Alexei V. Finkelstein

Making Optimal Use of Empirical Energy Functions: Force-Field Parameterization in Crystal Space

Todays energy functions are not able yet to distinguish reliably between correct and almost correct protein models. Improving these near‐native models is currently a major bottle‐neck in homology modeling or experimental structure determination at low resolution. Increasingly accurate energy functions are required to complete the “last mile of the protein folding problem,” for example during a molecular dynamics simulation. We present a new approach to reach this goal. For 50 high resolution X‐ray structures, the complete unit cell was reconstructed, including disordered water molecules, counter ions, and hydrogen atoms. Simulations were then run at the pH at which the crystal was solved, while force‐field parameters were iteratively adjusted so that the damage done to the structures was minimal. Starting with initial parameters from the AMBER force field, the optimization procedure converged at a new force field called YAMBER (Yet Another Model Building and Energy Refinement force field), which is shown to do significantly less damage to X‐ray structures, often move homology models in the right direction, and occasionally make them look like experimental structures. Application of YAMBER during the CASP5 structure prediction experiment yielded a model for target 176 that was ranked first among 150 submissions. Due to its compatibility with the well‐established AMBER format, YAMBER can be used by almost any molecular dynamics program. The parameters are freely available from www.yasara.org/yamber. Proteins 2004.

Contact order revisited: influence of protein size on the folding rate.

Guided by the recent success of empirical model predicting the folding rates of small two‐state folding proteins from the relative contact order (CO) of their native structures, by a theoretical model of protein folding that predicts that logarithm of the folding rate decreases with the protein chain length L as L2/3, and by the finding that the folding rates of multistate folding proteins strongly correlate with their sizes and have very bad correlation with CO, we reexamined the dependence of folding rate on CO and L in attempt to find a structural parameter that determines folding rates for the totality of proteins. We show that the Abs_CO = CO × L, is able to predict rather accurately folding rates for both two‐state and multistate folding proteins, as well as short peptides, and that this Abs_CO scales with the protein chain length as L0.70 ± 0.07 for the totality of studied single‐domain proteins and peptides.

Chain length is the main determinant of the folding rate for proteins with three-state folding kinetics.

We demonstrate that chain length is the main determinant of the folding rate for proteins with the three‐state folding kinetics. The logarithm of their folding rate in water (kf) strongly anticorrelates with their chain length L (the correlation coefficient being −0.80). At the same time, the chain length has no correlation with the folding rate for two‐state folding proteins (the correlation coefficient is −0.07). Another significant difference of these two groups of proteins is a strong anticorrelation between the folding rate and Bakers “relative contact order” for the two‐state folders and the complete absence of such correlation for the three‐state folders. Proteins 2003;51:162–166.

What is the probability of a chance prediction of a protein structure with an rmsd of 6 å

BACKGROUND The root mean square deviation (rmsd) between corresponding atoms of two protein chains is a commonly used measure of similarity between two protein structures. The smaller the rmsd is between two structures, the more similar are these two structures. In protein structure prediction, one needs the rmsd between predicted and experimental structures for which a prediction can be considered to be successful. Success is obvious only when the rmsd is as small as that for closely homologous proteins (< 3 A). To estimate the quality of the prediction in the more general case, one has to compare the native structure not only with the predicted one but also with randomly chosen protein-like folds. One can ask: how many such structures must be considered to find a structure with a given rmsd from the native structure? RESULTS We calculated the rmsd values between native structures of 142 proteins and all compact structures obtained in the threading of these protein chains over 364 non-homologous structures. The rmsd distributions have a Gaussian form, with the average rmsd approximately proportional to the radius of gyration. CONCLUSIONS We estimated the number of protein-like structures required to obtain a structure within an rmsd of 6 A to be 10(4)-10(5) for chains of 60-80 residues and 10(11)-10(12) structures for chains of 160-200 residues. The probability of obtaining a 6 A rmsd by chance is so remote that when such structures are obtained from a prediction algorithm, it should be considered quite successful.

Why are the same protein folds used to perform different functions

A small number of folding patterns describe in outline most of the known protein globules, the same folds being found in non‐homologous proteins with different functions. We show that the ‘popular’ folding patterns are those which, due to some thennodynamic advantages of their structure, can be stabilized by a lot of random sequences. In contrast, the folds which are rarely or never observed in natural globular proteins can be stabilized only by a tiny number of random sequences. The advantageous folds are few, they tolerate various primary structures, and therefore they can and ought to perform different functions. A connection between the inherent ‘weak points’ of protein folding patterns and positions of active sites are discussed.

Protein structure: what is it possible to predict now?

The computational techniques of sorting out protein folds (these techniques include dynamic programming, self-consistent field theory, etc.) have already ceased to be the bottleneck of predictions. The main problem is that all the methods of recognition and prediction of protein structure can actually use only some part of the interactions operating in the chain, and that even their energies are not known precisely. This is the principal source of errors now. The errors can be reduced by employment of many distant homologues, but this opens a possibility to predict a generalized folding pattern rather than a particular fold with all its details.

Folding nuclei in proteins.

When a protein folds or unfolds, it passes through many half‐folded microstates. Only a few of them can accumulate and be seen experimentally, and this happens only when the folding (or unfolding) occurs far from the point of thermodynamic equilibrium between the native and denatured states. The universal features of folding, though, are observed just close to the equilibrium point. Here the ‘two‐state’ transition proceeds without any accumulation of metastable intermediates, and only the transition state (‘folding nucleus’) is outlined by its key influence on the folding–unfolding kinetics. Our aim is to review recent experimental and theoretical studies of the folding nuclei.

Comparison of X-ray and NMR Structures: Is There a Systematic Difference in Residue Contacts between X-ray- and NMR-Resolved Protein Structures?

We have compared structures of 78 proteins determined by both NMR and X‐ray methods. It is shown that X‐ray and NMR structures of the same protein have more differences than various X‐ray structures obtained for the protein, and even more than various NMR structures of the protein. X‐ray and NMR structures of 18 of these 78 proteins have obvious large‐scale structural differences that seem to reflect a difference of crystal and solution structures. The other 60 pairs of structures have only small‐scale differences comparable with differences between various X‐ray or various NMR structures of a protein; we have analyzed these structures more attentively. One of the main differences between NMR and X‐ray structures concerns the number of contacts per residue: (1) NMR structures presented in PDB have more contacts than X‐ray structures at distances below 3.0 Å and 4.5–6.5 Å, and fewer contacts at distances of 3.0–4.5 Å and 6.5–8.0 Å; (2) this difference in the number of contacts is greater for internal residues than for external ones, and it is larger for β‐containing proteins than for all‐α proteins. Another significant difference is that the main‐chain hydrogen bonds identified in X‐ray and NMR structures often differ. Their correlation is 69% only. However, analogous difference is found for refined and rerefined NMR structures, allowing us to suggest that the observed difference in interresidue contacts of X‐ray and NMR structures of the same proteins is due mainly to a difference in mathematical treatment of experimental results. Proteins 2005.

Secondary structure of globular proteins at the early and the final stages in protein folding

The ellipticities for an early transient intermediate in refolding observed by kinetic circular dichroism measurements at 220–225 nm for 14 different proteins are summarized, and the ellipticity values are compared with those for the final native proteins and also with the ellipticities expected from a physical theory of protein and polypeptide secondary structure. The results show that a substantial part of the protein secondary structure is in general formed in the earliest detectable intermediate in refolding and that the ellipticities in both the native and the intermediate states are consistent with the physical theory of protein secondary structure.

Common features in structures and sequences of sandwich-like proteins

The goal of this work is to define the structural and sequence features common to sandwich-like proteins (SPs), a group of very different proteins now comprising 69 superfamilies in 38 protein folds. Analysis of the arrangements of strands within main sandwich sheets revealed a rigorously defined constraint on the supersecondary substructure that holds true for 94% of known SP structures. The invariant substructure consists of two interlocked pairs of neighboring β-strands. It is even more typical for centers of SP than the well-known “Greek key” strands arrangement for their edges. As homology among these proteins is not usually detectable even with the most powerful sequence-comparing algorithms, we employed a structure-based approach to sequence alignment. Within the interlocked strands we found 12 positions with fixed structural roles in SP. A residue at any of these positions possesses similar structural properties with residues in the same position of other SPs. The 12 positions lie at the center of the interface between the β-sheets and form the common geometrical core of SPs. Of the 12 positions, 8 are occupied by only four hydrophobic residues in 80% of all SPs.