Eugene I. Shakhnovich

Topological determinants of protein folding

The folding of many small proteins is kinetically a two-state process that represents overcoming the major free-energy barrier. A kinetic characteristic of a conformation, its probability to descend to the native state domain in the amount of time that represents a small fraction of total folding time, has been introduced to determine to which side of the free-energy barrier a conformation belongs. However, which features make a protein conformation on the folding pathway become committed to rapidly descending to the native state has been a mystery. Using two small, well characterized proteins, CI2 and C-Src SH3, we show how topological properties of protein conformations determine their kinetic ability to fold. We use a macroscopic measure of the protein contact network topology, the average graph connectivity, by constructing graphs that are based on the geometry of protein conformations. We find that the average connectivity is higher for conformations with a high folding probability than for those with a high probability to unfold. Other macroscopic measures of protein structural and energetic properties such as radius of gyration, rms distance, solvent-accessible surface area, contact order, and potential energy fail to serve as predictors of the probability of a given conformation to fold.

Discrete molecular dynamics studies of the folding of a protein-like model

BACKGROUND Many attempts have been made to resolve in time the folding of model proteins in computer simulations. Different computational approaches have emerged. Some of these approaches suffer from insensitivity to the geometrical properties of the proteins (lattice models), whereas others are computationally heavy (traditional molecular dynamics). RESULTS We used the recently proposed approach of Zhou and Karplus to study the folding of a protein model based on the discrete time molecular dynamics algorithm. We show that this algorithm resolves with respect to time the folding <--> unfolding transition. In addition, we demonstrate the ability to study the core of the model protein. CONCLUSIONS The algorithm along with the model of interresidue interactions can serve as a tool for studying the thermodynamics and kinetics of protein models.

Enumeration of all compact conformations of copolymers with random sequence of links

Exhaustive enumeration of all compact self‐avoiding conformations of a chain of 27 monomers on the 3*3*3 fragment of a simple cubic lattice is given. Total number of conformations unrelated by symmetry is 103 346. This number is relatively small which makes it possible to make a numerically exact calculation of all thermodynamic functions this chain. Heteropolymers with random sequence of links were considered, and the freezing transition at finite temperature was observed. This transition is analogous to folding transition in proteins where unique structure is formed. The numeric results demonstrate the equivalence between random 3‐dimensional heteropolymers and the random energy model found previously in analytical investigations. The possible application of these results to some problems of combinational optimization is discussed.

Protein and DNA Sequence Determinants of Thermophilic Adaptation

There have been considerable attempts in the past to relate phenotypic trait—habitat temperature of organisms—to their genotypes, most importantly compositions of their genomes and proteomes. However, despite accumulation of anecdotal evidence, an exact and conclusive relationship between the former and the latter has been elusive. We present an exhaustive study of the relationship between amino acid composition of proteomes, nucleotide composition of DNA, and optimal growth temperature (OGT) of prokaryotes. Based on 204 complete proteomes of archaea and bacteria spanning the temperature range from −10 °C to 110 °C, we performed an exhaustive enumeration of all possible sets of amino acids and found a set of amino acids whose total fraction in a proteome is correlated, to a remarkable extent, with the OGT. The universal set is Ile, Val, Tyr, Trp, Arg, Glu, Leu (IVYWREL), and the correlation coefficient is as high as 0.93. We also found that the G + C content in 204 complete genomes does not exhibit a significant correlation with OGT (R = −0.10). On the other hand, the fraction of A + G in coding DNA is correlated with temperature, to a considerable extent, due to codon patterns of IVYWREL amino acids. Further, we found strong and independent correlation between OGT and the frequency with which pairs of A and G nucleotides appear as nearest neighbors in genome sequences. This adaptation is achieved via codon bias. These findings present a direct link between principles of proteins structure and stability and evolutionary mechanisms of thermophylic adaptation. On the nucleotide level, the analysis provides an example of how nature utilizes codon bias for evolutionary adaptation to extreme conditions. Together these results provide a complete picture of how compositions of proteomes and genomes in prokaryotes adjust to the extreme conditions of the environment.

Chain Length Scaling of Protein Folding Time.

Folding of protein-like heteropolymers into unique 3D structures is investigated using Monte Carlo simulations on a cubic lattice. We found that folding time of chains of length

Free energy landscape for protein folding kinetics: Intermediates, traps, and multiple pathways in theory and lattice model simulations

N

Expanding protein universe and its origin from the biological Big Bang

scales as

The ensemble folding kinetics of protein G from an all-atom Monte Carlo simulation

N^\lambda

Kinetics, thermodynamics and evolution of non-native interactions in a protein folding nucleus.

at temperature of fastest folding. For chains with random sequences of monomers

Protein stability imposes limits on organism complexity and speed of molecular evolution

\lambda \approx 6