Dynamics of Linear and Comb DNA Solutions Using Efficient Brownian Dynamics Techniques

Excluded volume (EV) and hydrodynamic interactions (HI) play a central role in macromolecular dynamics under equilibrium and non-equilibrium settings, specifically in determining the concentration dependence of static and dynamic properties of semidilute polymer solutions. The high computational cost of incorporating the influence of HI in mesoscale Brownian dynamics simulations (BDS) of polymeric solutions has motivated much research on development of high-fidelity and cost efficient techniques. In this work, a Krylov subspace based technique is implemented to enable fast calculations of single chain dynamics with computational expense scaling as O(N_b²) where N_b is the number of beads in the bead-spring micromechanical model [1]. For simulations of coupled multichain systems, a matrix-free approach for calculation of HI is implemented which leads to O(NlogN) scaling of simulation time, where N is the total number of beads in the periodic box [2].

To investigate the properties of DNA solutions using coarse-grained bead-spring chains, a new technique is developed on the basis of properties of exact worm-like chain (WLC). In this approach, the correct correlation along the chain is modeled through the introduction of a bending potential and the spring force-law is obtained using asymptotic behavior of WLC at small and large forces. Using this model, the relaxation and stretching dynamics of linear and comb DNA molecules are evaluated and compared against experimental data [3].

References:

[1] A. Saadat and B. Khomami, J. Chem. Phys., 140, 184903 (2014).

[2] A. Saadat and B. Khomami, Phys. Rev. E, 92, 033307 (2015).

[3] D. J. Mai, A. B Marciel, C. E. Sing, C. M. Schroeder, ACS Macro Lett., 4, 446 (2015).