Solvent effects on supercoiled DNA dynamics explored by Langevin dynamics
simulations
The dynamical effects of solvent on supercoiled DNA are explored through
a simple, macroscopic energy model for DNA in the Langevin dynamics framework.
Closed-circular DNA is modeled by B splines, and both elastic and electrostatic
(screened Coulomb) potentials are included in the energy function. The
Langevin formalism describes approximately the influence of the solvent
on the motion of the solute. The collision frequency
determines the magnitude of the friction and the variance of the random
forces due to molecular collisions. Thus as a first approximation, the
Langevin equation of motion can be parametrized to capture the approximate
dynamics of DNA in a viscous medium. Solvent damping is well known to alter
the dynamical behavior of DNA and affect various hydrodynamic properties.
This work examines these effects systematically by varying the collision
frequency (viscosity) with the goal of better understanding the dynamical
behavior of supercoiled DNA. By varying
over ten orders of magnitude, we identify three distinct physical
regimes of DNA behavior: (i) low ,
dominated by globally harmonic motion; (ii) intermediate ,
characterized by maximal sampling and high mobility of the DNA; and (iii)
high , dominated by random
forces, where all of the global modes are effectively frozen by extreme
overdamping. These regimes are explored extensively by Langevin dynamics
simulations, offering insight into hydrodynamic effects on supercoiled
DNA. At low , the DNA exhibits
small, harmonic fluctuations. Transitions to other configurational regions
are more difficult to capture in finite simulations. In the intermediate
regime, the DNA exhibits maximal sampling of the writhe. Transition times
are accelerated and more readily captured in the simulations. A preferential
lowering
of the writhe from the value at the potential energy minimum is noted,
reflecting entropic effects. Only beyond a specific value
in this regime do we find reasonable convergence of the translational
diffusion constants and velocity autocorrelation functions. This brackets
the biologically relevant regime. At high
the DNA supercoil fluctuates about two distinct regions of
configuration space, one near the tightly wound potential energy minimum,
the other related to more open configurations. Transitions between the
two regions are infrequent. This behavior suggests two regions of free-energy
minima (potential and entropically favored) separated by a barrier. Indeed
the general dependence of the extent of configurational sampling on the
collision frequency is analogous to the isomerization behavior of a particle
in a bistable potential modeled by the Langevin equation in
motion. This intriguing parallelism suggests a favorable viscosity medium
where specific internal modes, namely, global twisting, are activated.
It is possible that physiological solvent densities correspond to this
region of optimal mobility for the DNA.
Click to go back to the publication list
Webpage design by Igor Zilberman