Relaxed annealing: a new search procedure for the most stable state of complex molecular systems

Abstract

Abstract A new algorithm is proposed for the determination of the maximum entropy state of complex molecular systems, as flexible macromolecules in solution. This method is called relaxed annealing (RAN) and is based on molecular dynamics simulations. In this paper it is applied to an elastin (the Rubber protein of vertebrates) polypeptide in aqueous solution, where the mobility of the peptide is increased gradually by decreasing an external force applied to the ends of the chain. The goal of the method is to optimize a thermodynamic potential by the relaxation of an external constraint that enhances the convergence velocity of the algorithm. The tetrapeptide Ac–Gly–Leu–Gly–Gly–NMe has been simulated for 2 ns, starting from the fully extended conformation with the ends constrained by harmonic potentials. The external force constants were reduced exponentially, and finally 2 ns of the free-running molecule were considered. Thus, the elasticity recoil process of the stretched chain has been simulated and the resilience of the elastin peptide to the experimented reversible deformations verified. The global dynamics of the peptide has been examined by the tools of nonlinear complex systems analysis. The evolution has been observed toward increasing entropy states, beginning from the essentially linear dynamics of the extended conformation, to the high entropy fractional Brownian chaotic behavior of the final folded state, typical of bounded diffusive fluctuations below the percolation threshold. In this way, the transition-to-chaos mechanism of the entropic driving force of elasticity and the soft-solution model of aggregation state of rubber proteins are confirmed.