A Combined Wormlike-Chain and Bead Model for Dynamic Simulations of Long Linear DNA

Abstract

A carefully parameterized and tested simulation procedure for studying the dynamic properties of long linear DNA, based on a representation that combines features of both wormlike-chain and bead models, is presented. Our goals are to verify the model parameters and protocols with respect to all relevant experimental data and equilibrium simulations, to choose the most efficient algorithms, and to test different approximations that increase the speed of the computations. The energy of the linear model chain includes stretching, bending, and electrostatic components. Beads are associated with each vertex of the chain in order to specify the hydrodynamic properties of the DNA. The value of the stretching rigidity constant is chosen to achieve a compromise between the efficiency of the dynamic simulations (since the timestep depends on the stretching constant) and realistic modeling of the DNA (i.e., small deviations of the input contour length); the bead hydrodynamic radius is set to yield agreement with known values of the translational diffusion coefficient. By comparing results from both a first- and a second-order Brownian dynamics algorithm, we find that the two schemes give reasonable accuracy for integration timesteps in the range 200–500 ps. However, the greater accuracy of the second-order algorithm permits timesteps of 600 ps to be used for better accuracy than the 300 ps used in the first-order method. We develop a more efficient second-order algorithm for our model by eliminating the auxiliary calculations of the translational diffusion tensor at each timestep. This treatment does not sacrifice accuracy and reduces the required CPU time by about 50%. We also show that an appropriate monitoring of the chain topology ensures essentially no intrachain crossing. The model details are assessed by comparing simulation-generated equilibrium and dynamic properties with results of Monte Carlo simulations for short linear DNA (300, 600 base pairs) and with experimental results. Very good agreement is obtained with Monte Carlo results for distributions of the end-to-end distance, bond lengths, bond angles between adjacent links, and translational diffusion measurements. Additionally, comparison of translational diffusion coefficients with experimentally-measured values for DNA chains (of 367, 762, 1010, 2311 base pairs) shows excellent agreement as well. This lends confidence to the predictive ability of our model and sets the groundwork for further work on circular DNA. We conclude with results of such a predictive measurement, the autocorrelation time, for the end-to-end distance and the bending angle as a function of DNA length. Rotational diffusion measurements for different DNA lengths (300 to 2311 base pairs) are also presented.