Effect of Finite Size on Cooperativity and Rates of Protein Folding

Abstract

We analyze the dependence of cooperativity of the thermal denaturation transition and folding rates of globular proteins on the number of amino acid residues, N , using lattice models with side chains, off-lattice Go models and the available experimental data. A dimensionless measure of cooperativity,The results of simulations and the analysis of experimental data further confirm the earlier prediction that ζ is universal with ζ = 1 + γ, where exponent γ characterizes the susceptibility of a self-avoiding walk. This finding suggests that the structural characteristics in the denaturated state are manifested in the folding cooperativity at the transition temperature. The folding rates k F for the Go models and a dataset of 69 proteins can be fit using k F = k 0 F exp(−cN β ). Both β = 1/2 and 2/3 provide a good fit of the data. We find that k F = k 0 F exp(−cN 1 2 ), with the average (over the dataset of proteins) k 0 F ≈ (0.2µs) −1 and c ≈ 1.1, can be used to estimate folding rates to within an order of magnitude in most cases. The minimal models give identical N dependence with c ≈ 1. The prefactor for off-lattice Go models is nearly four orders of magnitude larger than the experimental value.

Exploiting the downhill folding regime via experiment

“…Besides, these results indicate that there is a close connection between the broadness of the global unfolding curve and the structural heterogeneity at the atomic level. This relation is exactly what would be expected from statistical mechanical arguments (Kouza et al, 2006). In principle, the same argument can be taken beyond downhill folding to proteins with larger barriers (Klimov and Thirumalai, 2002).…”

Topography of funneled landscapes determines the thermodynamics and kinetics of protein folding

“…To explore the relationship between the landscape topography and kinetics, we have simulated folding and calculated the kinetic rates. We first investigated proteins of different sizes, using an energetically unfrustrated model that has been shown to produce folding kinetics that are correlated with experimental measurements (11,(45)(46)(47)(48)(49)(50)(51)(52)(53)(54)(55)(56)(57)(58). Kinetic simulations were performed at the temperature T χ , where 80% of the population occupies the native ensemble (38).…”

Protein Folding Thermodynamics and Dynamics: Where Physics, Chemistry, and Biology Meet

“…Firstly the chemical reaction analysis using SK order parameter Q as a global reaction coordinate predicts that barriers for protein folding are proportional to chain length N so that folding time scales with chain length as exp(αN) 117 126,127 ) At the conditions when the native state is stable the nucleation mechanism would predict that folding barrier is entropic due to loop closure entropy lost upon formation of specific nucleus 128,129 which implies much slower scaling of the folding time with chain length, as a power law N λ , which was indeed observed in simulations 128 and is also not inconsistent with experiment. Thus we see that the straightforward chemical reaction approach based on Q as a reaction coordinate, fails to predict correct and physically meaningful chain length scaling of protein folding time.…”