Dependence Of Folding Rate Research Articles

Dependence of internal friction on folding mechanism.

An outstanding challenge in protein folding is understanding the origin of “internal friction” in folding dynamics, experimentally identified from the dependence of folding rates on solvent viscosity. A possible origin suggested by simulation is the crossing of local torsion barriers. However, it was unclear why internal friction varied from protein to protein or for different folding barriers of the same protein. Using all-atom simulations with variable solvent viscosity, in conjunction with transition-path sampling to obtain reaction rates and analysis via Markov state models, we are able to determine the internal friction in the folding of several peptides and miniproteins. In agreement with experiment, we find that the folding events with greatest internal friction are those that mainly involve helix formation, while hairpin formation exhibits little or no evidence of friction. Via a careful analysis of folding transition paths, we show that internal friction arises when torsion angle changes are an important part of the folding mechanism near the folding free energy barrier. These results suggest an explanation for the variation of internal friction effects from protein to protein and across the energy landscape of the same protein.

Thermal denaturation and folding rates of single domain proteins: size matters

We analyze the dependence of thermal denaturation transition and folding rates of globular proteins on the number of amino acid residues, N. Using lattice Go models we show that Δ T/ T F∼ N −1, where T F is the folding transition temperature and Δ T is the transition width computed using the temperature dependence of the order parameter that distinguishes between the unfolded state and the native basin of attraction. This finding is consistent with finite size effects expected for the systems undergoing a phase transition from a disordered to an ordered phase. The dependence of the folding rates on N for lattice models and the dataset of 57 proteins and peptides shows that k F≃k F 0 exp(−CN β) with 0< β≤2/3 provides a good fit, where C is a β-dependent constant. We find that k F ≃k F 0 exp(−1.1N 1/2) with an average (over the dataset of proteins) k F 0≈(0.4 μs) −1, can estimate optimal protein folding rates, to within an order of magnitude in most cases. By using this fit for a set of proteins with β-sheet topology we find that k F 0≈ k U 0, the prefactor for unfolding. The maximum ratio of k U 0/ k F 0≈10 for this class of proteins.

Dependence of Folding Rates on Protein Length

Using three-dimensional Go lattice models with side chains for proteins, we investigate the dependence of folding times on protein length. In agreement with previous theoretical predictions, we find that the folding time grows as a power law with the chain length N with exponent $\lambda \approx 3.6$ for the Go model, in which all native interactions (i.e., between all side chains and backbone atoms) are uniform. If the interactions between side chains are given by pairwise statistical potentials, which introduce heterogeneity in the contact energies, then the power law fits yield large $\lambda$ values that typically signifies a crossover to an underlying activated process. Accordingly, the dependence of folding time is best described by the stretched exponential \exp(\sqrt{N}). The study also shows that the incorporation of side chains considerably slows down folding by introducing energetic and topological frustration.