From f0eb9de93a69de61b9857811a29663d4c003a0c3 Mon Sep 17 00:00:00 2001 From: "W. Trevor King" Date: Sun, 21 Feb 2010 20:16:37 -0500 Subject: [PATCH] Working through introductory citations, HGP and Levinthal. --- tex/src/introduction/main.tex | 73 ++++-- tex/src/wtk.bib | 427 ++++++++++++++++++++++++++++++++-- 2 files changed, 456 insertions(+), 44 deletions(-) diff --git a/tex/src/introduction/main.tex b/tex/src/introduction/main.tex index 06d59da..8f5c689 100644 --- a/tex/src/introduction/main.tex +++ b/tex/src/introduction/main.tex @@ -5,20 +5,45 @@ In biological systems the most important molecules, such as proteins, nucleic acids, and polysaccharides, are all polymers. Understanding the properties and functions of these polymeric molecules is crucial -in elucidating the molecular mechanisms of structures and processes in -cells. The large size of these molecules imposes certain limitations -on the information attainable from bulk measurements, because the -macromolecules in a population can have diverse conformations and -behaviors. The bulk measurement averages over these differences, -producing excelent statistics on the mean, but making it difficult to -understand the variation. The individualized, and sometimes rare, -behaviors of macromolecules can have important implications for their -functions inside the cell\cite{TODO}. Single molecule techniques, in -which the macromolecules are studied one at a time, allow direct -access to the variation within the population without averaging. This -provides important and complementary information about the functional +in understanding the molecular mechanisms behind structures and +processes in cells. The large size of these molecules imposes certain +limitations on the information attainable from bulk measurements, +because the macromolecules in a population can have diverse +conformations and behaviors. Bulk measurements average over these +differences, producing excellent statistics for the mean, but making +it difficult to understand the variation. The individualized, and +sometimes rare, behaviors of macromolecules can have important +implications for their functions inside the cell. For example, +...\citep{TODO}. Single molecule techniques, in which the +macromolecules are studied one at a time, allow direct access to the +variation within the population without averaging. This provides +important and complementary information about the functional mechanisms of several biological systems\citep{bustamante08}. +% What do genes do? + +DNA sequencing is a fairly well developed field, with fundamental work +such as the Human Genome Project seeing major development in the early +2000s\citep{wolfsberg01,mcpherson01,collins03}. It is estimated that +this genetic information contains approximately 25,000 genes, each +encoding a protein\citep{claverie01,venter01}. Knowing the amino acid +sequence for a particular protein, however, does not immediately shed +light on the protein's role in the body, or even the protein's +probable conformation. As pointed out by \citet{levinthal68}, a protein + + + +There has been a wealth of +information on the genetic code + +% Protein folding / unfolding + +One particularly interesting area of biophysics is protein folding. +Proteins are chains of amino acids, and from \emph{central dogma} of +molecular biology, DNA specifies the amino acid sequence +exactly\citep{TODO}. It is cur + + % why AFM & what an AFM is Single molecule techniques for the study of biological macromolecules include optical measurements, \ie, single molecule fluorescence @@ -27,7 +52,7 @@ individual macromolecules, \ie, force microscopy and spectroscopy using atomic force microscopes (AFMs), laser tweezers\citep{forde02}, magnetic tweezers\citep{smith92}, biomembrane force probes\citep{merkel99}, and centrifugal -microscopes\cite{halvorsen2010}. Of these mechanical manipulation +microscopes\citep{halvorsen2010}. Of these mechanical manipulation methods, AFM is the most widely used due to the availability of user-friendly commercial instruments. AFM has been employed on several types of biological macromolecules, mechanically unfolding @@ -38,16 +63,18 @@ sample. Cantilever bending is measured by a laser reflected off the cantilever and incident on a position sensitive photodetector (\cref{fig:afm-schematic}). When the bending force constant of the cantilever is known\citep{levy02}, the force applied to the sample can -be calculated. The forces that can be applied and measured with an -AFM range from tens of piconewtons to hundreds of nanonewtons. The -investigation of the unfolding and refolding processes of individual -protein molecules by the AFM is feasible because many globular -proteins unfold under external forces in this range. Since -elucidating the mechanism of protein folding is currently one of the -most important problems in biological sciences, the potential of the -AFM for revealing significant and unique information about protein -folding has stimulated much effort in both experimental and -theoretical research. +be calculated. + + +The forces that can be applied and measured with an AFM range from +tens of piconewtons to hundreds of nanonewtons. The investigation of +the unfolding and refolding processes of individual protein molecules +by the AFM is feasible because many globular proteins unfold under +external forces in this range. Since elucidating the mechanism of +protein folding is currently one of the most important problems in +biological sciences, the potential of the AFM for revealing +significant and unique information about protein folding has +stimulated much effort in both experimental and theoretical research. \begin{figure} \begin{center} diff --git a/tex/src/wtk.bib b/tex/src/wtk.bib index 8682192..c38af2e 100644 --- a/tex/src/wtk.bib +++ b/tex/src/wtk.bib @@ -55,7 +55,10 @@ @String{JCS = "J. Cell Sci."} #String{JCS = "Journal of Cell Science"} @String{JCP = "The Journal of Chemical Physics"} +@String{JCPPCB = "J. Chim. Phys."} +#String{JCPPCB = "Journal de Chimie Physique et de Physico-Chimie Biologique"} @String{JMB = "J. Mol. Biol."} +#String{JMB = "Journal of Molecular Biology"} @String{JPCM = "Journal of Physics: Condensed Matter"} @String{LANG = "Langmuir"} @String{NANOTECH = "Nanotechnology"} @@ -2990,7 +2993,7 @@ note = "Gives appropriate Einstein-S... relation for diffusion to damping", @Article{bell78, author = "G. I. Bell", title = "Models for the specific adhesion of cells to cells", - journal = "Science", + journal = SCI, year = "1978", month = may, day = "12", @@ -3876,12 +3879,12 @@ doi = {10.1063/1.439715} MCarrionVazquez #" and "# AOberhauser #" and K. Schulten and "# JFernandez, title = "Mechanical unfolding intermediates in titin modules", - journal = "Nature", - year = "1999", + journal = NAT, + year = 1999, month = nov, - day = "04", - volume = "402", - number = "6757", + day = 04, + volume = 402, + number = 6757, pages = "100--103", keywords = "Biomechanics", keywords = "Computer Simulation", @@ -4418,12 +4421,12 @@ doi = {10.1063/1.439715} and "# CBustamante, title = "Folding-unfolding transitions in single titin molecules characterized with laser tweezers", - journal = "Science", - year = "1997", + journal = SCI, + year = 1997, month = may, - day = "16", - volume = "276", - number = "5315", + day = 16, + volume = 276, + number = 5315, pages = "1112--1116", keywords = "Amino Acid Sequence", keywords = "Elasticity", @@ -4590,12 +4593,12 @@ doi = {10.1063/1.439715} title = "Overstretching {B}-{DNA}: the elastic response of individual double-stranded and single-stranded {DNA} molecules", - journal = "Science", - year = "1996", + journal = SCI, + year = 1996, month = feb, - day = "09", - volume = "271", - number = "5250", + day = 09, + volume = 271, + number = 5250, pages = "795--799", keywords = "Base Composition", keywords = "Chemistry, Physical", @@ -4953,12 +4956,12 @@ doi = {10.1063/1.439715} Bensimon and V. Croquette", title = "The elasticity of a single supercoiled {DNA} molecule", - journal = "Science", - year = "1996", + journal = SCI, + year = 1996, month = mar, - day = "29", - volume = "271", - number = "5257", + day = 29, + volume = 271, + number = 5257, pages = "1835--1837", keywords = "Bacteriophage lambda", keywords = "DNA, Superhelical", @@ -6907,3 +6910,385 @@ abstract = {Precise manipulation of single molecules has already led wider range of researchers and experimental systems.}, url = "http://arxiv.org/abs/0912.5370", } + +@Article{wolfsberg01, + author = "T. G. Wolfsberg and J. McEntyre and G. D. Schuler", + title = "Guide to the draft human genome.", + journal = NAT, + year = 2001, + month = feb, + day = 15, + volume = 409, + number = 6822, + pages = "824--826", + keywords = "Amino Acid Sequence", + keywords = "Chromosome Mapping", + keywords = "Computational Biology", + keywords = "Genes", + keywords = "Genetic Variation", + keywords = "Genome, Human", + keywords = "Human Genome Project", + keywords = "Humans", + keywords = "Internet", + keywords = "Molecular Sequence Data", + keywords = "Sequence Analysis, DNA", + abstract = "There are a number of ways to investigate the + structure, function and evolution of the human genome. + These include examining the morphology of normal and + abnormal chromosomes, constructing maps of genomic + landmarks, following the genetic transmission of + phenotypes and DNA sequence variations, and + characterizing thousands of individual genes. To this + list we can now add the elucidation of the genomic DNA + sequence, albeit at 'working draft' accuracy. The + current challenge is to weave together these disparate + types of data to produce the information infrastructure + needed to support the next generation of biomedical + research. Here we provide an overview of the different + sources of information about the human genome and how + modern information technology, in particular the + internet, allows us to link them together.", + ISSN = "0028-0836", + doi = "10.1038/35057000", + url = "http://www.nature.com/nature/journal/v409/n6822/full/409824a0.html", + eprint = "http://www.nature.com/nature/journal/v409/n6822/pdf/409824a0.pdf", +} + +@Article{mcpherson01, + author = "J. D. McPherson and M. Marra and L. Hillier and R. H. + Waterston and A. Chinwalla and J. Wallis and M. Sekhon + and K. Wylie and E. R. Mardis and R. K. Wilson and R. + Fulton and T. A. Kucaba and C. Wagner-McPherson and W. + B. Barbazuk and S. G. Gregory and S. J. Humphray and L. + French and R. S. Evans and G. Bethel and A. Whittaker + and J. L. Holden and O. T. McCann and A. Dunham and C. + Soderlund and C. E. Scott and D. R. Bentley and G. + Schuler and H. C. Chen and W. Jang and E. D. Green and + J. R. Idol and V. V. Maduro and K. T. Montgomery and E. + Lee and A. Miller and S. Emerling and Kucherlapati and + R. Gibbs and S. Scherer and J. H. Gorrell and E. + Sodergren and K. Clerc-Blankenburg and P. Tabor and S. + Naylor and D. Garcia and P. J. de Jong and J. J. + Catanese and N. Nowak and K. Osoegawa and S. Qin and L. + Rowen and A. Madan and M. Dors and L. Hood and B. Trask + and C. Friedman and H. Massa and V. G. Cheung and I. R. + Kirsch and T. Reid and R. Yonescu and J. Weissenbach + and T. Bruls and R. Heilig and E. Branscomb and A. + Olsen and N. Doggett and J. F. Cheng and T. Hawkins and + R. M. Myers and J. Shang and L. Ramirez and J. Schmutz + and O. Velasquez and K. Dixon and N. E. Stone and D. R. + Cox and D. Haussler and W. J. Kent and T. Furey and S. + Rogic and S. Kennedy and S. Jones and A. Rosenthal and + G. Wen and M. Schilhabel and G. Gloeckner and G. + Nyakatura and R. Siebert and B. Schlegelberger and J. + Korenberg and X. N. Chen and A. Fujiyama and M. Hattori + and A. Toyoda and T. Yada and H. S. Park and Y. Sakaki + and N. Shimizu and S. Asakawa and K. Kawasaki and T. + Sasaki and A. Shintani and A. Shimizu and K. Shibuya + and J. Kudoh and S. Minoshima and J. Ramser and P. + Seranski and C. Hoff and A. Poustka and R. Reinhardt + and H. Lehrach", + title = "A physical map of the human genome.", + journal = NAT, + year = 2001, + month = feb, + day = 15, + volume = 409, + number = 6822, + pages = "934--941", + keywords = "Chromosomes, Artificial, Bacterial", + keywords = "Cloning, Molecular", + keywords = "Contig Mapping", + keywords = "DNA Fingerprinting", + keywords = "Gene Duplication", + keywords = "Genome, Human", + keywords = "Humans", + keywords = "In Situ Hybridization, Fluorescence", + keywords = "Repetitive Sequences, Nucleic Acid", + abstract = "The human genome is by far the largest genome to be + sequenced, and its size and complexity present many + challenges for sequence assembly. The International + Human Genome Sequencing Consortium constructed a map of + the whole genome to enable the selection of clones for + sequencing and for the accurate assembly of the genome + sequence. Here we report the construction of the + whole-genome bacterial artificial chromosome (BAC) map + and its integration with previous landmark maps and + information from mapping efforts focused on specific + chromosomal regions. We also describe the integration + of sequence data with the map.", + ISSN = "0028-0836", + doi = "10.1038/35057157", + url = "http://www.nature.com/nature/journal/v409/n6822/full/409934a0.html", + eprint = "http://www.nature.com/nature/journal/v409/n6822/pdf/409934a0.pdf", +} + +@Article{venter01, +author = "Venter, J. C. and Adams, M. D. and Myers, E. W. and Li, + P. W. and Mural, R. J. and Sutton, G. G. and Smith, H. O. and + Yandell, M. and Evans, C. A. and Holt, R. A. and Gocayne, J. D. and + Amanatides, P. and Ballew, R. M. and Huson, D. H. and Wortman, + J. R. and Zhang, Q. and Kodira, C. D. and Zheng, X. H. and Chen, + L. and Skupski, M. and Subramanian, G. and Thomas, P. D. and Zhang, + J. and Gabor Miklos, G. L. and Nelson, C. and Broder, S. and Clark, + A. G. and Nadeau, J. and McKusick, V. A. and Zinder, N. and Levine, + A. J. and Roberts, R. J. and Simon, M. and Slayman, C. and + Hunkapiller, M. and Bolanos, R. and Delcher, A. and Dew, I. and + Fasulo, D. and Flanigan, M. and Florea, L. and Halpern, A. and + Hannenhalli, S. and Kravitz, S. and Levy, S. and Mobarry, C. and + Reinert, K. and Remington, K. and Abu-Threideh, J. and Beasley, + E. and Biddick, K. and Bonazzi, V. and Brandon, R. and Cargill, + M. and Chandramouliswaran, I. and Charlab, R. and Chaturvedi, K. and + Deng, Z. and Di Francesco, V. and Dunn, P. and Eilbeck, K. and + Evangelista, C. and Gabrielian, A. E. and Gan, W. and Ge, W. and + Gong, F. and Gu, Z. and Guan, P. and Heiman, T. J. and Higgins, + M. E. and Ji, R. R. and Ke, Z. and Ketchum, K. A. and Lai, Z. and + Lei, Y. and Li, Z. and Li, J. and Liang, Y. and Lin, X. and Lu, + F. and Merkulov, G. V. and Milshina, N. and Moore, H. M. and Naik, + A. K. and Narayan, V. A. and Neelam, B. and Nusskern, D. and Rusch, + D. B. and Salzberg, S. and Shao, W. and Shue, B. and Sun, J. and + Wang, Z. and Wang, A. and Wang, X. and Wang, J. and Wei, M. and + Wides, R. and Xiao, C. and Yan, C. and Yao, A. and Ye, J. and Zhan, + M. and Zhang, W. and Zhang, H. and Zhao, Q. and Zheng, L. and + Zhong, F. and Zhong, W. and Zhu, S. and Zhao, S. and Gilbert, + D. and Baumhueter, S. and Spier, G. and Carter, C. and Cravchik, + A. and Woodage, T. and Ali, F. and An, H. and Awe, A. and Baldwin, + D. and Baden, H. and Barnstead, M. and Barrow, I. and Beeson, + K. and Busam, D. and Carver, A. and Center, A. and Cheng, M. L. and + Curry, L. and Danaher, S. and Davenport, L. and Desilets, R. and + Dietz, S. and Dodson, K. and Doup, L. and Ferriera, S. and Garg, + N. and Gluecksmann, A. and Hart, B. and Haynes, J. and Haynes, + C. and Heiner, C. and Hladun, S. and Hostin, D. and Houck, J. and + Howland, T. and Ibegwam, C. and Johnson, J. and Kalush, F. and + Kline, L. and Koduru, S. and Love, A. and Mann, F. and May, D. and + McCawley, S. and McIntosh, T. and McMullen, I. and Moy, M. and Moy, + L. and Murphy, B. and Nelson, K. and Pfannkoch, C. and Pratts, + E. and Puri, V. and Qureshi, H. and Reardon, M. and Rodriguez, + R. and Rogers, Y. H. and Romblad, D. and Ruhfel, B. and Scott, + R. and Sitter, C. and Smallwood, M. and Stewart, E. and Strong, + R. and Suh, E. and Thomas, R. and Tint, N. N. and Tse, S. and Vech, + C. and Wang, G. and Wetter, J. and Williams, S. and Williams, + M. and Windsor, S. and Winn-Deen, E. and Wolfe, K. and Zaveri, + J. and Zaveri, K. and Abril, J. F. and Guig{\'o}, R. and Campbell, + M. J. and Sjolander, K. V. and Karlak, B. and Kejariwal, A. and Mi, + H. and Lazareva, B. and Hatton, T. and Narechania, A. and Diemer, + K. and Muruganujan, A. and Guo, N. and Sato, S. and Bafna, V. and + Istrail, S. and Lippert, R. and Schwartz, R. and Walenz, B. and + Yooseph, S. and Allen, D. and Basu, A. and Baxendale, J. and Blick, + L. and Caminha, M. and Carnes-Stine, J. and Caulk, P. and Chiang, + Y. H. and Coyne, M. and Dahlke, C. and Mays, A. and Dombroski, + M. and Donnelly, M. and Ely, D. and Esparham, S. and Fosler, C. and + Gire, H. and Glanowski, S. and Glasser, K. and Glodek, A. and + Gorokhov, M. and Graham, K. and Gropman, B. and Harris, M. and Heil, + J. and Henderson, S. and Hoover, J. and Jennings, D. and Jordan, + C. and Jordan, J. and Kasha, J. and Kagan, L. and Kraft, C. and + Levitsky, A. and Lewis, M. and Liu, X. and Lopez, J. and Ma, D. and + Majoros, W. and McDaniel, J. and Murphy, S. and Newman, M. and + Nguyen, T. and Nguyen, N. and Nodell, M. and Pan, S. and Peck, + J. and Peterson, M. and Rowe, W. and Sanders, R. and Scott, J. and + Simpson, M. and Smith, T. and Sprague, A. and Stockwell, T. and + Turner, R. and Venter, E. and Wang, M. and Wen, M. and Wu, D. and + Wu, M. and Xia, A. and Zandieh, A. and Zhu, X.", +title="The sequence of the human genome.", +journal=SCI, +year=2001, +month="Feb", +day=16, +volume=291, +number=5507, +pages="1304--1351", +keywords="Algorithms", +keywords="Animals", +keywords="Chromosome Banding", +keywords="Chromosome Mapping", +keywords="Chromosomes, Artificial, Bacterial", +keywords="Computational Biology", +keywords="Consensus Sequence", +keywords="CpG Islands", +keywords="DNA, Intergenic", +keywords="Databases, Factual", +keywords="Evolution, Molecular", +keywords="Exons", +keywords="Female", +keywords="Gene Duplication", +keywords="Genes", +keywords="Genetic Variation", +keywords="Genome, Human", +keywords="Human Genome Project", +keywords="Humans", +keywords="Introns", +keywords="Male", +keywords="Phenotype", +keywords="Physical Chromosome Mapping", +keywords="Polymorphism, Single Nucleotide", +keywords="Proteins", +keywords="Pseudogenes", +keywords="Repetitive Sequences, Nucleic Acid", +keywords="Retroelements", +keywords="Sequence Analysis, DNA", +keywords="Species Specificity", +abstract="A 2.91-billion base pair (bp) consensus sequence of the +euchromatic portion of the human genome was generated by the +whole-genome shotgun sequencing method. The 14.8-billion bp DNA +sequence was generated over 9 months from 27,271,853 high-quality +sequence reads (5.11-fold coverage of the genome) from both ends of +plasmid clones made from the DNA of five individuals. Two assembly +strategies-a whole-genome assembly and a regional chromosome +assembly-were used, each combining sequence data from Celera and the +publicly funded genome effort. The public data were shredded into +550-bp segments to create a 2.9-fold coverage of those genome regions +that had been sequenced, without including biases inherent in the +cloning and assembly procedure used by the publicly funded group. This +brought the effective coverage in the assemblies to eightfold, +reducing the number and size of gaps in the final assembly over what +would be obtained with 5.11-fold coverage. The two assembly strategies +yielded very similar results that largely agree with independent +mapping data. The assemblies effectively cover the euchromatic regions +of the human chromosomes. More than 90\% of the genome is in scaffold +assemblies of 100,000 bp or more, and 25\% of the genome is in +scaffolds of 10 million bp or larger. Analysis of the genome sequence +revealed 26,588 protein-encoding transcripts for which there was +strong corroborating evidence and an additional approximately 12,000 +computationally derived genes with mouse matches or other weak +supporting evidence. Although gene-dense clusters are obvious, almost +half the genes are dispersed in low G+C sequence separated by large +tracts of apparently noncoding sequence. Only 1.1\% of the genome is +spanned by exons, whereas 24\% is in introns, with 75\% of the genome +being intergenic DNA. Duplications of segmental blocks, ranging in +size up to chromosomal lengths, are abundant throughout the genome and +reveal a complex evolutionary history. Comparative genomic analysis +indicates vertebrate expansions of genes associated with neuronal +function, with tissue-specific developmental regulation, and with the +hemostasis and immune systems. DNA sequence comparisons between the +consensus sequence and publicly funded genome data provided locations +of 2.1 million single-nucleotide polymorphisms (SNPs). A random pair +of human haploid genomes differed at a rate of 1 bp per 1250 on +average, but there was marked heterogeneity in the level of +polymorphism across the genome. Less than 1\% of all SNPs resulted in +variation in proteins, but the task of determining which SNPs have +functional consequences remains an open challenge.", +issn="0036-8075", +doi="10.1126/science.1058040", +url="http://www.sciencemag.org/cgi/content/short/291/5507/1304", +eprint="http://www.sciencemag.org/cgi/content/pdf/291/5507/1304", +} + +@Article{claverie01, + author = "J. M. Claverie", + title = "Gene number. What if there are only 30,000 human + genes?", + journal = SCI, + year = 2001, + month = feb, + day = 16, + volume = 291, + number = 5507, + pages = "1255--1257", + keywords = "Animals", + keywords = "Computational Biology", + keywords = "Drug Industry", + keywords = "Expressed Sequence Tags", + keywords = "Gene Expression", + keywords = "Gene Expression Regulation", + keywords = "Genes", + keywords = "Genetic Techniques", + keywords = "Genome, Human", + keywords = "Genomics", + keywords = "Human Genome Project", + keywords = "Humans", + keywords = "Models, Genetic", + keywords = "Polymorphism, Single Nucleotide", + keywords = "Proteins", + keywords = "RNA, Messenger", + ISSN = "0036-8075", + url = "http://www.sciencemag.org/cgi/content/full/291/5507/1255", +} + +@Article{collins03, + author = "Francis S. Collins and Michael Morgan and Aristides + Patrinos", + title = "The Human Genome Project: lessons from large-scale + biology.", + journal = SCI, + year = 2003, + month = apr, + day = 11, + volume = 300, + number = 5617, + pages = "286--290", + keywords = "Access to Information", + keywords = "Computational Biology", + keywords = "Databases, Nucleic Acid", + keywords = "Genome, Human", + keywords = "Genomics", + keywords = "Government Agencies", + keywords = "History, 20th Century", + keywords = "Human Genome Project", + keywords = "Humans", + keywords = "International Cooperation", + keywords = "National Institutes of Health (U.S.)", + keywords = "Private Sector", + keywords = "Public Policy", + keywords = "Public Sector", + keywords = "Publishing", + keywords = "Quality Control", + keywords = "Sequence Analysis, DNA", + keywords = "United States", + ISSN = "1095-9203", + doi = "10.1126/science.1084564", + url = "http://www.sciencemag.org/cgi/content/summary/300/5617/277", + eprint = "http://www.sciencemag.org/cgi/reprint/300/5617/286.pdf", + note = "See also: \href{http://www.ornl.gov/sci/techresources/Human_Genome/project/journals/journals.shtml}{Landmark HPG Papers}", +} + +@Article{levinthal68, + author = "Levinthal, Cyrus", + title = "Are there pathways for protein folding?", + journal = JCPPCB, + volume = 65, + number = 1, + pages = "44--45", + year = 1968, + eprint = "http://www.biochem.wisc.edu/courses/biochem704/Reading/Levinthal1968.pdf", + note = "\emph{Not} Levinthal's paradox.", +} + +@Inproceedings{levinthal69, + author = "Levinthal, Cyrus", + title = "How to Fold Graciously.", + booktitle = "Mossbauer Spectroscopy in Biological Systems", + year = 1969, + editor = {Debrunner, P. and Tsibris, J.C.M. and M\"unck, E.}, + pages = "22--24", + address = "Allerton House, Monticello, IL", + publisher = "University of Illinois Press, Urbana", + url = "http://www-miller.ch.cam.ac.uk/levinthal/levinthal.html" +} + +@Article{zwanzig92, + author = "R. Zwanzig and A. Szabo and B. Bagchi", + title = "Levinthal's paradox.", + journal = PNAS, + year = 1992, + month = jan, + day = 01, + volume = 89, + number = 1, + pages = "20--22", + keywords = "Mathematics", + keywords = "Models, Theoretical", + keywords = "Protein Conformation", + keywords = "Proteins", + abstract = "Levinthal's paradox is that finding the native folded + state of a protein by a random search among all + possible configurations can take an enormously long + time. Yet proteins can fold in seconds or less. + Mathematical analysis of a simple model shows that a + small and physically reasonable energy bias against + locally unfavorable configurations, of the order of a + few kT, can reduce Levinthal's time to a biologically + significant size.", + ISSN = "0027-8424", + url = "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC48166/", + eprint = "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC48166/pdf/pnas01075-0036.pdf", +} -- 2.26.2