  Using molecular dynamics simulations, the kinetics of bundle formation for
stiff polyelectrolytes such as actin is studied in the solution of multivalent
salt. The dominant kinetic mode of aggregation is found to be the case of one
end of one rod meeting others at right angle due to electrostatic interactions.
The kinetic pathway to bundle formation involves a hierarchical structure of
small clusters forming initially and then feeding into larger clusters, which
is reminiscent of the flocculation dynamics of colloids. For the first few
cluster sizes, the Smoluchowski formula for the time evolution of the cluster
size gives a reasonable account for the results of our simulation without a
single fitting parameter. The description using Smoluchowski formula provides
evidence for the aggregation time scale to be controlled by diffusion, with no
appreciable energy barrier to overcome.
