1 % Good, very basic tutorial
2 % http://cmtw.harvard.edu/Documentation/TeX/Bibtex/Example.html
3 % More detail on the whole process
4 % http://www.andy-roberts.net/misc/latex/latextutorial3.html
5 % Entry types reference
6 % http://newton.ex.ac.uk/tex/pack/bibtex/btxdoc/node6.html
8 % http://newton.ex.ac.uk/tex/pack/bibtex/btxdoc/node7.html
9 % Entry and field reference, but with little discussion
10 % http://en.wikipedia.org/wiki/BibTeX
11 % Examples of assorted styles
12 % http://www.cs.stir.ac.uk/~kjt/software/latex/showbst.html
13 % Assorted BibTeX tools
14 % http://liinwww.ira.uka.de/bibliography/Bib.Format.html
16 % at some point in your latex document
17 % \bibliographystyle{prsty} % Phys. Rev. style
18 % other syles include abbrv, alpha, plain, unsrt
20 % and in your latex document where you want the bibliography:
21 % \bibliography{wtk} % wtk.bib is the name of the database
23 % compile (using latex for example) with
29 % See possibly the Natbib package for other citation styles & link formats
30 % Customize bibliography with Makebst (`latex makebst`),
31 % makes .bst bib-style format files according to your specifications.
33 % My key style is '<lowercase-main-author-last-name><four-digit-year>',
34 % which I can kindof achieve with
35 % $ bibtool -f '%-1n(author)%2d(year)' wtk.bib -o wtk1.bib
36 % Except any paper with more than one author has a '.ea' appended to the name
37 % and bibtool removes all comments :(.
39 % Define some Journal name shortcuts
40 % @String{PRL = "Phys. Rev. Lett."}
42 % @String{RMP = "Rev. Mod. Phys."}
44 % @String{LANG = "Langmuir"}
46 % @String(PNAS="Proc. Nat. Acad. Sci.")
47 % @String{RSI = "Rev. Sci. Instrum."}
50 author = "Changbong Hyeon and D. Thirumalai",
51 title = "Can energy landscape roughness of proteins and {RNA}
52 be measured by using mechanical unfolding
54 journal = "Proc Natl Acad Sci U S A",
60 pages = "10249--10253",
61 keywords = "Protein Folding",
62 keywords = "Proteins",
64 keywords = "Temperature",
65 keywords = "Thermodynamics",
66 abstract = "By considering temperature effects on the mechanical
67 unfolding rates of proteins and RNA, whose energy
68 landscape is rugged, the question posed in the title is
69 answered in the affirmative. Adopting a theory by
70 Zwanzig [Zwanzig, R. (1988) Proc. Natl. Acad. Sci. USA
71 85, 2029-2030], we show that, because of roughness
72 characterized by an energy scale epsilon, the unfolding
73 rate at constant force is retarded. Similarly, in
74 nonequilibrium experiments done at constant loading
75 rates, the most probable unfolding force increases
76 because of energy landscape roughness. The effects are
77 dramatic at low temperatures. Our analysis suggests
78 that, by using temperature as a variable in mechanical
79 unfolding experiments of proteins and RNA, the
80 ruggedness energy scale epsilon, can be directly
83 doi = "10.1073/pnas.1833310100",
84 URL = "http://www.pnas.org/cgi/content/abstract/100/18/10249",
85 eprint = "http://www.pnas.org/cgi/reprint/100/18/10249.pdf",
86 note = "Derives the major theory behind my thesis. The Kramers rate equation is Hanggi Eq. 4.56c (page 275)\cite{hanggi90}.",
87 project = "Energy Landscape Roughness",
91 author = "Reinat Nevo and Vlad Brumfeld and Ruti Kapon and Peter
92 Hinterdorfer and Ziv Reich",
93 title = "Direct measurement of protein energy landscape
101 keywords = "Models, Molecular",
102 keywords = "Protein Binding",
103 keywords = "Protein Folding",
104 keywords = "Spectrum Analysis",
105 keywords = "Thermodynamics",
106 keywords = "beta Karyopherins",
107 keywords = "ran GTP-Binding Protein",
108 abstract = "The energy landscape of proteins is thought to have an
109 intricate, corrugated structure. Such roughness should
110 have important consequences on the folding and binding
111 kinetics of proteins, as well as on their equilibrium
112 fluctuations. So far, no direct measurement of protein
113 energy landscape roughness has been made. Here, we
114 combined a recent theory with single-molecule dynamic
115 force spectroscopy experiments to extract the overall
116 energy scale of roughness epsilon for a complex
117 consisting of the small GTPase Ran and the nuclear
118 transport receptor importin-beta. The results gave
119 epsilon > 5k(B)T, indicating a bumpy energy surface,
120 which is consistent with the ability of importin-beta
121 to accommodate multiple conformations and to interact
122 with different, structurally distinct ligands.",
124 doi = "10.1038/sj.embor.7400403",
125 URL = "http://www.nature.com/embor/journal/v6/n5/abs/7400403.html",
126 eprint = "http://www.nature.com/embor/journal/v6/n5/pdf/7400403.pdf",
127 note = "Applies H&T\cite{hyeon03} to ligand-receptor
129 project = "Energy Landscape Roughness",
132 % Altered from original 'Download citation' from Rev Sci Instrum website
134 author = "Yao Yang and Fan-Chi Lin and Guoliang Yang",
136 title = "Temperature control device for single molecule
137 measurements using the atomic force microscope",
140 journal = "Review of Scientific Instruments",
146 keywords = "temperature control; atomic force microscopy;
147 thermocouples; heat sinks",
148 URL = "http://link.aip.org/link/?RSI/77/063701/1",
149 doi = "10.1063/1.2204580",
150 note = "Introduces our temperature control system",
151 project = "Energy Landscape Roughness",
154 % Altered from original 'Download to citation manager' from Highwire Press
156 author = "Matthias Rief and Mathias Gautel and Filipp Oesterhelt
157 and Julio M. Fernandez and Hermann E. Gaub",
158 title = "{Reversible Unfolding of Individual Titin
159 Immunoglobulin Domains by AFM}",
163 pages = "1109--1112",
164 doi = "10.1126/science.276.5315.1109",
166 URL = "http://www.sciencemag.org/cgi/content/abstract/276/5315/1109",
167 eprint = "http://www.sciencemag.org/cgi/reprint/276/5315/1109.pdf",
168 note = "Seminal paper for force spectroscopy on Titin. Cited
169 by Dietz '04\cite{dietz04} (ref 9) as an example of how
170 unfolding large proteins is easily interpreted (vs.
171 confusing unfolding in bulk), but Titin is a rather
172 simple example of that, because of it's globular-chain
174 project = "Energy Landscape Roughness",
177 % Altered from original 'Download to citation manager' from scitation.aip.org
179 author = "Jeffrey L. Hutter and John Bechhoefer",
181 title = "Calibration of atomic-force microscope tips",
184 journal = "Review of Scientific Instruments",
187 pages = "1868--1873",
188 keywords = "ATOMIC FORCE MICROSCOPY; CALIBRATION; QUALITY FACTOR;
189 PROBES; RESONANCE; SILICON NITRIDES; MICA; VAN DER
191 URL = "http://link.aip.org/link/?RSI/64/1868/1",
192 doi = "10.1063/1.1143970",
193 note = "Seminal paper for thermal calibration of AFM
195 project = "Cantilever Calibration",
198 % Originals from PNAS 'download to citation manager'
201 author = "Hendrik Dietz and Matthias Rief",
202 title = "{Exploring the energy landscape of GFP by
203 single-molecule mechanical experiments}",
204 journal = "Proceedings of the National Academy of Sciences",
207 pages = "16192--16197",
208 doi = "10.1073/pnas.0404549101",
210 abstract = "We use single-molecule force spectroscopy to drive
211 single GFP molecules from the native state through
212 their complex energy landscape into the completely
213 unfolded state. Unlike many smaller proteins,
214 mechanical GFP unfolding proceeds by means of two
215 subsequent intermediate states. The transition from the
216 native state to the first intermediate state occurs
217 near thermal equilibrium at {approx}35 pN and is
218 characterized by detachment of a seven-residue
219 N-terminal {alpha}-helix from the beta barrel. We
220 measure the equilibrium free energy cost associated
221 with this transition as 22 kBT. Detachment of this
222 small {alpha}-helix completely destabilizes GFP
223 thermodynamically even though the {beta}-barrel is
224 still intact and can bear load. Mechanical stability of
225 the protein on the millisecond timescale, however, is
226 determined by the activation barrier of unfolding the
227 {beta}-barrel out of this thermodynamically unstable
228 intermediate state. High bandwidth, time-resolved
229 measurements of the cantilever relaxation phase upon
230 unfolding of the {beta}-barrel revealed a second
231 metastable mechanical intermediate with one complete
232 {beta}-strand detached from the barrel. Quantitative
233 analysis of force distributions and lifetimes lead to a
234 detailed picture of the complex mechanical unfolding
235 pathway through a rough energy landscape.",
236 URL = "http://www.pnas.org/cgi/content/abstract/101/46/16192",
237 eprint = "http://www.pnas.org/cgi/reprint/101/46/16192.pdf",
238 note = "Nice energy-landscape-to-one-dimension compression
239 graphic. Unfolding Green Flourescent Protein (GFP)
240 towards using it as an embedded force probe.",
241 project = "Energy landscape roughness",
245 author = "Takehiro Sato and Masatoshi Esaki and Julio M.
246 Fernandez and Toshiya Endo",
247 title = "{Comparison of the protein-unfolding pathways between
248 mitochondrial protein import and atomic-force
249 microscopy measurements}",
250 journal = "Proceedings of the National Academy of Sciences",
253 pages = "17999--18004",
254 doi = "10.1073/pnas.0504495102",
256 abstract = "Many newly synthesized proteins have to become
257 unfolded during translocation across biological
258 membranes. We have analyzed the effects of various
259 stabilization/destabilization mutations in the Ig-like
260 module of the muscle protein titin upon its import from
261 the N terminus or C terminus into mitochondria. The
262 effects of mutations on the import of the titin module
263 from the C terminus correlate well with those on forced
264 mechanical unfolding in atomic-force microscopy (AFM)
265 measurements. On the other hand, as long as turnover of
266 the mitochondrial Hsp70 system is not rate-limiting for
267 the import, import of the titin module from the N
268 terminus is sensitive to mutations in the N-terminal
269 region but not the ones in the C-terminal region that
270 affect resistance to global unfolding in AFM
271 experiments. We propose that the mitochondrial-import
272 system can catalyze precursor-unfolding by reducing the
273 stability of unfolding intermediates.",
274 URL = "http://www.pnas.org/cgi/content/abstract/102/50/17999",
275 eprint = "http://www.pnas.org/cgi/reprint/102/50/17999.pdf",
279 author = "Qing Peng and Hongbin Li",
280 title = "{Atomic force microscopy reveals parallel mechanical
281 unfolding pathways of T4 lysozyme: Evidence for a
282 kinetic partitioning mechanism}",
283 journal = "Proceedings of the National Academy of Sciences",
286 pages = "1885--1890",
287 doi = "10.1073/pnas.0706775105",
289 abstract = "Kinetic partitioning is predicted to be a general
290 mechanism for proteins to fold into their well defined
291 native three-dimensional structure from unfolded states
292 following multiple folding pathways. However,
293 experimental evidence supporting this mechanism is
294 still limited. By using single-molecule atomic force
295 microscopy, here we report experimental evidence
296 supporting the kinetic partitioning mechanism for
297 mechanical unfolding of T4 lysozyme, a small protein
298 composed of two subdomains. We observed that on
299 stretching from its N and C termini, T4 lysozyme
300 unfolds by multiple distinct unfolding pathways: the
301 majority of T4 lysozymes unfold in an all-or-none
302 fashion by overcoming a dominant unfolding kinetic
303 barrier; and a small fraction of T4 lysozymes unfold in
304 three-state fashion involving unfolding intermediate
305 states. The three-state unfolding pathways do not
306 follow well defined routes, instead they display
307 variability and diversity in individual unfolding
308 pathways. The unfolding intermediate states are local
309 energy minima along the mechanical unfolding pathways
310 and are likely to result from the residual structures
311 present in the two subdomains after crossing the main
312 unfolding barrier. These results provide direct
313 evidence for the kinetic partitioning of the mechanical
314 unfolding pathways of T4 lysozyme, and the complex
315 unfolding behaviors reflect the stochastic nature of
316 kinetic barrier rupture in mechanical unfolding
317 processes. Our results demonstrate that single-molecule
318 atomic force microscopy is an ideal tool to investigate
319 the folding/unfolding dynamics of complex multimodule
320 proteins that are otherwise difficult to study using
321 traditional methods.",
322 URL = "http://www.pnas.org/cgi/content/abstract/105/6/1885",
323 eprint = "http://www.pnas.org/cgi/reprint/105/6/1885.pdf",
327 author = "Deepak Sharma and Ognjen Perisic and Qing Peng and Yi
328 Cao and Canaan Lam and Hui Lu and Hongbin Li",
329 title = "{Single-molecule force spectroscopy reveals a
330 mechanically stable protein fold and the rational
331 tuning of its mechanical stability}",
332 journal = "Proceedings of the National Academy of Sciences",
335 pages = "9278--9283",
336 doi = "10.1073/pnas.0700351104",
338 abstract = "It is recognized that shear topology of two directly
339 connected force-bearing terminal [beta]-strands is a
340 common feature among the vast majority of mechanically
341 stable proteins known so far. However, these proteins
342 belong to only two distinct protein folds, Ig-like
343 [beta] sandwich fold and [beta]-grasp fold,
344 significantly hindering delineating molecular
345 determinants of mechanical stability and rational
346 tuning of mechanical properties. Here we combine
347 single-molecule atomic force microscopy and steered
348 molecular dynamics simulation to reveal that the de
349 novo designed Top7 fold [Kuhlman B, Dantas G, Ireton
350 GC, Varani G, Stoddard BL, Baker D (2003) Science
351 302:13641368] represents a mechanically stable protein
352 fold that is distinct from Ig-like [beta] sandwich and
353 [beta]-grasp folds. Although the two force-bearing
354 [beta] strands of Top7 are not directly connected, Top7
355 displays significant mechanical stability,
356 demonstrating that the direct connectivity of
357 force-bearing [beta] strands in shear topology is not
358 mandatory for mechanical stability. This finding
359 broadens our understanding of the design of
360 mechanically stable proteins and expands the protein
361 fold space where mechanically stable proteins can be
362 screened. Moreover, our results revealed a
363 substructure-sliding mechanism for the mechanical
364 unfolding of Top7 and the existence of two possible
365 unfolding pathways with different height of energy
366 barrier. Such insights enabled us to rationally tune
367 the mechanical stability of Top7 by redesigning its
368 mechanical unfolding pathway. Our study demonstrates
369 that computational biology methods (including de novo
370 design) offer great potential for designing proteins of
371 defined topology to achieve significant and tunable
372 mechanical properties in a rational and systematic
374 URL = "http://www.pnas.org/cgi/content/abstract/104/22/9278",
375 eprint = "http://www.pnas.org/cgi/reprint/104/22/9278.pdf",
378 @Article{oberhauser01,
379 author = "Andres F. Oberhauser and Paul K. Hansma and Mariano
380 Carrion-Vazquez and Julio M. Fernandez",
381 title = "{Stepwise unfolding of titin under force-clamp atomic
383 journal = "Proceedings of the National Academy of Sciences",
387 doi = "10.1073/pnas.021321798",
390 URL = "http://www.pnas.org/cgi/content/abstract/98/2/468",
391 eprint = "http://www.pnas.org/cgi/reprint/98/2/468.pdf",
395 author = "Kirstin A. Walther and Frauke Grater and Lorna Dougan
396 and Carmen L. Badilla and Bruce J. Berne and Julio M.
398 title = "{Signatures of hydrophobic collapse in extended
399 proteins captured with force spectroscopy}",
400 journal = "Proceedings of the National Academy of Sciences",
403 pages = "7916--7921",
404 doi = "10.1073/pnas.0702179104",
406 abstract = "We unfold and extend single proteins at a high force
407 and then linearly relax the force to probe their
408 collapse mechanisms. We observe a large variability in
409 the extent of their recoil. Although chain entropy
410 makes a small contribution, we show that the observed
411 variability results from hydrophobic interactions with
412 randomly varying magnitude from protein to protein.
413 This collapse mechanism is common to highly extended
414 proteins, including nonfolding elastomeric proteins
415 like PEVK from titin. Our observations explain the
416 puzzling differences between the folding behavior of
417 highly extended proteins, from those folding after
418 chemical or thermal denaturation. Probing the collapse
419 of highly extended proteins with force spectroscopy
420 allows separation of the different driving forces in
422 URL = "http://www.pnas.org/cgi/content/abstract/104/19/7916",
423 eprint = "http://www.pnas.org/cgi/reprint/104/19/7916.pdf",
427 author = "Hendrik Dietz and Felix Berkemeier and Morten Bertz
429 title = "{Anisotropic deformation response of single protein
431 journal = "Proceedings of the National Academy of Sciences",
434 pages = "12724--12728",
435 doi = "10.1073/pnas.0602995103",
437 abstract = "Single-molecule methods have given experimental access
438 to the mechanical properties of single protein
439 molecules. So far, access has been limited to mostly
440 one spatial direction of force application. Here, we
441 report single-molecule experiments that explore the
442 mechanical properties of a folded protein structure in
443 precisely controlled directions by applying force to
444 selected amino acid pairs. We investigated the
445 deformation response of GFP in five selected
446 directions. We found fracture forces widely varying
447 from 100 pN up to 600 pN. We show that straining the
448 GFP structure in one of the five directions induces
449 partial fracture of the protein into a half-folded
450 intermediate structure. From potential widths we
451 estimated directional spring constants of the GFP
452 structure and found values ranging from 1 N/m up to 17
453 N/m. Our results show that classical continuum
454 mechanics and simple mechanistic models fail to
455 describe the complex mechanics of the GFP protein
456 structure and offer insights into the mechanical design
457 of protein materials.",
458 URL = "http://www.pnas.org/cgi/content/abstract/103/34/12724",
459 eprint = "http://www.pnas.org/cgi/reprint/103/34/12724.pdf",
463 author = "Michael Schlierf and Hongbin Li and Julio M.
465 title = "{The unfolding kinetics of ubiquitin captured with
466 single-molecule force-clamp techniques}",
467 journal = "Proceedings of the National Academy of Sciences",
470 pages = "7299--7304",
471 doi = "10.1073/pnas.0400033101",
473 abstract = "We use single-molecule force spectroscopy to study the
474 kinetics of unfolding of the small protein ubiquitin.
475 Upon a step increase in the stretching force, a
476 ubiquitin polyprotein extends in discrete steps of 20.3
477 {+/-} 0.9 nm marking each unfolding event. An average
478 of the time course of these unfolding events was well
479 described by a single exponential, which is a necessary
480 condition for a memoryless Markovian process. Similar
481 ensemble averages done at different forces showed that
482 the unfolding rate was exponentially dependent on the
483 stretching force. Stretching a ubiquitin polyprotein
484 with a force that increased at a constant rate
485 (force-ramp) directly measured the distribution of
486 unfolding forces. This distribution was accurately
487 reproduced by the simple kinetics of an all-or-none
488 unfolding process. Our force-clamp experiments directly
489 demonstrate that an ensemble average of ubiquitin
490 unfolding events is well described by a two-state
491 Markovian process that obeys the Arrhenius equation.
492 However, at the single-molecule level, deviant behavior
493 that is not well represented in the ensemble average is
494 readily observed. Our experiments make an important
495 addition to protein spectroscopy by demonstrating an
496 unambiguous method of analysis of the kinetics of
497 protein unfolding by a stretching force.",
498 URL = "http://www.pnas.org/cgi/content/abstract/101/19/7299",
499 eprint = "http://www.pnas.org/cgi/reprint/101/19/7299.pdf",
503 author = "Dietmar Labeit and Kaori Watanabe and Christian Witt
504 and Hideaki Fujita and Yiming Wu and Sunshine Lahmers
505 and Theodor Funck and Siegfried Labeit and Henk
507 title = "Calcium-dependent molecular spring elements in the
508 giant protein titin",
509 journal = "Proceedings of the National Academy of Sciences",
512 pages = "13716--13721",
513 doi = "10.1073/pnas.2235652100",
515 abstract = "Titin (also known as connectin) is a giant protein
516 with a wide range of cellular functions, including
517 providing muscle cells with elasticity. Its
518 physiological extension is largely derived from the
519 PEVK segment, rich in proline (P), glutamate (E),
520 valine (V), and lysine (K) residues. We studied
521 recombinant PEVK molecules containing the two conserved
522 elements: {approx}28-residue PEVK repeats and E-rich
523 motifs. Single molecule experiments revealed that
524 calcium-induced conformational changes reduce the
525 bending rigidity of the PEVK fragments, and
526 site-directed mutagenesis identified four glutamate
527 residues in the E-rich motif that was studied (exon
528 129), as critical for this process. Experiments with
529 muscle fibers showed that titin-based tension is
530 calcium responsive. We propose that the PEVK segment
531 contains E-rich motifs that render titin a
532 calcium-dependent molecular spring that adapts to the
533 physiological state of the cell.",
534 URL = "http://www.pnas.org/cgi/content/abstract/100/23/13716",
535 eprint = "http://www.pnas.org/cgi/reprint/100/23/13716.pdf",
539 author = "Moritz Mickler and Ruxandra I. Dima and Hendrik Dietz
540 and Changbong Hyeon and D. Thirumalai and Matthias
542 title = "Revealing the bifurcation in the unfolding pathways
543 of {GFP} by using single-molecule experiments and
545 journal = "Proceedings of the National Academy of Sciences",
548 pages = "20268--20273",
549 doi = "10.1073/pnas.0705458104",
551 keywords = "AFM experiments, coarse-grained simulations, cross-link mutants,
552 pathway bifurcation, plasticity of energy landscape",
553 abstract = "Nanomanipulation of biomolecules by using
554 single-molecule methods and computer simulations has
555 made it possible to visualize the energy landscape of
556 biomolecules and the structures that are sampled during
557 the folding process. We use simulations and
558 single-molecule force spectroscopy to map the complex
559 energy landscape of GFP that is used as a marker in
560 cell biology and biotechnology. By engineering internal
561 disulfide bonds at selected positions in the GFP
562 structure, mechanical unfolding routes are precisely
563 controlled, thus allowing us to infer features of the
564 energy landscape of the wild-type GFP. To elucidate the
565 structures of the unfolding pathways and reveal the
566 multiple unfolding routes, the experimental results are
567 complemented with simulations of a self-organized
568 polymer (SOP) model of GFP. The SOP representation of
569 proteins, which is a coarse-grained description of
570 biomolecules, allows us to perform forced-induced
571 simulations at loading rates and time scales that
572 closely match those used in atomic force microscopy
573 experiments. By using the combined approach, we show
574 that forced unfolding of GFP involves a bifurcation in
575 the pathways to the stretched state. After detachment
576 of an N-terminal {alpha}-helix, unfolding proceeds
577 along two distinct pathways. In the dominant pathway,
578 unfolding starts from the detachment of the primary
579 N-terminal -strand, while in the minor pathway rupture
580 of the last, C-terminal -strand initiates the unfolding
581 process. The combined approach has allowed us to map
582 the features of the complex energy landscape of GFP
583 including a characterization of the structures, albeit
584 at a coarse-grained level, of the three metastable
586 URL = "http://www.pnas.org/cgi/content/abstract/104/51/20268",
587 eprint = "http://www.pnas.org/cgi/reprint/104/51/20268.pdf",
588 note = "Hiccup in unfolding leg corresponds to unfolding intermediate
589 (See Figure 2). The unfolding timescale in GFP is about 6 ms.",
593 author = "Arun P. Wiita and Sri Rama Koti Ainavarapu and Hector
594 H. Huang and Julio M. Fernandez",
595 title = "{From the Cover: Force-dependent chemical kinetics of
596 disulfide bond reduction observed with single-molecule
598 journal = "Proceedings of the National Academy of Sciences",
601 pages = "7222--7227",
602 doi = "10.1073/pnas.0511035103",
604 abstract = "The mechanism by which mechanical force regulates the
605 kinetics of a chemical reaction is unknown. Here, we
606 use single-molecule force-clamp spectroscopy and
607 protein engineering to study the effect of force on the
608 kinetics of thiol/disulfide exchange. Reduction of
609 disulfide bonds through the thiol/disulfide exchange
610 chemical reaction is crucial in regulating protein
611 function and is known to occur in mechanically stressed
612 proteins. We apply a constant stretching force to
613 single engineered disulfide bonds and measure their
614 rate of reduction by DTT. Although the reduction rate
615 is linearly dependent on the concentration of DTT, it
616 is exponentially dependent on the applied force,
617 increasing 10-fold over a 300-pN range. This result
618 predicts that the disulfide bond lengthens by 0.34 A at
619 the transition state of the thiol/disulfide exchange
620 reaction. Our work at the single bond level directly
621 demonstrates that thiol/disulfide exchange in proteins
622 is a force-dependent chemical reaction. Our findings
623 suggest that mechanical force plays a role in disulfide
624 reduction in vivo, a property that has never been
625 explored by traditional biochemistry. Furthermore, our
626 work also indicates that the kinetics of any chemical
627 reaction that results in bond lengthening will be
629 URL = "http://www.pnas.org/cgi/content/abstract/103/19/7222",
630 eprint = "http://www.pnas.org/cgi/reprint/103/19/7222.pdf",
634 author = "Belinda Bullard and Tzintzuni Garcia and Vladimir
635 Benes and Mark C. Leake and Wolfgang A. Linke and
636 Andres F. Oberhauser",
637 title = "{The molecular elasticity of the insect flight muscle
638 proteins projectin and kettin}",
639 journal = "Proceedings of the National Academy of Sciences",
642 pages = "4451--4456",
643 doi = "10.1073/pnas.0509016103",
645 abstract = "Projectin and kettin are titin-like proteins mainly
646 responsible for the high passive stiffness of insect
647 indirect flight muscles, which is needed to generate
648 oscillatory work during flight. Here we report the
649 mechanical properties of kettin and projectin by
650 single-molecule force spectroscopy. Force-extension and
651 force-clamp curves obtained from Lethocerus projectin
652 and Drosophila recombinant projectin or kettin
653 fragments revealed that fibronectin type III domains in
654 projectin are mechanically weaker (unfolding force, Fu
655 {approx} 50-150 pN) than Ig-domains (Fu {approx}
656 150-250 pN). Among Ig domains in Sls/kettin, the
657 domains near the N terminus are less stable than those
658 near the C terminus. Projectin domains refolded very
659 fast [85% at 15 s-1 (25{degrees}C)] and even under high
660 forces (15-30 pN). Temperature affected the unfolding
661 forces with a Q10 of 1.3, whereas the refolding speed
662 had a Q10 of 2-3, probably reflecting the cooperative
663 nature of the folding mechanism. High bending
664 rigidities of projectin and kettin indicated that
665 straightening the proteins requires low forces. Our
666 results suggest that titin-like proteins in indirect
667 flight muscles could function according to a
668 folding-based-spring mechanism.",
669 URL = "http://www.pnas.org/cgi/content/abstract/103/12/4451",
670 eprint = "http://www.pnas.org/cgi/reprint/103/12/4451.pdf",
674 author = "Hendrik Dietz and Matthias Rief",
675 title = "{Protein structure by mechanical triangulation}",
676 journal = "Proceedings of the National Academy of Sciences",
679 pages = "1244--1247",
680 doi = "10.1073/pnas.0509217103",
682 abstract = "Knowledge of protein structure is essential to
683 understand protein function. High-resolution protein
684 structure has so far been the domain of ensemble
685 methods. Here, we develop a simple single-molecule
686 technique to measure spatial position of selected
687 residues within a folded and functional protein
688 structure in solution. Construction and mechanical
689 unfolding of cysteine-engineered polyproteins with
690 controlled linkage topology allows measuring
691 intramolecular distance with angstrom precision. We
692 demonstrate the potential of this technique by
693 determining the position of three residues in the
694 structure of green fluorescent protein (GFP). Our
695 results perfectly agree with the GFP crystal structure.
696 Mechanical triangulation can find many applications
697 where current bulk structural methods fail.",
698 URL = "http://www.pnas.org/cgi/content/abstract/103/5/1244",
699 eprint = "http://www.pnas.org/cgi/reprint/103/5/1244.pdf",
703 author = "Alexander J. Wilcox and Jason Choy and Carlos
704 Bustamante and Andreas Matouschek",
705 title = "{Effect of protein structure on mitochondrial
707 journal = "Proceedings of the National Academy of Sciences",
710 pages = "15435--15440",
711 doi = "10.1073/pnas.0507324102",
713 abstract = "Most proteins that are to be imported into the
714 mitochondrial matrix are synthesized as precursors,
715 each composed of an N-terminal targeting sequence
716 followed by a mature domain. Precursors are recognized
717 through their targeting sequences by receptors at the
718 mitochondrial surface and are then threaded through
719 import channels into the matrix. Both the targeting
720 sequence and the mature domain contribute to the
721 efficiency with which proteins are imported into
722 mitochondria. Precursors must be in an unfolded
723 conformation during translocation. Mitochondria can
724 unfold some proteins by changing their unfolding
725 pathways. The effectiveness of this unfolding mechanism
726 depends on the local structure of the mature domain
727 adjacent to the targeting sequence. This local
728 structure determines the extent to which the unfolding
729 pathway can be changed and, therefore, the unfolding
730 rate increased. Atomic force microscopy studies find
731 that the local structures of proteins near their N and
732 C termini also influence their resistance to mechanical
733 unfolding. Thus, protein unfolding during import
734 resembles mechanical unfolding, and the specificity of
735 import is determined by the resistance of the mature
736 domain to unfolding as well as by the properties of the
737 targeting sequence.",
738 URL = "http://www.pnas.org/cgi/content/abstract/102/43/15435",
739 eprint = "http://www.pnas.org/cgi/reprint/102/43/15435.pdf",
742 @Article{marszalek02,
743 author = "Piotr E. Marszalek and Hongbin Li and Andres F.
744 Oberhauser and Julio M. Fernandez",
745 title = "{Chair-boat transitions in single polysaccharide
746 molecules observed with force-ramp AFM}",
747 journal = "Proceedings of the National Academy of Sciences",
750 pages = "4278--4283",
751 doi = "10.1073/pnas.072435699",
753 abstract = "Under a stretching force, the sugar ring of
754 polysaccharide molecules switches from the chair to the
755 boat-like or inverted chair conformation. This
756 conformational change can be observed by stretching
757 single polysaccharide molecules with an atomic force
758 microscope. In those early experiments, the molecules
759 were stretched at a constant rate while the resulting
760 force changed over wide ranges. However, because the
761 rings undergo force-dependent transitions, an
762 experimental arrangement where the force is the free
763 variable introduces an undesirable level of complexity
764 in the results. Here we demonstrate the use of
765 force-ramp atomic force microscopy to capture the
766 conformational changes in single polysaccharide
767 molecules. Force-ramp atomic force microscopy readily
768 captures the ring transitions under conditions where
769 the entropic elasticity of the molecule is separated
770 from its conformational transitions, enabling a
771 quantitative analysis of the data with a simple
772 two-state model. This analysis directly provides the
773 physico-chemical characteristics of the ring
774 transitions such as the width of the energy barrier,
775 the relative energy of the conformers, and their
776 enthalpic elasticity. Our experiments enhance the
777 ability of single-molecule force spectroscopy to make
778 high-resolution measurements of the conformations of
779 single polysaccharide molecules under a stretching
780 force, making an important addition to polysaccharide
782 URL = "http://www.pnas.org/cgi/content/abstract/99/7/4278",
783 eprint = "http://www.pnas.org/cgi/reprint/99/7/4278.pdf",
787 author = "David Craig and Andre Krammer and Klaus Schulten and
789 title = "{Comparison of the early stages of forced unfolding
790 for fibronectin type III modules}",
791 journal = "Proceedings of the National Academy of Sciences",
794 pages = "5590--5595",
795 doi = "10.1073/pnas.101582198",
798 URL = "http://www.pnas.org/cgi/content/abstract/98/10/5590",
799 eprint = "http://www.pnas.org/cgi/reprint/98/10/5590.pdf",
802 @Article{carrion-vazquez99a,
803 author = "Mariano Carrion-Vazquez and Piotr E. Marszalek and
804 Andres F. Oberhauser and Julio M. Fernandez",
805 title = "Atomic force microscopy captures length phenotypes in
807 journal = "Proceedings of the National Academy of Sciences",
810 pages = "11288--11292",
811 doi = "10.1073/pnas.96.20.11288",
814 URL = "http://www.pnas.org/cgi/content/abstract/96/20/11288",
815 eprint = "http://www.pnas.org/cgi/reprint/96/20/11288.pdf",
819 author = "Yi Cao and M. M. Balamurali and Deepak Sharma and
821 title = "{A functional single-molecule binding assay via force
823 journal = "Proceedings of the National Academy of Sciences",
826 pages = "15677--15681",
827 doi = "10.1073/pnas.0705367104",
829 abstract = "Proteinligand interactions, including proteinprotein
830 interactions, are ubiquitously essential in biological
831 processes and also have important applications in
832 biotechnology. A wide range of methodologies have been
833 developed for quantitative analysis of proteinligand
834 interactions. However, most of them do not report
835 direct functional/structural consequence of ligand
836 binding. Instead they only detect the change of
837 physical properties, such as fluorescence and
838 refractive index, because of the colocalization of
839 protein and ligand, and are susceptible to false
840 positives. Thus, important information about the
841 functional state of proteinligand complexes cannot be
842 obtained directly. Here we report a functional
843 single-molecule binding assay that uses force
844 spectroscopy to directly probe the functional
845 consequence of ligand binding and report the functional
846 state of proteinligand complexes. As a proof of
847 principle, we used protein G and the Fc fragment of IgG
848 as a model system in this study. Binding of Fc to
849 protein G does not induce major structural changes in
850 protein G but results in significant enhancement of its
851 mechanical stability. Using mechanical stability of
852 protein G as an intrinsic functional reporter, we
853 directly distinguished and quantified Fc-bound and
854 Fc-free forms of protein G on a single-molecule basis
855 and accurately determined their dissociation constant.
856 This single-molecule functional binding assay is
857 label-free, nearly background-free, and can detect
858 functional heterogeneity, if any, among proteinligand
859 interactions. This methodology opens up avenues for
860 studying proteinligand interactions in a functional
861 context, and we anticipate that it will find broad
862 application in diverse proteinligand systems.",
863 URL = "http://www.pnas.org/cgi/content/abstract/104/40/15677",
864 eprint = "http://www.pnas.org/cgi/reprint/104/40/15677.pdf",
868 author = "Weichang Yu and Jonathan C. Lamb and Fangpu Han and
870 title = "{Telomere-mediated chromosomal truncation in maize}",
871 journal = "Proceedings of the National Academy of Sciences",
874 pages = "17331--17336",
875 doi = "10.1073/pnas.0605750103",
877 abstract = "Direct repeats of Arabidopsis telomeric sequence were
878 constructed to test telomere-mediated chromosomal
879 truncation in maize. Two constructs with 2.6 kb of
880 telomeric sequence were used to transform maize
881 immature embryos by Agrobacterium-mediated
882 transformation. One hundred seventy-six transgenic
883 lines were recovered in which 231 transgene loci were
884 revealed by a FISH analysis. To analyze chromosomal
885 truncations that result in transgenes located near
886 chromosomal termini, Southern hybridization analyses
887 were performed. A pattern of smear in truncated lines
888 was seen as compared with discrete bands for internal
889 integrations, because telomeres in different cells are
890 elongated differently by telomerase. When multiple
891 restriction enzymes were used to map the transgene
892 positions, the size of the smears shifted in accordance
893 with the locations of restriction sites on the
894 construct. This result demonstrated that the transgene
895 was present at the end of the chromosome immediately
896 before the integrated telomere sequence. Direct
897 evidence for chromosomal truncation came from the
898 results of FISH karyotyping, which revealed broken
899 chromosomes with transgene signals at the ends. These
900 results demonstrate that telomere-mediated chromosomal
901 truncation operates in plant species. This technology
902 will be useful for chromosomal engineering in maize as
903 well as other plant species.",
904 URL = "http://www.pnas.org/cgi/content/abstract/103/46/17331",
905 eprint = "http://www.pnas.org/cgi/reprint/103/46/17331.pdf",
909 author = "Jason Ming Zhao and Haeshin Lee and Rene A. Nome and
910 Sophia Majid and Norbert F. Scherer and Wouter D.
912 title = "{Single-molecule detection of structural changes
913 during Per-Arnt-Sim (PAS) domain activation}",
914 journal = "Proceedings of the National Academy of Sciences",
917 pages = "11561--11566",
918 doi = "10.1073/pnas.0601567103",
920 abstract = "The Per-Arnt-Sim (PAS) domain is a ubiquitous protein
921 module with a common three-dimensional fold involved in
922 a wide range of regulatory and sensory functions in all
923 domains of life. The activation of these functions is
924 thought to involve partial unfolding of N- or
925 C-terminal helices attached to the PAS domain. Here we
926 use atomic force microscopy to probe receptor
927 activation in single molecules of photoactive yellow
928 protein (PYP), a prototype of the PAS domain family.
929 Mechanical unfolding of Cys-linked PYP multimers in the
930 presence and absence of illumination reveals that, in
931 contrast to previous studies, the PAS domain itself is
932 extended by {approx}3 nm (at the 10-pN detection limit
933 of the measurement) and destabilized by {approx}30% in
934 the light-activated state of PYP. Comparative
935 measurements and steered molecular dynamics simulations
936 of two double-Cys PYP mutants that probe different
937 regions of the PAS domain quantify the anisotropy in
938 stability and changes in local structure, thereby
939 demonstrating the partial unfolding of their PAS domain
940 upon activation. These results establish a generally
941 applicable single-molecule approach for mapping
942 functional conformational changes to selected regions
943 of a protein. In addition, the results have profound
944 implications for the molecular mechanism of PAS domain
945 activation and indicate that stimulus-induced partial
946 protein unfolding can be used as a signaling
948 URL = "http://www.pnas.org/cgi/content/abstract/103/31/11561",
949 eprint = "http://www.pnas.org/cgi/reprint/103/31/11561.pdf",
953 author = "Mu Gao and David Craig and Olivier Lequin and Iain D.
954 Campbell and Viola Vogel and Klaus Schulten",
955 title = "{Structure and functional significance of mechanically
956 unfolded fibronectin type III1 intermediates}",
957 journal = "Proceedings of the National Academy of Sciences",
960 pages = "14784--14789",
961 doi = "10.1073/pnas.2334390100",
963 abstract = "Fibronectin (FN) forms fibrillar networks coupling
964 cells to the extracellular matrix. The formation of FN
965 fibrils, fibrillogenesis, is a tightly regulated
966 process involving the exposure of cryptic binding sites
967 in individual FN type III (FN-III) repeats presumably
968 exposed by mechanical tension. The FN-III1 module has
969 been previously proposed to contain such cryptic sites
970 that promote the assembly of extracellular matrix FN
971 fibrils. We have combined NMR and steered molecular
972 dynamics simulations to study the structure and
973 mechanical unfolding pathway of FN-III1. This study
974 finds that FN-III1 consists of a {beta}-sandwich
975 structure that unfolds to a mechanically stable
976 intermediate about four times the length of the native
977 folded state. Considering previous experimental
978 findings, our studies provide a structural model by
979 which mechanical stretching of FN-III1 may induce
980 fibrillogenesis through this partially unfolded
982 URL = "http://www.pnas.org/cgi/content/abstract/100/25/14784",
983 eprint = "http://www.pnas.org/cgi/reprint/100/25/14784.pdf",
987 author = "Christiane A. Opitz and Michael Kulke and Mark C.
988 Leake and Ciprian Neagoe and Horst Hinssen and Roger J.
989 Hajjar and Wolfgang A. Linke",
990 title = "{Damped elastic recoil of the titin spring in
991 myofibrils of human myocardium}",
992 journal = "Proceedings of the National Academy of Sciences",
995 pages = "12688--12693",
996 doi = "10.1073/pnas.2133733100",
998 abstract = "The giant protein titin functions as a molecular
999 spring in muscle and is responsible for most of the
1000 passive tension of myocardium. Because the titin spring
1001 is extended during diastolic stretch, it will recoil
1002 elastically during systole and potentially may
1003 influence the overall shortening behavior of cardiac
1004 muscle. Here, titin elastic recoil was quantified in
1005 single human heart myofibrils by using a high-speed
1006 charge-coupled device-line camera and a nanonewtonrange
1007 force sensor. Application of a slack-test protocol
1008 revealed that the passive shortening velocity (Vp) of
1009 nonactivated cardiomyofibrils depends on: (i) initial
1010 sarcomere length, (ii) release-step amplitude, and
1011 (iii) temperature. Selective digestion of titin, with
1012 low doses of trypsin, decelerated myofibrillar passive
1013 recoil and eventually stopped it. Selective extraction
1014 of actin filaments with a Ca2+-independent gelsolin
1015 fragment greatly reduced the dependency of Vp on
1016 release-step size and temperature. These results are
1017 explained by the presence of viscous forces opposing
1018 myofibrillar passive recoil that are caused mainly by
1019 weak actin-titin interactions. Thus, Vp is determined
1020 by two distinct factors: titin elastic recoil and
1021 internal viscous drag forces. The recoil could be
1022 modeled as that of a damped entropic spring consisting
1023 of independent worm-like chains. The functional
1024 importance of myofibrillar elastic recoil was addressed
1025 by comparing instantaneous Vp to unloaded shortening
1026 velocity, which was measured in demembranated, fully
1027 Ca2+-activated, human cardiac fibers. Titin-driven
1028 passive recoil was much faster than active unloaded
1029 shortening velocity in early phases of isotonic
1030 contraction. Damped myofibrillar elastic recoil could
1031 help accelerate active contraction speed of human
1032 myocardium during early systolic shortening.",
1033 URL = "http://www.pnas.org/cgi/content/abstract/100/22/12688",
1034 eprint = "http://www.pnas.org/cgi/reprint/100/22/12688.pdf",
1038 author = "Robert B. Best and Susan B. Fowler and Jose L.
1039 Toca-Herrera and Jane Clarke",
1040 title = "{A simple method for probing the mechanical unfolding
1041 pathway of proteins in detail}",
1042 journal = "Proceedings of the National Academy of Sciences",
1045 pages = "12143--12148",
1046 doi = "10.1073/pnas.192351899",
1048 abstract = "Atomic force microscopy is an exciting new
1049 single-molecule technique to add to the toolbox of
1050 protein (un)folding methods. However, detailed analysis
1051 of the unfolding of proteins on application of force
1052 has, to date, relied on protein molecular dynamics
1053 simulations or a qualitative interpretation of mutant
1054 data. Here we describe how protein engineering {Phi}
1055 value analysis can be adapted to characterize the
1056 transition states for mechanical unfolding of proteins.
1057 Single-molecule studies also have an advantage over
1058 bulk experiments, in that partial {Phi} values arising
1059 from partial structure in the transition state can be
1060 clearly distinguished from those averaged over
1061 alternate pathways. We show that unfolding rate
1062 constants derived in the standard way by using Monte
1063 Carlo simulations are not reliable because of the
1064 errors involved. However, it is possible to circumvent
1065 these problems, providing the unfolding mechanism is
1066 not changed by mutation, either by a modification of
1067 the Monte Carlo procedure or by comparing mutant and
1068 wild-type data directly. The applicability of the
1069 method is tested on simulated data sets and
1070 experimental data for mutants of titin I27.",
1071 URL = "http://www.pnas.org/cgi/content/abstract/99/19/12143",
1072 eprint = "http://www.pnas.org/cgi/reprint/99/19/12143.pdf",
1076 author = "Th. Basche and S. Nie and J. M. Fernandez",
1077 title = "{Single molecules}",
1078 journal = "Proceedings of the National Academy of Sciences",
1081 pages = "10527--10528",
1082 doi = "10.1073/pnas.191365898",
1084 URL = "http://www.pnas.org",
1085 eprint = "http://www.pnas.org/cgi/reprint/98/19/10527.pdf",
1089 author = "Hongbin Li and Andres F. Oberhauser and Sambra D.
1090 Redick and Mariano Carrion-Vazquez and Harold P.
1091 Erickson and Julio M. Fernandez",
1092 title = "{Multiple conformations of PEVK proteins detected by
1093 single-molecule techniques}",
1094 journal = "Proceedings of the National Academy of Sciences",
1097 pages = "10682--10686",
1098 doi = "10.1073/pnas.191189098",
1100 abstract = "An important component of muscle elasticity is the
1101 PEVK region of titin, so named because of the
1102 preponderance of these amino acids. However, the PEVK
1103 region, similar to other elastomeric proteins, is
1104 thought to form a random coil and therefore its
1105 structure cannot be determined by standard techniques.
1106 Here we combine single-molecule electron microscopy and
1107 atomic force microscopy to examine the conformations of
1108 the human cardiac titin PEVK region. In contrast to a
1109 simple random coil, we have found that cardiac PEVK
1110 shows a wide range of elastic conformations with
1111 end-to-end distances ranging from 9 to 24 nm and
1112 persistence lengths from 0.4 to 2.5 nm. Individual PEVK
1113 molecules retained their distinctive elastic
1114 conformations through many stretch-relaxation cycles,
1115 consistent with the view that these PEVK conformers
1116 cannot be interconverted by force. The multiple elastic
1117 conformations of cardiac PEVK may result from varying
1118 degrees of proline isomerization. The single-molecule
1119 techniques demonstrated here may help elucidate the
1120 conformation of other proteins that lack a well-defined
1122 URL = "http://www.pnas.org/cgi/content/abstract/98/19/10682",
1123 eprint = "http://www.pnas.org/cgi/reprint/98/19/10682.pdf",
1127 author = "Philippe Carl and Carol H. Kwok and Gavin Manderson
1128 and David W. Speicher and Dennis E. Discher",
1129 title = "{Forced unfolding modulated by disulfide bonds in the
1130 Ig domains of a cell adhesion molecule}",
1131 journal = "Proceedings of the National Academy of Sciences",
1134 pages = "1565--1570",
1135 doi = "10.1073/pnas.031409698",
1138 URL = "http://www.pnas.org/cgi/content/abstract/98/4/1565",
1139 eprint = "http://www.pnas.org/cgi/reprint/98/4/1565.pdf",
1143 author = "D. K. Klimov and D. Thirumalai",
1144 title = "{Native topology determines force-induced unfolding
1145 pathways in globular proteins}",
1146 journal = "Proceedings of the National Academy of Sciences",
1149 pages = "7254--7259",
1150 doi = "10.1073/pnas.97.13.7254",
1154 keywords = "Animals",
1155 keywords = "Humans",
1156 keywords = "Protein Folding",
1157 keywords = "Proteins",
1158 keywords = "Spectrin",
1159 abstract = "Single-molecule manipulation techniques reveal that
1160 stretching unravels individually folded domains in the
1161 muscle protein titin and the extracellular matrix
1162 protein tenascin. These elastic proteins contain tandem
1163 repeats of folded domains with beta-sandwich
1164 architecture. Herein, we propose by stretching two
1165 model sequences (S1 and S2) with four-stranded
1166 beta-barrel topology that unfolding forces and pathways
1167 in folded domains can be predicted by using only the
1168 structure of the native state. Thermal refolding of S1
1169 and S2 in the absence of force proceeds in an
1170 all-or-none fashion. In contrast, phase diagrams in the
1171 force-temperature (f,T) plane and steered Langevin
1172 dynamics studies of these sequences, which differ in
1173 the native registry of the strands, show that S1
1174 unfolds in an allor-none fashion, whereas unfolding of
1175 S2 occurs via an obligatory intermediate. Force-induced
1176 unfolding is determined by the native topology. After
1177 proving that the simulation results for S1 and S2 can
1178 be calculated by using native topology alone, we
1179 predict the order of unfolding events in Ig domain
1180 (Ig27) and two fibronectin III type domains ((9)FnIII
1181 and (10)FnIII). The calculated unfolding pathways for
1182 these proteins, the location of the transition states,
1183 and the pulling speed dependence of the unfolding
1184 forces reflect the differences in the way the strands
1185 are arranged in the native states. We also predict the
1186 mechanisms of force-induced unfolding of the
1187 coiled-coil spectrin (a three-helix bundle protein) for
1188 all 20 structures deposited in the Protein Data Bank.
1189 Our approach suggests a natural way to measure the
1190 phase diagram in the (f,C) plane, where C is the
1191 concentration of denaturants.",
1193 URL = "http://www.pnas.org/cgi/content/abstract/97/13/7254",
1194 URLB = "http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=16532",
1195 eprint = "http://www.pnas.org/cgi/reprint/97/13/7254.pdf",
1196 note = "Simulated unfolding timescales for Ig27-like S1 and S2 domains",
1200 author = "Hongbin Li and Andres F. Oberhauser and Susan B.
1201 Fowler and Jane Clarke and Julio M. Fernandez",
1202 title = "{Atomic force microscopy reveals the mechanical design
1203 of a modular protein}",
1204 journal = "Proceedings of the National Academy of Sciences",
1207 pages = "6527--6531",
1208 doi = "10.1073/pnas.120048697",
1211 URL = "http://www.pnas.org/cgi/content/abstract/97/12/6527",
1212 eprint = "http://www.pnas.org/cgi/reprint/97/12/6527.pdf",
1216 author = "Rene A. Nome and Jason Ming Zhao and Wouter D. Hoff
1217 and Norbert F. Scherer",
1218 title = "Axis-dependent anisotropy in protein unfolding from
1219 integrated nonequilibrium single-molecule experiments,
1220 analysis, and simulation",
1221 journal = "Proceedings of the National Academy of Sciences",
1224 pages = "20799--20804",
1225 doi = "10.1073/pnas.0701281105",
1229 keywords = "Anisotropy",
1230 keywords = "Bacterial Proteins",
1231 keywords = "Biophysics",
1232 keywords = "Computer Simulation",
1233 keywords = "Cysteine",
1234 keywords = "Halorhodospira halophila",
1235 keywords = "Hydrogen Bonding",
1236 keywords = "Kinetics",
1237 keywords = "Luminescent Proteins",
1238 keywords = "Microscopy, Atomic Force",
1239 keywords = "Molecular Conformation",
1240 keywords = "Protein Binding",
1241 keywords = "Protein Conformation",
1242 keywords = "Protein Denaturation",
1243 keywords = "Protein Folding",
1244 keywords = "Protein Structure, Secondary",
1245 abstract = "We present a comprehensive study that integrates
1246 experimental and theoretical nonequilibrium techniques
1247 to map energy landscapes along well defined pull-axis
1248 specific coordinates to elucidate mechanisms of protein
1249 unfolding. Single-molecule force-extension experiments
1250 along two different axes of photoactive yellow protein
1251 combined with nonequilibrium statistical mechanical
1252 analysis and atomistic simulation reveal energetic and
1253 mechanistic anisotropy. Steered molecular dynamics
1254 simulations and free-energy curves constructed from the
1255 experimental results reveal that unfolding along one
1256 axis exhibits a transition-state-like feature where six
1257 hydrogen bonds break simultaneously with weak
1258 interactions observed during further unfolding. The
1259 other axis exhibits a constant (unpeaked) force profile
1260 indicative of a noncooperative transition, with
1261 enthalpic (e.g., H-bond) interactions being broken
1262 throughout the unfolding process. Striking qualitative
1263 agreement was found between the force-extension curves
1264 derived from steered molecular dynamics calculations
1265 and the equilibrium free-energy curves obtained by
1266 JarzynskiHummerSzabo analysis of the nonequilibrium
1267 work data. The anisotropy persists beyond pulling
1268 distances of more than twice the initial dimensions of
1269 the folded protein, indicating a rich energy landscape
1270 to the mechanically fully unfolded state. Our findings
1271 challenge the notion that cooperative unfolding is a
1272 universal feature in protein stability.",
1274 doi = "10.1073/pnas.0701281105",
1275 URL = "http://www.pnas.org/cgi/content/abstract/104/52/20799",
1276 eprint = "http://www.pnas.org/cgi/reprint/104/52/20799.pdf",
1280 author = "Sean P. Ng and Kate S. Billings and Tomoo Ohashi and
1281 Mark D. Allen and Robert B. Best and Lucy G. Randles
1282 and Harold P. Erickson and Jane Clarke",
1283 title = "{Designing an extracellular matrix protein with
1284 enhanced mechanical stability}",
1285 journal = "Proceedings of the National Academy of Sciences",
1288 pages = "9633--9637",
1289 doi = "10.1073/pnas.0609901104",
1291 abstract = "The extracellular matrix proteins tenascin and
1292 fibronectin experience significant mechanical forces in
1293 vivo. Both contain a number of tandem repeating
1294 homologous fibronectin type III (fnIII) domains, and
1295 atomic force microscopy experiments have demonstrated
1296 that the mechanical strength of these domains can vary
1297 significantly. Previous work has shown that mutations
1298 in the core of an fnIII domain from human tenascin
1299 (TNfn3) reduce the unfolding force of that domain
1300 significantly: The composition of the core is
1301 apparently crucial to the mechanical stability of these
1302 proteins. Based on these results, we have used rational
1303 redesign to increase the mechanical stability of the
1304 10th fnIII domain of human fibronectin, FNfn10, which
1305 is directly involved in integrin binding. The
1306 hydrophobic core of FNfn10 was replaced with that of
1307 the homologous, mechanically stronger TNfn3 domain.
1308 Despite the extensive substitution, FNoTNc retains both
1309 the three-dimensional structure and the cell adhesion
1310 activity of FNfn10. Atomic force microscopy experiments
1311 reveal that the unfolding forces of the engineered
1312 protein FNoTNc increase by {approx}20% to match those
1313 of TNfn3. Thus, we have specifically designed a protein
1314 with increased mechanical stability. Our results
1315 demonstrate that core engineering can be used to change
1316 the mechanical strength of proteins while retaining
1317 functional surface interactions.",
1318 URL = "http://www.pnas.org/cgi/content/abstract/104/23/9633",
1319 eprint = "http://www.pnas.org/cgi/reprint/104/23/9633.pdf",
1323 author = "Wei Zhuang and Darius Abramavicius and Shaul Mukamel",
1324 title = "{Two-dimensional vibrational optical probes for
1325 peptide fast folding investigation}",
1326 journal = "Proceedings of the National Academy of Sciences",
1329 pages = "18934--18938",
1330 doi = "10.1073/pnas.0606912103",
1332 abstract = "A simulation study shows that early protein folding
1333 events may be investigated by using a recently
1334 developed family of nonlinear infrared techniques that
1335 combine the high temporal and spatial resolution of
1336 multidimensional spectroscopy with the
1337 chirality-specific sensitivity of amide vibrations to
1338 structure. We demonstrate how the structural
1339 sensitivity of cross-peaks in two-dimensional
1340 correlation plots of chiral signals of an {alpha} helix
1341 and a [beta] hairpin may be used to clearly resolve
1342 structural and dynamical details undetectable by
1343 one-dimensional techniques (e.g. circular dichroism)
1344 and identify structures indistinguishable by NMR.",
1345 URL = "http://www.pnas.org/cgi/content/abstract/103/50/18934",
1346 eprint = "http://www.pnas.org/cgi/reprint/103/50/18934.pdf",
1350 author = "Dennis E. Discher and Nishant Bhasin and Colin P.
1352 title = "{Covalent chemistry on distended proteins}",
1353 journal = "Proceedings of the National Academy of Sciences",
1356 pages = "7533--7534",
1357 doi = "10.1073/pnas.0602388103",
1359 URL = "http://www.pnas.org",
1360 eprint = "http://www.pnas.org/cgi/reprint/103/20/7533.pdf",
1364 author = "Mai Suan Li and Chin-Kun Hu and Dmitri K. Klimov and
1366 title = "{Multiple stepwise refolding of immunoglobulin domain
1367 I27 upon force quench depends on initial conditions}",
1368 journal = "Proceedings of the National Academy of Sciences",
1372 doi = "10.1073/pnas.0503758103",
1374 abstract = "Mechanical folding trajectories for polyproteins
1375 starting from initially stretched conformations
1376 generated by single-molecule atomic force microscopy
1377 experiments [Fernandez, J. M. & Li, H. (2004) Science
1378 303, 1674-1678] show that refolding, monitored by the
1379 end-to-end distance, occurs in distinct multiple
1380 stages. To clarify the molecular nature of folding
1381 starting from stretched conformations, we have probed
1382 the folding dynamics, upon force quench, for the single
1383 I27 domain from the muscle protein titin by using a
1384 C{alpha}-Go model. Upon temperature quench, collapse
1385 and folding of I27 are synchronous. In contrast,
1386 refolding from stretched initial structures not only
1387 increases the folding and collapse time scales but also
1388 decouples the two kinetic processes. The increase in
1389 the folding times is associated primarily with the
1390 stretched state to compact random coil transition.
1391 Surprisingly, force quench does not alter the nature of
1392 the refolding kinetics, but merely increases the height
1393 of the free-energy folding barrier. Force quench
1394 refolding times scale as f1.gif, where {Delta}xf
1395 {approx} 0.6 nm is the location of the average
1396 transition state along the reaction coordinate given by
1397 end-to-end distance. We predict that {tau}F and the
1398 folding mechanism can be dramatically altered by the
1399 initial and/or final values of force. The implications
1400 of our results for design and analysis of experiments
1402 URL = "http://www.pnas.org/cgi/content/abstract/103/1/93",
1403 eprint = "http://www.pnas.org/cgi/reprint/103/1/93.pdf",
1407 author = "Anders Irback and Simon Mitternacht and Sandipan
1409 title = "{Dissecting the mechanical unfolding of ubiquitin}",
1410 journal = "Proceedings of the National Academy of Sciences",
1413 pages = "13427--13432",
1414 doi = "10.1073/pnas.0501581102",
1416 abstract = "The unfolding behavior of ubiquitin under the
1417 influence of a stretching force recently was
1418 investigated experimentally by single-molecule
1419 constant-force methods. Many observed unfolding traces
1420 had a simple two-state character, whereas others showed
1421 clear evidence of intermediate states. Here, we use
1422 Monte Carlo simulations to investigate the
1423 force-induced unfolding of ubiquitin at the atomic
1424 level. In agreement with experimental data, we find
1425 that the unfolding process can occur either in a single
1426 step or through intermediate states. In addition to
1427 this randomness, we find that many quantities, such as
1428 the frequency of occurrence of intermediates, show a
1429 clear systematic dependence on the strength of the
1430 applied force. Despite this diversity, one common
1431 feature can be identified in the simulated unfolding
1432 events, which is the order in which the
1433 secondary-structure elements break. This order is the
1434 same in two- and three-state events and at the
1435 different forces studied. The observed order remains to
1436 be verified experimentally but appears physically
1438 URL = "http://www.pnas.org/cgi/content/abstract/102/38/13427",
1439 eprint = "http://www.pnas.org/cgi/reprint/102/38/13427.pdf",
1443 author = "Atom Sarkar and Ragan B. Robertson and Julio M.
1445 title = "{Simultaneous atomic force microscope and fluorescence
1446 measurements of protein unfolding using a calibrated
1448 journal = "Proceedings of the National Academy of Sciences",
1451 pages = "12882--12886",
1452 doi = "10.1073/pnas.0403534101",
1454 abstract = "Fluorescence techniques for monitoring single-molecule
1455 dynamics in the vertical dimension currently do not
1456 exist. Here we use an atomic force microscope to
1457 calibrate the distance-dependent intensity decay of an
1458 evanescent wave. The measured evanescent wave transfer
1459 function was then used to convert the vertical motions
1460 of a fluorescent particle into displacement (SD = <1
1461 nm). We demonstrate the use of the calibrated
1462 evanescent wave to resolve the 20.1 {+/-} 0.5-nm step
1463 increases in the length of the small protein ubiquitin
1464 during forced unfolding. The experiments that we report
1465 here make an important contribution to fluorescence
1466 microscopy by demonstrating the unambiguous optical
1467 tracking of a single molecule with a resolution
1468 comparable to that of an atomic force microscope.",
1469 URL = "http://www.pnas.org/cgi/content/abstract/101/35/12882",
1470 eprint = "http://www.pnas.org/cgi/reprint/101/35/12882.pdf",
1473 @Article{bustanji03,
1474 author = "Yasser Bustanji and Carla Renata Arciola and Matteo
1475 Conti and Enrico Mandello and Lucio Montanaro and Bruno
1477 title = "{Dynamics of the interaction between a fibronectin
1478 molecule and a living bacterium under mechanical
1480 journal = "Proceedings of the National Academy of Sciences",
1483 pages = "13292--13297",
1484 doi = "10.1073/pnas.1735343100",
1486 abstract = "Fibronectin (Fn) is an important mediator of bacterial
1487 invasions and of persistent infections like that of
1488 Staphylococcus epidermis. Similar to many other types
1489 of cell-protein adhesion, the binding between Fn and S.
1490 epidermidis takes place under physiological shear
1491 rates. We investigated the dynamics of the interaction
1492 between individual living S. epidermidis cells and
1493 single Fn molecules under mechanical force by using the
1494 scanning force microscope. The mechanical strength of
1495 this interaction and the binding site in the Fn
1496 molecule were determined. The energy landscape of the
1497 binding/unbinding process was mapped, and the force
1498 spectrum and the association and dissociation rate
1499 constants of the binding pair were measured. The
1500 interaction between S. epidermidis cells and Fn
1501 molecules is compared with those of two other
1502 protein/ligand pairs known to mediate different dynamic
1503 states of adhesion of cells under a hydrodynamic flow:
1504 the firm adhesion mediated by biotin/avidin
1505 interactions, and the rolling adhesion, mediated by
1506 L-selectin/P-selectin glycoprotein ligand-1
1507 interactions. The inner barrier in the energy landscape
1508 of the Fn case characterizes a high-energy binding mode
1509 that can sustain larger deformations and for
1510 significantly longer times than the correspondent
1511 high-strength L-selectin/P-selectin glycoprotein
1512 ligand-1 binding mode. The association kinetics of the
1513 former interaction is much slower to settle than the
1514 latter. On this basis, the observations made at the
1515 macroscopic scale by other authors of a strong lability
1516 of the bacterial adhesions mediated by Fn under high
1517 turbulent flow are rationalized at the molecular
1519 URL = "http://www.pnas.org/cgi/content/abstract/100/23/13292",
1520 eprint = "http://www.pnas.org/cgi/reprint/100/23/13292.pdf",
1524 author = "W. Liu and Vedrana Montana and Edwin R. Chapman and U.
1525 Mohideen and Vladimir Parpura",
1526 title = "{Botulinum toxin type B micromechanosensor}",
1527 journal = "Proceedings of the National Academy of Sciences",
1530 pages = "13621--13625",
1531 doi = "10.1073/pnas.2233819100",
1533 abstract = "Botulinum neurotoxin (BoNT) types A, B, E, and F are
1534 toxic to humans; early and rapid detection is essential
1535 for adequate medical treatment. Presently available
1536 tests for detection of BoNTs, although sensitive,
1537 require hours to days. We report a BoNT-B sensor whose
1538 properties allow detection of BoNT-B within minutes.
1539 The technique relies on the detection of an agarose
1540 bead detachment from the tip of a micromachined
1541 cantilever resulting from BoNT-B action on its
1542 substratum, the synaptic protein synaptobrevin 2,
1543 attached to the beads. The mechanical resonance
1544 frequency of the cantilever is monitored for the
1545 detection. To suspend the bead off the cantilever we
1546 use synaptobrevin's molecular interaction with another
1547 synaptic protein, syntaxin 1A, that was deposited onto
1548 the cantilever tip. Additionally, this bead detachment
1549 technique is general and can be used in any
1550 displacement reaction, such as in receptor-ligand
1551 pairs, where the introduction of one chemical leads to
1552 the displacement of another. The technique is of broad
1553 interest and will find uses outside toxicology.",
1554 URL = "http://www.pnas.org/cgi/content/abstract/100/23/13621",
1555 eprint = "http://www.pnas.org/cgi/reprint/100/23/13621.pdf",
1558 @Article{oroudjev02,
1559 author = "E. Oroudjev and J. Soares and S. Arcidiacono and J. B.
1560 Thompson and S. A. Fossey and H. G. Hansma",
1561 title = "{Segmented nanofibers of spider dragline silk: Atomic
1562 force microscopy and single-molecule force
1564 journal = "Proceedings of the National Academy of Sciences",
1567 pages = "6460--6465",
1568 doi = "10.1073/pnas.082526499",
1570 abstract = "Despite its remarkable materials properties, the
1571 structure of spider dragline silk has remained
1572 unsolved. Results from two probe microscopy techniques
1573 provide new insights into the structure of spider
1574 dragline silk. A soluble synthetic protein from
1575 dragline silk spontaneously forms nanofibers, as
1576 observed by atomic force microscopy. These nanofibers
1577 have a segmented substructure. The segment length and
1578 amino acid sequence are consistent with a slab-like
1579 shape for individual silk protein molecules. The height
1580 and width of nanofiber segments suggest a stacking
1581 pattern of slab-like molecules in each nanofiber
1582 segment. This stacking pattern produces nano-crystals
1583 in an amorphous matrix, as observed previously by NMR
1584 and x-ray diffraction of spider dragline silk. The
1585 possible importance of nanofiber formation to native
1586 silk production is discussed. Force spectra for single
1587 molecules of the silk protein demonstrate that this
1588 protein unfolds through a number of rupture events,
1589 indicating a modular substructure within single silk
1590 protein molecules. A minimal unfolding module size is
1591 estimated to be around 14 nm, which corresponds to the
1592 extended length of a single repeated module, 38 amino
1593 acids long. The structure of this spider silk protein
1594 is distinctly different from the structures of other
1595 proteins that have been analyzed by single-molecule
1596 force spectroscopy, and the force spectra show
1597 correspondingly novel features.",
1598 URL = "http://www.pnas.org/cgi/content/abstract/99/suppl_2/6460",
1599 eprint = "http://www.pnas.org/cgi/reprint/99/suppl_2/6460.pdf",
1603 author = "Gretchen Baneyx and Loren Baugh and Viola Vogel",
1604 title = "{Supramolecular Chemistry And Self-assembly Special
1605 Feature: Fibronectin extension and unfolding within
1606 cell matrix fibrils controlled by cytoskeletal
1608 journal = "Proceedings of the National Academy of Sciences",
1611 pages = "5139--5143",
1612 doi = "10.1073/pnas.072650799",
1614 abstract = "Evidence is emerging that mechanical stretching can
1615 alter the functional states of proteins. Fibronectin
1616 (Fn) is a large, extracellular matrix protein that is
1617 assembled by cells into elastic fibrils and subjected
1618 to contractile forces. Assembly into fibrils coincides
1619 with expression of biological recognition sites that
1620 are buried in Fn's soluble state. To investigate how
1621 supramolecular assembly of Fn into fibrillar matrix
1622 enables cells to mechanically regulate its structure,
1623 we used fluorescence resonance energy transfer (FRET)
1624 as an indicator of Fn conformation in the fibrillar
1625 matrix of NIH 3T3 fibroblasts. Fn was randomly labeled
1626 on amine residues with donor fluorophores and
1627 site-specifically labeled on cysteine residues in
1628 modules FnIII7 and FnIII15 with acceptor fluorophores.
1629 Intramolecular FRET was correlated with known
1630 structural changes of Fn in denaturing solution, then
1631 applied in cell culture as an indicator of Fn
1632 conformation within the matrix fibrils of NIH 3T3
1633 fibroblasts. Based on the level of FRET, Fn in many
1634 fibrils was stretched by cells so that its dimer arms
1635 were extended and at least one FnIII module unfolded.
1636 When cytoskeletal tension was disrupted using
1637 cytochalasin D, FRET increased, indicating refolding of
1638 Fn within fibrils. These results suggest that
1639 cell-generated force is required to maintain Fn in
1640 partially unfolded conformations. The results support a
1641 model of Fn fibril elasticity based on unraveling and
1642 refolding of FnIII modules. We also observed variation
1643 of FRET between and along single fibrils, indicating
1644 variation in the degree of unfolding of Fn in fibrils.
1645 Molecular mechanisms by which mechanical force can
1646 alter the structure of Fn, converting tensile forces
1647 into biochemical cues, are discussed.",
1648 URL = "http://www.pnas.org/cgi/content/abstract/99/8/5139",
1649 eprint = "http://www.pnas.org/cgi/reprint/99/8/5139.pdf",
1652 @Article{brower-toland02,
1653 author = "Brent D. Brower-Toland and Corey L. Smith and Richard
1654 C. Yeh and John T. Lis and Craig L. Peterson and
1656 title = "{From the Cover: Mechanical disruption of individual
1657 nucleosomes reveals a reversible multistage release of
1659 journal = "Proceedings of the National Academy of Sciences",
1662 pages = "1960--1965",
1663 doi = "10.1073/pnas.022638399",
1665 abstract = "The dynamic structure of individual nucleosomes was
1666 examined by stretching nucleosomal arrays with a
1667 feedback-enhanced optical trap. Forced disassembly of
1668 each nucleosome occurred in three stages. Analysis of
1669 the data using a simple worm-like chain model yields 76
1670 bp of DNA released from the histone core at low
1671 stretching force. Subsequently, 80 bp are released at
1672 higher forces in two stages: full extension of DNA with
1673 histones bound, followed by detachment of histones.
1674 When arrays were relaxed before the dissociated state
1675 was reached, nucleosomes were able to reassemble and to
1676 repeat the disassembly process. The kinetic parameters
1677 for nucleosome disassembly also have been determined.",
1678 URL = "http://www.pnas.org/cgi/content/abstract/99/4/1960",
1679 eprint = "http://www.pnas.org/cgi/reprint/99/4/1960.pdf",
1683 author = "Gerhard Hummer and Attila Szabo",
1684 title = "{From the Cover: Free energy reconstruction from
1685 nonequilibrium single-molecule pulling experiments}",
1686 journal = "Proceedings of the National Academy of Sciences",
1689 pages = "3658--3661",
1690 doi = "10.1073/pnas.071034098",
1692 URL = "http://www.pnas.org/cgi/content/abstract/98/7/3658",
1693 eprint = "http://www.pnas.org/cgi/reprint/98/7/3658.pdf",
1697 author = "David S. Talaga and Wai Leung Lau and Heinrich Roder
1698 and Jianyong Tang and Yiwei Jia and William F. DeGrado
1699 and Robin M. Hochstrasser",
1700 title = "{Dynamics and folding of single two-stranded
1701 coiled-coil peptides studied by fluorescent energy
1702 transfer confocal microscopy}",
1703 journal = "Proceedings of the National Academy of Sciences",
1706 pages = "13021--13026",
1707 doi = "10.1073/pnas.97.24.13021",
1709 URL = "http://www.pnas.org/cgi/content/abstract/97/24/13021",
1710 eprint = "http://www.pnas.org/cgi/reprint/97/24/13021.pdf",
1714 author = "C. Gergely and J.-C. Voegel and P. Schaaf and B.
1715 Senger and M. Maaloum and J. K. H. Horber and J.
1717 title = "{Unbinding process of adsorbed proteins under external
1718 stress studied by atomic force microscopy
1720 journal = "Proceedings of the National Academy of Sciences",
1723 pages = "10802--10807",
1724 doi = "10.1073/pnas.180293097",
1726 URL = "http://www.pnas.org/cgi/content/abstract/97/20/10802",
1727 eprint = "http://www.pnas.org/cgi/reprint/97/20/10802.pdf",
1731 author = "Emanuele Paci and Martin Karplus",
1732 title = "{Unfolding proteins by external forces and
1733 temperature: The importance of topology and
1735 journal = "Proceedings of the National Academy of Sciences",
1738 pages = "6521--6526",
1739 doi = "10.1073/pnas.100124597",
1741 URL = "http://www.pnas.org/cgi/content/abstract/97/12/6521",
1742 eprint = "http://www.pnas.org/cgi/reprint/97/12/6521.pdf",
1746 author = "Guoliang Yang and Ciro Cecconi and Walter A. Baase and
1747 Ingrid R. Vetter and Wendy A. Breyer and Julie A. Haack
1748 and Brian W. Matthews and Frederick W. Dahlquist and
1750 title = "{Solid-state synthesis and mechanical unfolding of
1751 polymers of T4 lysozyme}",
1752 journal = "Proceedings of the National Academy of Sciences",
1756 doi = "10.1073/pnas.97.1.139",
1758 URL = "http://www.pnas.org/cgi/content/abstract/97/1/139",
1759 eprint = "http://www.pnas.org/cgi/reprint/97/1/139.pdf",
1763 author = "Torsten Strunz and Krisztina Oroszlan and Rolf Schafer
1764 and Hans-Joachim Guntherodt",
1765 title = "{Dynamic force spectroscopy of single DNA molecules}",
1766 journal = "Proceedings of the National Academy of Sciences",
1769 pages = "11277--11282",
1770 doi = "10.1073/pnas.96.20.11277",
1772 URL = "http://www.pnas.org/cgi/content/abstract/96/20/11277",
1773 eprint = "http://www.pnas.org/cgi/reprint/96/20/11277.pdf",
1776 @Article{carrion-vazquez99b,
1777 author = "Mariano Carrion-Vazquez and Andres F. Oberhauser and
1778 Susan B. Fowler and Piotr E. Marszalek and Sheldon E.
1779 Broedel and Jane Clarke and Julio M. Fernandez",
1780 title = "Mechanical and chemical unfolding of a single
1781 protein: A comparison",
1782 journal = "Proceedings of the National Academy of Sciences",
1785 pages = "3694--3699",
1786 doi = "10.1073/pnas.96.7.3694",
1788 URL = "http://www.pnas.org/cgi/content/abstract/96/7/3694",
1789 eprint = "http://www.pnas.org/cgi/reprint/96/7/3694.pdf",
1793 author = "Reinat Nevo and Vlad Brumfeld and Michael Elbaum and
1794 Peter Hinterdorfer and Ziv Reich",
1795 title = "Direct discrimination between models of protein
1796 activation by single-molecule force measurements.",
1797 journal = "Biophys J",
1802 pages = "2630--2634",
1803 keywords = "Elasticity",
1804 keywords = "Enzyme Activation",
1805 keywords = "Micromanipulation",
1806 keywords = "Microscopy, Atomic Force",
1807 keywords = "Models, Chemical",
1808 keywords = "Models, Molecular",
1809 keywords = "Multiprotein Complexes",
1810 keywords = "Nuclear Proteins",
1811 keywords = "Physical Stimulation",
1812 keywords = "Protein Binding",
1813 keywords = "Stress, Mechanical",
1814 keywords = "Structure-Activity Relationship",
1815 keywords = "beta Karyopherins",
1816 keywords = "ran GTP-Binding Protein",
1817 abstract = "The limitations imposed on the analyses of complex
1818 chemical and biological systems by ensemble averaging
1819 can be overcome by single-molecule experiments. Here,
1820 we used a single-molecule technique to discriminate
1821 between two generally accepted mechanisms of a key
1822 biological process--the activation of proteins by
1823 molecular effectors. The two mechanisms, namely
1824 induced-fit and population-shift, are normally
1825 difficult to discriminate by ensemble approaches. As a
1826 model, we focused on the interaction between the
1827 nuclear transport effector, RanBP1, and two related
1828 complexes consisting of the nuclear import receptor,
1829 importin beta, and the GDP- or GppNHp-bound forms of
1830 the small GTPase, Ran. We found that recognition by the
1831 effector proceeds through either an induced-fit or a
1832 population-shift mechanism, depending on the substrate,
1833 and that the two mechanisms can be differentiated by
1836 doi = "10.1529/biophysj.104.041889",
1837 URL = "http://www.biophysj.org/cgi/content/abstract/87/4/2630",
1838 eprint = "http://www.biophysj.org/cgi/reprint/87/4/2630.pdf",
1842 author = "Reinat Nevo and Cordula Stroh and Ferry Kienberger and
1843 David Kaftan and Vlad Brumfeld and Michael Elbaum and
1844 Ziv Reich and Peter Hinterdorfer",
1845 title = "A molecular switch between alternative conformational
1846 states in the complex of Ran and importin beta1.",
1847 journal = "Nat Struct Biol",
1853 keywords = "Guanosine Diphosphate",
1854 keywords = "Guanosine Triphosphate",
1855 keywords = "Microscopy, Atomic Force",
1856 keywords = "Protein Binding",
1857 keywords = "Protein Conformation",
1858 keywords = "beta Karyopherins",
1859 keywords = "ran GTP-Binding Protein",
1860 abstract = "Several million macromolecules are exchanged each
1861 minute between the nucleus and cytoplasm by
1862 receptor-mediated transport. Most of this traffic is
1863 controlled by the small GTPase Ran, which regulates
1864 assembly and disassembly of the receptor-cargo
1865 complexes in the appropriate cellular compartment. Here
1866 we applied dynamic force spectroscopy to study the
1867 interaction of Ran with the nuclear import receptor
1868 importin beta1 (impbeta) at the single-molecule level.
1869 We found that the complex alternates between two
1870 distinct conformational states of different adhesion
1871 strength. The application of an external mechanical
1872 force shifts equilibrium toward one of these states by
1873 decreasing the height of the interstate activation
1874 energy barrier. The other state can be stabilized by a
1875 functional Ran mutant that increases this barrier.
1876 These results support a model whereby functional
1877 control of Ran-impbeta is achieved by a population
1878 shift between pre-existing alternative conformations.",
1880 doi = "10.1038/nsb940",
1881 URL = "http://www.nature.com/nsmb/journal/v10/n7/abs/nsb940.html",
1882 eprint = "http://www.nature.com/nsmb/journal/v10/n7/pdf/nsb940.pdf",
1885 @Article{grossman05,
1886 title = "Optical Tweezers Advanced Lab",
1887 author = "C. Grossman and A. Stout",
1891 eprint = "http://chirality.swarthmore.edu/PHYS81/OpticalTweezers.pdf",
1892 note = "Fairly complete overdamped PSD derivation in section
1893 4.3., cites \cite{tlusty98} and \cite{bechhoefer02} for
1894 further details. However, Tlusty (listed as reference
1895 8) doesn't contain the thermal response fn.\ derivation
1896 it was cited for. Also, the single sided PSD definition
1897 credited to reference 9 (listed as Bechhoefer) looks
1898 more like Press (listed as reference 10). I imagine
1899 Grossman and Stout mixed up their references, and meant
1900 to refer to \cite{bechhoefer02} and \cite{press92}
1901 respectively instead.",
1902 project = "Cantilever Calibration",
1906 title = "Optical Gradient Forces of Strongly Localized Fields",
1907 author = "Tsvi Tlusty and Amit Meller and Roy Bar-Ziv",
1908 journal = "Phys. Rev. Lett.",
1911 pages = "1738--1741",
1915 doi = "10.1103/PhysRevLett.81.1738",
1916 publisher = "American Physical Society",
1917 eprint = "http://prola.aps.org/pdf/PRL/v81/i8/p1738_1",
1919 \url{http://nanoscience.bu.edu/papers/p1738_1_Meller.pdf}.
1920 Cited by \cite{grossman05} for derivation of thermal
1921 response fn. However, I only see a referenced thermal
1922 energy when they list the likelyhood of a small
1923 partical (radius < $R_c$) escaping due to thermal
1924 energy, where $R_c$ is roughly $R_c \sim (k_B T /
1925 \alpha I_0)^(1/3)$, $\alpha$ is a dielectric scaling
1926 term, and $I_0$ is the maximum beam energy density. I
1927 imagine Grossman and Stout mixed up this reference.",
1928 project = "Cantilever Calibration",
1931 @Article{bechhoefer02,
1932 author = "John Bechhoefer and Scott Wilson",
1934 title = "Faster, cheaper, safer optical tweezers for the
1935 undergraduate laboratory",
1938 journal = "American Journal of Physics",
1942 keywords = "student experiments; safety; radiation pressure; laser
1944 URL = "http://link.aip.org/link/?AJP/70/393/1",
1945 doi = "10.1119/1.1445403",
1946 project = "Cantilever Calibration",
1947 note = "Good discussion of the effect of correlation time on
1948 calibration. Excellent detail on power spectrum
1949 derivation and thermal noise for extremely overdamped
1950 oscillators in Appendix A (references \cite{reif65}).
1951 References work on deconvolving thermal noise from
1952 other noise\cite{cowan98}",
1956 title = "Numerical Recipies in {C}: The Art of Scientific
1958 author = "W. Press and S. Teukolsky and W. Vetterling and B.
1961 publisher = "Cambridge University Press",
1962 address = "New York",
1964 eprint = "http://www.nrbook.com/a/bookcpdf.php",
1965 note = "See sections 12.0, 12.1, 12.3, and 13.4 for a good
1966 introduction to Fourier transforms and power spectrum
1968 project = "Cantilever Calibration",
1972 title = "Statistical Data Analysis",
1973 author = "Glen Cowan",
1974 publisher = "Oxford University Press",
1975 address = "New York",
1977 note = "Noise deconvolution in Chapter 11",
1978 project = "Cantilever Calibration",
1982 title = "Fundamentals of Statistical and Thermal Physics",
1983 author = "Frederick Rief",
1984 publisher = "McGraw-Hill",
1985 address = "New York",
1987 note = "Thermal noise for SHOs, in Chapter 15, Sections 6 and
1989 project = "Cantilever Calibration",
1992 @Article{schlierf06,
1993 author = "Michael Schlierf and Matthias Rief",
1994 title = "Single-molecule unfolding force distributions reveal a
1995 funnel-shaped energy landscape.",
1996 journal = "Biophys J",
2003 keywords = "Models, Molecular",
2004 keywords = "Protein Folding",
2005 keywords = "Proteins",
2006 keywords = "Thermodynamics",
2007 abstract = "The protein folding process is described as diffusion
2008 on a high-dimensional energy landscape. Experimental
2009 data showing details of the underlying energy surface
2010 are essential to understanding folding. So far in
2011 single-molecule mechanical unfolding experiments a
2012 simplified model assuming a force-independent
2013 transition state has been used to extract such
2014 information. Here we show that this so-called Bell
2015 model, although fitting well to force velocity data,
2016 fails to reproduce full unfolding force distributions.
2017 We show that by applying Kramers' diffusion model, we
2018 were able to reconstruct a detailed funnel-like
2019 curvature of the underlying energy landscape and
2020 establish full agreement with the data. We demonstrate
2021 that obtaining spatially resolved details of the
2022 unfolding energy landscape from mechanical
2023 single-molecule protein unfolding experiments requires
2024 models that go beyond the Bell model.",
2026 doi = "10.1529/biophysj.105.077982",
2027 URL = "http://www.biophysj.org/cgi/content/abstract/90/4/L33",
2028 note = "The inspiration behind my sawtooth simulation.
2029 Bell model fit to $f_{unfold}(v)$, but
2030 Kramers model fit to unfolding distribution for a given $v$.
2031 Eqn.~3 in the supplement is Evans-Ritchie 1999's Eqn.~2\cite{evans99}, but it is just ``[dying percent] * [surviving population] = [deaths]'' (TODO, check).
2032 $\nu \equiv k$ is the force/time-dependent off rate... (TODO)
2033 The Kramers' rate equation (second equation in the paper) is Hanggi Eq.~4.56b (page 275)\cite{hanggi90}.
2034 It is important to extract $k_0$ and $\Delta x$ using every
2039 author = "John F. Marko and Eric D. Siggia",
2040 title = "Stretching {DNA}",
2041 journal = "Macromolecules",
2044 pages = "8759--8770",
2047 URL = "http://pubs3.acs.org/acs/journals/doilookup?in_doi=10.1021/ma00130a008",
2050 eprint = "http://pubs.acs.org/cgi-bin/archive.cgi/mamobx/1995/28/i26/pdf/ma00130a008.pdf",
2051 note = "Derivation of the Worm-like Chain interpolation
2055 % 0021-4922 is the print ISSN. The online ISSN is 1347-4065.
2057 author = "Hendrik Dietz and Matthias Rief",
2058 title = "Detecting Molecular Fingerprints in Single Molecule
2059 Force Spectroscopy Using Pattern Recognition",
2060 journal = "Japanese Journal of Applied Physics",
2063 pages = "5540--5542",
2065 keywords = "single molecule, protein mechanics, force
2066 spectroscopy, AFM, pattern recognition, GFP",
2067 abstract = "Single molecule force spectroscopy has given
2068 experimental access to the mechanical properties of
2069 protein molecules. Typically, less than 1% of the
2070 experimental recordings reflect true single molecule
2071 events due to abundant surface and multiple-molecule
2072 interactions. A key issue in single molecule force
2073 spectroscopy is thus to identify the characteristic
2074 mechanical `fingerprint' of a specific protein in noisy
2075 data sets. Here, we present an objective pattern
2076 recognition algorithm that is able to identify
2077 fingerprints in such noisy data sets.",
2079 URL = "http://jjap.ipap.jp/link?JJAP/46/5540/",
2080 doi = "10.1143/JJAP.46.5540",
2081 note = "Automatic force curve selection. Seems a bit shoddy.
2086 author = "Ariel Kleiner and Eugene Shakhnovich",
2087 title = "The mechanical unfolding of ubiquitin through all-atom
2088 Monte Carlo simulation with a Go-type potential.",
2089 journal = "Biophys J",
2095 pages = "2054--2061",
2096 keywords = "Computer Simulation",
2097 keywords = "Models, Chemical",
2098 keywords = "Models, Molecular",
2099 keywords = "Models, Statistical",
2100 keywords = "Monte Carlo Method",
2101 keywords = "Motion",
2102 keywords = "Protein Conformation",
2103 keywords = "Protein Denaturation",
2104 keywords = "Protein Folding",
2105 keywords = "Ubiquitin",
2106 abstract = "The mechanical unfolding of proteins under a
2107 stretching force has an important role in living
2108 systems and is a logical extension of the more general
2109 protein folding problem. Recent advances in
2110 experimental methodology have allowed the stretching of
2111 single molecules, thus rendering this process ripe for
2112 computational study. We use all-atom Monte Carlo
2113 simulation with a G?-type potential to study the
2114 mechanical unfolding pathway of ubiquitin. A detailed,
2115 robust, well-defined pathway is found, confirming
2116 existing results in this vein though using a different
2117 model. Additionally, we identify the protein's
2118 fundamental stabilizing secondary structure
2119 interactions in the presence of a stretching force and
2120 show that this fundamental stabilizing role does not
2121 persist in the absence of mechanical stress. The
2122 apparent success of simulation methods in studying
2123 ubiquitin's mechanical unfolding pathway indicates
2124 their potential usefulness for future study of the
2125 stretching of other proteins and the relationship
2126 between protein structure and the response to
2127 mechanical deformation.",
2129 doi = "10.1529/biophysj.106.081257",
2130 URL = "http://www.biophysj.org/cgi/content/full/92/6/2054",
2131 eprint = "http://www.biophysj.org/cgi/reprint/92/6/2054",
2135 author = "Dmitrii E. Makarov and Paul K. Hansma and Horia
2138 title = "Kinetic Monte Carlo simulation of titin unfolding",
2141 journal = "The Journal of Chemical Physics",
2144 pages = "9663--9673",
2145 keywords = "proteins; hydrogen bonds; digital simulation; Monte
2146 Carlo methods; molecular biophysics; intramolecular
2147 mechanics; macromolecules; atomic force microscopy",
2148 URL = "http://link.aip.org/link/?JCP/114/9663/1",
2149 eprint = "http://hansmalab.physics.ucsb.edu/pdf/297%20-%20Makarov,%20D.E._J.Chem.Phys._2001.pdf",
2150 doi = "10.1063/1.1369622",
2154 title = "Elastically Coupled Two-Level Systems as a Model for
2155 Biopolymer Extensibility",
2156 author = "Matthias Rief and Julio M. Fernandez and Hermann E.
2158 journal = "Phys. Rev. Lett.",
2161 pages = "4764--4767",
2165 doi = "10.1103/PhysRevLett.81.4764",
2166 eprint = "http://prola.aps.org/pdf/PRL/v81/i21/p4764_1",
2167 publisher = "American Physical Society",
2171 author = "Rebecca C. Zinober and David J. Brockwell and Godfrey
2172 S. Beddard and Anthony W. Blake and Peter D. Olmsted
2173 and Sheena E. Radford and D. Alastair Smith",
2174 title = "Mechanically unfolding proteins: the effect of
2175 unfolding history and the supramolecular scaffold.",
2176 journal = "Protein Sci",
2181 pages = "2759--2765",
2182 keywords = "Computer Simulation",
2183 keywords = "Models, Molecular",
2184 keywords = "Monte Carlo Method",
2185 keywords = "Protein Folding",
2186 keywords = "Protein Structure, Tertiary",
2187 keywords = "Proteins",
2188 abstract = "The mechanical resistance of a folded domain in a
2189 polyprotein of five mutant I27 domains (C47S, C63S
2190 I27)(5)is shown to depend on the unfolding history of
2191 the protein. This observation can be understood on the
2192 basis of competition between two effects, that of the
2193 changing number of domains attempting to unfold, and
2194 the progressive increase in the compliance of the
2195 polyprotein as domains unfold. We present Monte Carlo
2196 simulations that show the effect and experimental data
2197 that verify these observations. The results are
2198 confirmed using an analytical model based on transition
2199 state theory. The model and simulations also predict
2200 that the mechanical resistance of a domain depends on
2201 the stiffness of the surrounding scaffold that holds
2202 the domain in vivo, and on the length of the unfolded
2203 domain. Together, these additional factors that
2204 influence the mechanical resistance of proteins have
2205 important consequences for our understanding of natural
2206 proteins that have evolved to withstand force.",
2208 doi = "10.1110/ps.0224602",
2209 URL = "http://www.proteinscience.org/cgi/content/abstract/11/12/2759",
2210 eprint = "http://www.proteinscience.org/cgi/reprint/11/12/2759.pdf",
2212 project = "sawtooth simulation",
2215 @Article{brockwell02,
2216 author = "David J. Brockwell and Godfrey S. Beddard and John
2217 Clarkson and Rebecca C. Zinober and Anthony W. Blake
2218 and John Trinick and Peter D. Olmsted and D. Alastair
2219 Smith and Sheena E. Radford",
2220 title = "The effect of core destabilization on the mechanical
2221 resistance of {I27}.",
2222 journal = "Biophys J",
2228 keywords = "Amino Acid Sequence",
2229 keywords = "Dose-Response Relationship, Drug",
2230 keywords = "Kinetics",
2231 keywords = "Magnetic Resonance Spectroscopy",
2232 keywords = "Models, Molecular",
2233 keywords = "Molecular Sequence Data",
2234 keywords = "Monte Carlo Method",
2235 keywords = "Muscle Proteins",
2236 keywords = "Mutation",
2237 keywords = "Peptide Fragments",
2238 keywords = "Protein Denaturation",
2239 keywords = "Protein Folding",
2240 keywords = "Protein Kinases",
2241 keywords = "Protein Structure, Secondary",
2242 keywords = "Protein Structure, Tertiary",
2243 keywords = "Proteins",
2244 keywords = "Thermodynamics",
2245 abstract = "It is still unclear whether mechanical unfolding
2246 probes the same pathways as chemical denaturation. To
2247 address this point, we have constructed a concatamer of
2248 five mutant I27 domains (denoted (I27)(5)*) and used it
2249 for mechanical unfolding studies. This protein consists
2250 of four copies of the mutant C47S, C63S I27 and a
2251 single copy of C63S I27. These mutations severely
2252 destabilize I27 (DeltaDeltaG(UN) = 8.7 and 17.9 kJ
2253 mol(-1) for C63S I27 and C47S, C63S I27, respectively).
2254 Both mutations maintain the hydrogen bond network
2255 between the A' and G strands postulated to be the major
2256 region of mechanical resistance for I27. Measuring the
2257 speed dependence of the force required to unfold
2258 (I27)(5)* in triplicate using the atomic force
2259 microscope allowed a reliable assessment of the
2260 intrinsic unfolding rate constant of the protein to be
2261 obtained (2.0 x 10(-3) s(-1)). The rate constant of
2262 unfolding measured by chemical denaturation is over
2263 fivefold faster (1.1 x 10(-2) s(-1)), suggesting that
2264 these techniques probe different unfolding pathways.
2265 Also, by comparing the parameters obtained from the
2266 mechanical unfolding of a wild-type I27 concatamer with
2267 that of (I27)(5)*, we show that although the observed
2268 forces are considerably lower, core destabilization has
2269 little effect on determining the mechanical sensitivity
2272 URL = "http://www.biophysj.org/cgi/content/abstract/83/1/458",
2273 eprint = {http://www.biophysj.org/cgi/reprint/83/1/458.pdf},
2276 @Article{Hummer2003,
2277 author = "Gerhard Hummer and Attila Szabo",
2278 title = "Kinetics from nonequilibrium single-molecule pulling
2280 journal = "Biophys J",
2286 keywords = "Computer Simulation",
2287 keywords = "Crystallography",
2288 keywords = "Energy Transfer",
2289 keywords = "Kinetics",
2290 keywords = "Lasers",
2291 keywords = "Micromanipulation",
2292 keywords = "Microscopy, Atomic Force",
2293 keywords = "Models, Molecular",
2294 keywords = "Molecular Conformation",
2295 keywords = "Motion",
2296 keywords = "Muscle Proteins",
2297 keywords = "Nanotechnology",
2298 keywords = "Physical Stimulation",
2299 keywords = "Protein Conformation",
2300 keywords = "Protein Denaturation",
2301 keywords = "Protein Folding",
2302 keywords = "Protein Kinases",
2303 keywords = "Stress, Mechanical",
2304 abstract = "Mechanical forces exerted by laser tweezers or atomic
2305 force microscopes can be used to drive rare transitions
2306 in single molecules, such as unfolding of a protein or
2307 dissociation of a ligand. The phenomenological
2308 description of pulling experiments based on Bell's
2309 expression for the force-induced rupture rate is found
2310 to be inadequate when tested against computer
2311 simulations of a simple microscopic model of the
2312 dynamics. We introduce a new approach of comparable
2313 complexity to extract more accurate kinetic information
2314 about the molecular events from pulling experiments.
2315 Our procedure is based on the analysis of a simple
2316 stochastic model of pulling with a harmonic spring and
2317 encompasses the phenomenological approach, reducing to
2318 it in the appropriate limit. Our approach is tested
2319 against computer simulations of a multimodule titin
2320 model with anharmonic linkers and then an illustrative
2321 application is made to the forced unfolding of I27
2322 subunits of the protein titin. Our procedure to extract
2323 kinetic information from pulling experiments is simple
2324 to implement and should prove useful in the analysis of
2325 experiments on a variety of systems.",
2327 URL = "http://www.biophysj.org/cgi/content/abstract/85/1/5",
2328 eprint = "http://www.biophysj.org/cgi/reprint/85/1/5.pdf",
2329 project = "sawtooth simulation",
2333 @Article{thirumalai05,
2334 author = "D. Thirumalai and C. Hyeon",
2335 title = "{RNA} and Protein Folding: Common Themes and
2337 journal = "Biochemistry",
2340 pages = "4957--4970",
2342 abstract = "Visualizing the navigation of an ensemble of unfolded
2343 molecules through the bumpy energy landscape in search
2344 of the native state gives a pictorial view of
2345 biomolecular folding. This picture, when combined with
2346 concepts in polymer theory, provides a unified theory
2347 of RNA and protein folding. Just as for proteins, the
2348 major folding free energy barrier for RNA scales
2349 sublinearly with the number of nucleotides, which
2350 allows us to extract the elusive prefactor for RNA
2351 folding. Several folding scenarios can be anticipated
2352 by considering variations in the energy landscape that
2353 depend on sequence, native topology, and external
2354 conditions. RNA and protein folding mechanism can be
2355 described by the kinetic partitioning mechanism (KPM)
2356 according to which a fraction () of molecules reaches
2357 the native state directly, whereas the remaining
2358 fraction gets kinetically trapped in metastable
2359 conformations. For two-state folders 1. Molecular
2360 chaperones are recruited to assist protein folding
2361 whenever is small. We show that the iterative annealing
2362 mechanism, introduced to describe chaperonin-mediated
2363 folding, can be generalized to understand
2364 protein-assisted RNA folding. The major differences
2365 between the folding of proteins and RNA arise in the
2366 early stages of folding. For RNA, folding can only
2367 begin after the polyelectrolyte problem is solved,
2368 whereas protein collapse requires burial of hydrophobic
2369 residues. Cross-fertilization of ideas between the two
2370 fields should lead to an understanding of how RNA and
2371 proteins solve their folding problems.",
2372 URL = "http://pubs3.acs.org/acs/journals/doilookup?in_doi=10.1021/bi047314+",
2373 affiliation = "Biophysics Program, and Department of Chemistry and
2374 Biochemistry, Institute for Physical Science and
2375 Technology, University of Maryland, College Park,
2378 note = "unfolding-refolding",
2381 @article{schwaiger05,
2382 author = "Ingo Schwaiger and Michael Schleicher and Angelika A.
2383 Noegel and Matthias Rief",
2384 title = "The folding pathway of a fast-folding immunoglobulin
2385 domain revealed by single-molecule mechanical
2387 journal = "EMBO Rep",
2393 keywords = "Animals",
2394 keywords = "Contractile Proteins",
2395 keywords = "Dictyostelium",
2396 keywords = "Immunoglobulins",
2397 keywords = "Kinetics",
2398 keywords = "Microfilament Proteins",
2399 keywords = "Models, Molecular",
2400 keywords = "Protein Folding",
2401 keywords = "Protein Structure, Tertiary",
2402 abstract = "The F-actin crosslinker filamin from Dictyostelium
2403 discoideum (ddFLN) has a rod domain consisting of six
2404 structurally similar immunoglobulin domains. When
2405 subjected to a stretching force, domain 4 unfolds at a
2406 lower force than all the other domains in the chain.
2407 Moreover, this domain shows a stable intermediate along
2408 its mechanical unfolding pathway. We have developed a
2409 mechanical single-molecule analogue to a double-jump
2410 stopped-flow experiment to investigate the folding
2411 kinetics and pathway of this domain. We show that an
2412 obligatory and productive intermediate also occurs on
2413 the folding pathway of the domain. Identical mechanical
2414 properties suggest that the unfolding and refolding
2415 intermediates are closely related. The folding process
2416 can be divided into two consecutive steps: in the first
2417 step 60 C-terminal amino acids form an intermediate at
2418 the rate of 55 s(-1); and in the second step the
2419 remaining 40 amino acids are packed on this core at the
2420 rate of 179 s(-1). This division increases the overall
2421 folding rate of this domain by a factor of ten compared
2422 with all other homologous domains of ddFLN that lack
2423 the folding intermediate.",
2425 doi = "10.1038/sj.embor.7400317",
2426 url = "http://www.nature.com/embor/journal/v6/n1/index.html",
2427 eprint = "http://www.nature.com/embor/journal/v6/n1/pdf/7400317.pdf",
2431 author = "E. Evans and K. Ritchie",
2432 title = "Strength of a weak bond connecting flexible polymer
2434 journal = "Biophys J",
2439 pages = "2439--2447",
2440 keywords = "Animals",
2441 keywords = "Biophysics",
2442 keywords = "Biopolymers",
2443 keywords = "Microscopy, Atomic Force",
2444 keywords = "Models, Chemical",
2445 keywords = "Muscle Proteins",
2446 keywords = "Protein Folding",
2447 keywords = "Protein Kinases",
2448 keywords = "Stochastic Processes",
2449 keywords = "Stress, Mechanical",
2450 keywords = "Thermodynamics",
2451 abstract = "Bond dissociation under steadily rising force occurs
2452 most frequently at a time governed by the rate of
2453 loading (Evans and Ritchie, 1997 Biophys. J.
2454 72:1541-1555). Multiplied by the loading rate, the
2455 breakage time specifies the force for most frequent
2456 failure (called bond strength) that obeys the same
2457 dependence on loading rate. The spectrum of bond
2458 strength versus log(loading rate) provides an image of
2459 the energy landscape traversed in the course of
2460 unbonding. However, when a weak bond is connected to
2461 very compliant elements like long polymers, the load
2462 applied to the bond does not rise steadily under
2463 constant pulling speed. Because of nonsteady loading,
2464 the most frequent breakage force can differ
2465 significantly from that of a bond loaded at constant
2466 rate through stiff linkages. Using generic models for
2467 wormlike and freely jointed chains, we have analyzed
2468 the kinetic process of failure for a bond loaded by
2469 pulling the polymer linkages at constant speed. We find
2470 that when linked by either type of polymer chain, a
2471 bond is likely to fail at lower force under steady
2472 separation than through stiff linkages. Quite
2473 unexpectedly, a discontinuous jump can occur in bond
2474 strength at slow separation speed in the case of long
2475 polymer linkages. We demonstrate that the predictions
2476 of strength versus log(loading rate) can rationalize
2477 conflicting results obtained recently for unfolding Ig
2478 domains along muscle titin with different force
2481 URL = {http://www.biophysj.org/cgi/content/abstract/76/5/2439},
2482 eprint = {http://www.biophysj.org/cgi/reprint/76/5/2439.pdf},
2483 note= {Develops Kramers improvement on Bell model for domain unfolding.
2484 Presents unfolding under variable loading rates.
2485 Often cited as the ``Bell-Evans'' model?
2486 They derive a unitless treatment, scaling force by $f_\beta$, TODO;
2487 time by $\tau_f$, TODO; elasiticity by compliance $c(f)$.
2488 The appendix has relaxation time formulas for WLC and FJC polymer models.},
2489 project = "sawtooth simulation",
2493 author = "E. Evans and K. Ritchie",
2494 title = "Dynamic strength of molecular adhesion bonds.",
2495 journal = "Biophys J",
2500 pages = "1541--1555",
2501 keywords = "Avidin",
2502 keywords = "Biotin",
2503 keywords = "Chemistry, Physical",
2504 keywords = "Computer Simulation",
2505 keywords = "Mathematics",
2506 keywords = "Monte Carlo Method",
2507 keywords = "Protein Binding",
2508 abstract = "In biology, molecular linkages at, within, and beneath
2509 cell interfaces arise mainly from weak noncovalent
2510 interactions. These bonds will fail under any level of
2511 pulling force if held for sufficient time. Thus, when
2512 tested with ultrasensitive force probes, we expect
2513 cohesive material strength and strength of adhesion at
2514 interfaces to be time- and loading rate-dependent
2515 properties. To examine what can be learned from
2516 measurements of bond strength, we have extended
2517 Kramers' theory for reaction kinetics in liquids to
2518 bond dissociation under force and tested the
2519 predictions by smart Monte Carlo (Brownian dynamics)
2520 simulations of bond rupture. By definition, bond
2521 strength is the force that produces the most frequent
2522 failure in repeated tests of breakage, i.e., the peak
2523 in the distribution of rupture forces. As verified by
2524 the simulations, theory shows that bond strength
2525 progresses through three dynamic regimes of loading
2526 rate. First, bond strength emerges at a critical rate
2527 of loading (> or = 0) at which spontaneous dissociation
2528 is just frequent enough to keep the distribution peak
2529 at zero force. In the slow-loading regime immediately
2530 above the critical rate, strength grows as a weak power
2531 of loading rate and reflects initial coupling of force
2532 to the bonding potential. At higher rates, there is
2533 crossover to a fast regime in which strength continues
2534 to increase as the logarithm of the loading rate over
2535 many decades independent of the type of attraction.
2536 Finally, at ultrafast loading rates approaching the
2537 domain of molecular dynamics simulations, the bonding
2538 potential is quickly overwhelmed by the rapidly
2539 increasing force, so that only naked frictional drag on
2540 the structure remains to retard separation. Hence, to
2541 expose the energy landscape that governs bond strength,
2542 molecular adhesion forces must be examined over an
2543 enormous span of time scales. However, a significant
2544 gap exists between the time domain of force
2545 measurements in the laboratory and the extremely fast
2546 scale of molecular motions. Using results from a
2547 simulation of biotin-avidin bonds (Izrailev, S., S.
2548 Stepaniants, M. Balsera, Y. Oono, and K. Schulten.
2549 1997. Molecular dynamics study of unbinding of the
2550 avidin-biotin complex. Biophys. J., this issue), we
2551 describe how Brownian dynamics can help bridge the gap
2552 between molecular dynamics and probe tests.",
2554 URL = {http://www.biophysj.org/cgi/content/abstract/72/4/1541},
2555 eprint = {http://www.biophysj.org/cgi/reprint/72/4/1541.pdf},
2556 project = "sawtooth simulation",
2559 @Article{shillcock98,
2560 title = {Escape from a metastable well under a time-ramped force},
2561 author = {Shillcock, Julian and Seifert, Udo },
2562 journal = {Phys. Rev. E},
2565 pages = {7301--7304},
2569 doi = {10.1103/PhysRevE.57.7301},
2570 publisher = {American Physical Society},
2571 url = "http://link.aps.org/abstract/PRE/v57/p7301",
2572 eprint = "http://prola.aps.org/pdf/PRE/v57/i6/p7301_1",
2573 project = "sawtooth simulation",
2576 @Article{hatfield99,
2577 title = {Dynamic Properties of an Extended Polymer in Solution},
2578 author = {Hatfield, John William and Quake, Stephen R.},
2579 journal = {Phys. Rev. Lett.},
2582 pages = {3548--3551},
2586 doi = {10.1103/PhysRevLett.82.3548},
2587 url = "http://link.aps.org/abstract/PRL/v82/p3548",
2588 publisher = {American Physical Society},
2589 note = "Defines WLC and FJC models, citing textbooks.",
2590 project = "sawtooth simulation",
2594 title = {Reaction-rate theory: fifty years after Kramers},
2595 author = {H\"anggi, Peter and Talkner, Peter and Borkovec, Michal },
2596 journal = {Rev. Mod. Phys.},
2603 doi = {10.1103/RevModPhys.62.251},
2604 url = {http://prola.aps.org/abstract/RMP/v62/i2/p251_1},
2605 eprint = {http://www.physik.uni-augsburg.de/theo1/hanggi/Papers/112.pdf},
2606 publisher = {American Physical Society},
2607 note = "\emph{The} Kramers' theory review article. See pages 268--279 for the Kramers-specific introduction.",
2608 project = "sawtooth simulation",
2611 % onuchic, contacting the folding funnnel with NMR, pnas 1997?
2613 @Article{onuchic1996,
2614 author = "J. N. Onuchic and N. D. Socci and Z. Luthey-Schulten
2616 title = "Protein folding funnels: the nature of the transition
2618 journal = "Fold Des",
2623 keywords = "Animals",
2624 keywords = "Cytochrome c Group",
2625 keywords = "Humans",
2626 keywords = "Infant",
2627 keywords = "Protein Folding",
2628 abstract = "BACKGROUND: Energy landscape theory predicts that the
2629 folding funnel for a small fast-folding alpha-helical
2630 protein will have a transition state half-way to the
2631 native state. Estimates of the position of the
2632 transition state along an appropriate reaction
2633 coordinate can be obtained from linear free energy
2634 relationships observed for folding and unfolding rate
2635 constants as a function of denaturant concentration.
2636 The experimental results of Huang and Oas for lambda
2637 repressor, Fersht and collaborators for C12, and Gray
2638 and collaborators for cytochrome c indicate a free
2639 energy barrier midway between the folded and unfolded
2640 regions. This barrier arises from an entropic
2641 bottleneck for the folding process. RESULTS: In keeping
2642 with the experimental results, lattice simulations
2643 based on the folding funnel description show that the
2644 transition state is not just a single conformation, but
2645 rather an ensemble of a relatively large number of
2646 configurations that can be described by specific values
2647 of one or a few order parameters (e.g. the fraction of
2648 native contacts). Analysis of this transition state or
2649 bottleneck region from our lattice simulations and from
2650 atomistic models for small alpha-helical proteins by
2651 Boczko and Brooks indicates a broad distribution for
2652 native contact participation in the transition state
2653 ensemble centered around 50\%. Importantly, however,
2654 the lattice-simulated transition state ensemble does
2655 include some particularly hot contacts, as seen in the
2656 experiments, which have been termed by others a folding
2657 nucleus. CONCLUSIONS: Linear free energy relations
2658 provide a crude spectroscopy of the transition state,
2659 allowing us to infer the values of a reaction
2660 coordinate based on the fraction of native contacts.
2661 This bottleneck may be thought of as a collection of
2662 delocalized nuclei where different native contacts will
2663 have different degrees of participation. The agreement
2664 between the experimental results and the theoretical
2665 predictions provides strong support for the landscape
2671 author = {N. D. Socci and J. N. Onuchic and P. G. Wolynes},
2673 title = {Diffusive dynamics of the reaction coordinate for protein folding funnels},
2676 journal = {The Journal of Chemical Physics},
2679 pages = {5860-5868},
2680 keywords = {PROTEINS; FOLDS; DIFFUSION; MONTE CARLO METHOD; SIMULATION; FREE ENERGY},
2681 abstract = {The quantitative description
2682 of model protein folding kinetics using a diffusive
2683 collective reaction coordinate is examined.
2684 Direct folding kinetics, diffusional coefficients
2685 and free energy profiles are determined
2686 from Monte Carlo simulations of a 27-mer, 3
2687 letter code lattice model, which corresponds
2688 roughly to a small helical protein. Analytic
2689 folding calculations, using simple diffusive rate
2690 theory, agree extremely well with the full simulation
2691 results. Folding in this system is best
2692 seen as a diffusive, funnel-like process.},
2693 url = {http://link.aip.org/link/?JCP/104/5860/1},
2694 doi = {10.1063/1.471317},
2695 eprint = {http://arxiv.org/pdf/cond-mat/9601091},
2696 note = {A nice introduction to some quantitative ramifications of the funnel energy landscape. There's also a bit of Kramers' theory and graph theory thrown in for good measure.},
2700 @Article{Schwaiger04,
2701 author = "Ingo Schwaiger and Angelika Kardinal and Michael
2702 Schleicher and Angelika A. Noegel and Matthias Rief",
2703 title = "A mechanical unfolding intermediate in an
2704 actin-crosslinking protein.",
2705 journal = "Nat Struct Mol Biol",
2712 keywords = "Actins",
2713 keywords = "Animals",
2714 keywords = "Contractile Proteins",
2715 keywords = "Cross-Linking Reagents",
2716 keywords = "Dictyostelium",
2717 keywords = "Dimerization",
2718 keywords = "Microfilament Proteins",
2719 keywords = "Microscopy, Atomic Force",
2720 keywords = "Mutagenesis, Site-Directed",
2721 keywords = "Protein Denaturation",
2722 keywords = "Protein Folding",
2723 keywords = "Protein Structure, Tertiary",
2724 keywords = "Protozoan Proteins",
2725 abstract = "Many F-actin crosslinking proteins consist of two
2726 actin-binding domains separated by a rod domain that
2727 can vary considerably in length and structure. In this
2728 study, we used single-molecule force spectroscopy to
2729 investigate the mechanics of the immunoglobulin (Ig)
2730 rod domains of filamin from Dictyostelium discoideum
2731 (ddFLN). We find that one of the six Ig domains unfolds
2732 at lower forces than do those of all other domains and
2733 exhibits a stable unfolding intermediate on its
2734 mechanical unfolding pathway. Amino acid inserts into
2735 various loops of this domain lead to contour length
2736 changes in the single-molecule unfolding pattern. These
2737 changes allowed us to map the stable core of
2738 approximately 60 amino acids that constitutes the
2739 unfolding intermediate. Fast refolding in combination
2740 with low unfolding forces suggest a potential in vivo
2741 role for this domain as a mechanically extensible
2742 element within the ddFLN rod.",
2744 doi = "10.1038/nsmb705",
2745 url = "http://www.nature.com/nsmb/journal/v11/n1/full/nsmb705.html",
2746 eprint = "http://www.nature.com/nsmb/journal/v11/n1/pdf/nsmb705.pdf",
2747 note = "ddFLN unfolding with WLC params for sacrificial domains.
2748 Gives persistence length $p = 0.5\mbox{ nm}$ in ``high force regime'', $p = 0.9\mbox{ nm}$ in ``low force regime'', with a transition at $F = 30\mbox{ pN}$.",
2749 project = "sawtooth simulation",
2753 author = {Yu-Jane Sheng and Shaoyi Jiang and Heng-Kwong Tsao},
2755 title = {Forced Kramers escape in single-molecule pulling experiments},
2758 journal = {The Journal of Chemical Physics},
2764 keywords = {molecular biophysics; bonds (chemical); proteins},
2765 url = {http://link.aip.org/link/?JCP/123/091102/1},
2766 doi = {10.1063/1.2046632},
2767 project = "sawtooth simulation",
2768 note = "Gives appropriate Einstein-S... relation for diffusion to damping",
2772 author = "G. I. Bell",
2773 title = "Models for the specific adhesion of cells to cells.",
2774 journal = "Science",
2781 keywords = "Antigen-Antibody Reactions",
2782 keywords = "Cell Adhesion",
2783 keywords = "Cell Membrane",
2784 keywords = "Chemistry, Physical",
2785 keywords = "Electrophysiology",
2786 keywords = "Enzymes",
2787 keywords = "Glycoproteins",
2788 keywords = "Kinetics",
2789 keywords = "Ligands",
2790 keywords = "Membrane Proteins",
2791 keywords = "Models, Biological",
2792 keywords = "Receptors, Drug",
2793 abstract = "A theoretical framework is proposed for the analysis
2794 of adhesion between cells or of cells to surfaces when
2795 the adhesion is mediated by reversible bonds between
2796 specific molecules such as antigen and antibody, lectin
2797 and carbohydrate, or enzyme and substrate. From a
2798 knowledge of the reaction rates for reactants in
2799 solution and of their diffusion constants both in
2800 solution and on membranes, it is possible to estimate
2801 reaction rates for membrane-bound reactants. Two models
2802 are developed for predicting the rate of bond formation
2803 between cells and are compared with experiments. The
2804 force required to separate two cells is shown to be
2805 greater than the expected electrical forces between
2806 cells, and of the same order of magnitude as the forces
2807 required to pull gangliosides and perhaps some integral
2808 membrane proteins out of the cell membrane.",
2810 url = "http://www.jstor.org/stable/1746930",
2811 note = "The Bell model and a fair bit of cell bonding background.",
2812 project = "sawtooth simulation",
2816 author = "Cecilia C. Mello and Doug Barrick",
2817 title = "An experimentally determined protein folding energy
2819 journal = "Proc Natl Acad Sci U S A",
2825 pages = "14102--14107",
2826 keywords = "Animals",
2827 keywords = "Ankyrin Repeat",
2828 keywords = "Circular Dichroism",
2829 keywords = "Drosophila Proteins",
2830 keywords = "Drosophila melanogaster",
2831 keywords = "Gene Deletion",
2832 keywords = "Models, Chemical",
2833 keywords = "Models, Molecular",
2834 keywords = "Protein Denaturation",
2835 keywords = "Protein Folding",
2836 keywords = "Protein Structure, Tertiary",
2837 keywords = "Spectrometry, Fluorescence",
2838 keywords = "Thermodynamics",
2840 abstract = "Energy landscapes have been used to conceptually
2841 describe and model protein folding but have been
2842 difficult to measure experimentally, in large part
2843 because of the myriad of partly folded protein
2844 conformations that cannot be isolated and
2845 thermodynamically characterized. Here we experimentally
2846 determine a detailed energy landscape for protein
2847 folding. We generated a series of overlapping
2848 constructs containing subsets of the seven ankyrin
2849 repeats of the Drosophila Notch receptor, a protein
2850 domain whose linear arrangement of modular structural
2851 units can be fragmented without disrupting structure.
2852 To a good approximation, stabilities of each construct
2853 can be described as a sum of energy terms associated
2854 with each repeat. The magnitude of each energy term
2855 indicates that each repeat is intrinsically unstable
2856 but is strongly stabilized by interactions with its
2857 nearest neighbors. These linear energy terms define an
2858 equilibrium free energy landscape, which shows an early
2859 free energy barrier and suggests preferred low-energy
2860 routes for folding.",
2862 doi = "10.1073/pnas.0403386101",
2865 @Article{Bryngelson1995,
2866 author = "J. D. Bryngelson and J. N. Onuchic and N. D. Socci and
2868 title = "Funnels, pathways, and the energy landscape of protein
2869 folding: a synthesis.",
2870 journal = "Proteins",
2876 keywords = "Amino Acid Sequence",
2877 keywords = "Chemistry, Physical",
2878 keywords = "Computer Simulation",
2879 keywords = "Data Interpretation, Statistical",
2880 keywords = "Kinetics",
2881 keywords = "Models, Chemical",
2882 keywords = "Molecular Sequence Data",
2883 keywords = "Protein Biosynthesis",
2884 keywords = "Protein Conformation",
2885 keywords = "Protein Folding",
2886 keywords = "Proteins",
2887 keywords = "Thermodynamics",
2888 abstract = "The understanding, and even the description of protein
2889 folding is impeded by the complexity of the process.
2890 Much of this complexity can be described and understood
2891 by taking a statistical approach to the energetics of
2892 protein conformation, that is, to the energy landscape.
2893 The statistical energy landscape approach explains when
2894 and why unique behaviors, such as specific folding
2895 pathways, occur in some proteins and more generally
2896 explains the distinction between folding processes
2897 common to all sequences and those peculiar to
2898 individual sequences. This approach also gives new,
2899 quantitative insights into the interpretation of
2900 experiments and simulations of protein folding
2901 thermodynamics and kinetics. Specifically, the picture
2902 provides simple explanations for folding as a two-state
2903 first-order phase transition, for the origin of
2904 metastable collapsed unfolded states and for the curved
2905 Arrhenius plots observed in both laboratory experiments
2906 and discrete lattice simulations. The relation of these
2907 quantitative ideas to folding pathways, to
2908 uniexponential vs. multiexponential behavior in protein
2909 folding experiments and to the effect of mutations on
2910 folding is also discussed. The success of energy
2911 landscape ideas in protein structure prediction is also
2912 described. The use of the energy landscape approach for
2913 analyzing data is illustrated with a quantitative
2914 analysis of some recent simulations, and a qualitative
2915 analysis of experiments on the folding of three
2916 proteins. The work unifies several previously proposed
2917 ideas concerning the mechanism protein folding and
2918 delimits the regions of validity of these ideas under
2919 different thermodynamic conditions.",
2921 doi = "10.1002/prot.340210302",
2924 @Article{Bryngelson1987,
2925 author = "J. D. Bryngelson and P. G. Wolynes",
2926 title = "Spin glasses and the statistical mechanics of protein
2928 journal = "Proc Natl Acad Sci U S A",
2933 pages = "7524--7528",
2934 keywords = "Kinetics",
2935 keywords = "Mathematics",
2936 keywords = "Models, Theoretical",
2937 keywords = "Protein Conformation",
2938 keywords = "Proteins",
2939 keywords = "Stochastic Processes",
2940 abstract = "The theory of spin glasses was used to study a simple
2941 model of protein folding. The phase diagram of the
2942 model was calculated, and the results of dynamics
2943 calculations are briefly reported. The relation of
2944 these results to folding experiments, the relation of
2945 these hypotheses to previous protein folding theories,
2946 and the implication of these hypotheses for protein
2947 folding prediction schemes are discussed.",
2949 note = "Seminal protein folding via energy landscape paper.",
2952 @Article{bustamante94,
2953 author = "C. Bustamante and J. F. Marko and E. D. Siggia and S.
2955 title = "Entropic elasticity of lambda-phage {DNA}.",
2956 journal = "Science",
2962 pages = "1599--1600",
2963 keywords = "Bacteriophage lambda",
2964 keywords = "DNA, Viral",
2965 keywords = "Least-Squares Analysis",
2966 keywords = "Thermodynamics",
2968 note = "WLC interpolation formula.",
2971 % see the list of BibTeX databases Beebe has compiled
2972 % http://www.math.utah.edu/~beebe/bibliographies.html
2974 % Beebe: http://www.math.utah.edu/pub/tex/bib/gnu.html
2975 @String{pub-NETWORK-THEORY = "Network Theory Ltd."}
2976 @String{pub-NETWORK-THEORY:adr = "Bristol, UK"}
2978 author = "Mark Galassi and Jim Davies and James Theiler and
2979 Brian Gough and Gerard Jungman and Michael Booth and
2981 title = "{GNU} Scientific Library: Reference Manual",
2982 publisher = pub-NETWORK-THEORY,
2983 address = pub-NETWORK-THEORY:adr,
2984 edition = "Second Revised",
2985 pages = "xvi + 601",
2987 ISBN = "0-9541617-3-4",
2988 ISBN-13 = "978-0-9541617-3-6",
2989 LCCN = "QA76.73.C15",
2990 bibdate = "Wed Oct 30 10:44:22 2002",
2991 acknowledgement = ack-nhfb,
2992 remark = "This is the revised and updated second edition of the
2993 manual, and corresponds to version 1.6 of the
2995 URL = "http://www.network-theory.co.uk/gsl/manual/",
2996 xxpages = "xvi + 580",
3001 author = {Arien Malec and Chris Pickett and Fredrik Hugosson and Robert Lemmen},
3002 version = {version 0.9.4},
3006 abstract = "Check is a unit testing framework for C. It features a simple interface for defining unit tests, putting little in the way of the developer. Tests are run in a separate address space, so Check can catch both assertion failures and code errors that cause segmentation faults or other signals. The output from unit tests can be used within source code editors and IDEs.",
3007 url = {http://check.sourceforge.net},
3012 author = {Norman Ramsey},
3013 version = {version 2.11b},
3017 abstract = "Noweb is a simple, extensible literate programming tool.",
3018 url = {http://www.eecs.harvard.edu/nr/noweb/},
3019 note = {Debian package by Federico Di Gregorio},
3024 author = {Guido {van Rossum} and others},
3025 version = {version 2.5.1},
3029 abstract = "Python is a dynamic object-oriented programming language.",
3030 url = {http://www.python.org/},
3034 author = {Eric Jones and Travis Oliphant and Pearu Peterson and others},
3035 title = {{SciPy}: Open source scientific tools for {Python}},
3037 url = "http://www.scipy.org/"
3041 author = {Nummela, Jeremiah and Andricioaei, Ioan},
3042 title = {{Exact Low-Force Kinetics from High-Force Single-Molecule Unfolding Events}},
3043 journal = {Biophys. J.},
3046 pages = {3373-3381},
3047 doi = {10.1529/biophysj.107.111658},
3049 abstract = {Mechanical forces play a key role in crucial cellular processes involving force-bearing biomolecules, as well as in novel single-molecule pulling experiments. We present an exact method that enables one to extrapolate, to low (or zero) forces, entire time-correlation functions and kinetic rate constants from the conformational dynamics either simulated numerically or measured experimentally at a single, relatively higher, external force. The method has twofold relevance: 1), to extrapolate the kinetics at physiological force conditions from molecular dynamics trajectories generated at higher forces that accelerate conformational transitions; and 2), to extrapolate unfolding rates from experimental force-extension single-molecule curves. The theoretical formalism, based on stochastic path integral weights of Langevin trajectories, is presented for the constant-force, constant loading rate, and constant-velocity modes of the pulling experiments. For the first relevance, applications are described for simulating the conformational isomerization of alanine dipeptide; and for the second relevance, the single-molecule pulling of RNA is considered. The ability to assign a weight to each trace in the single-molecule data also suggests a means to quantitatively compare unfolding pathways under different conditions.
3051 URL = {http://www.biophysj.org/cgi/content/abstract/93/10/3373},
3052 eprint = {http://www.biophysj.org/cgi/reprint/93/10/3373.pdf}
3055 @article{gompertz25,
3056 jstor_articletype = {primary_article},
3057 title = {On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies},
3058 author = {Gompertz, Benjamin},
3059 journal = {Philosophical Transactions of the Royal Society of London},
3060 jstor_issuetitle = {},
3063 jstor_formatteddate = {1825},
3065 url = {http://www.jstor.org/stable/107756},
3068 publisher = {The Royal Society},
3070 copyright = {Copyright © 1825 The Royal Society},
3075 author = "Olga K. Dudko and J{\'e}r{\^o}me Math{\'e} and Attila
3076 Szabo and Amit Meller and Gerhard Hummer",
3077 title = "Extracting kinetics from single-molecule force
3078 spectroscopy: nanopore unzipping of {DNA} hairpins.",
3079 journal = "Biophys J",
3085 pages = "4188--4195",
3086 keywords = "Computer Simulation",
3088 keywords = "Elasticity",
3089 keywords = "Mechanics",
3090 keywords = "Micromanipulation",
3091 keywords = "Microscopy, Atomic Force",
3092 keywords = "Models, Chemical",
3093 keywords = "Models, Molecular",
3094 keywords = "Nanostructures",
3095 keywords = "Nucleic Acid Conformation",
3096 keywords = "Porosity",
3097 keywords = "Stress, Mechanical",
3098 abstract = "Single-molecule force experiments provide powerful new
3099 tools to explore biomolecular interactions. Here, we
3100 describe a systematic procedure for extracting kinetic
3101 information from force-spectroscopy experiments, and
3102 apply it to nanopore unzipping of individual DNA
3103 hairpins. Two types of measurements are considered:
3104 unzipping at constant voltage, and unzipping at
3105 constant voltage-ramp speeds. We perform a global
3106 maximum-likelihood analysis of the experimental data at
3107 low-to-intermediate ramp speeds. To validate the
3108 theoretical models, we compare their predictions with
3109 two independent sets of data, collected at high ramp
3110 speeds and at constant voltage, by using a quantitative
3111 relation between the two types of measurements.
3112 Microscopic approaches based on Kramers theory of
3113 diffusive barrier crossing allow us to estimate not
3114 only intrinsic rates and transition state locations, as
3115 in the widely used phenomenological approach based on
3116 Bell's formula, but also free energies of activation.
3117 The problem of extracting unique and accurate kinetic
3118 parameters of a molecular transition is discussed in
3119 light of the apparent success of the microscopic
3120 theories in reproducing the experimental data.",
3122 doi = "10.1529/biophysj.106.102855",
3123 eprint = "http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1877759&blobtype=pdf",
3127 author = "Olga K. Dudko and Gerhard Hummer and Attila Szabo",
3128 title = "Intrinsic rates and activation free energies from
3129 single-molecule pulling experiments.",
3130 journal = "Phys Rev Lett",
3137 keywords = "Biophysics",
3138 keywords = "Computer Simulation",
3139 keywords = "Data Interpretation, Statistical",
3140 keywords = "Kinetics",
3141 keywords = "Micromanipulation",
3142 keywords = "Models, Chemical",
3143 keywords = "Models, Molecular",
3144 keywords = "Molecular Conformation",
3145 keywords = "Muscle Proteins",
3146 keywords = "Nucleic Acid Conformation",
3147 keywords = "Protein Binding",
3148 keywords = "Protein Denaturation",
3149 keywords = "Protein Folding",
3150 keywords = "Protein Kinases",
3152 keywords = "Stress, Mechanical",
3153 keywords = "Thermodynamics",
3154 keywords = "Time Factors",
3155 abstract = "We present a unified framework for extracting kinetic
3156 information from single-molecule pulling experiments at
3157 constant force or constant pulling speed. Our procedure
3158 provides estimates of not only (i) the intrinsic rate
3159 coefficient and (ii) the location of the transition
3160 state but also (iii) the free energy of activation. By
3161 analyzing simulated data, we show that the resulting
3162 rates of force-induced rupture are significantly more
3163 reliable than those obtained by the widely used
3164 approach based on Bell's formula. We consider the
3165 uniqueness of the extracted kinetic information and
3166 suggest guidelines to avoid over-interpretation of
3169 doi = "10.1103/PhysRevLett.96.108101",
3173 author = "Jong-Wuu Wu and Wen-Liang Hung and Chih-Hui Tsai",
3174 title = "Estimation of parameters of the {G}ompertz distribution using the least squares method.",
3175 journal = "Applied Mathematics and Computation",
3182 keywords = "Gompertz distribution; Least squares estimate; Maximum likelihood estimate; First failure-censored; Series system",
3183 abstract = "The Gompertz distribution has been used to describe human mortality and establish actuarial tables. Recently, this distribution has been again studied by some authors. The maximum likelihood estimates for the parameters of the Gompertz distribution has been discussed by Garg et al. [J. R. Statist. Soc. C 19 (1970) 152]. The purpose of this paper is to propose unweighted and weighted least squares estimates for parameters of the Gompertz distribution under the complete data and the first failure-censored data (series systems; see [J. Statist. Comput. Simulat. 52 (1995) 337]). A simulation study is carried out to compare the proposed estimators and the maximum likelihood estimators. Results of the simulation studies show that the performance of the weighted least squares estimators is acceptable.",
3185 doi = "10.1016/j.amc.2003.08.086",
3186 url = "http://www.sciencedirect.com/science/article/B6TY8-4B3NR1W-B/1/bbaa47878ada03c6ef8e681d03bb65d3",
3192 @Article{braverman08,
3193 author = "Elena Braverman and Reneeta Mamdani",
3194 title = "Continuous versus pulse harvesting for population
3195 models in constant and variable environment.",
3196 journal = "J Math Biol",
3203 abstract = "We consider both autonomous and nonautonomous
3204 population models subject to either impulsive or
3205 continuous harvesting. It is demonstrated in the paper
3206 that the impulsive strategy can be as good as the
3207 continuous one, but cannot outperform it. We introduce
3208 a model, where certain harm to the population is
3209 incorporated in each harvesting event, and study it for
3210 the logistic and the Gompertz laws of growth. In this
3211 case, impulsive harvesting is not only the optimal
3212 strategy but is the only possible one.",
3214 doi = "10.1007/s00285-008-0169-z",
3215 url = "http://www.springerlink.com/content/a1m23v50201m2401/",
3216 eprint = "http://www.springerlink.com/content/a1m23v50201m2401/fulltext.pdf",
3217 note = "An example of non-exponential Gomperz law.",
3220 @Article{gavrilov01,
3221 author = "L. A. Gavrilov and N. S. Gavrilova",
3222 title = "The reliability theory of aging and longevity.",
3223 journal = "J Theor Biol",
3233 keywords = "Animals",
3234 keywords = "Humans",
3235 keywords = "Longevity",
3236 keywords = "Middle Aged",
3237 keywords = "Models, Biological",
3238 keywords = "Survival Rate",
3239 keywords = "Systems Theory",
3240 abstract = "Reliability theory is a general theory about systems
3241 failure. It allows researchers to predict the
3242 age-related failure kinetics for a system of given
3243 architecture (reliability structure) and given
3244 reliability of its components. Reliability theory
3245 predicts that even those systems that are entirely
3246 composed of non-aging elements (with a constant failure
3247 rate) will nevertheless deteriorate (fail more often)
3248 with age, if these systems are redundant in
3249 irreplaceable elements. Aging, therefore, is a direct
3250 consequence of systems redundancy. Reliability theory
3251 also predicts the late-life mortality deceleration with
3252 subsequent leveling-off, as well as the late-life
3253 mortality plateaus, as an inevitable consequence of
3254 redundancy exhaustion at extreme old ages. The theory
3255 explains why mortality rates increase exponentially
3256 with age (the Gompertz law) in many species, by taking
3257 into account the initial flaws (defects) in newly
3258 formed systems. It also explains why organisms
3259 ``prefer'' to die according to the Gompertz law, while
3260 technical devices usually fail according to the Weibull
3261 (power) law. Theoretical conditions are specified when
3262 organisms die according to the Weibull law: organisms
3263 should be relatively free of initial flaws and defects.
3264 The theory makes it possible to find a general failure
3265 law applicable to all adult and extreme old ages, where
3266 the Gompertz and the Weibull laws are just special
3267 cases of this more general failure law. The theory
3268 explains why relative differences in mortality rates of
3269 compared populations (within a given species) vanish
3270 with age, and mortality convergence is observed due to
3271 the exhaustion of initial differences in redundancy
3272 levels. Overall, reliability theory has an amazing
3273 predictive and explanatory power with a few, very
3274 general and realistic assumptions. Therefore,
3275 reliability theory seems to be a promising approach for
3276 developing a comprehensive theory of aging and
3277 longevity integrating mathematical methods with
3278 specific biological knowledge.",
3280 doi = "10.1006/jtbi.2001.2430",
3281 note = "An example of exponential (standard) Gomperz law.",
3284 @Article{olshansky97,
3285 author = "S. J. Olshansky and B. A. Carnes",
3286 title = "Ever since Gompertz.",
3287 journal = "Demography",
3294 keywords = "Biometry",
3295 keywords = "History, 19th Century",
3296 keywords = "History, 20th Century",
3297 keywords = "Humans",
3298 keywords = "Life Tables",
3299 keywords = "Mortality",
3300 keywords = "Sexual Maturation",
3301 abstract = "In 1825 British actuary Benjamin Gompertz made a
3302 simple but important observation that a law of
3303 geometrical progression pervades large portions of
3304 different tables of mortality for humans. The simple
3305 formula he derived describing the exponential rise in
3306 death rates between sexual maturity and old age is
3307 commonly, referred to as the Gompertz equation-a
3308 formula that remains a valuable tool in demography and
3309 in other scientific disciplines. Gompertz's observation
3310 of a mathematical regularity in the life table led him
3311 to believe in the presence of a low of mortality that
3312 explained why common age patterns of death exist. This
3313 law of mortality has captured the attention of
3314 scientists for the past 170 years because it was the
3315 first among what are now several reliable empirical
3316 tools for describing the dying-out process of many
3317 living organisms during a significant portion of their
3318 life spans. In this paper we review the literature on
3319 Gompertz's law of mortality and discuss the importance
3320 of his observations and insights in light of research
3321 on aging that has taken place since then.",
3323 notes = "Hardly any actual math, but the references might be interesting.
3324 I'll look into them if I have the time.
3325 Available through several repositories.",
3326 url = "http://www.jstor.org/stable/2061656",
3330 author = "D. A. Juckett and B. Rosenberg",
3331 title = "Comparison of the Gompertz and Weibull functions as
3332 descriptors for human mortality distributions and their
3334 journal = "Mech Ageing Dev",
3340 keywords = "Adolescent",
3343 keywords = "Aged, 80 and over",
3345 keywords = "Biometry",
3347 keywords = "Child, Preschool",
3348 keywords = "Data Interpretation, Statistical",
3349 keywords = "Female",
3350 keywords = "Humans",
3351 keywords = "Infant",
3352 keywords = "Infant, Newborn",
3353 keywords = "Longitudinal Studies",
3355 keywords = "Middle Aged",
3356 keywords = "Models, Biological",
3357 keywords = "Models, Statistical",
3358 keywords = "Mortality",
3359 abstract = "The Gompertz and Weibull functions are compared with
3360 respect to goodness-of-fit to human mortality
3361 distributions; ability to describe mortality curve
3362 intersections; and, parameter interpretation. The
3363 Gompertz function is shown to be a better descriptor
3364 for 'all-causes' of deaths and combined disease
3365 categories while the Weibull function is shown to be a
3366 better descriptor of purer, single causes-of-death. A
3367 modified form of the Weibull function maps directly to
3368 the inherent degrees of freedom of human mortality
3369 distributions while the Gompertz function does not.
3370 Intersections in the old-age tails of mortality are
3371 explored in the context of both functions and, in
3372 particular, the relationship between distribution
3373 intersections, and the Gompertz ln[R0] versus alpha
3374 regression is examined. Evidence is also presented that
3375 mortality intersections are fundamental to the
3376 survivorship form and not the rate (hazard) form.
3377 Finally, comparisons are made to the parameter
3378 estimates in recent longitudinal Gompertzian analyses
3379 and the probable errors in those analyses are
3382 notes = "Nice table of various functions associated with Gompertz and Weibull models.",
3383 doi = "10.1016/0047-6374(93)90068-3"
3387 author = "Matthias Rief and Helmut Grubm{\"u}ller",
3388 title = "Force spectroscopy of single biomolecules.",
3389 journal = "Chemphyschem",
3396 keywords = "Ligands",
3397 keywords = "Microscopy, Atomic Force",
3398 keywords = "Polysaccharides",
3399 keywords = "Protein Denaturation",
3400 keywords = "Proteins",
3401 abstract = "Many processes in the body are effected and regulated
3402 by highly specialized protein molecules: These
3403 molecules certainly deserve the name ``biochemical
3404 nanomachines''. Recent progress in single-molecule
3405 experiments and corresponding simulations with
3406 supercomputers enable us to watch these
3407 ``nanomachines'' at work, revealing a host of
3408 astounding mechanisms. Examples are the fine-tuned
3409 movements of the binding pocket of a receptor protein
3410 locking into its ligand molecule and the forced
3411 unfolding of titin, which acts as a molecular shock
3412 absorber to protect muscle cells. At present, we are
3413 not capable of designing such high precision machines,
3414 but we are beginning to understand their working
3415 principles and to simulate and predict their
3418 doi = "10.1002/1439-7641(20020315)3:3<255::AID-CPHC255>3.0.CO;2-M",
3419 url = "http://www3.interscience.wiley.com/journal/91016383/abstract",
3420 note = "Nice, general review of force spectroscopy to 2002, but not much detail.",
3424 author = "M. Raible and M. Evstigneev and P. Reimann and F. W.
3425 Bartels and R. Ros",
3426 title = "Theoretical analysis of dynamic force spectroscopy
3427 experiments on ligand-receptor complexes.",
3428 journal = "J Biotechnol",
3435 keywords = "Binding Sites",
3436 keywords = "Computer Simulation",
3438 keywords = "DNA-Binding Proteins",
3439 keywords = "Elasticity",
3440 keywords = "Ligands",
3441 keywords = "Macromolecular Substances",
3442 keywords = "Micromanipulation",
3443 keywords = "Microscopy, Atomic Force",
3444 keywords = "Models, Chemical",
3445 keywords = "Molecular Biology",
3446 keywords = "Nucleic Acid Conformation",
3447 keywords = "Physical Stimulation",
3448 keywords = "Protein Binding",
3449 keywords = "Protein Conformation",
3450 keywords = "Stress, Mechanical",
3451 abstract = "The forced rupture of single chemical bonds in
3452 biomolecular compounds (e.g. ligand-receptor systems)
3453 as observed in dynamic force spectroscopy experiments
3454 is addressed. Under the assumption that the probability
3455 of bond rupture depends only on the instantaneously
3456 acting force, a data collapse onto a single master
3457 curve is predicted. For rupture data obtained
3458 experimentally by dynamic AFM force spectroscopy of a
3459 ligand-receptor bond between a DNA and a regulatory
3460 protein we do not find such a collapse. We conclude
3461 that the above mentioned, generally accepted assumption
3462 is not satisfied and we discuss possible
3465 doi = "10.1016/j.jbiotec.2004.04.017",
3469 author = "M. Raible and M. Evstigneev and F. W. Bartels and R.
3470 Eckel and M. Nguyen-Duong and R. Merkel and R. Ros and
3471 D. Anselmetti and P. Reimann",
3472 title = "Theoretical analysis of single-molecule force
3473 spectroscopy experiments: heterogeneity of chemical
3475 journal = "Biophys J",
3481 pages = "3851--3864",
3482 keywords = "Biomechanics",
3483 keywords = "Microscopy, Atomic Force",
3484 keywords = "Models, Molecular",
3485 keywords = "Statistical Distributions",
3486 keywords = "Thermodynamics",
3487 abstract = "We show that the standard theoretical framework in
3488 single-molecule force spectroscopy has to be extended
3489 to consistently describe the experimental findings. The
3490 basic amendment is to take into account heterogeneity
3491 of the chemical bonds via random variations of the
3492 force-dependent dissociation rates. This results in a
3493 very good agreement between theory and rupture data
3494 from several different experiments.",
3496 doi = "10.1529/biophysj.105.077099",
3497 url = "http://www.biophysj.org/cgi/content/abstract/90/11/3851",
3498 eprint = "http://www.biophysj.org/cgi/reprint/90/11/3851.pdf",
3502 author = {Attila Szabo and Klaus Schulten and Zan Schulten},
3504 title = {First passage time approach to diffusion controlled reactions},
3507 journal = {The Journal of Chemical Physics},
3510 pages = {4350-4357},
3511 keywords = {DIFFUSION; CHEMICAL REACTIONS; CHEMICAL REACTION KINETICS; PROBABILITY; DIFFERENTIAL EQUATIONS},
3512 url = {http://link.aip.org/link/?JCP/72/4350/1},
3513 doi = {10.1063/1.439715}
3517 author = "O. K. Dudko and A. E. Filippov and J. Klafter and M.
3519 title = "Beyond the conventional description of dynamic force
3520 spectroscopy of adhesion bonds.",
3521 journal = "Proc Natl Acad Sci U S A",
3527 pages = "11378--11381",
3528 keywords = "Spectrum Analysis",
3529 keywords = "Temperature",
3530 abstract = "Dynamic force spectroscopy of single molecules is
3531 described by a model that predicts a distribution of
3532 rupture forces, the corresponding mean rupture force,
3533 and variance, which are all amenable to experimental
3534 tests. The distribution has a pronounced asymmetry,
3535 which has recently been observed experimentally. The
3536 mean rupture force follows a (lnV)2/3 dependence on the
3537 pulling velocity, V, and differs from earlier
3538 predictions. Interestingly, at low pulling velocities,
3539 a rebinding process is obtained whose signature is an
3540 intermittent behavior of the spring force, which delays
3541 the rupture. An extension to include conformational
3542 changes of the adhesion complex is proposed, which
3543 leads to the possibility of bimodal distributions of
3546 doi = "10.1073/pnas.1534554100",
3547 url = "http://www.pnas.org/content/100/20/11378.abstract",
3548 eprint = "http://www.pnas.org/content/100/20/11378.full.pdf",
3552 author = "M. Balsera and S. Stepaniants and S. Izrailev and Y.
3553 Oono and K. Schulten",
3554 title = "Reconstructing potential energy functions from
3555 simulated force-induced unbinding processes.",
3556 journal = "Biophys J",
3561 pages = "1281--1287",
3562 keywords = "Binding Sites",
3563 keywords = "Biopolymers",
3564 keywords = "Kinetics",
3565 keywords = "Ligands",
3566 keywords = "Microscopy, Atomic Force",
3567 keywords = "Models, Chemical",
3568 keywords = "Molecular Conformation",
3569 keywords = "Protein Conformation",
3570 keywords = "Proteins",
3571 keywords = "Reproducibility of Results",
3572 keywords = "Stochastic Processes",
3573 keywords = "Thermodynamics",
3574 abstract = "One-dimensional stochastic models demonstrate that
3575 molecular dynamics simulations of a few nanoseconds can
3576 be used to reconstruct the essential features of the
3577 binding potential of macromolecules. This can be
3578 accomplished by inducing the unbinding with the help of
3579 external forces applied to the molecules, and
3580 discounting the irreversible work performed on the
3581 system by these forces. The fluctuation-dissipation
3582 theorem sets a fundamental limit on the precision with
3583 which the binding potential can be reconstructed by
3584 this method. The uncertainty in the resulting potential
3585 is linearly proportional to the irreversible component
3586 of work performed on the system during the simulation.
3587 These results provide an a priori estimate of the
3588 energy barriers observable in molecular dynamics
3591 url = "http://www.biophysj.org/cgi/content/abstract/73/3/1281",
3592 eprint = "http://www.biophysj.org/cgi/reprint/73/3/1281.pdf",
3595 @Article{izrailev97,
3596 author = "S. Izrailev and S. Stepaniants and M. Balsera and Y.
3597 Oono and K. Schulten",
3598 title = "Molecular dynamics study of unbinding of the
3599 avidin-biotin complex.",
3600 journal = "Biophys J",
3605 pages = "1568--1581",
3606 keywords = "Avidin",
3607 keywords = "Binding Sites",
3608 keywords = "Biotin",
3609 keywords = "Computer Simulation",
3610 keywords = "Hydrogen Bonding",
3611 keywords = "Mathematics",
3612 keywords = "Microscopy, Atomic Force",
3613 keywords = "Microspheres",
3614 keywords = "Models, Molecular",
3615 keywords = "Molecular Structure",
3616 keywords = "Protein Binding",
3617 keywords = "Protein Conformation",
3618 keywords = "Protein Folding",
3619 keywords = "Sepharose",
3620 abstract = "We report molecular dynamics simulations that induce,
3621 over periods of 40-500 ps, the unbinding of biotin from
3622 avidin by means of external harmonic forces with force
3623 constants close to those of AFM cantilevers. The
3624 applied forces are sufficiently large to reduce the
3625 overall binding energy enough to yield unbinding within
3626 the measurement time. Our study complements earlier
3627 work on biotin-streptavidin that employed a much larger
3628 harmonic force constant. The simulations reveal a
3629 variety of unbinding pathways, the role of key residues
3630 contributing to adhesion as well as the spatial range
3631 over which avidin binds biotin. In contrast to the
3632 previous studies, the calculated rupture forces exceed
3633 by far those observed. We demonstrate, in the framework
3634 of models expressed in terms of one-dimensional
3635 Langevin equations with a schematic binding potential,
3636 the associated Smoluchowski equations, and the theory
3637 of first passage times, that picosecond to nanosecond
3638 simulation of ligand unbinding requires such strong
3639 forces that the resulting protein-ligand motion
3640 proceeds far from the thermally activated regime of
3641 millisecond AFM experiments, and that simulated
3642 unbinding cannot be readily extrapolated to the
3643 experimentally observed rupture.",
3645 url = "http://www.biophysj.org/cgi/content/abstract/72/4/1568",
3646 eprint = "http://www.biophysj.org/cgi/reprint/72/4/1568.pdf",
3650 author = "B. Heymann and H. Grubm{\"u}ller",
3651 title = "Dynamic force spectroscopy of molecular adhesion
3653 journal = "Phys Rev Lett",
3659 pages = "6126--6129",
3660 abstract = "Recent advances in atomic force microscopy,
3661 biomembrane force probe experiments, and optical
3662 tweezers allow one to measure the response of single
3663 molecules to mechanical stress with high precision.
3664 Such experiments, due to limited spatial resolution,
3665 typically access only one single force value in a
3666 continuous force profile that characterizes the
3667 molecular response along a reaction coordinate. We
3668 develop a theory that allows one to reconstruct force
3669 profiles from force spectra obtained from measurements
3670 at varying loading rates, without requiring increased
3671 resolution. We show that spectra obtained from
3672 measurements with different spring constants contain
3673 complementary information.",
3675 doi = "10.1103/PhysRevLett.84.6126",
3676 url = "http://prola.aps.org/abstract/PRL/v84/p6126",
3677 eprint = "http://prola.aps.org/pdf/PRL/v84/i26/p6126_1",
3681 author = "Ioan Kosztin and Bogdan Barz and Lorant Janosi",
3682 title = "Calculating potentials of mean force and diffusion coefficients from nonequilibrium processes without Jarzynski's equality.",
3683 journal = "J. Chem. Phys.",
3690 doi = "10.1063/1.2166379",
3691 url = "http://link.aip.org/link/?JCPSA6/124/064106/1",
3695 author = "H.A.~Kramers",
3696 title = "Brownian motion in a field of force and the diffusion model of chemical reactions.",
3697 journal = "Physica",
3704 abstract = "A particle which is caught in a potential hole and which, through the shuttling action of Brownian motion, can escape over a potential barrier yields a suitable model for elucidating the applicability of the transition state method for calculating the rate of chemical reactions.",
3705 doi = "10.1016/S0031-8914(40)90098-2",
3706 url = "http://www.sciencedirect.com/science/article/B6X42-4CB752H-3G/1/1d9e8dc558b822877c9e1ad55bb08831",
3707 note = "Seminal paper on thermally activated barrier crossings.",
3711 title = "Stochastic Processes in Physics and Chemistry",
3712 author = "N.G. {van Kampen}",
3714 publisher = "Elsevier, North-Holland Personal Library",
3715 address = "Amsterdam",
3718 project = "sawtooth simulation",
projects / sawsim.git / blob