Cooperativity in protein folding: from lattice models with sidechains to real proteins.

BACKGROUND Over the past few years novel folding mechanisms of globular proteins have been proposed using minimal lattice and off-lattice models. The factors determining the cooperativity of folding in these models and especially their explicit relation to experiments have not been fully established, however. RESULTS We consider equilibrium folding transitions in lattice models with and without sidechains. A dimensionless measure, omega c, is introduced to quantitatively assess the degree of cooperativity in lattice models and in real proteins. We show that larger values of omega c resembling the values seen in proteins are obtained in lattice models with sidechains. The enhanced cooperativity of such models results from possible denser packing of sidechains in the interior of the model polypeptide chain. We also establish that omega c correlates extremely well with sigma T = (T o - T f) /T o, where T o and T f are collapse and folding transition temperatures, respectively. These theoretical ideas are used to analyze folding transitions in two-state folders (RNase A, chymotrypsin inhibitor 2, fibronectin type III modules and tendamistat) and three-state folders (apomyoglobin and lysozyme). The values of omega c extracted from experiments show a correlation with sigma T (suitably generalized when folding is induced by denaturants or acid). CONCLUSIONS A quantitative description of the cooperative transition of real proteins can be made by lattice models with sidechains. The degree of cooperativity in minimal models and real proteins can be expressed in terms of the single parameter sigma, which can be estimated from experimental data.

[1]  D Thirumalai,et al.  Factors governing the foldability of proteins , 1996, Proteins.

[2]  Klimov,et al.  Criterion that determines the foldability of proteins. , 1996, Physical review letters.

[3]  A. Godzik,et al.  A general method for the prediction of the three dimensional structure and folding pathway of globular proteins: Application to designed helical proteins , 1993 .

[4]  I D Campbell,et al.  A comparison of the folding kinetics and thermodynamics of two homologous fibronectin type III modules. , 1997, Journal of molecular biology.

[5]  Christopher M. Dobson,et al.  Following protein folding in real time using NMR spectroscopy , 1995, Nature Structural Biology.

[6]  E. Shakhnovich,et al.  A new approach to the design of stable proteins. , 1993, Protein engineering.

[7]  R. Jernigan,et al.  Estimation of effective interresidue contact energies from protein crystal structures: quasi-chemical approximation , 1985 .

[8]  C. Brooks,et al.  Exploring the folding free energy surface of a three-helix bundle protein. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[9]  R. Jernigan,et al.  Residue-residue potentials with a favorable contact pair term and an unfavorable high packing density term, for simulation and threading. , 1996, Journal of molecular biology.

[10]  Alan M. Ferrenberg,et al.  Optimized Monte Carlo data analysis. , 1989, Physical review letters.

[11]  S Doniach,et al.  A lysozyme folding intermediate revealed by solution X-ray scattering. , 1996, Journal of molecular biology.

[12]  D. Eisenberg,et al.  A method to identify protein sequences that fold into a known three-dimensional structure. , 1991, Science.

[13]  U. Arnold,et al.  Kinetic and thermodynamic thermal stabilities of ribonuclease A and ribonuclease B. , 1997, Biochemistry.

[14]  T. Kiefhaber,et al.  Folding of the disulfide-bonded beta-sheet protein tendamistat: rapid two-state folding without hydrophobic collapse. , 1997, Journal of molecular biology.

[15]  J. Onuchic,et al.  Toward an outline of the topography of a realistic protein-folding funnel. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[16]  E. Shakhnovich,et al.  Proteins with selected sequences fold into unique native conformation. , 1994, Physical review letters.

[17]  D. Yee,et al.  Principles of protein folding — A perspective from simple exact models , 1995, Protein science : a publication of the Protein Society.

[18]  D. Thirumalai,et al.  Kinetic partitioning mechanism as a unifying theme in the folding of biomolecules , 1997, cond-mat/9704067.

[19]  M. Hao,et al.  STATISTICAL THERMODYNAMICS OF PROTEIN FOLDING : SEQUENCE DEPENDENCE , 1994 .

[20]  J. Trewhella,et al.  Denatured states of ribonuclease A have compact dimensions and residual secondary structure. , 1992, Biochemistry.

[21]  D. Thirumalai,et al.  Protein folding kinetics: timescales, pathways and energy landscapes in terms of sequence-dependent properties. , 1996, Folding & design.

[22]  Andrzej Kolinski,et al.  On the origin of the cooperativity of protein folding: Implications from model simulations , 1996, Proteins.

[23]  R Elber,et al.  Kinetics of peptide folding: computer simulations of SYPFDV and peptide variants in water. , 1997, Journal of molecular biology.

[24]  K. Dill,et al.  From Levinthal to pathways to funnels , 1997, Nature Structural Biology.

[25]  J. Onuchic,et al.  Navigating the folding routes , 1995, Science.

[26]  M. Fukugita,et al.  Kinematics and thermodynamics of a folding heteropolymer. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[27]  Cooperativity of folding of the apomyoglobin pH 4 intermediate studied by glycine and proline mutations , 1997, Nature Structural Biology.

[28]  A. Fersht,et al.  Folding of chymotrypsin inhibitor 2. 1. Evidence for a two-state transition. , 1991, Biochemistry.

[29]  F M Richards,et al.  An analysis of packing in the protein folding problem , 1993, Quarterly Reviews of Biophysics.

[30]  F M Richards,et al.  Areas, volumes, packing and protein structure. , 1977, Annual review of biophysics and bioengineering.

[31]  E I Shakhnovich,et al.  Theory of cooperative transitions in protein molecules. I. Why denaturation of globular protein is a first‐order phase transition , 1989, Biopolymers.

[32]  R. L. Baldwin,et al.  Three-state analysis of sperm whale apomyoglobin folding. , 1993, Biochemistry.

[33]  D Thirumalai,et al.  Kinetics and thermodynamics of folding in model proteins. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[34]  J. Onuchic,et al.  Funnels, pathways, and the energy landscape of protein folding: A synthesis , 1994, Proteins.

[35]  M. Karplus,et al.  Folding thermodynamics of a model three-helix-bundle protein. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[36]  A. Fersht,et al.  An N-terminal fragment of barnase has residual helical structure similar to that in a refolding intermediate. , 1992, Journal of molecular biology.

[37]  Harold A. Scheraga,et al.  MONTE CARLO SIMULATION OF A FIRST-ORDER TRANSITION FOR PROTEIN FOLDING , 1994 .

[38]  L A Mirny,et al.  Universality and diversity of the protein folding scenarios: a comprehensive analysis with the aid of a lattice model. , 1996, Folding & design.

[39]  H. Scheraga,et al.  Experimental and theoretical aspects of protein folding. , 1975, Advances in protein chemistry.

[40]  K A Dill,et al.  Side‐chain entropy and packing in proteins , 1994, Protein science : a publication of the Protein Society.