How to perform Monte Carlo simulations for protein chains far from equilibrium concerning to the solvent

When we perform Monte Carlo (MC) simulations in order to emulate the protein folding process we handle with a chain-solvent system. The first component is a finite (nanometric) sub-system, while the second one, the solvent (the thermal reservoir), is a large and homogeneous system well characterized by the thermodynamic equilibrium. However, at nanoscale domain, thermal fluctuations emerge as a fundamental feature, because thermal noise plays an important role over chain' configurations. In order to incorporate this aspect in our MC sampling we adopt the Tsallis? weight instead of the usual Boltzmann? factor [1]. Once we choose the Tsallis' weight, the entropic index \textit{q} is regarded as a dynamical variable; \textit{q} values are associated with instantaneous degrees of freedom \textit{n} of an evolving chain. As the chain packing goes on, the number of inter-residue contacts changes, so \textit{n} becomes a function of the globule surface, which is roughly estimated by the square of the gyration radius \textit{RG}. In our point of view, \textit{q} reflects the effect of local thermal fluctuations on the chain, which are more critical over compact configurations (\textit{q}$>$1) than over those extended ones (\textit{q}$\rightarrow$1). The effect of \textit{q}$>$1 on the transition probability, faced to the standard Boltzmann factor, is quite equivalent to the conventional exponential factor in which its argument has been effectively decreased (increased temperature of the thermal reservoir). Therefore, for more compact configurations, larger \textit{q} values are needed. Which is equivalent to the situation in which the chain is submitted to a little higher temperature than the pre-established thermal reservoir temperature [1]. The net effect on the chain evolution is that wrongly compacted configurations can escape more easily from energetic/steric traps. In order to stress our point of view we will show an extended set of MC simulations for the folding process performed with both statistical weights.

[1] Dal Molin JP, da Silva MAA, Caliri A, Effect of local thermal fluctuations on folding kinetics: A study from the perspective of nonextensive statistical mechanics, Phys. Rev. E 2011,84:041903.