Sequencing of folding events in Go-like proteins

We have studied folding mechanisms of three small globular proteins: crambin (CRN), chymotrypsin inhibitor 2 (CI2) and the fyn Src Homology 3 domain (SH3) which are modelled by a Go-like Hamiltonian with the Lennard-Jones interactions. It is shown that folding is dominated by a well-defined sequencing of events as determined by establishment of particular contacts. The order of events depends primarily on the geometry of the native state. Variations in temperature, coupling strengths and viscosity affect the sequencing scenarios to a rather small extent. The sequencing is strongly correlated with the distance of the contacting aminoacids along the sequence. Thus $\alpha$-helices get established first. Crambin is found to behave like a single-route folder, whereas in CI2 and SH3 the folding trajectories are more diversified. The folding scenarios for CI2 and SH3 are consistent with experimental studies of their transition states.Comment: REVTeX, 12 pages, 11 EPS figures, J. Chem. Phys (in press

Origins of Chevron Rollovers in Non-Two-State Protein Folding Kinetics

Chevron rollovers of some proteins imply that their logarithmic folding rates are nonlinear in native stability. This is predicted by lattice and continuum G\=o models to arise from diminished accessibilities of the ground state from transiently populated compact conformations under strongly native conditions. Despite these models' native-centric interactions, the slowdown is due partly to kinetic trapping caused by some of the folding intermediates' nonnative topologies. Notably, simple two-state folding kinetics of small single-domain proteins are not reproduced by common G\=o-like schemes.Comment: 10 pages, 4 Postscript figures (will appear on PRL

Nucleation phenomena in protein folding: The modulating role of protein sequence

For the vast majority of naturally occurring, small, single domain proteins folding is often described as a two-state process that lacks detectable intermediates. This observation has often been rationalized on the basis of a nucleation mechanism for protein folding whose basic premise is the idea that after completion of a specific set of contacts forming the so-called folding nucleus the native state is achieved promptly. Here we propose a methodology to identify folding nuclei in small lattice polymers and apply it to the study of protein molecules with chain length N=48. To investigate the extent to which protein topology is a robust determinant of the nucleation mechanism we compare the nucleation scenario of a native-centric model with that of a sequence specific model sharing the same native fold. To evaluate the impact of the sequence's finner details in the nucleation mechanism we consider the folding of two non- homologous sequences. We conclude that in a sequence-specific model the folding nucleus is, to some extent, formed by the most stable contacts in the protein and that the less stable linkages in the folding nucleus are solely determined by the fold's topology. We have also found that independently of protein sequence the folding nucleus performs the same `topological' function. This unifying feature of the nucleation mechanism results from the residues forming the folding nucleus being distributed along the protein chain in a similar and well-defined manner that is determined by the fold's topological features.Comment: 10 Figures. J. Physics: Condensed Matter (to appear

Thermodynamically Important Contacts in Folding of Model Proteins

We introduce a quantity, the entropic susceptibility, that measures the thermodynamic importance-for the folding transition-of the contacts between amino acids in model proteins. Using this quantity, we find that only one equilibrium run of a computer simulation of a model protein is sufficient to select a subset of contacts that give rise to the peak in the specific heat observed at the folding transition. To illustrate the method, we identify thermodynamically important contacts in a model 46-mer. We show that only about 50% of all contacts present in the protein native state are responsible for the sharp peak in the specific heat at the folding transition temperature, while the remaining 50% of contacts do not affect the specific heat.Comment: 5 pages, 5 figures; to be published in PR

Modeling study on the validity of a possibly simplified representation of proteins

The folding characteristics of sequences reduced with a possibly simplified representation of five types of residues are shown to be similar to their original ones with the natural set of residues (20 types or 20 letters). The reduced sequences have a good foldability and fold to the same native structure of their optimized original ones. A large ground state gap for the native structure shows the thermodynamic stability of the reduced sequences. The general validity of such a five-letter reduction is further studied via the correlation between the reduced sequences and the original ones. As a comparison, a reduction with two letters is found not to reproduce the native structure of the original sequences due to its homopolymeric features.Comment: 6 pages with 4 figure

Protein structures and optimal folding emerging from a geometrical variational principle

Novel numerical techniques, validated by an analysis of barnase and chymotrypsin inhibitor, are used to elucidate the paramount role played by the geometry of the protein backbone in steering the folding to the correct native state. It is found that, irrespective of the sequence, the native state of a protein has exceedingly large number of conformations with a given amount of structural overlap compared to other compact artificial backbones; moreover the conformational entropies of unrelated proteins of the same length are nearly equal at any given stage of folding. These results are suggestive of an extremality principle underlying protein evolution, which, in turn, is shown to be associated with the emergence of secondary structures.Comment: Revtex, 5 pages, 5 postscript figure

Conformations of Proteins in Equilibrium

We introduce a simple theoretical approach for an equilibrium study of proteins with known native state structures. We test our approach with results on well-studied globular proteins, Chymotrypsin Inhibitor (2ci2), Barnase and the alpha spectrin SH3 domain and present evidence for a hierarchical onset of order on lowering the temperature with significant organization at the local level even at high temperatures. A further application to the folding process of HIV-1 protease shows that the model can be reliably used to identify key folding sites that are responsible for the development of drug resistance .Comment: 6 pages, 3 eps figure

Role of Secondary Motifs in Fast Folding Polymers: A Dynamical Variational Principle

A fascinating and open question challenging biochemistry, physics and even geometry is the presence of highly regular motifs such as alpha-helices in the folded state of biopolymers and proteins. Stimulating explanations ranging from chemical propensity to simple geometrical reasoning have been invoked to rationalize the existence of such secondary structures. We formulate a dynamical variational principle for selection in conformation space based on the requirement that the backbone of the native state of biologically viable polymers be rapidly accessible from the denatured state. The variational principle is shown to result in the emergence of helical order in compact structures.Comment: 4 pages, RevTex, 4 eps figure

Geometric and Statistical Properties of the Mean-Field HP Model, the LS Model and Real Protein Sequences

Lattice models, for their coarse-grained nature, are best suited for the study of the ``designability problem'', the phenomenon in which most of the about 16,000 proteins of known structure have their native conformations concentrated in a relatively small number of about 500 topological classes of conformations. Here it is shown that on a lattice the most highly designable simulated protein structures are those that have the largest number of surface-core switchbacks. A combination of physical, mathematical and biological reasons that causes the phenomenon is given. By comparing the most foldable model peptides with protein sequences in the Protein Data Bank, it is shown that whereas different models may yield similar designabilities, predicted foldable peptides will simulate natural proteins only when the model incorporates the correct physics and biology, in this case if the main folding force arises from the differing hydrophobicity of the residues, but does not originate, say, from the steric hindrance effect caused by the differing sizes of the residues.Comment: 12 pages, 10 figure