Azat Ya. Badretdinov

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.

Boltzmann-like Statistics of Protein Architectures

Inspection of globular proteins shows that the most common protein structures are those that have some advantage in stability. This would cause no wonder if the advantages were not so small and the difference in occurrence was not so great.

Rate of protein folding near the point of thermodynamic equilibrium between the coil and the most stable chain fold: Influence of chain knotting on the rate of folding

In our original paper [1], the time of achievement of the most stable chain was estimated (near the point of thermodynamic equilibrium between the fold and the coil) as:

Evolution of protein 3D structures as diffusion in multidimensional conformational space

A theory of protein spatial-structure evolution in terms of random walks in multidimensional conformational space is proposed. It is shown that the spatial divergence in pairs of homologous proteins depends only on their sequence similarity and is independent of the protein size. X-ray data are reasonably well described in terms of the theory developed.

S6 permutein shows that the unusual target topology is not responsible for the absence of rigid tertiary structure in de novo protein albebetin

Ribosomal protein S6 from Thermus thermophilus was modified to form the unusual unique topology designed earlier for a de novo protein albebetin. The S6 gene was cloned, sequenced and circularly permutated by means of genetic engineering methods. The permutated gene was expressed in Escherichia coli and the permutein was isolated and investigated by means of circular dichroism, fluorescence spectroscopy and scanning microcalorimetry. The permutated protein revealed a pronounced secondary structure close to that of the wild type S6 protein and a rigid tertiary structure possessing cooperative temperature melting. It means that the unusual new topology of albebetin is compatible with a rigid tertiary structure, it may be realized in natural proteins and it is not responsible for the absence of rigid structure in albebetin.

How fast a protein chain can fold to its most stable structure

Having -lO’oo of possible folds [l], how does the protein chain spontaneously [2] choose its native structure: as the most stable fold but how the chain can find time to single it among 10roo f other folds? as the mes atinkel@sun.ipr.serpukhov.su ‘Present address: Rockefeller University, Box 270, 1230 York Ave., New York, NY 10021, USA; azat@guitar.rockefeller.edu Permission to make digitzd5ard copies of all or pat of this material for personal or classroom use is granted without fee provided tithe copies are not made or diiiuted for profit or ccmmerckl advantage, the copyright notice, the title of the publication and its date appear, and notice is given that copyright is by permission of the ACM, Inc. To copy otherwise, to republish, to post on servers or to rediiiute to lii requires specitic permission and/or fee. RECOMB 98 New York NY USA copyright 1998 o-89791-976-919s13...%.00 1 Folding pathway An N-residue chain can fold in N steps, each of which adds of one residue to a growing native structure (Fig.1). Here we will consider folding pathways of this kind. The additional pathways can only accelerate the folding since the rates of parallel reactions are additive. If the free energy would be downhill along all the pathway, a loo-residue chain would fold in -100 nsec, since the growth of a structure (e.g., an cl-helix) by 1 residue takes a few nanoseconds [7]. If protein folding takes more than 100 ns, this is because the free energy increases at some steps of folding, and most of the folding time is spent climbing the free energy barrier and falling back, rather‘than moving along the folding pathway. A simple, based on the transition state theory [S] estimate of the transition time is: FOLDING TIME +p(AG#IRT) Here T is the absolute temperature, R the gas constant, AG’ the free energy of the transition state counted off the initial free energy miniium, and t1 ns is the time of adding of one residue to the growing structure. Let AE,, A& and AG,, = Al?,, -TM,, be the interaction energy, the conformational entropy and the free energy, respectively, of the intermediate where n links are already fixed in the final positions while other N-n links are disordered counted off those of the disordered chain (hence, all the A

Rate of protein folding near the point of thermodynamic equilibrium between the coil and the most stable chain fold

< 0). One can see that AG,/RT = (-MN/R) x (w4 -hE,lA4v)+ (1) (GVIRT) +-w%~