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E Shakhnovich

Publications and source records attributed to E Shakhnovich.

10 recordsLinked to original sources
PubMed2001

Dynamic charge-density correlation function in weakly charged polyampholyte globules.

We study solutions of statistically neutral polyampholyte chains containing a large fraction of neutral monomers. It is known that such solutions phase separate at very low concentrations, even if the quality of the solvent with respect to the neutral monomers is good. The precipitate is semidilute if the chains are weakly charged. This paper considers straight theta solvents and good solvents, and we calculate the dynamic charge density correlation function g(k,t) in the precipitate, using the quadratic approximation to the Martin-Siggia-Rose generating functional. It is convenient to express the results in terms of dimensionless space and time variables. Let xi be the blob size, and let tau be the characteristic time scale at the blob level. Define the dimensionless wave vector q=xik, and the dimensionless time s=t/tau. In the regime q<1, corresponding to length scales larger than the blob size, and 1 0.1, where entanglements are unimportant.

Journal Article↗
PubMed2001

Evolutionary conservation of the folding nucleus.

Here, we present statistical analysis of conservation profiles in families of homologous sequences for nine proteins whose folding nucleus was determined by protein engineering methods. We show that in all but one protein (AcP) folding nucleus residues are significantly more conserved than the rest of the protein. Two aspects of our study are especially important: (i) grouping of amino acid residues into classes according to their physical-chemical properties and (ii) proper normalization of amino acid probabilities that reflects the fact that evolutionary pressure to conserve some amino acid types may itself affect concentration of various amino acid types in protein families. Neglect of any of those two factors may make physical and biological "signals" from conservation profiles disappear.

Conserved Sequence↗
PubMed2001

Protein folding theory: from lattice to all-atom models.

This review focuses on recent advances in understanding protein folding kinetics in the context of nucleation theory. We present basic concepts such as nucleation, folding nucleus, and transition state ensemble and then discuss recent advances and challenges in theoretical understanding of several key aspects of protein folding kinetics. We cover recent topology-based approaches as well as evolutionary studies and molecular dynamics approaches to determine protein folding nucleus and analyze other aspects of folding kinetics. Finally, we briefly discuss successful all-atom Monte-Carlo simulations of protein folding and conclude with a brief outlook for the future.

Cell Nucleus↗
PubMed1999

Factors that affect the folding ability of proteins.

The folding ability of a heteropolymer model for proteins subject to Monte Carlo dynamics on a simple cubic lattice is shown to be strongly correlated with the stability of the native state. We consider a number of estimates of the stability that can be determined without simulation, including the energy gap between the native state and the structurally dissimilar part of the spectrum (Z score) and, for sequences with fully compact native states, the gap in energy between the native and first excited fully compact states. These estimates are found to be more robust predictors of folding ability than a parameter sigma that requires simulation for its evaluation: sigma = 1 - Tf/Ttheta, where Tf is the temperature at which the fluctuation of an order parameter is at its maximum and Ttheta is the temperature at which the specific heat is at its maximum. We show that the interpretation of Ttheta as the collapse transition temperature is not correct in general and that the correlation between sigma and the folding ability arises from the fact that sigma is related to the energy gap (Z score).

Monte Carlo Method↗
PubMed1998

A strategy for detecting the conservation of folding-nucleus residues in protein superfamilies.

BACKGROUND: Nucleation-growth theory predicts that fast-folding peptide sequences fold to their native structure via structures in a transition-state ensemble that share a small number of native contacts (the folding nucleus). Experimental and theoretical studies of proteins suggest that residues participating in folding nuclei are conserved among homologs. We attempted to determine if this is true in proteins with highly diverged sequences but identical folds (superfamilies). RESULTS: We describe a strategy based on comparisons of residue conservation in natural superfamily sequences with simulated sequences (generated with a Monte-Carlo sequence design strategy) for the same proteins. The basic assumptions of the strategy were that natural sequences will conserve residues needed for folding and stability plus function, the simulated sequences contain no functional conservation, and nucleus residues make native contacts with each other. Based on these assumptions, we identified seven potential nucleus residues in ubiquitin superfamily members. Non-nucleus conserved residues were also identified; these are proposed to be involved in stabilizing native interactions. We found that all superfamily members conserved the same potential nucleus residue positions, except those for which the structural topology is significantly different. CONCLUSIONS: Our results suggest that the conservation of the nucleus of a specific fold can be predicted by comparing designed simulated sequences with natural highly diverged sequences that fold to the same structure. We suggest that such a strategy could be used to help plan protein folding and design experiments, to identify new superfamily members, and to subdivide superfamilies further into classes having a similar folding mechanism.

Algorithms↗
PubMed1996

Conserved residues and the mechanism of protein folding.

Experimental and simulation studies show that small monomeric proteins fold in one kinetic step, which entails overcoming the free-energy barrier between the unfolded and the native protein through a transition state. Two models of transition state formation have been proposed: a 'nonspecific' one in which it depends on the formation of a sufficient number of native-like contacts regardless of what amino acids are involved, and a 'specific' one, in which it depends on formation of a specific subset of the native structure (a folding nucleus). The latter requires that some amino acids form most of their contacts in the transition state, whereas others only do so on reaching the native conformation. If so, mutations affecting the stability of the transition state nucleus should have a greater effect on the folding kinetics than mutations elsewhere, and the residues involved should be evolutionarily conserved. Lattice-model simulations and experiments suggest that such mutations exist. Here we present a method for determining the folding nucleus of a protein with known structure with two-state folding kinetics. This method is based on the alignment of many sequences designed to fold into the native conformation of a protein to identify the positions where amino acids are most conserved in designed sequences. The method is applied to chymotrypsin inhibitor 2 (CI2), a protein whose transition state has been previously studied by protein engineering. The involvement of residues in folding nucleus of CI2 is clearly correlated with their conservation in design, and the residues forming the nucleus are highly conserved in 23 natural sequences homologous to CI2.

Amino Acid Sequence↗
PubMed1994

How does a protein fold?

The number of all possible conformations of a polypeptide chain is too large to be sampled exhaustively. Nevertheless, protein sequences do fold into unique native states in seconds (the Levinthal paradox). To determine how the Levinthal paradox is resolved, we use a lattice Monte Carlo model in which the global minimum (native state) is known. The necessary and sufficient condition for folding in this model is that the native state be a pronounced global minimum on the potential surface. This guarantees thermodynamic stability of the native state at a temperature where the chain does not get trapped in local minima. Folding starts by a rapid collapse from a random-coil state to a random semi-compact globule. It then proceeds by a slow, rate-determining search through the semi-compact states to find a transition state from which the chain folds rapidly to the native state. The elements of the folding mechanism that lead to the resolution of the Levinthal paradox are the reduced number of conformations that need to be searched in the semi-compact globule (approximately 10(10) versus approximately 10(16) for the random coil) and the existence of many (approximately 10(3)) transition states. The results have evolutionary implications and suggest principles for the folding of real proteins.

Models, Chemical↗
PubMed1994

Kinetics of protein folding. A lattice model study of the requirements for folding to the native state.

A three-dimensional lattice model of a protein is used to investigate the properties required for its folding to the native state. The polypeptide chain is represented as a 27 bead heteropolymer whose lowest energy (native) state can be determined by an exhaustive enumeration of all fully compact conformations. A total of 200 sequences with random interactions are generated and subjected to Monte Carlo simulations to determine which chains find the ground state in a short time; i.e. which sequences overcome the folding problem referred to as the Levinthal paradox. Comparison of the folding and non-folding sequences is used to identify the features that are required for fast folding to the global energy minimum. It is shown that successful folding does not require certain attributes that have been previously proposed as necessary for folding; these include a high number of short versus long-range contacts in the native state, a high content of the secondary structure in the native state, a strong correlation between the native contact map and the interaction parameters, and the existence of a high number of low energy states with near-native conformation. Instead, the essential difference between the folding and the non-folding sequences is the nature of the energy spectrum. The necessary and sufficient condition for a sequence to fold rapidly in the present model is that the native state is a pronounced energy minimum. As a consequence, the thermodynamic stability of the native state of a folding sequence has a sigmoidal dependence on temperature. This permits such a sequence to satisfy both the thermodynamic and the kinetic requirements for folding; i.e. the native state predominates thermodynamically at temperatures that are high enough for folding to be kinetically possible. The applicability of the present results to real proteins is discussed.

Algorithms↗