year = {2001--},
url = "http://www.scipy.org/"
}
+
+@article{nummela07,
+author = {Nummela, Jeremiah and Andricioaei, Ioan},
+title = {{Exact Low-Force Kinetics from High-Force Single-Molecule Unfolding Events}},
+journal = {Biophys. J.},
+volume = {93},
+number = {10},
+pages = {3373-3381},
+doi = {10.1529/biophysj.107.111658},
+year = {2007},
+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.
+},
+URL = {http://www.biophysj.org/cgi/content/abstract/93/10/3373},
+eprint = {http://www.biophysj.org/cgi/reprint/93/10/3373.pdf}
+}
+
+ @article{gompertz25,
+ jstor_articletype = {primary_article},
+ 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},
+ author = {Gompertz, Benjamin},
+ journal = {Philosophical Transactions of the Royal Society of London},
+ jstor_issuetitle = {},
+ volume = {115},
+ number = {},
+ jstor_formatteddate = {1825},
+ pages = {513--583},
+ url = {http://www.jstor.org/stable/107756},
+ ISSN = {02610523},
+ abstract = {},
+ publisher = {The Royal Society},
+ language = {},
+ copyright = {Copyright © 1825 The Royal Society},
+ year = {1825},
+ }
+
+@Article{dudko07,
+ author = "Olga K. Dudko and J{\'e}r{\^o}me Math{\'e} and Attila
+ Szabo and Amit Meller and Gerhard Hummer",
+ title = "Extracting kinetics from single-molecule force
+ spectroscopy: nanopore unzipping of {DNA} hairpins.",
+ journal = "Biophys J",
+ year = "2007",
+ month = jun,
+ day = "15",
+ volume = "92",
+ number = "12",
+ pages = "4188--4195",
+ keywords = "Computer Simulation",
+ keywords = "DNA",
+ keywords = "Elasticity",
+ keywords = "Mechanics",
+ keywords = "Micromanipulation",
+ keywords = "Microscopy, Atomic Force",
+ keywords = "Models, Chemical",
+ keywords = "Models, Molecular",
+ keywords = "Nanostructures",
+ keywords = "Nucleic Acid Conformation",
+ keywords = "Porosity",
+ keywords = "Stress, Mechanical",
+ abstract = "Single-molecule force experiments provide powerful new
+ tools to explore biomolecular interactions. Here, we
+ describe a systematic procedure for extracting kinetic
+ information from force-spectroscopy experiments, and
+ apply it to nanopore unzipping of individual DNA
+ hairpins. Two types of measurements are considered:
+ unzipping at constant voltage, and unzipping at
+ constant voltage-ramp speeds. We perform a global
+ maximum-likelihood analysis of the experimental data at
+ low-to-intermediate ramp speeds. To validate the
+ theoretical models, we compare their predictions with
+ two independent sets of data, collected at high ramp
+ speeds and at constant voltage, by using a quantitative
+ relation between the two types of measurements.
+ Microscopic approaches based on Kramers theory of
+ diffusive barrier crossing allow us to estimate not
+ only intrinsic rates and transition state locations, as
+ in the widely used phenomenological approach based on
+ Bell's formula, but also free energies of activation.
+ The problem of extracting unique and accurate kinetic
+ parameters of a molecular transition is discussed in
+ light of the apparent success of the microscopic
+ theories in reproducing the experimental data.",
+ ISSN = "0006-3495",
+ doi = "10.1529/biophysj.106.102855",
+ eprint = "http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1877759&blobtype=pdf",
+}
+
+@Article{dudko06,
+ author = "Olga K. Dudko and Gerhard Hummer and Attila Szabo",
+ title = "Intrinsic rates and activation free energies from
+ single-molecule pulling experiments.",
+ journal = "Phys Rev Lett",
+ year = "2006",
+ month = mar,
+ day = "17",
+ volume = "96",
+ number = "10",
+ pages = "108101",
+ keywords = "Biophysics",
+ keywords = "Computer Simulation",
+ keywords = "Data Interpretation, Statistical",
+ keywords = "Kinetics",
+ keywords = "Micromanipulation",
+ keywords = "Models, Chemical",
+ keywords = "Models, Molecular",
+ keywords = "Molecular Conformation",
+ keywords = "Muscle Proteins",
+ keywords = "Nucleic Acid Conformation",
+ keywords = "Protein Binding",
+ keywords = "Protein Denaturation",
+ keywords = "Protein Folding",
+ keywords = "Protein Kinases",
+ keywords = "RNA",
+ keywords = "Stress, Mechanical",
+ keywords = "Thermodynamics",
+ keywords = "Time Factors",
+ abstract = "We present a unified framework for extracting kinetic
+ information from single-molecule pulling experiments at
+ constant force or constant pulling speed. Our procedure
+ provides estimates of not only (i) the intrinsic rate
+ coefficient and (ii) the location of the transition
+ state but also (iii) the free energy of activation. By
+ analyzing simulated data, we show that the resulting
+ rates of force-induced rupture are significantly more
+ reliable than those obtained by the widely used
+ approach based on Bell's formula. We consider the
+ uniqueness of the extracted kinetic information and
+ suggest guidelines to avoid over-interpretation of
+ experiments.",
+ ISSN = "0031-9007",
+ doi = "10.1103/PhysRevLett.96.108101",
+}
+
+@Article{wu04,
+ author = "Jong-Wuu Wu and Wen-Liang Hung and Chih-Hui Tsai",
+ title = "Estimation of parameters of the {G}ompertz distribution using the least squares method.",
+ journal = "Applied Mathematics and Computation",
+ year = "2004",
+ month = oct,
+ day = "25",
+ volume = "158",
+ number = "1",
+ pages = "133--147",
+ keywords = "Gompertz distribution; Least squares estimate; Maximum likelihood estimate; First failure-censored; Series system",
+ 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.",
+ ISSN = "0096-3003",
+ doi = "10.1016/j.amc.2003.08.086",
+ url = "http://www.sciencedirect.com/science/article/B6TY8-4B3NR1W-B/1/bbaa47878ada03c6ef8e681d03bb65d3",
+}
+
+
+
+
+@Article{braverman08,
+ author = "Elena Braverman and Reneeta Mamdani",
+ title = "Continuous versus pulse harvesting for population
+ models in constant and variable environment.",
+ journal = "J Math Biol",
+ year = "2008",
+ month = sep,
+ day = "18",
+ volume = "57",
+ number = "3",
+ pages = "413--434",
+ abstract = "We consider both autonomous and nonautonomous
+ population models subject to either impulsive or
+ continuous harvesting. It is demonstrated in the paper
+ that the impulsive strategy can be as good as the
+ continuous one, but cannot outperform it. We introduce
+ a model, where certain harm to the population is
+ incorporated in each harvesting event, and study it for
+ the logistic and the Gompertz laws of growth. In this
+ case, impulsive harvesting is not only the optimal
+ strategy but is the only possible one.",
+ ISSN = "0303-6812",
+ doi = "10.1007/s00285-008-0169-z",
+ url = "http://www.springerlink.com/content/a1m23v50201m2401/",
+ eprint = "http://www.springerlink.com/content/a1m23v50201m2401/fulltext.pdf",
+ note = "An example of non-exponential Gomperz law.",
+}
+
+@Article{gavrilov01,
+ author = "L. A. Gavrilov and N. S. Gavrilova",
+ title = "The reliability theory of aging and longevity.",
+ journal = "J Theor Biol",
+ year = "2001",
+ month = dec,
+ day = "21",
+ volume = "213",
+ number = "4",
+ pages = "527--545",
+ keywords = "Adult",
+ keywords = "Aged",
+ keywords = "Aging",
+ keywords = "Animals",
+ keywords = "Humans",
+ keywords = "Longevity",
+ keywords = "Middle Aged",
+ keywords = "Models, Biological",
+ keywords = "Survival Rate",
+ keywords = "Systems Theory",
+ abstract = "Reliability theory is a general theory about systems
+ failure. It allows researchers to predict the
+ age-related failure kinetics for a system of given
+ architecture (reliability structure) and given
+ reliability of its components. Reliability theory
+ predicts that even those systems that are entirely
+ composed of non-aging elements (with a constant failure
+ rate) will nevertheless deteriorate (fail more often)
+ with age, if these systems are redundant in
+ irreplaceable elements. Aging, therefore, is a direct
+ consequence of systems redundancy. Reliability theory
+ also predicts the late-life mortality deceleration with
+ subsequent leveling-off, as well as the late-life
+ mortality plateaus, as an inevitable consequence of
+ redundancy exhaustion at extreme old ages. The theory
+ explains why mortality rates increase exponentially
+ with age (the Gompertz law) in many species, by taking
+ into account the initial flaws (defects) in newly
+ formed systems. It also explains why organisms
+ ``prefer'' to die according to the Gompertz law, while
+ technical devices usually fail according to the Weibull
+ (power) law. Theoretical conditions are specified when
+ organisms die according to the Weibull law: organisms
+ should be relatively free of initial flaws and defects.
+ The theory makes it possible to find a general failure
+ law applicable to all adult and extreme old ages, where
+ the Gompertz and the Weibull laws are just special
+ cases of this more general failure law. The theory
+ explains why relative differences in mortality rates of
+ compared populations (within a given species) vanish
+ with age, and mortality convergence is observed due to
+ the exhaustion of initial differences in redundancy
+ levels. Overall, reliability theory has an amazing
+ predictive and explanatory power with a few, very
+ general and realistic assumptions. Therefore,
+ reliability theory seems to be a promising approach for
+ developing a comprehensive theory of aging and
+ longevity integrating mathematical methods with
+ specific biological knowledge.",
+ ISSN = "0022-5193",
+ doi = "10.1006/jtbi.2001.2430",
+ note = "An example of exponential (standard) Gomperz law.",
+}
+
+@Article{olshansky97,
+ author = "S. J. Olshansky and B. A. Carnes",
+ title = "Ever since Gompertz.",
+ journal = "Demography",
+ year = "1997",
+ month = feb,
+ volume = "34",
+ number = "1",
+ pages = "1--15",
+ keywords = "Aging",
+ keywords = "Biometry",
+ keywords = "History, 19th Century",
+ keywords = "History, 20th Century",
+ keywords = "Humans",
+ keywords = "Life Tables",
+ keywords = "Mortality",
+ keywords = "Sexual Maturation",
+ abstract = "In 1825 British actuary Benjamin Gompertz made a
+ simple but important observation that a law of
+ geometrical progression pervades large portions of
+ different tables of mortality for humans. The simple
+ formula he derived describing the exponential rise in
+ death rates between sexual maturity and old age is
+ commonly, referred to as the Gompertz equation-a
+ formula that remains a valuable tool in demography and
+ in other scientific disciplines. Gompertz's observation
+ of a mathematical regularity in the life table led him
+ to believe in the presence of a low of mortality that
+ explained why common age patterns of death exist. This
+ law of mortality has captured the attention of
+ scientists for the past 170 years because it was the
+ first among what are now several reliable empirical
+ tools for describing the dying-out process of many
+ living organisms during a significant portion of their
+ life spans. In this paper we review the literature on
+ Gompertz's law of mortality and discuss the importance
+ of his observations and insights in light of research
+ on aging that has taken place since then.",
+ ISSN = "0070-3370",
+notes = "Hardly any actual math, but the references might be interesting.
+I'll look into them if I have the time.
+Available through several repositories.",
+url = "http://www.jstor.org/stable/2061656",
+}
+
+@Article{juckett93,
+ author = "D. A. Juckett and B. Rosenberg",
+ title = "Comparison of the Gompertz and Weibull functions as
+ descriptors for human mortality distributions and their
+ intersections.",
+ journal = "Mech Ageing Dev",
+ year = "1993",
+ month = jun,
+ volume = "69",
+ number = "1-2",
+ pages = "1--31",
+ keywords = "Adolescent",
+ keywords = "Adult",
+ keywords = "Aged",
+ keywords = "Aged, 80 and over",
+ keywords = "Aging",
+ keywords = "Biometry",
+ keywords = "Child",
+ keywords = "Child, Preschool",
+ keywords = "Data Interpretation, Statistical",
+ keywords = "Female",
+ keywords = "Humans",
+ keywords = "Infant",
+ keywords = "Infant, Newborn",
+ keywords = "Longitudinal Studies",
+ keywords = "Male",
+ keywords = "Middle Aged",
+ keywords = "Models, Biological",
+ keywords = "Models, Statistical",
+ keywords = "Mortality",
+ abstract = "The Gompertz and Weibull functions are compared with
+ respect to goodness-of-fit to human mortality
+ distributions; ability to describe mortality curve
+ intersections; and, parameter interpretation. The
+ Gompertz function is shown to be a better descriptor
+ for 'all-causes' of deaths and combined disease
+ categories while the Weibull function is shown to be a
+ better descriptor of purer, single causes-of-death. A
+ modified form of the Weibull function maps directly to
+ the inherent degrees of freedom of human mortality
+ distributions while the Gompertz function does not.
+ Intersections in the old-age tails of mortality are
+ explored in the context of both functions and, in
+ particular, the relationship between distribution
+ intersections, and the Gompertz ln[R0] versus alpha
+ regression is examined. Evidence is also presented that
+ mortality intersections are fundamental to the
+ survivorship form and not the rate (hazard) form.
+ Finally, comparisons are made to the parameter
+ estimates in recent longitudinal Gompertzian analyses
+ and the probable errors in those analyses are
+ discussed.",
+ ISSN = "0047-6374",
+notes = "Nice table of various functions associated with Gompertz and Weibull models.",
+doi = "10.1016/0047-6374(93)90068-3"
+}
+
+@Article{rief02,
+ author = "Matthias Rief and Helmut Grubm{\"u}ller",
+ title = "Force spectroscopy of single biomolecules.",
+ journal = "Chemphyschem",
+ year = "2002",
+ month = mar,
+ day = "12",
+ volume = "3",
+ number = "3",
+ pages = "255--261",
+ keywords = "Ligands",
+ keywords = "Microscopy, Atomic Force",
+ keywords = "Polysaccharides",
+ keywords = "Protein Denaturation",
+ keywords = "Proteins",
+ abstract = "Many processes in the body are effected and regulated
+ by highly specialized protein molecules: These
+ molecules certainly deserve the name ``biochemical
+ nanomachines''. Recent progress in single-molecule
+ experiments and corresponding simulations with
+ supercomputers enable us to watch these
+ ``nanomachines'' at work, revealing a host of
+ astounding mechanisms. Examples are the fine-tuned
+ movements of the binding pocket of a receptor protein
+ locking into its ligand molecule and the forced
+ unfolding of titin, which acts as a molecular shock
+ absorber to protect muscle cells. At present, we are
+ not capable of designing such high precision machines,
+ but we are beginning to understand their working
+ principles and to simulate and predict their
+ function.",
+ ISSN = "1439-4235",
+ doi = "10.1002/1439-7641(20020315)3:3<255::AID-CPHC255>3.0.CO;2-M",
+ url = "http://www3.interscience.wiley.com/journal/91016383/abstract",
+ note = "Nice, general review of force spectroscopy to 2002, but not much detail.",
+}
+
+@Article{raible04,
+ author = "M. Raible and M. Evstigneev and P. Reimann and F. W.
+ Bartels and R. Ros",
+ title = "Theoretical analysis of dynamic force spectroscopy
+ experiments on ligand-receptor complexes.",
+ journal = "J Biotechnol",
+ year = "2004",
+ month = aug,
+ day = "26",
+ volume = "112",
+ number = "1-2",
+ pages = "13--23",
+ keywords = "Binding Sites",
+ keywords = "Computer Simulation",
+ keywords = "DNA",
+ keywords = "DNA-Binding Proteins",
+ keywords = "Elasticity",
+ keywords = "Ligands",
+ keywords = "Macromolecular Substances",
+ keywords = "Micromanipulation",
+ keywords = "Microscopy, Atomic Force",
+ keywords = "Models, Chemical",
+ keywords = "Molecular Biology",
+ keywords = "Nucleic Acid Conformation",
+ keywords = "Physical Stimulation",
+ keywords = "Protein Binding",
+ keywords = "Protein Conformation",
+ keywords = "Stress, Mechanical",
+ abstract = "The forced rupture of single chemical bonds in
+ biomolecular compounds (e.g. ligand-receptor systems)
+ as observed in dynamic force spectroscopy experiments
+ is addressed. Under the assumption that the probability
+ of bond rupture depends only on the instantaneously
+ acting force, a data collapse onto a single master
+ curve is predicted. For rupture data obtained
+ experimentally by dynamic AFM force spectroscopy of a
+ ligand-receptor bond between a DNA and a regulatory
+ protein we do not find such a collapse. We conclude
+ that the above mentioned, generally accepted assumption
+ is not satisfied and we discuss possible
+ explanations.",
+ ISSN = "0168-1656",
+ doi = "10.1016/j.jbiotec.2004.04.017",
+}
+
+@Article{raible06,
+ author = "M. Raible and M. Evstigneev and F. W. Bartels and R.
+ Eckel and M. Nguyen-Duong and R. Merkel and R. Ros and
+ D. Anselmetti and P. Reimann",
+ title = "Theoretical analysis of single-molecule force
+ spectroscopy experiments: heterogeneity of chemical
+ bonds.",
+ journal = "Biophys J",
+ year = "2006",
+ month = jun,
+ day = "01",
+ volume = "90",
+ number = "11",
+ pages = "3851--3864",
+ keywords = "Biomechanics",
+ keywords = "Microscopy, Atomic Force",
+ keywords = "Models, Molecular",
+ keywords = "Statistical Distributions",
+ keywords = "Thermodynamics",
+ abstract = "We show that the standard theoretical framework in
+ single-molecule force spectroscopy has to be extended
+ to consistently describe the experimental findings. The
+ basic amendment is to take into account heterogeneity
+ of the chemical bonds via random variations of the
+ force-dependent dissociation rates. This results in a
+ very good agreement between theory and rupture data
+ from several different experiments.",
+ ISSN = "0006-3495",
+ doi = "10.1529/biophysj.105.077099",
+ url = "http://www.biophysj.org/cgi/content/abstract/90/11/3851",
+ eprint = "http://www.biophysj.org/cgi/reprint/90/11/3851.pdf",
+}
+
+@article{szabo80,
+author = {Attila Szabo and Klaus Schulten and Zan Schulten},
+collaboration = {},
+title = {First passage time approach to diffusion controlled reactions},
+publisher = {AIP},
+year = {1980},
+journal = {The Journal of Chemical Physics},
+volume = {72},
+number = {8},
+pages = {4350-4357},
+keywords = {DIFFUSION; CHEMICAL REACTIONS; CHEMICAL REACTION KINETICS; PROBABILITY; DIFFERENTIAL EQUATIONS},
+url = {http://link.aip.org/link/?JCP/72/4350/1},
+doi = {10.1063/1.439715}
+}
+
+@Article{dudko03,
+ author = "O. K. Dudko and A. E. Filippov and J. Klafter and M.
+ Urbakh",
+ title = "Beyond the conventional description of dynamic force
+ spectroscopy of adhesion bonds.",
+ journal = "Proc Natl Acad Sci U S A",
+ year = "2003",
+ month = sep,
+ day = "30",
+ volume = "100",
+ number = "20",
+ pages = "11378--11381",
+ keywords = "Spectrum Analysis",
+ keywords = "Temperature",
+ abstract = "Dynamic force spectroscopy of single molecules is
+ described by a model that predicts a distribution of
+ rupture forces, the corresponding mean rupture force,
+ and variance, which are all amenable to experimental
+ tests. The distribution has a pronounced asymmetry,
+ which has recently been observed experimentally. The
+ mean rupture force follows a (lnV)2/3 dependence on the
+ pulling velocity, V, and differs from earlier
+ predictions. Interestingly, at low pulling velocities,
+ a rebinding process is obtained whose signature is an
+ intermittent behavior of the spring force, which delays
+ the rupture. An extension to include conformational
+ changes of the adhesion complex is proposed, which
+ leads to the possibility of bimodal distributions of
+ rupture forces.",
+ ISSN = "0027-8424",
+ doi = "10.1073/pnas.1534554100",
+ url = "http://www.pnas.org/content/100/20/11378.abstract",
+ eprint = "http://www.pnas.org/content/100/20/11378.full.pdf",
+}
+
+@Article{balsera97,
+ author = "M. Balsera and S. Stepaniants and S. Izrailev and Y.
+ Oono and K. Schulten",
+ title = "Reconstructing potential energy functions from
+ simulated force-induced unbinding processes.",
+ journal = "Biophys J",
+ year = "1997",
+ month = sep,
+ volume = "73",
+ number = "3",
+ pages = "1281--1287",
+ keywords = "Binding Sites",
+ keywords = "Biopolymers",
+ keywords = "Kinetics",
+ keywords = "Ligands",
+ keywords = "Microscopy, Atomic Force",
+ keywords = "Models, Chemical",
+ keywords = "Molecular Conformation",
+ keywords = "Protein Conformation",
+ keywords = "Proteins",
+ keywords = "Reproducibility of Results",
+ keywords = "Stochastic Processes",
+ keywords = "Thermodynamics",
+ abstract = "One-dimensional stochastic models demonstrate that
+ molecular dynamics simulations of a few nanoseconds can
+ be used to reconstruct the essential features of the
+ binding potential of macromolecules. This can be
+ accomplished by inducing the unbinding with the help of
+ external forces applied to the molecules, and
+ discounting the irreversible work performed on the
+ system by these forces. The fluctuation-dissipation
+ theorem sets a fundamental limit on the precision with
+ which the binding potential can be reconstructed by
+ this method. The uncertainty in the resulting potential
+ is linearly proportional to the irreversible component
+ of work performed on the system during the simulation.
+ These results provide an a priori estimate of the
+ energy barriers observable in molecular dynamics
+ simulations.",
+ ISSN = "0006-3495",
+ url = "http://www.biophysj.org/cgi/content/abstract/73/3/1281",
+ eprint = "http://www.biophysj.org/cgi/reprint/73/3/1281.pdf",
+}
+
+@Article{izrailev97,
+ author = "S. Izrailev and S. Stepaniants and M. Balsera and Y.
+ Oono and K. Schulten",
+ title = "Molecular dynamics study of unbinding of the
+ avidin-biotin complex.",
+ journal = "Biophys J",
+ year = "1997",
+ month = apr,
+ volume = "72",
+ number = "4",
+ pages = "1568--1581",
+ keywords = "Avidin",
+ keywords = "Binding Sites",
+ keywords = "Biotin",
+ keywords = "Computer Simulation",
+ keywords = "Hydrogen Bonding",
+ keywords = "Mathematics",
+ keywords = "Microscopy, Atomic Force",
+ keywords = "Microspheres",
+ keywords = "Models, Molecular",
+ keywords = "Molecular Structure",
+ keywords = "Protein Binding",
+ keywords = "Protein Conformation",
+ keywords = "Protein Folding",
+ keywords = "Sepharose",
+ abstract = "We report molecular dynamics simulations that induce,
+ over periods of 40-500 ps, the unbinding of biotin from
+ avidin by means of external harmonic forces with force
+ constants close to those of AFM cantilevers. The
+ applied forces are sufficiently large to reduce the
+ overall binding energy enough to yield unbinding within
+ the measurement time. Our study complements earlier
+ work on biotin-streptavidin that employed a much larger
+ harmonic force constant. The simulations reveal a
+ variety of unbinding pathways, the role of key residues
+ contributing to adhesion as well as the spatial range
+ over which avidin binds biotin. In contrast to the
+ previous studies, the calculated rupture forces exceed
+ by far those observed. We demonstrate, in the framework
+ of models expressed in terms of one-dimensional
+ Langevin equations with a schematic binding potential,
+ the associated Smoluchowski equations, and the theory
+ of first passage times, that picosecond to nanosecond
+ simulation of ligand unbinding requires such strong
+ forces that the resulting protein-ligand motion
+ proceeds far from the thermally activated regime of
+ millisecond AFM experiments, and that simulated
+ unbinding cannot be readily extrapolated to the
+ experimentally observed rupture.",
+ ISSN = "0006-3495",
+ url = "http://www.biophysj.org/cgi/content/abstract/72/4/1568",
+ eprint = "http://www.biophysj.org/cgi/reprint/72/4/1568.pdf",
+}
+
+@Article{heymann00,
+ author = "B. Heymann and H. Grubm{\"u}ller",
+ title = "Dynamic force spectroscopy of molecular adhesion
+ bonds.",
+ journal = "Phys Rev Lett",
+ year = "2000",
+ month = jun,
+ day = "26",
+ volume = "84",
+ number = "26 Pt 1",
+ pages = "6126--6129",
+ abstract = "Recent advances in atomic force microscopy,
+ biomembrane force probe experiments, and optical
+ tweezers allow one to measure the response of single
+ molecules to mechanical stress with high precision.
+ Such experiments, due to limited spatial resolution,
+ typically access only one single force value in a
+ continuous force profile that characterizes the
+ molecular response along a reaction coordinate. We
+ develop a theory that allows one to reconstruct force
+ profiles from force spectra obtained from measurements
+ at varying loading rates, without requiring increased
+ resolution. We show that spectra obtained from
+ measurements with different spring constants contain
+ complementary information.",
+ ISSN = "0031-9007",
+ doi = "10.1103/PhysRevLett.84.6126",
+ url = "http://prola.aps.org/abstract/PRL/v84/p6126",
+ eprint = "http://prola.aps.org/pdf/PRL/v84/i26/p6126_1",
+}
+
+@Article{kosztin06,
+ author = "Ioan Kosztin and Bogdan Barz and Lorant Janosi",
+ title = "Calculating potentials of mean force and diffusion coefficients from nonequilibrium processes without Jarzynski's equality.",
+ journal = "J. Chem. Phys.",
+ year = "2006",
+ month = feb,
+ day = "10",
+ volume = "124",
+ pages = "064106",
+ ISSN = "0031-9007",
+ doi = "10.1063/1.2166379",
+ url = "http://link.aip.org/link/?JCPSA6/124/064106/1",
+}
+
+@Article{kramers40,
+ author = "H.A.~Kramers",
+ title = "Brownian motion in a field of force and the diffusion model of chemical reactions.",
+ journal = "Physica",
+ year = "1940",
+ month = apr,
+ volume = "7",
+ number = "4",
+ pages = "284--304",
+ ISSN = "0031-8914",
+ 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.",
+ doi = "10.1016/S0031-8914(40)90098-2",
+ url = "http://www.sciencedirect.com/science/article/B6X42-4CB752H-3G/1/1d9e8dc558b822877c9e1ad55bb08831",
+ note = "Seminal paper on thermally activated barrier crossings.",
+}
+
+@Book{vanKampen07,
+ title = "Stochastic Processes in Physics and Chemistry",
+ author = "N.G. {van Kampen}",
+ editin = "3",
+ publisher = "Elsevier, North-Holland Personal Library",
+ address = "Amsterdam",
+ year = "2007",
+ note = "",
+ project = "sawtooth simulation",
+}
projects / sawsim.git / commitdiff