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.

Folding kinetics of villin 14T, a protein domain with a central beta-sheet and two hydrophobic cores

The thermodynamics and kinetics of folding are characterized for villin 14T, a 126-residue protein domain. Equilibrium fluorescence measurements reveal that villin 14T unfolds and refolds reversibly. The folding kinetics was monitored using stopped-flow with fluorescence and quenched-flow with NMR and mass spectrometry. Unfolding occurs in a single-exponential phase in the stopped-flow experiments, and about 75% of the total amplitude is recovered in the fast phase of refolding. The remaining 25% of the amplitude probably represents trapping in cis-trans proline isomerization pathways. At 25 degreesC, the stability estimate obtained by extrapolation from the transition region of the stopped-flow chevron matches the stability value from equilibrium urea titrations (DeltaG = 9.7 kcal/mol, m value = 2.2 kcal mol-1 M-1). At low final urea concentrations, however, the refolding kinetics deviates from the two-state model, indicating the formation of an intermediate. Under these conditions, quenched-flow followed by NMR and mass spectrometry show no detectable hydrogen-bonded intermediate in the fast refolding phase. In contrast, agreement is observed between the equilibrium and kinetic estimates of stability at 37 degreesC (DeltaG = 6.0 kcal/mol, m value = 1.6 kcal mol-1 M-1), at all observed urea concentrations, demonstrating apparent two-state folding at this temperature. This result shows that the two-state folding model, previously applied to small domains with single, central hydrophobic cores, can also describe the folding of a larger domain with multiple core structures.

A protein engineering analysis of the transition state for protein folding: simulation in the lattice model

BACKGROUND

Protein engineering has been used extensively to evaluate the properties of transition states in protein folding. Although the method has proved useful, its limitations and the details of interpretation of the obtained results remain largely unexplored.

RESULTS

Lattice model simulations are used to test and verify the protein engineering analysis of the transition state in protein folding. It is shown that in some cases - but not always - this method is able to determine the transition state with reasonable accuracy. Limitations of protein engineering are revealed and analyzed. In particular, the change in non-native interactions as a result of mutations is shown to influence the results of the protein engineering analysis. Furthermore, the temperature dependencies of phi values (which are a measure of the participation of a residue in the transition state) and the character of the transition state ensemble are studied. It is shown that as a general trend phi values decrease when the temperature decreases, a finding consistent with recent experimental results. Our analysis suggests that this trend results primarily from the formation of some contacts (native and non-native) in the unfolded state at a lower temperature, when the barrier for folding is energetic.

CONCLUSIONS

Our analysis helps to interpret the results of protein engineering and allows observed φ values to be directly related to structural features of the unfolded state, the transition state and the native state.

Protein design: a perspective from simple tractable models

Recent progress in computational approaches to protein design builds on advances in statistical mechanical protein folding theory. Here, the number of sequences folding into a given conformation is evaluated and a simple condition for a protein model's designability is outlined.

Theory of kinetic partitioning in protein folding with possible applications to prions

This study focuses of the phenomenon of kinetic partitioning when a polypeptide chain has two ground-state conformations, one of which is kinetically more reachable than the other. We designed sequences for lattice model proteins with two different conformations of equal energy corresponding to the global energy minimum. Folding simulations revealed that one of these conformations was indeed much more kinetically accessible than the other. We found that the number and strength of local contacts in the ground-state conformation are the major factors that determine which conformation is reached faster; the greater the number of local contacts, the more kinetically reachable a conformation is. We present simple statistical-mechanical arguments to explain these findings. Our results may be relevant in explaining the phenomenology of such proteins as human plasminogen activator inhibitor-1 (PAI-1), photosystem II, and prions.

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.

Computer simulations of prebiotic evolution

This paper is a review of our previous work on the field of possible ways of prebiotic evolution. We propose an algorithm providing sequences of model proteins with rapid folding into a given native conformation. Thermodynamical analysis shows that the increase in speed is matched by an increase in stability: the evolved sequences are much more stable in their native conformation than the initial random sequence. We discuss a possible origin of the first biopolymers, having stable unique structure. We suggest that at the prebiotic stage of evolution, long organic polymers had to be compact in order to avoid hydrolysis and had to be soluble and thus must not be exceedingly hydrophobic. We present an algorithm that generates such sequences of model proteins. The evolved sequences turn out to have a stable unique structure, into which they quickly fold. This result illustrates the idea that the unique three-dimensional native structure of first biopolymers could have evolved as a side effect of a nonspecific physico-chemical factors acting at the prebiotic stage of evolution.

Theoretical studies of protein-folding thermodynamics and kinetics

Recently, protein-folding models have advanced to the point where folding simulations of protein-like chains of reasonable length (up to 125 amino acids) are feasible, and the major physical features of folding proteins, such as cooperativity in thermodynamics and nucleation mechanisms in kinetics, can be reproduced. This has allowed deep insight into the physical mechanism of folding, including the solution of the so-called 'Levinthal paradox'.

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.

How the first biopolymers could have evolved

In this work, we discuss a possible origin of the first biopolymers with stable unique structures. We suggest that at the prebiotic stage of evolution, long organic polymers had to be compact to avoid hydrolysis and had to be soluble and thus must not be exceedingly hydrophobic. We present an algorithm that generates such sequences for model proteins. The evolved sequences turn out to have a stable unique structure, into which they quickly fold. This result illustrates the idea that the unique three-dimensional native structures of first biopolymers could have evolved as a side effect of nonspecific physicochemical factors acting at the prebiotic stage of evolution.