Folding kinetics of proteins: A model study

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Abstract
We study the kinetics of folding of a heteropolymer containing a specific sequence of hydrophobic, hydrophilic, and neutral residues. The heteropolymer, representing the alpha carbon sequence of a model protein, folds into a β‐barrel structure below a characteristic folding transition temperature. Several measures are introduced to probe the dynamics of approach to a folded state with particular emphasis on the kinetics of formation of nonbonded contacts starting from a high temperature random configuration. The measures of compactness are used to argue that even below the folding temperature, nonbonded contacts are formed at a very slow rate. This result is further corroborated by analyzing the dynamics of relaxation of the nonbonded interactions which are responsible for the formation of folded structures at low temperatures. We also show that below the folding transition temperature and for short times, the heteropolymer undergoes large structural fluctuations. Examination of the time dependence of the radius of gyration Rg shows that the heteropolymer is trapped in one minimum (characterized by a roughly constant Rg ) for arbitrary times followed by sudden excursions to neighboring minima. In this regime, multistate kinetics is appropriate. However, at longer times when the heteropolymer becomes trapped in one of the minima corresponding to the folded conformation, the folding process appears to be an all or none process. The implication of our results for the kinetics of in vitro folding of proteins are discussed.