Multiple protein folding nuclei and the transition state ensemble in two‐state proteins

Using exhaustive simulations of lattice models with side‐chains, we show that optimized two‐state folders reach the native state by a nucleation‐collapse mechanism with multiple folding nuclei (MFN). For both the full model and the Go version, there are certain contacts that on an average participate in the critical nuclei with higher probability than the others. The high‐ (≳0.5) probability contacts are largely determined by the structure of the native state. Comparison of the results for the full sequence and the Go model shows that non‐native interactions compromise the degree of cooperativity and stability of the native state. From an extremely detailed analysis of the folding kinetics, we find that non‐native interactions are present in the folding nuclei. The folding times decrease if the non‐native interactions in the folding nuclei are made neutral or repulsive. Using cluster analysis and making no prior assumption about reaction coordinate, we show that both full and Go models have three distinct transition states that give a structural description for the MFN. In the transition states, on an average, about two‐thirds of the sequence is structured, whereas the rest is disordered, reminiscent of the polarized transition state in the SH3 domain. Our studies show that Go models cannot describe the transition state characteristics of two‐state folders at the molecular level. As a byproduct of our investigations, we establish that our method of computing the transition state ensemble is numerically equivalent to the technique based on the stochastic separatrix, which also does not require a priori knowledge of the folding reaction coordinate. Proteins 2001;43:465–475. © 2001 Wiley‐Liss, Inc.

[1]  D. Thirumalai,et al.  Deciphering the timescales and mechanisms of protein folding using minimal off-lattice models. , 1999, Current opinion in structural biology.

[2]  R. Zwanzig,et al.  Two-state models of protein folding kinetics. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[3]  J. Onuchic,et al.  Theory of protein folding: the energy landscape perspective. , 1997, Annual review of physical chemistry.

[4]  V. Pande,et al.  On the transition coordinate for protein folding , 1998 .

[5]  P. Wolynes,et al.  Folding funnels and energy landscapes of larger proteins within the capillarity approximation. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[6]  D. Thirumalai,et al.  Thermodynamic stability of folded proteins against mutations , 1997, cond-mat/9709078.

[7]  V. Pande,et al.  Pathways for protein folding: is a new view needed? , 1998, Current opinion in structural biology.

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

[9]  D. Thirumalai,et al.  LINKING RATES OF FOLDING IN LATTICE MODELS OF PROTEINS WITH UNDERLYING THERMODYNAMIC CHARACTERISTICS , 1998, cond-mat/9805061.

[10]  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 .

[11]  E. Shakhnovich,et al.  Conserved residues and the mechanism of protein folding , 1996, Nature.

[12]  D. Thirumalai,et al.  Kinetics of protein folding: Nucleation mechanism, time scales, and pathways , 1995 .

[13]  R A Sayle,et al.  RASMOL: biomolecular graphics for all. , 1995, Trends in biochemical sciences.

[14]  V. Muñoz,et al.  Submillisecond kinetics of protein folding. , 1997, Current opinion in structural biology.

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

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

[17]  A. R. Fresht Structure and Mechanism in Protein Science: A Guide to Enzyme Catalysis and Protein Folding , 1999 .

[18]  D Thirumalai,et al.  Cooperativity in protein folding: from lattice models with sidechains to real proteins. , 1998, Folding & design.

[19]  D. Thirumalai,et al.  Fishing for folding nuclei in lattice models and proteins. , 1998, Folding & design.

[20]  J. Straub,et al.  The MaxFlux algorithm for calculating variationally optimized reaction paths for conformational transitions in many body systems at finite temperature , 1997 .

[21]  A. Fersht Nucleation mechanisms in protein folding. , 1997, Current opinion in structural biology.

[22]  J. Onuchic,et al.  Protein folding funnels: the nature of the transition state ensemble. , 1996, Folding & design.

[23]  D Thirumalai,et al.  Lattice models for proteins reveal multiple folding nuclei for nucleation-collapse mechanism. , 1998, Journal of molecular biology.

[24]  J. Onuchic,et al.  DIFFUSIVE DYNAMICS OF THE REACTION COORDINATE FOR PROTEIN FOLDING FUNNELS , 1996, cond-mat/9601091.

[25]  David Baker,et al.  Important role of hydrogen bonds in the structurally polarized transition state for folding of the src SH3 domain , 1998, Nature Structural &Molecular Biology.

[26]  Eugene I. Shakhnovich,et al.  Kinetics, thermodynamics and evolution of non-native interactions in a protein folding nucleus , 2000, Nature Structural Biology.

[27]  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.

[28]  D. Thirumalai,et al.  The nucleation-collapse mechanism in protein folding: evidence for the non-uniqueness of the folding nucleus. , 1997, Folding & design.

[29]  Bernard J. Matkowsky,et al.  The Kramers Problem in the Turnover Regime: The Role of the Stochastic Separatrix , 1991 .

[30]  N. Go Theoretical studies of protein folding. , 1983, Annual review of biophysics and bioengineering.

[31]  C. Brooks,et al.  Exploring the space of protein folding Hamiltonians: The balance of forces in a minimalist β-barrel model , 1998 .

[32]  J. Onuchic,et al.  How native-state topology affects the folding of dihydrofolate reductase and interleukin-1beta. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[33]  Peter G. Wolynes,et al.  A simple statistical field theory of heteropolymer collapse with application to protein folding , 1990 .