Modulated charge patterns and noise effect in a twisted DNA model with solvent interaction

We modify the Peyrard-Bishop-Holstein model and bring out the influence of the torsion and solvent interactions on charge transport in DNA. Through the linear stability analysis, we detect regions of instability and we compare the results with those of the standard Peyrard-Bishop-Holstein model. There are two regimes where modulated charge patterns can occur: the undertwisted and the overtwisted conformations. Numerical simulations are used to confirm our analytical predictions. Charge patterns are obtained and propagate more easily in an overwinded helix than in an underwinded one. The effects of dissipation and thermal fluctuations are also studied, which confirm the robustness of the obtained modulated patterns. On the one hand, we argue that in the absence of twisting, temperature can lead to the breaking of the hydrogen bonds between bases and prevent charges from propagating. On the other hand, when the molecule is overtwisted, the solvent and the temperature will rather enhance charge spreading patterns with random features.