A Combined Wormlike-Chain and Bead Model for Dynamic Simulations of Long
Linear DNA
A carefully parametrized and tested simulation procedure for studying 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 to specify 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 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 second-order Brownian dynamics algorithm, we find
that the two schemes give reasonable accuracy for integration timesteps
in the range of 200-500 ps. However, the greater accuracy of the second-order
algorithm permits timesteps of 600 ps to be used for better accuracy than
300 ps 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 and random force at each timestep. This
treatment does not sacrifice accuracy and reduces the required CPU time
by 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 experiment. 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 in the predictive ability of our model
and sets the ground 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 (300-2311
base pairs) are also presented.
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