Salt Effects on the Thermodynamics of a Frameshifting RNA Pseudoknot under Tension

Naoto Hori; Natalia A. Denesyuk; D. Thirumalai

We performed Langevin dynamics simulations by solving the equation of motion, mẍ = − ∂UTIS ∂x − γẋ + R, where m is mass; γ, the friction coefficient, depends on the size of the particle type (P, S, or B); and R is a Gaussian random force, which satisfies the fluctuationdissipation relation. The [C, f ] phase diagram is calculated at a somewhat elevated temperature, T =50 • C, in order to observe multiple folding-unfolding transitions when the monovalent salt concentration is varied over a wide range, from 5 to 1200 mM. The numerical integration is performed using the leap-frog algorithm with time step length δt L = 0.05τ , where τ is the unit of time. We performed low friction Langevin dynamics simulations to enhance the rate of conformational sampling [56] . For each condition (C and f ), we performed 50 independent simulations for 6 × 10 8 time steps and the last two-third of trajectories are used for data analyses. In addition, we also performed a set of simulations using the replicaexchange molecular dynamics (REMD) to confirm the validity of the results obtained by the low friction Langevin dynamics simulations [57] . In the REMD simulations, both C and f are treated as replica variables and are exchanged between 256 replicas, by covering C from 1 to 1200 mM and f from 0 to 20 pN. The replicas are distributed over 16 × 16 grid. The combined set of simulations using different protocols assures us that the simulations are converged at all conditions. Our simulations are done at constant forces under equilibrium conditions in which we observe multiple transitions between the various states. We have made comparison to LOT experiments, which are performed by pulling the RNA at a constant velocity. In general, if RNA is stretched at a constant velocity, then one has to be concerned about non-equilibrium effects. However, in optical tweezer experiments, the pulling speed is low enough so that the tension propagates uniformly throughout the RNA prior to initiation of unfolding [58] . Thus, the unfolding of PK studied using LOT experiments [19] occurs at equilibrium, justifying comparisons to our explicit equilibrium simulations.