where R is the column vector of all bead positions, D is the 3N × 3N diffusivity tensor (N being the total number of beads), U = U s + U ev + U b is the total interaction potential, δt is the time step, and x is a column vector of length 3N containing random numbers drawn from a normal distribution N (0, 1). The third term √ 2δt D 1/2 • x represents displacement only due to Brownian motion. The right hand side of the above equation is evaluated using the positions at time t and left hand side gives the bead positions at time t + δt. Note that eq (11) is in non-dimensionalized form with respect to the units mentioned in the preceding paragraph. Furthermore, for computational expediency we neglect hydrodynamic interaction (HI) between the beads, therefore the diffusivity tensor D degenerates to the identity matrix. A simulation run for a given condition starts with equilibration, using the slow pushoff method descibed by Auhl et al 3 (originally in the context of polymer melts), but applied to a single molecule. Six independent trajectories were generated for each case. The time step δt for advancing the beads was 10 -4 τ . A pivot move was performed after every 50 BD time steps and a double bridging sweep was performed after every 11 BD time steps.