We investigate the dynamics and pathways of the collapse of a single, semiflexible polymer in a poor solvent via three-dimensional Brownian Dynamics simulations. An example of this phenomenon is DNA condensation induced by multivalent cations. Earlier work indicates that the collapse of semiflexible polymers generically proceeds via a cascade through metastable racquet-shaped, long-lived intermediates towards the stable torus state. We investigate the rate of decay of uncollapsed states, analyze the preferential pathways of condensation, and describe the likelihood and lifespan of the different metastable states. The simulations are performed with a bead-stiff spring model with excluded volume interaction, bending stiffness, and exponentially decaying attractive potential. The semiflexible chain collapse is studied as a function of the three relevant length scales of the phenomenon, i.e., the total chain length L, the persistence length $L_p,$ and the condensation length $L_0=\sqrt{k_B{\mathrm{TL}}_p{/u}_0},$ where $u_0$ is a measure of the attractive potential per unit length. Two dimensionless ratios, ${L/L}_p$ and $L_0{/L}_p,$ suffice to describe the dimensionless decay rate of uncollapsed states, which appears to scale as ${(L/L}_p{)}^{1/3}{(L}_0{/L}_p).\mathrm{}$ The condensation sequence is described in terms of the time series of the well separated energy levels associated with each metastable collapsed state. The collapsed states are described quantitatively through the spatial correlation of tangent vectors along the chain. We also compare the results obtained with a locally inextensible bead-rod chain and with a phantom bead-spring chain. Finally, we show preliminary results on how steady shear flow influences the kinetics of collapse.

• Received 29 August 2003

DOI:https://doi.org/10.1103/PhysRevE.69.021916