One-Dimensional and Two-Dimensional Simulations of Helical Homopolymers: A Comparative Analysis of Efficiency and Funnel Folding

The purpose of our work is to analyze the results of a two-dimensional parallel tempering simulation of a coarse-grained helical homopolymer. We aim to measure the efficiency of the simulation and apply this efficiency to the theoretical protein free energy landscape.The stable states for helical homopolymers will be analyzed using the folding funnel theory of free energy landscapes for given polymer configurations. The genesis of each simulation is defined by a randomly configured polymer; as time progresses, the energy of each structure decreases until equilibrium is reached. Data collected after equilibrium is reached is used to understand polymer behavior for each model and simulated temperature. A rolling average algorithm has been designed to establish the time step at which energy stabilization is reached for each model. The simulation is considered to be stable when the rolling average of the energy is within a set fraction of the standard deviation of the rolling window based on the standard deviation and mean of previous windows. Efficiency and equilibration time of the 1D and 2D simulations are compared to determine the value of the two dimensional exchange scheme and analyze the free energy landscape of the polymer configuration.