A simple measure of native‐state topology and chain connectivity predicts the folding rates of two‐state proteins with and without crosslinks

The folding rates of two‐state proteins have been found to correlate with simple measures of native‐state topology. The most prominent among these measures is the relative contact order (CO), which is the average CO, or localness, of all contacts in the native protein structure, divided by the chain length. Here, we test whether such measures can be generalized to capture the effect of chain crosslinks on the folding rate. Crosslinks change the chain connectivity and therefore also the localness of some of the native contacts. These changes in localness can be taken into account by the graph‐theoretical concept of effective contact order (ECO). The relative ECO, however, the natural extension of the relative CO for proteins with crosslinks, overestimates the changes in the folding rates caused by crosslinks. We suggest here a novel measure of native‐state topology, the relative logCO, and its natural extension, the relative logECO. The relative logCO is the average value for the logarithm of the CO of all contacts, divided by the logarithm of the chain length. The relative log(E)CO reproduces the folding rates of a set of 26 two‐state proteins without crosslinks with essentially the same high correlation coefficient as the relative CO. In addition, it also captures the folding rates of eight two‐state proteins with crosslinks. Proteins 2006. © 2006 Wiley‐Liss, Inc.

[1]  D. Baker,et al.  Contact order, transition state placement and the refolding rates of single domain proteins. , 1998, Journal of molecular biology.

[2]  Huan-Xiang Zhou,et al.  Effect of backbone cyclization on protein folding stability: chain entropies of both the unfolded and the folded states are restricted. , 2003, Journal of molecular biology.

[3]  K. Dill,et al.  Protein core assembly processes , 1993 .

[4]  Kevin W Plaxco,et al.  Contact order revisited: Influence of protein size on the folding rate , 2003, Protein science : a publication of the Protein Society.

[5]  Kevin W Plaxco,et al.  The topomer search model: A simple, quantitative theory of two‐state protein folding kinetics , 2003, Protein science : a publication of the Protein Society.

[6]  T. Kameda.  Importance of sequence specificity for predicting protein folding pathways: Perturbed Gaussian chain model , 2003, Proteins.

[7]  Homer Jacobson,et al.  Intramolecular Reaction in Polycondensations. I. The Theory of Linear Systems , 1950 .

[8]  D Baker,et al.  Mechanisms of protein folding. , 2001, Current opinion in structural biology.

[9]  Hongyi Zhou,et al.  Folding rate prediction using total contact distance. , 2002, Biophysical journal.

[10]  D. Baker,et al.  A surprising simplicity to protein folding , 2000, Nature.

[11]  E. Shakhnovich,et al.  Constructing, verifying, and dissecting the folding transition state of chymotrypsin inhibitor 2 with all-atom simulations , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Jeanette Tångrot,et al.  Complete change of the protein folding transition state upon circular permutation , 2002, Nature Structural Biology.

[13]  D Baker,et al.  Topology, stability, sequence, and length: defining the determinants of two-state protein folding kinetics. , 2000, Biochemistry.

[14]  A. Flammini,et al.  Energy landscape and native-state structure of proteins: A simplified model , 2002 .

[15]  K. Dill,et al.  The effects of internal constraints on the configurations of chain molecules , 1990 .

[16]  Marek Cieplak,et al.  Sequencing of folding events in Go-type proteins , 2000, cond-mat/0008201.

[17]  D Thirumalai,et al.  Stiffness of the distal loop restricts the structural heterogeneity of the transition state ensemble in SH3 domains. , 2002, Journal of molecular biology.

[18]  A. Finkelstein,et al.  Folding of circular permutants with decreased contact order: general trend balanced by protein stability. , 2001, Journal of molecular biology.

[19]  Thomas R Weikl,et al.  Loop‐closure events during protein folding: Rationalizing the shape of Φ‐value distributions , 2005, Proteins.

[20]  T. Oas,et al.  Microsecond protein folding through a compact transition state. , 1996, Journal of molecular biology.

[21]  A. Fersht,et al.  Folding of circular and permuted chymotrypsin inhibitor 2: retention of the folding nucleus. , 1998, Biochemistry.

[22]  D Thirumalai,et al.  Theoretical predictions of folding pathways by using the proximity rule, with applications to bovine pancreatic trypsin inhibitor. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[23]  A. Finkelstein,et al.  A theoretical search for folding/unfolding nuclei in three-dimensional protein structures. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Kevin W Plaxco,et al.  How the folding rate constant of simple, single-domain proteins depends on the number of native contacts , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[25]  Cristian Micheletti,et al.  Prediction of folding rates and transition‐state placement from native‐state geometry , 2002, Proteins.

[26]  Loops, Linkages, Rings, Catenanes, Cages, and Crowders: Entropy‐Based Strategies for Stabilizing Proteins , 2004 .

[27]  S. Marqusee,et al.  Experimental evaluation of topological parameters determining protein-folding rates , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[28]  D Baker,et al.  Long-range order in the src SH3 folding transition state. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[29]  J. Onuchic,et al.  Topological and energetic factors: what determines the structural details of the transition state ensemble and "en-route" intermediates for protein folding? An investigation for small globular proteins. , 2000, Journal of molecular biology.

[30]  David Baker,et al.  Simple physical models connect theory and experiment in protein folding kinetics. , 2002, Journal of molecular biology.

[31]  V. Muñoz,et al.  A simple model for calculating the kinetics of protein folding from three-dimensional structures. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[32]  K. Dill,et al.  Cooperativity in protein-folding kinetics. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[33]  K. Dill,et al.  Folding rates and low-entropy-loss routes of two-state proteins. , 2003, Journal of molecular biology.

[34]  M. Gromiha,et al.  Comparison between long-range interactions and contact order in determining the folding rate of two-state proteins: application of long-range order to folding rate prediction. , 2001, Journal of molecular biology.

[35]  E. Alm,et al.  Prediction of protein-folding mechanisms from free-energy landscapes derived from native structures. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[36]  Alessandro Pelizzola,et al.  Exact solution of the Muñoz-Eaton model for protein folding. , 2002, Physical review letters.

[37]  T. Kiefhaber,et al.  Effect of preformed correct tertiary interactions on rapid two-state tendamistat folding: evidence for hairpins as initiation sites for beta-sheet formation. , 1997, Biochemistry.

[38]  Haipeng Gong,et al.  Local secondary structure content predicts folding rates for simple, two-state proteins. , 2003, Journal of molecular biology.

[39]  L Serrano,et al.  The SH3-fold family: experimental evidence and prediction of variations in the folding pathways. , 2000, Journal of molecular biology.

[40]  W. Goddard,et al.  First principles prediction of protein folding rates. , 1999, Journal of molecular biology.

[41]  Hue Sun Chan,et al.  A critical assessment of the topomer search model of protein folding using a continuum explicit‐chain model with extensive conformational sampling , 2005, Protein science : a publication of the Protein Society.

[42]  Luis Serrano,et al.  Different folding transition states may result in the same native structure , 1996, Nature Structural Biology.

[43]  T. Muir,et al.  Rescuing a destabilized protein fold through backbone cyclization. , 2001, Journal of molecular biology.

[44]  Ken A Dill,et al.  Folding kinetics of two-state proteins: effect of circularization, permutation, and crosslinks. , 2003, Journal of molecular biology.

[45]  Martin Gruebele,et al.  Folding at the speed limit , 2003, Nature.

[46]  A. Fersht.  Structure and mechanism in protein science , 1998 .

[47]  S. Jackson,et al.  How do small single-domain proteins fold? , 1998, Folding & design.

[48]  David Baker,et al.  Experiment and theory highlight role of native state topology in SH3 folding , 1999, Nature Structural Biology.

[49]  Shoji Takada,et al.  Microscopic theory of protein folding rates. I. Fine structure of the free energy profile and folding routes from a variational approach , 2000, cond-mat/0008454.