Heteropolymer freezing and design: Towards physical models of protein folding
Abstract
Protein folding has become one of the most actively studied problems in modern molecular biophysics. Approaches to the problem combine ideas from the physics of disordered systems, polymer physics, and molecular biology. Much can be learned from the statistical properties of model heteropolymers, the chain molecules having different monomers in irregular sequences. Even in highly evolved proteins, there is a strong random element in the sequences, which gives rise to a statistical ensemble of sequences for a given folded shape. Simple analytic models give rise to phase transitions between random, glassy, and folded states, depending on the temperature T and the design temperature ${T}^{\mathrm{des}}$ of the ensemble of sequences. Besides considering the analytic results obtainable in a random-energy model and in the Flory mean-field model of polymers, the article reports on confirming numerical simulations.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Proteins are not random heteropolymers but their sequences are formed following a tentative design.
“Only recently it has been realized that proteins are not random heteropolymers but their sequences are formed following a tentative design (for a review see [39], [40]).”
From Lethal mutants and truncated selection together solve a paradox of the origin of life (2011) · cites this paper as [39]
Cites
Principles of polymer chemistry
(1995) · Choice Reviews Online · doi:10.5860/choice.33-2140 · Cited by 15,292 · see citing works
<i>Scaling Concepts in Polymer Physics</i>
de Gennes, P. G., & Witten, T. A. (1980) · Physics Today · doi:10.1063/1.2914118 · Cited by 9,348 · see citing works
The theory of polymer dynamics
Doi, M., & Edwards, S. F. (1986) · Cited by 8,964 · see citing works
The Neutral Theory of Molecular Evolution
Kimura, M. (1979) · Scientific American · doi:10.1038/scientificamerican1179-98 · Cited by 7,698 · see citing works
Principles that Govern the Folding of Protein Chains
Anfinsen, C. B. (1973) · Science · doi:10.1126/science.181.4096.223 · Cited by 7,096 · see citing works
Statistical mechanics of chain molecules
Flory, P. J., & Volkenstein, M. V. (1969) · Biopolymers · doi:10.1002/bip.1969.360080514 · Cited by 6,449 · see citing works
Spin glasses: Experimental facts, theoretical concepts, and open questions
Binder, K., & Young, A. P. (1986) · Reviews of Modern Physics · doi:10.1103/revmodphys.58.801 · Cited by 5,134 · see citing works
Mézard, M., Giorgio Parisi, A., VIRASORO, M. A., & Thouless, D. J. (1988) · Physics Today · doi:10.1063/1.2811676 · Cited by 2,683 · see citing works
Lectures On Phase Transitions And The Renormalization Group
Goldenfeld, N. (1972) · CRC Press eBooks · doi:10.1201/9780429493492 · Cited by 2,654 · see citing works
Funnels, pathways, and the energy landscape of protein folding: A synthesis
Bryngelson, J. D., Onuchic, J. N., Socci, N. D., & Wolynes, P. G. (1995) · Proteins: Structure, Function, and Bioinformatics · doi:10.1002/prot.340210302 · Cited by 2,648 · see citing works
From Levinthal to pathways to funnels
Dill, K. A., & Chan, H. S. (1997) · Nature Structural & Molecular Biology · doi:10.1038/nsb0197-10 · Cited by 2,293 · see citing works
Stability of Proteins Small Globular Proteins
Privalov, P. L. (1979) · Advances in protein chemistry · doi:10.1016/s0065-3233(08)60460-x · Cited by 2,163 · see citing works
Tanford, C. (1968) · Advances in protein chemistry · doi:10.1016/s0065-3233(08)60401-5 · Cited by 2,135 · see citing works
Statistical Physics of Macromolecules
Grosberg, A. Y., Khokhlov, A. R., Stanley, H. E., et al. (1995) · Computers in Physics · doi:10.1063/1.4823390 · Cited by 1,683 · see citing works
Self-citationSpin glasses and the statistical mechanics of protein folding.
Bryngelson, J. D., & Wolynes, P. G. (1987) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.84.21.7524 · Cited by 1,647 · see citing works
Miyazawa, S., & Jernigan, R. L. (1985) · Macromolecules · doi:10.1021/ma00145a039 · Cited by 1,588 · see citing works
Creighton, T. E. (1992) · Cited by 1,572 · see citing works
Kuwajima, K. (1989) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.340060202 · Cited by 1,440 · see citing works
Monte Carlo and Molecular Dynamics Simulations in Polymer Science
Binder, K. (1995) · doi:10.1093/oso/9780195094381.001.0001 · Cited by 1,263 · see citing works
Molten Globule and Protein Folding
Ptitsyn, O. B. (1995) · Advances in protein chemistry · doi:10.1016/s0065-3233(08)60546-x · Cited by 1,222 · see citing works
De Novo Protein Design: Fully Automated Sequence Selection
Dahiyat, B. I., & Mayo, S. L. (1997) · Science · doi:10.1126/science.278.5335.82 · Cited by 1,142 · see citing works
Wolynes, P., Onuchic, J., & Thirumalai, D. (1995) · Science · doi:10.1126/science.7886447 · Cited by 1,080 · see citing works
Computer simulation of protein folding
Levitt, M., & Warshel, A. (1975) · Nature · doi:10.1038/253694a0 · Cited by 1,051 · see citing works
A lattice statistical mechanics model of the conformational and sequence spaces of proteins
Lau, K. F., & Dill, K. A. (1989) · Macromolecules · doi:10.1021/ma00200a030 · Cited by 954 · see citing works
Protein folding funnels: a kinetic approach to the sequence-structure relationship.
Leopold, P., Montal, M., & Onuchic, J. N. (1992) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.89.18.8721 · Cited by 929 · see citing works
Statistical mechanics of neural networks near saturation
Amit, D. J., Gutfreund, H., & Sompolinsky, H. (1987) · Annals of Physics · doi:10.1016/0003-4916(87)90092-3 · Cited by 843 · see citing works
Theoretical Studies of Protein Folding
Gō, N. (1983) · Annual Review of Biophysics and Bioengineering · doi:10.1146/annurev.bb.12.060183.001151 · Cited by 833 · see citing works
Random-Energy Model: Limit of a Family of Disordered Models
Derrida, B. (1980) · Physical Review Letters · doi:10.1103/physrevlett.45.79 · Cited by 821 · see citing works
Intermediates and barrier crossing in a random energy model (with applications to protein folding)
Bryngelson, J. D., & Wolynes, P. G. (1989) · The Journal of Physical Chemistry · doi:10.1021/j100356a007 · Cited by 746 · see citing works
Abola, E. E., Bernstein, F. C., & Koetzle, T. F. (1984) · Springer eBooks · doi:10.1007/978-1-4899-0375-4_26 · Cited by 739 · see citing works
Some problems of the statistical physics of polymer chains with volume interaction
Lifshitz, I. M., Grosberg, A. Y., & Khokhlov, A. R. (1978) · Reviews of Modern Physics · doi:10.1103/revmodphys.50.683 · Cited by 737 · see citing works
Self-citationSTUDIES ON PROTEIN FOLDING, UNFOLDING AND FLUCTUATIONS BY COMPUTER SIMULATION
Taketomi, H., Ueda, Y., & Gō, N. (1975) · International journal of peptide & protein research · doi:10.1111/j.1399-3011.1975.tb02465.x · Cited by 679 · see citing works
Emergence of Preferred Structures in a Simple Model of Protein Folding
Li, H., Helling, R. C., Tang, C., & Wingreen, N. S. (1996) · Science · doi:10.1126/science.273.5275.666 · Cited by 650 · see citing works
Characterization of a Helical Protein Designed from First Principles
Regan, L., & DeGrado, W. F. (1988) · Science · doi:10.1126/science.3043666 · Cited by 543 · see citing works
Toward an outline of the topography of a realistic protein-folding funnel.
Onuchic, J. N., Wolynes, P. G., Luthey-Schulten, Z., & Socci, N. D. (1995) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.92.8.3626 · Cited by 523 · see citing works
On the Structure of Native, Denatured, and Coagulated Proteins
Mirsky, A. E., & Pauling, L. C. (1936) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.22.7.439 · Cited by 521 · see citing works
Engineering of stable and fast-folding sequences of model proteins.
Shakhnovich, E. I., & Gutin, A. M. (1993) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.90.15.7195 · Cited by 516 · see citing works
Diffusive dynamics of the reaction coordinate for protein folding funnels
Socci, N. D., Onuchic, J. N., & Wolynes, P. G. (1996) · The Journal of Chemical Physics · doi:10.1063/1.471317 · Cited by 504 · see citing works
On the transition coordinate for protein folding
Du, R., Pande, V. S., Grosberg, A. Y., Tanaka, T., & Shakhnovich, E. I. (1998) · The Journal of Chemical Physics · doi:10.1063/1.475393 · Cited by 486 · see citing works
Self-citationSpecific Nucleus as the Transition State for Protein Folding: Evidence from the Lattice Model
Abkevich, V., Gutin, A. M., & Shakhnovich, E. I. (1994) · Biochemistry · doi:10.1021/bi00199a029 · Cited by 477 · see citing works
Fersht, A. R. (1995) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.92.24.10869 · Cited by 473 · see citing works
The role of topological constraints in the kinetics of collapse of macromolecules
Grosberg, A. Y., Nechaev, S. K., & Shakhnovich, E. I. (1988) · Journal de physique · doi:10.1051/jphys:0198800490120209500 · Cited by 437 · see citing works
Self-citationThe denatured state (the other half of the folding equation) and its role in protein stability
Shortle, D. (1996) · The FASEB Journal · doi:10.1096/fasebj.10.1.8566543 · Cited by 405 · see citing works
Theory of polyampholyte solutions
Higgs, P. G., & Joanny, J. (1991) · The Journal of Chemical Physics · doi:10.1063/1.460012 · Cited by 397 · see citing works
First-Principles Calculation of the Folding Free Energy of a Three-Helix Bundle Protein
Boczko, E. M., & Brooks, C. L. (1995) · Science · doi:10.1126/science.7618103 · Cited by 394 · see citing works
Proteins with selected sequences fold into unique native conformation
Shakhnovich, E. I. (1994) · Physical Review Letters · doi:10.1103/physrevlett.72.3907 · Cited by 393 · see citing works
Hecht, M. H., Richardson, J. S., Richardson, D. C., & Ogden, R. C. (1990) · Science · doi:10.1126/science.2392678 · Cited by 391 · see citing works
Theoretical studies of protein-folding thermodynamics and kinetics
Shakhnovich, E. I. (1997) · Current Opinion in Structural Biology · doi:10.1016/s0959-440x(97)80005-x · Cited by 379 · see citing works
Validity of the “two‐state” hypothesis for conformational transitions of proteins
Lumry, R. W., Biltonen, R. L., & Brandts, J. F. (1966) · Biopolymers · doi:10.1002/bip.1966.360040808 · Cited by 359 · see citing works
Kinetics and thermodynamics of folding in model proteins.
Camacho, C. J., & Thirumalai, D. (1993) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.90.13.6369 · Cited by 357 · see citing works
Optimal protein-folding codes from spin-glass theory.
Goldstein, R. A., Luthey-Schulten, Z. A., & Wolynes, P. G. (1992) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.89.11.4918 · Cited by 351 · see citing works
Protein folding funnels: the nature of the transition state ensemble
Onuchic, J. N., Socci, N. D., Luthey-Schulten, Z. A., & Wolynes, P. G. (1996) · Folding and Design · doi:10.1016/s1359-0278(96)00060-0 · Cited by 330 · see citing works
Formation of unique structure in polypeptide chains
Shakhnovich, E. I., & Gutin, A. M. (1989) · Biophysical Chemistry · doi:10.1016/0301-4622(89)80058-4 · Cited by 321 · see citing works
Polymer Principles in Protein Structure and Stability
Chan, H. S., & Dill, K. A. (1991) · Annual Review of Biophysics and Biophysical Chemistry · doi:10.1146/annurev.bb.20.060191.002311 · Cited by 308 · see citing works
Chan, H. S., & Dill, K. A. (1993) · Physics Today · doi:10.1063/1.881371 · Cited by 308 · see citing works
Dahiyat, B. I., & Mayo, S. L. (1996) · Protein Science · doi:10.1002/pro.5560050511 · Cited by 298 · see citing works
Folding kinetics of proteinlike heteropolymers
Socci, N. D., & Onuchic, J. N. (1994) · The Journal of Chemical Physics · doi:10.1063/1.467775 · Cited by 297 · see citing works
Monte carlo simulations of protein folding. I. Lattice model and interaction scheme
Koliński, A., & Skolnick, J. (1994) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.340180405 · Cited by 295 · see citing works
Shakhnovich, E. I., & Finkelstein, A. V. (1989) · Biopolymers · doi:10.1002/bip.360281003 · Cited by 290 · see citing works
A test of lattice protein folding algorithms.
Yue, K., Fiebig, K. M., Thomas, P. D., Chan, H. S., Shakhnovich, E. I., & Dill, K. A. (1995) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.92.1.325 · Cited by 286 · see citing works
How to Derive a Protein Folding Potential? A New Approach to an Old Problem
Mirny, L. A., & Shakhnovich, E. I. (1996) · Journal of Molecular Biology · doi:10.1006/jmbi.1996.0704 · Cited by 277 · see citing works
Enumeration of all compact conformations of copolymers with random sequence of links
Shakhnovich, E. I., & Gutin, A. M. (1990) · The Journal of Chemical Physics · doi:10.1063/1.459480 · Cited by 259 · see citing works
An iterative method for extracting energy-like quantities from protein structures.
Thomas, P. D., & Dill, K. A. (1996) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.93.21.11628 · Cited by 254 · see citing works
Pathways for protein folding: is a new view needed?
Pande, V. S., Grosberg, A. Y., Tanaka, T., & Rokhsar, D. S. (1998) · Current Opinion in Structural Biology · doi:10.1016/s0959-440x(98)80012-2 · Cited by 252 · see citing works
Self-citationLi, A., & Daggett, V. (1994) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.91.22.10430 · Cited by 248 · see citing works
A generalization of the Random Energy Model which includes correlations between energies
Derrida, B. (1985) · Journal de Physique Lettres · doi:10.1051/jphyslet:01985004609040100 · Cited by 239 · see citing works
Statistical physics of polymer gels
Panyukov, S., & Rabin, Y. (1996) · Physics Reports · doi:10.1016/0370-1573(95)00068-2 · Cited by 238 · see citing works
The complexity and accuracy of discrete state models of protein structure
Park, B. H., & Levitt, M. (1995) · Journal of Molecular Biology · doi:10.1006/jmbi.1995.0311 · Cited by 232 · see citing works
HENRY, C. H., & Kazarinov, R. F. (1996) · Reviews of Modern Physics · doi:10.1103/revmodphys.68.801 · Cited by 220 · see citing works
Biomolecules: Where the Physics of Complexity and Simplicity Meet
Frauenfelder, H., & Wolynes, P. G. (1994) · Physics Today · doi:10.1063/1.881414 · Cited by 217 · see citing works
Why do protein architectures have boltzmann‐like statistics?
Finkelstein, A. V., Badretdinov, A. Y., & Gutin, A. M. (1995) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.340230204 · Cited by 200 · see citing works
Criterion that Determines the Foldability of Proteins
Klimov, D. K., & Thirumalai, D. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.4070 · Cited by 197 · see citing works
Koliński, A., Godzik, A., & Skolnick, J. (1993) · The Journal of Chemical Physics · doi:10.1063/1.464706 · Cited by 193 · see citing works
Mean-Field Model for Protein Folding
Garel, T., & Orland, H. (1988) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/6/4/005 · Cited by 189 · see citing works
Levitt, M., Gerstein, M., Huang, E. S., Subbiah, S., & Tsai, J. W. (1997) · Annual Review of Biochemistry · doi:10.1146/annurev.biochem.66.1.549 · Cited by 189 · see citing works
Equilibrium swelling properties of polyampholytic hydrogels
English, A. E., Mafé, S., Manzanares, J. A., et al. (1996) · The Journal of Chemical Physics · doi:10.1063/1.471560 · Cited by 188 · see citing works
Abe, H., & Gō, N. (1981) · Biopolymers · doi:10.1002/bip.1981.360200512 · Cited by 184 · see citing works
De novo design of the hydrophobic core of ubiquitin
Lazar, G. A., Desjarlais, J. R., & Handel, T. M. (1997) · Protein Science · doi:10.1002/pro.5560060605 · Cited by 184 · see citing works
How evolution makes proteins fold quickly
Mirny, L. A., Abkevich, V., & Shakhnovich, E. I. (1998) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.95.9.4976 · Cited by 183 · see citing works
Kinetic and thermodynamic analysis of proteinlike heteropolymers: Monte Carlo histogram technique
Socci, N. D., & Onuchic, J. N. (1995) · The Journal of Chemical Physics · doi:10.1063/1.470610 · Cited by 180 · see citing works
First-Order Disorder-to-Order Transition in an Isolated Homopolymer Model
Zhou, Y., Hall, C. K., & Karplus, M. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.2822 · Cited by 179 · see citing works
Molecular Dynamics Simulations of the Unfolding of Barnase in Water and 8 M Aqueous Urea
Tirado‐Rives, J., Orozco, M., & Jorgensen, W. L. (1997) · Biochemistry · doi:10.1021/bi970096i · Cited by 179 · see citing works
The molten globule is a third thermodynamical state of protein molecules
Ptitsyn, O. B., & Uversky, V. N. (1994) · FEBS Letters · doi:10.1016/0014-5793(94)80231-9 · Cited by 178 · see citing works
Grosberg, A. Y., & Kuznetsov, D. V. (1992) · Macromolecules · doi:10.1021/ma00033a022 · Cited by 177 · see citing works
Self-citationKinetics and Thermodynamics of Folding of ade NovoDesigned Four-helix Bundle Protein
Guo, Z., & Thirumalai, D. (1996) · Journal of Molecular Biology · doi:10.1006/jmbi.1996.0578 · Cited by 169 · see citing works
A model of the molten globule state from molecular dynamics simulations.
Daggett, V., & Levitt, M. (1992) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.89.11.5142 · Cited by 163 · see citing works
Solution of the generalised random energy model
Derrida, B., & Gardner, E. (1986) · Journal of Physics C Solid State Physics · doi:10.1088/0022-3719/19/13/015 · Cited by 162 · see citing works
Caflisch, A., & Karplus, M. (1994) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.91.5.1746 · Cited by 162 · see citing works
Instabilities of charged polyampholytes
Kantor, Y., & Mehran Kardar, A. (1995) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.51.1299 · Cited by 158 · see citing works
Structural energetics of the molten globule state
Haynie, D. T., & Freire, E. (1993) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.340160202 · Cited by 156 · see citing works
Exploring conformational space with a simple lattice model for protein structure
Hinds, D. A., & Levitt, M. (1994) · Journal of Molecular Biology · doi:10.1016/0022-2836(94)90040-x · Cited by 153 · see citing works
Toward Protein Tertiary Structure Recognition by Means of Associative Memory Hamiltonians
Friedrichs, M. S., & Wolynes, P. G. (1989) · Science · doi:10.1126/science.246.4928.371 · Cited by 148 · see citing works
Statistical mechanics of a correlated energy landscape model for protein folding funnels
Plotkin, S. S., Wang, J., & Wolynes, P. G. (1997) · The Journal of Chemical Physics · doi:10.1063/1.473355 · Cited by 147 · see citing works
Frozen states of a disordered globular heteropolymer
Shakhnovich, E. I., & Gutin, A. M. (1989) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/22/10/019 · Cited by 146 · see citing works
Are proteins ideal mixtures of amino acids? Analysis of energy parameter sets
Godzik, A., Skolnick, J., & Koliński, A. (1995) · Protein Science · doi:10.1002/pro.5560041016 · Cited by 144 · see citing works
Evolution-like selection of fast-folding model proteins.
Gutin, A. M., Abkevich, V., & Shakhnovich, E. I. (1995) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.92.5.1282 · Cited by 141 · see citing works
Protein-like copolymers: computer simulation
Khokhlov, A. R., & Khalatur, P. G. (1998) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(97)00473-1 · Cited by 140 · see citing works
Monte Carlo and Molecular Dynamics Simulations
Clementi, E., Corongiu, G., Aida, M., Niesar, U., & Kneller, G. R. (1990) · Springer eBooks · doi:10.1007/978-94-009-2219-8_17 · Cited by 139 · see citing works
Why are some proteins structures so common?
Govindarajan, S., & Goldstein, R. A. (1996) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.93.8.3341 · Cited by 135 · see citing works
Cooperativity in protein folding: from lattice models with sidechains to real proteins
Klimov, D., & Thirumalai, D. (1998) · Folding and Design · doi:10.1016/s1359-0278(98)00018-2 · Cited by 129 · see citing works
Random and Alternating Polyampholytes
Wittmer, J. P., Johner, A., & Joanny, J. (1993) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/24/4/005 · Cited by 128 · see citing works
New Algorithm for Protein Design
Deutsch, J. M., & Kurosky, T. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.323 · Cited by 127 · see citing works
Statistical mechanics of simple models of protein folding and design
Pande, V. S., Grosberg, A. Y., & Tanaka, T. (1997) · Biophysical Journal · doi:10.1016/s0006-3495(97)78345-0 · Cited by 125 · see citing works
Self-citationPhase diagram of random copolymers
Sfatos, C. D., Gutin, A. M., & Shakhnovich, E. I. (1993) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.48.465 · Cited by 117 · see citing works
Factors governing the foldability of proteins
Klimov, D. K., & Thirumalai, D. (1996) · Proteins Structure Function and Bioinformatics · doi:10.1002/(sici)1097-0134(199612)26:4 · Cited by 115 · see citing works
Nonrandomness in protein sequences: evidence for a physically driven stage of evolution?
Pande, V. S., Grosberg, A. Y., & Tanaka, T. (1994) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.91.26.12972 · Cited by 111 · see citing works
Self-citationDesigning amino acid sequences to fold with good hydrophobic cores
Sun, S., Brem, R. B., Chan, H. S., & Dill, K. A. (1995) · Protein Engineering Design and Selection · doi:10.1093/protein/8.12.1205 · Cited by 109 · see citing works
Sequence-structure relationships in proteins and copolymers
Yue, K., & Dill, K. A. (1993) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.48.2267 · Cited by 108 · see citing works
Alexandrov, N. N., & Fischer, D. (1996) · Proteins Structure Function and Bioinformatics · doi:10.1002/(sici)1097-0134(199607)25:3 · Cited by 107 · see citing works
Aqueous solution properties of ampholytic copolymers prepared in microemulsions
Corpart, J., & Candau, F. (1993) · Macromolecules · doi:10.1021/ma00058a023 · Cited by 106 · see citing works
Phase diagram of a semiflexible polymer chain in a θ solvent: Application to protein folding
Doniach, S., Garel, T., & Orland, H. (1996) · The Journal of Chemical Physics · doi:10.1063/1.472031 · Cited by 106 · see citing works
Evidence for nonrandom hydrophobicity structures in protein chains.
Irbäck, A., Peterson, C., & Potthast, F. (1996) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.93.18.9533 · Cited by 103 · see citing works
Is the molten globule a third phase of proteins?
Pande, V. S., & Rokhsar, D. S. (1998) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.95.4.1490 · Cited by 103 · see citing works
Self-citationFast-folding eriments and the topography of protein folding energy landscapes
Wolynes, P. G., Luthey-Schulten, Z. A., & Onuchic, J. N. (1996) · Chemistry & Biology · doi:10.1016/s1074-5521(96)90090-3 · Cited by 98 · see citing works
Correlated energy landscape model for finite, random heteropolymers
Plotkin, S. S., Wang, J., & Wolynes, P. G. (1996) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.53.6271 · Cited by 93 · see citing works
Optimal Protein Design Procedure
Seno, F., Vendruscolo, M., Maritan, A., & Banavar, J. R. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.1901 · Cited by 91 · see citing works
Pande, V. S., Grosberg, A. Y., & Tanaka, T. (1994) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.91.26.12976 · Cited by 87 · see citing works
Self-citationWhy are the same protein folds used to perform different functions?
Finkelstein, A. V., Gutun, A. M., & Badretdinov, A. Y. (1993) · FEBS Letters · doi:10.1016/0014-5793(93)81407-q · Cited by 86 · see citing works
Thirumalai, D., & Guo, Z. (1995) · Biopolymers · doi:10.1002/bip.360350114 · Cited by 85 · see citing works
Molecular theory of associative memory Hamiltonian models of protein folding
Sasai, M., & Wolynes, P. G. (1990) · Physical Review Letters · doi:10.1103/physrevlett.65.2740 · Cited by 83 · see citing works
Phase changes in polyampholytes
Edwards, S. F., King, P., & Pincus, P. A. (1980) · Ferroelectrics · doi:10.1080/00150198008209479 · Cited by 81 · see citing works
Statistical mechanics of polyampholytes
Kantor, Y., Kardar, M., & Li, H. (1994) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.49.1383 · Cited by 81 · see citing works
Physical Approaches to Biological Evolution
Volkenstein, M. V. (1994) · Springer eBooks · doi:10.1007/978-3-642-78788-1 · Cited by 80 · see citing works
The foldability landscape of model proteins
Govindarajan, S., & Goldstein, R. A. (1997) · Biopolymers · doi:10.1002/(sici)1097-0282(19971005)42:4 · Cited by 77 · see citing works
Ground state of random copolymers and the discrete random energy model
Gutin, A. M., & Shakhnovich, E. I. (1993) · The Journal of Chemical Physics · doi:10.1063/1.464522 · Cited by 76 · see citing works
Protein Structures and Neutral Theory of Evolution
Ptitsyn, O. B., & Volkenstein, M. V. (1986) · Journal of Biomolecular Structure and Dynamics · doi:10.1080/07391102.1986.10507651 · Cited by 76 · see citing works
Statistical mechanics of proteins with ‘‘evolutionary selected’’ sequences
Ramanathan, S., & Shakhnovich, E. I. (1994) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.50.1303 · Cited by 75 · see citing works
Uversky, V. N., & Ptitsyn, O. B. (1996) · Folding and Design · doi:10.1016/s1359-0278(96)00020-x · Cited by 72 · see citing works
Modelling protein folding: the beauty and power of simplicity
Shakhnovich, E. I. (1996) · Folding and Design · doi:10.1016/s1359-0278(96)00027-2 · Cited by 69 · see citing works
How accurate must potentials be for successful modeling of protein folding?
Pande, V. S., Grosberg, A. Y., & Tanaka, T. (1995) · The Journal of Chemical Physics · doi:10.1063/1.470009 · Cited by 67 · see citing works
Self-citationChemical Sequence and Spatial Structure in Simple Models of Biopolymers
Garel, T., & Orland, H. (1988) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/6/7/005 · Cited by 66 · see citing works
Enumerations of the Hamiltonian walks on a cubic sublattice
Pande, V. S., Joerg, C., Grosberg, A. Y., et al. (1994) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/27/18/030 · Cited by 65 · see citing works
Self-citationDesign of proteins with selected thermal properties
Morrissey, M., & Shakhnovich, E. I. (1996) · Folding and Design · doi:10.1016/s1359-0278(96)00054-5 · Cited by 63 · see citing works
Protein structure: what is it possible to predict now?
Finkelstein, A. V. (1997) · Current Opinion in Structural Biology · doi:10.1016/s0959-440x(97)80008-5 · Cited by 62 · see citing works
Helix-Coil, Liquid Crystal, and Spin Glass Transitions of a Collapsed Heteropolymer
Luthey-Schulten, Z. A., Ramirez, B. E., & Wolynes, P. G. (1995) · The Journal of Physical Chemistry · doi:10.1021/j100007a057 · Cited by 58 · see citing works
Properties and origins of protein secondary structure
Socci, N. D., Bialek, W., & Onuchic, J. N. (1994) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.49.3440 · Cited by 57 · see citing works
Phase diagram of a model protein derived by exhaustive enumeration of the conformations
Dinner, A. R., Šali, A., Karplus, M., et al. (1994) · The Journal of Chemical Physics · doi:10.1063/1.467769 · Cited by 55 · see citing works
Statistical Mechanics, Protein Structure, and Protein Substrate Interactions
(1994) · NATO ASI series. Series B : Physics · doi:10.1007/978-1-4899-1349-4 · Cited by 53 · see citing works
Partially Folded States of Proteins: Characterization by X-ray Scattering
Doniach, S., Bascle, J., Garel, T., et al. (1995) · Journal of Molecular Biology · doi:10.1006/jmbi.1995.0668 · Cited by 53 · see citing works
Randomly charged polymers: An exact enumeration study
Kantor, Y., & Mehran Kardar, A. (1995) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.52.835 · Cited by 52 · see citing works
Magnetic properties and the function q(x) of the generalised random-energy model
Derrida, B., & Gardner, E. (1986) · Journal of Physics C Solid State Physics · doi:10.1088/0022-3719/19/29/005 · Cited by 51 · see citing works
Freezing transition of random heteropolymers consisting of an arbitrary set of monomers
Pande, V. S., Grosberg, A. Y., & Tanaka, T. (1995) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.51.3381 · Cited by 50 · see citing works
Self-citationOn the theory of folding kinetics for short proteins
Pande, V. S., Grosberg, A. Y., & Tanaka, T. (1997) · Folding and Design · doi:10.1016/s1359-0278(97)00015-1 · Cited by 47 · see citing works
Self-citationIs Heteropolymer Freezing Well Described by the Random Energy Model?
Pande, V. S., Grosberg, A. Y., Joerg, C., & Tanaka, T. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.3987 · Cited by 47 · see citing works
Self-citationProtein Design in a Lattice Model of Hydrophobic and Polar Amino Acids
Micheletti, C., Seno, F., Maritan, A., & Banavar, J. R. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.2237 · Cited by 46 · see citing works
Phase Diagram of Heteropolymers with an Imprinted Conformation
Pande, V. S., Grosberg, A. Y., & Tanaka, T. (1995) · Macromolecules · doi:10.1021/ma00111a016 · Cited by 45 · see citing works
Self-citationBryngelson, J. D. (1994) · The Journal of Chemical Physics · doi:10.1063/1.467114 · Cited by 43 · see citing works
Computer modeling and folding of four‐helix bundles
Rey, A., & Skolnick, J. (1993) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.340160103 · Cited by 43 · see citing works
How the first biopolymers could have evolved.
Abkevich, V., Gutin, A. M., & Shakhnovich, E. I. (1996) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.93.2.839 · Cited by 42 · see citing works
DeGrado, W. F. (1997) · Science · doi:10.1126/science.278.5335.80 · Cited by 41 · see citing works
Domains in folding of model proteins
Abkevich, V., Gutin, A. M., & Shakhnovich, E. I. (1995) · Protein Science · doi:10.1002/pro.5560040615 · Cited by 41 · see citing works
Protein folding from a combinatorial perspective
Sauer, R. T. (1996) · Folding and Design · doi:10.1016/s1359-0278(96)00015-6 · Cited by 40 · see citing works
[THE THEORY OF HELIX-COIL TRANSITIONS IN MACROMOLECULES].
Ptitsyn, O. B., & EIZNER, I. E. (1965) · PubMed · Cited by 37 · see citing works
Molecular dynamics simulations of apocytochrome b562– the highly ordered limit of molten globules
Laidig, K. E., & Daggett, V. (1996) · Folding and Design · doi:10.1016/s1359-0278(96)00049-1 · Cited by 36 · see citing works
Statistical mechanics of polymers with distance constraints
Gutin, A. M., & Shakhnovich, E. I. (1994) · The Journal of Chemical Physics · doi:10.1063/1.467193 · Cited by 35 · see citing works
Stability Threshold as a Selection Principle for Protein Design
Vendruscolo, M., Maritan, A., & Banavar, J. R. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.3967 · Cited by 35 · see citing works
Protein-like copolymers: Computer simulation
Khalatur, P. G., Иванов, В. А., Shusharina, N., & Khokhlov, A. R. (1998) · Russian Chemical Bulletin · doi:10.1007/bf02498152 · Cited by 33 · see citing works
Freezing Transition of Compact Polyampholytes
Pande, V. S., Grosberg, A. Y., Joerg, C., et al. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.3565 · Cited by 30 · see citing works
Self-citationThermodynamics of the coil to frozen globule transition in heteropolymers
Pande, V. S., Grosberg, A. Y., & Tanaka, T. (1997) · The Journal of Chemical Physics · doi:10.1063/1.474875 · Cited by 29 · see citing works
Self-citation[The theory of cooperative transitions in protein globules].
Shakhnovich, E. I., & Finkel'shteĭn (1982) · PubMed · Cited by 28 · see citing works
Steric Constraints in Model Proteins
Micheletti, C., Banavar, J. R., Maritan, A., et al. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.5683 · Cited by 26 · see citing works
Design of copolymeric materials
Kurosky, T., & Deutsch, J. M. (1995) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/28/14/003 · Cited by 26 · see citing works
Investigation of protein unfolding and stability by computer simulation
van Gunsteren, W. F., Hünenberger, P. H., Kovacs, H., et al. (1995) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.1995.0045 · Cited by 25 · see citing works
Kauffman, S. A., & Ellington, A. D. (1999) · Current Opinion in Chemical Biology · doi:10.1016/s1367-5931(99)80040-4 · Cited by 19 · see citing works
Freezing of compact random heteropolymers with correlated sequence fluctuations
Chakraborty, A. K., Shakhnovich, E. I., & Pande, V. S. (1998) · The Journal of Chemical Physics · doi:10.1063/1.475539 · Cited by 16 · see citing works
Self-citationTanaka, T., Enoki, T., Grosberg, A. Y., Masamune, S., Oya, T., Takaoka, Y., Tanaka, K., Wang, C., & Wang, G. (1998) · Berichte der Bunsengesellschaft für physikalische Chemie · doi:10.1002/bbpc.19981021103 · Cited by 16 · see citing works
Self-citationModels of protein interactions: how to choose one
Du, R., Grosberg, A. Y., & Tanaka, T. (1998) · Folding and Design · doi:10.1016/s1359-0278(98)00028-5 · Cited by 13 · see citing works
Self-citationON THE MEAN FIELD THEORY OF RANDOM HETEROPOLYMERS
Franz, S., Mézard, M., & Parisi, G. (1992) · International Journal of Neural Systems · doi:10.1142/s0129065792000528 · Cited by 11 · see citing works
On the properties of polymer globules in the high density limit
Witelski, T. P., Grosberg, A. Y., & Tanaka, T. (1998) · The Journal of Chemical Physics · doi:10.1063/1.476361 · Cited by 11 · see citing works
Self-citationThe coil–globule transition of polymers of long rigid monomers connected by flexible spacers
Sear, R. P. (1997) · The Journal of Chemical Physics · doi:10.1063/1.474987 · Cited by 8 · see citing works
Analyticity of the partition function of the random energy model
Koukiou, F. (1993) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/26/23/003 · Cited by 7 · see citing works
Grosberg, A. Y., & Shakhnovich, E. I. (1987) · PubMed · Cited by 3 · see citing works
Self-citationHolden, C. (1995) · Science · doi:10.1126/science.269.5231.1675 · Cited by 3 · see citing works
Overlap properties and adsorption transition of two Hamiltonian paths
Franz, S., Garel, T., & Orland, H. (1999) · The European Physical Journal B · doi:10.1007/s100510050957 · Cited by 2 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Finding low-energy conformations of lattice protein models by quantum annealing
Perdomo-Ortiz, A., Dickson, N., Drew-Brook, M., Rose, G., & Aspuru-Guzik, A. (2012) · Scientific Reports · doi:10.1038/srep00571 · Cited by 366 · see citing works
Simulating Chemistry Using Quantum Computers
Kassal, I., Whitfield, J. D., Perdomo-Ortiz, A., Yung, M.-H., & Aspuru-Guzik, A. (2011) · Annual Review of Physical Chemistry · doi:10.1146/annurev-physchem-032210-103512 · Cited by 352 · see citing works
Li, W., Wolynes, P. G., & Takada, S. (2011) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1018983108 · Cited by 159 · see citing works
Babbush, R., Perdomo‐Ortiz, A., O'Gorman, B., Macready, W., & Aspuru‐Guzik, A. (2014) · Advances in Chemical Physics · doi:10.1002/9781118755815.ch05 · Cited by 45 · see citing works
Lethal mutants and truncated selection together solve a paradox of the origin of life
Saakian, D. B., Biebricher, C. K., & Hu, C.-K. (2011) · PLoS ONE · doi:10.1371/journal.pone.0021904 · Cited by 27 · see citing works
- Authors
- Pande, V. S., Grosberg, A. Y., & Tanaka, T.
- Affiliations
- Stanford University (US)
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 2000-01-01
- Volume
- 72
- Issue
- 1
- Pages
- 259-314
- ISSN
- 0034-6861 (ISSN-L)
- 1539-0756
- OpenAlex
- W1998893348
- Cited by
- 284
- References
- 174
- Citations by year
- 2026: 2 · 2025: 5 · 2024: 5 · 2023: 4 · 2022: 5 · 2021: 7 · 2020: 9 · 2019: 5 · 2018: 10 · 2017: 9 · 2016: 5 · 2015: 5 · 2014: 8 · 2013: 8 · 2012: 9
- FWCI
- 8.68
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Reviews of Modern Physics (publishedVersion)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › RNA and protein synthesis mechanisms
- Keywords
- protein folding, heteropolymers, random energy model, design temperature, glass transition, phase transitions, polymer physics, disordered systems, sequence statistics
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review