Regular article
Contact order, transition state placement and the refolding rates of single domain proteins1

This paper is dedicated to W. A. Goddard III, on the occasion of his 60th birthday.
https://doi.org/10.1006/jmbi.1998.1645Get rights and content

Abstract

Theoretical studies have suggested relationships between the size, stability and topology of a protein fold and the rate and mechanisms by which it is achieved. The recent characterization of the refolding of a number of simple, single domain proteins has provided a means of testing these assertions. Our investigations have revealed statistically significant correlations between the average sequence separation between contacting residues in the native state and the rate and transition state placement of folding for a non-homologous set of simple, single domain proteins. These indicate that proteins featuring primarily sequence-local contacts tend to fold more rapidly and exhibit less compact folding transition states than those characterized by more non-local interactions. No significant relationship is apparent between protein length and folding rates, but a weak correlation is observed between length and the fraction of solvent-exposed surface area buried in the transition state. Anticipated strong relationships between equilibrium folding free energy and folding kinetics, or between chemical denaturant and temperature dependence-derived measures of transition state placement, are not apparent. The observed correlations are consistent with a model of protein folding in which the size and stability of the polypeptide segments organized in the transition state are largely independent of protein length, but are related to the topological complexity of the native state. The correlation between topological complexity and folding rates may reflect chain entropy contributions to the folding barrier.

Introduction

Numerous theoretical studies have suggested that the size Wolynes 1997, Finkelstein and Badretdinov 1997, Klimov and Thirumalai 1997, Gutin et al 1996, Thirumalai 1995, stability Finkelstein 1991, Sali et al 1994, Bryngelson et al 1995, Onuchic et al 1995, Pande et al 1997 and topology Doyle et al 1997, Gross 1996, Unger and Moult 1996, Wolynes 1996, Abkevich et al 1995, Fersht 1995a, Fersht 1995b, Govindarajan and Goldstein 1995, Karplus and Weaver 1994, Orengo et al 1994, Dill et al 1993 of a protein influence the rate and mechanisms by which it folds. Unfortunately, attempts to demonstrate such relationships (e.g. see Munoz and Serrano 1996, Scalley et al 1998) have been hindered by the difficulties associated with analyzing complex, multiphasic folding kinetics and by the limited amount of experimental evidence available. The recent characterization of the refolding of a number of single domain proteins lacking cis proline residues or disulfide bonds, however, motivated us to re-investigate these relationships. Here we report potentially significant correlations between the folding kinetics and the native, equilibrium properties of a set of kinetically simple, single domain proteins.

Comparisons of the refolding of proteins under differing experimental conditions, of mutant proteins (e.g. Fersht 1995b, Burton et al 1996) and of homologous proteins Kragelund et al 1996, Mines et al 1996, Plaxco et al 1997, Plaxco et al 1998 indicate that minor changes in solvent or sequence can dramatically alter the kinetics of folding. The large range of kinetic behaviors exhibited by a single protein under differing solvent conditions, or by multiple proteins adopting nearly identical folds, suggests that the resolution of sequence and experiment specific effects from the potentially more subtle effects of size, stability and topology might prove very difficult. Our solution to this problem is to search for relationships in a large, diverse data set so that the kinetic consequences of equilibrium properties may be assessed despite this noise. Causal relationships should thus appear as statistically significant, albeit imperfect, correlations between kinetic parameters and equilibrium properties.

Section snippets

Results

We have investigated the influence of three general equilibrium properties, the size, stability and topological complexity of the native state, on the folding kinetics of a non-homologous set of simple single domain proteins. The size (length) and stability (ΔGu) of the native state are easily quantified and were taken directly from the literature. Topological complexity is somewhat more difficult to specify numerically. We have used relative contact order, (CO), which reflects the relative

Discussion

Recent years have seen a large increase in studies of the refolding of simple, single domain proteins. We have used this rapidly increasing data base to investigate the roles played by general, equilibrium properties such as length, topology or stability in defining the rates and mechanisms by which proteins fold. Due to the relatively small size of the data set presently available the results of these investigations should be considered preliminary. However, several statistically significant

Conclusions

The recent characterization of the refolding properties of a number of simple, single domain proteins has provided an opportunity to demonstrate that the relative contact order of the native state is a determinant of both the height and placement of the folding transition state barrier. The influences of other factors, such as equilibrium stability and chain length, are either not apparent or only weakly supported by the test set presently available. No doubt the rapidly increasing protein

Materials and methods

We are aware of 22 monomeric, single domain proteins which lack disulfide bonds and cis proline residues, which have been suggested to fold via two-state kinetics under at least some conditions and for which most of the appropriate structural and kinetic data are available. Multiple members of homologous families were not included in the test set in order to avoid over representation of a single topology or length. Thus, eight of the 22 proteins were excluded because they exhibit significant

Acknowledgements

The authors gratefully acknowledge a long-standing collaboration with Chris Dobson as the source of much of the data used in this analysis. The authors also thank R. Baldwin, H. S. Chan, F. Chiti, K. Dill, V. Daggett, C. Dobson, K. Fiebig, H. Gray, M. Gross, B. Kragelund, T. Oas, M. Scalley, D. Shortle, D. Teller and D. Thirumalai for helpful reviews of this paper and L. Plaxco and I. Ruczinski for invaluable aid and advice on the statistical analysis. We are also deeply indebted to F. Chiti,

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