Entropic formulation for the protein folding process: Hydrophobic stability correlates with folding rates

Here we focus on the conformational search for the native structure when it is ruled by the hydrophobic effect and steric specificities coming from amino acids. Our main tool of investigation is a 3D lattice model provided by a ten-letter alphabet, the stereochemical model. This minimalist model was conceived for Monte Carlo (MC) simulations when one keeps in mind the kinetic behavior of protein-like chains in solution. We have three central goals here. The first one is to characterize the folding time (τ) by two distinct sampling methods, so we present two sets of 103 MC simulations for a fast protein-like sequence. The resulting sets of characteristic folding times, τ and τq were obtained by the application of the standard Metropolis algorithm (MA), as well as by an enhanced algorithm (MqA). The finding for τq shows two things: (i) the chain-solvent hydrophobic interactions {hk} plus a set of inter-residues steric constraints {ci,j} are able to emulate the conformational search for the native structure. For each one of the 103MC performed simulations, the target is always found within a finite time window; (ii) the ratio τq∕τ≅1∕10 suggests that the effect of local thermal fluctuations, encompassed by the Tsallis weight, provides to the chain an innate efficiency to escape from energetic and steric traps. We performed additional MC simulations with variations of our design rule to attest this first result, both algorithms the MA and the MqA were applied to a restricted set of targets, a physical insight is provided. Our second finding was obtained by a set of 600 independent MC simulations, only performed with the MqA applied to an extended set of 200 representative targets, our native structures. The results show how structural patterns should modulate τq, which cover four orders of magnitude; this finding is our second goal. The third, and last result, was obtained with a special kind of simulation performed with the purpose to explore a possible connection between the hydrophobic component of protein stability and the native structural topology. We simulated those same 200 targets again with the MqA, only. However, this time we evaluated the relative frequency {ϕq} in which each target visits its corresponding native structure along an appropriate simulation time. Due to the presence of the hydrophobic effect in our approach we obtained a strong correlation between the stability and the folding rate (R=0.85). So, as faster a sequence found its target, as larger is the hydrophobic component of its stability. The strong correlation fulfills our last goal. This final finding suggests that the hydrophobic effect could not be a general stabilizing factor for proteins.