Biomedical subjects

L A Mirny

Publications and source records attributed to L A Mirny.

8 recordsLinked to original sources

PubMed2000

Comparison of two optimization methods to derive energy parameters for protein folding: perceptron and Z score.

Two methods were proposed recently to derive energy parameters from known native protein conformations and corresponding sets of decoys. One is based on finding, by means of a perceptron learning scheme, energy parameters such that the native conformations have lower energies than the decoys. The second method maximizes the difference between the native energy and the average energy of the decoys, measured in terms of the width of the decoys' energy distribution (Z-score). Whereas the perceptron method is sensitive mainly to "outlier" (i.e., extremal) decoys, the Z-score optimization is governed by the high density regions in decoy-space. We compare the two methods by deriving contact energies for two very different sets of decoys: the first obtained for model lattice proteins and the second by threading. We find that the potentials derived by the two methods are of similar quality and fairly closely related. This finding indicates that standard, naturally occurring sets of decoys are distributed in a way that yields robust energy parameters (that are quite insensitive to the particular method used to derive them). The main practical implication of this finding is that it is not necessary to fine-tune the potential search method to the particular set of decoys used.

Algorithms↗

PubMed2000

Statistical significance of protein structure prediction by threading.

In this study, we estimate the statistical significance of structure prediction by threading. We introduce a single parameter epsilon that serves as a universal measure determining the probability that the best alignment is indeed a native-like analog. Parameter epsilon takes into account both length and composition of the query sequence and the number of decoys in threading simulation. It can be computed directly from the query sequence and potential of interactions, eliminating the need for sequence reshuffling and realignment. Although our theoretical analysis is general, here we compare its predictions with the results of gapless threading. Finally we estimate the number of decoys from which the native structure can be found by existing potentials of interactions. We discuss how this analysis can be extended to determine the optimal gap penalties for any sequence-structure alignment (threading) method, thus optimizing it to maximum possible performance.

Models, Statistical↗

PubMed2000

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

A lattice model with side chains was used to investigate protein folding with computer simulations. In this model, we rigorously demonstrate the existence of a specific folding nucleus. This nucleus contains specific interactions not present in the native state that, when weakened, slow folding but do not change protein stability. Such a decoupling of folding kinetics from thermodynamics has been observed experimentally for real proteins. From our results, we conclude that specific non-native interactions in the transition state would give rise to straight phi-values that are negative or larger than unity. Furthermore, we demonstrate that residue Ile 34 in src SH3, which has been shown to be kinetically, but not thermodynamically, important, is universally conserved in proteins with the SH3 fold. This is a clear example of evolution optimizing the folding rate of a protein independent of its stability and function.

Amino Acid Sequence↗

PubMed1999

Universally conserved positions in protein folds: reading evolutionary signals about stability, folding kinetics and function.

Here, we provide an analysis of molecular evolution of five of the most populated protein folds: immunoglobulin fold, oligonucleotide-binding fold, Rossman fold, alpha/beta plait, and TIM barrels. In order to distinguish between "historic", functional and structural reasons for amino acid conservations, we consider proteins that acquire the same fold and have no evident sequence homology. For each fold we identify positions that are conserved within each individual family and coincide when non-homologous proteins are structurally superimposed. As a baseline for statistical assessment we use the conservatism expected based on the solvent accessibility. The analysis is based on a new concept of "conservatism-of-conservatism". This approach allows us to identify the structural features that are stabilized in all proteins having a given fold, despite the fact that actual interactions that provide such stabilization may vary from protein to protein. Comparison with experimental data on thermodynamics, folding kinetics and function of the proteins reveals that such universally conserved clusters correspond to either: (i) super-sites (common location of active site in proteins having common tertiary structures but not function) or (ii) folding nuclei whose stability is an important determinant of folding rate, or both (in the case of Rossman fold). The analysis also helps to clarify the relation between folding and function that is apparent for some folds.

Amino Acid Sequence↗

PubMed1998

Protein structure prediction by threading. Why it works and why it does not.

We developed a novel Monte Carlo threading algorithm which allows gaps and insertions both in the template structure and threaded sequence. The algorithm is able to find the optimal sequence-structure alignment and sample suboptimal alignments. Using our algorithm we performed sequence-structure alignments for a number of examples for three protein folds (ubiquitin, immunoglobulin and globin) using both "ideal" set of potentials (optimized to provide the best Z-score for a given protein) and more realistic knowledge-based potentials. Two physically different scenarios emerged. If a template structure is similar to the native one (within 2 A RMS), then (i) the optimal threading alignment is correct and robust with respect to deviations of the potential from the "ideal" one; (ii) suboptimal alignments are very similar to the optimal one; (iii) as Monte Carlo temperature decreases a sharp cooperative transition to the optimal alignment is observed. In contrast, if the template structure is only moderately close to the native structure (RMS greater than 3.5 A), then (i) the optimal alignment changes dramatically when an "ideal" potential is substituted by the real one; (ii) the structures of suboptimal alignments are very different from the optimal one, reducing the reliability of the alignment; (iii) the transition to the apparently optimal alignment is non-cooperative. In the intermediate cases when the RMS between the template and the native conformations is in the range between 2 A and 3.5 A, the success of threading alignment may depend on the quality of potentials used. These results are rationalized in terms of a threading free energy landscape. Possible ways to overcome the fundamental limitations of threading are discussed briefly.

Algorithms↗

PubMed1998

How evolution makes proteins fold quickly.

Sequences of fast-folding model proteins (48 residues long on a cubic lattice) were generated by an evolution-like selection toward fast folding. We find that fast-folding proteins exhibit a specific folding mechanism in which all transition state conformations share a smaller subset of common contacts (folding nucleus). Acceleration of folding was accompanied by dramatic strengthening of interactions in the folding nucleus whereas average energy of nonnucleus interactions remained largely unchanged. Furthermore, the residues involved in the nucleus are the most conserved ones within families of evolved sequences. Our results imply that for each protein structure there is a small number of conserved positions that are key determinants of fast folding into that structure. This conjecture was tested on two protein superfamilies: the first having the classical monophosphate binding fold (CMBF; 98 families) and the second having type-III repeat fold (47 families). For each superfamily, we discovered a few positions that exhibit very strong and statistically significant "conservatism of conservatism"-amino acids in those positions are conserved within every family whereas the actual types of amino acids varied from family to family. Those amino acids are in spatial contact with each other. The experimental data of Serrano and coworkers [Lopez-Hernandez, E. & Serrano, L. (1996) Fold. Des. (London) 1, 43-55]. for one of the proteins of the CMBF superfamily (CheY) show that residues identified this way indeed belong to the folding nucleus. Further analysis revealed deep connections between nucleation in CMBF proteins and their function.

Bacterial Proteins↗

PubMed1996

How to derive a protein folding potential? A new approach to an old problem.

In this paper we introduce a novel method of deriving a pairwise potential for protein folding. The potential is obtained by an optimization procedure that simultaneously maximizes thermodynamic stability for all proteins in the database. When applied to the representative dataset of proteins and with the energy function taken in pairwise contact approximation, our potential scored somewhat better than existing ones. However, the discrimination of the native structure from decoys is still not strong enough to make the potential useful for ab initio folding. Our results suggest that the problem lies with pairwise amino acid contact approximation and/or simplified presentation of proteins rather than with the derivation of potential. We argue that more detail of protein structure and energetics should be taken into account to achieve energy gaps. The suggested method is general enough to allow us to systematically derive parameters for more sophisticated energy functions. The internal control of validity for the potential derived by our method is convergence to a unique solution upon addition of new proteins to the database. The method is tested on simple model systems where sequences are designed, using the preset "true" potential, to have low energy in a dataset of structures. Our procedure is able to recover the potential with correlation r approximately 91% with the true one and we were able to fold all model structures using the recovered potential. Other statistical knowledge-based approaches were tested using this model and the results indicate that they also can recover the true potential with high degree of accuracy.

Databases, Factual↗

PubMed1996

Universality and diversity of the protein folding scenarios: a comprehensive analysis with the aid of a lattice model.

BACKGROUND: The role of intermediates in protein folding has been a matter of great controversy. Although it was widely believed that intermediates play a key role in minimizing the search problem associated with the Levinthal paradox, experimental evidence has been accumulating that small proteins fold fast without any detectable intermediates. RESULTS: We study the thermodynamics and kinetics of folding using a simple lattice model. Two folding sequences obtained by the design procedure exhibit different folding scenarios. The first sequence folds fast to the native state and does not exhibit any populated intermediates during folding. In contrast, the second sequence folds much slower, often being trapped in misfolded low-energy conformations. However, a small fraction of folding molecules for the second sequence fold on a fast track avoiding misfolded traps. In equilibrium at the same temperature the second sequence has a highly populated intermediate with structure similar to that of the kinetics intermediate. CONCLUSIONS: Our analysis suggests that intermediates may often destabilize native conformations and derail the folding process leading it to traps. Less-optimized sequences fold via parallel pathways involving misfolded intermediates. A better designed sequence is more stable in the native state and folds fast without intermediates in a two-state process.

Amino Acid Sequence↗