DNA Solvation Dynamics.

Experiments have revealed that DNA solvation dynamics is characterized by multiple time scales ranging from a few picoseconds to a few hundred nanoseconds and in some cases even up to several microseconds. The last part of decay is not only slow but can also be described by a power law (PL). The microscopic origin of this PL is yet to be clearly established. Here we present a theoretical study employing multiple approaches from time dependent statistical mechanics and computer simulations. The present study shows that water dynamics may not account for the slow PL decay because the longest time scales describing water dynamics could be at most of the order of 100 ps. We find that the DNA solvation dynamics is complex, due to multiple different contributions to solvation energy. Our investigations also show that the primary candidates for this exotic nature of solvation dynamics are the response of the counterions and ions of the buffer solution. We first employ the well-known Oosawa model of polyelectrolyte solution that includes effects of counterion fluctuations to construct a frequency dependent dielectric function. We use it in the continuum model of Bagchi, Fleming, and Oxtoby (BOF). We find that it fails to explain the slow PL decay of DNA solvation dynamics. We then extend the Oosawa model by employing the continuous time random walk technique developed by Scher, Montroll and Lax. We find that this approach could explain the long time PL decay, in terms of the collective response of the counterions. To check the nature of random walk of counterions along the phosphate backbone, we carry out atomistic molecular dynamics (MD) simulations with a long (38 base pair) DNA. We indeed find frequent occurrence of random walk of tagged counterions along the phosphate backbone. We next propose a generalized random walk model for counterion hopping on phosphate backbone (observed in our MD simulations) and carry out kinetic Monte Carlo simulations to show that the nonexponential contribution to solvation dynamics can indeed come from dynamics of such ions. We also employ a mode coupling theory (MCT) analysis to understand the slow relaxation that can originate from ions in solution due to the use of the buffer. Explicit evaluation suggests that buffer ion contribution could explain a logarithmic time dependence in the nanosecond time scale but not a power law. To further understand the nonexponentiality of solvation dynamics at relatively shorter times (less than 100 ps) we carry out atomistic MD simulations with explicit water molecules. Log-normal distributions of relaxation times of water dynamics inside the grooves may be responsible for the initial multiexponential decay of solvation dynamics. We find that the observed faster solvation of groove bound probe than that of the intercalated probe could arise from the self-motion of the probe.