A lattice model for cytoskeletons’ dynamics: analysis of growth and shrinkage

We analyze growth–shrinkage dynamics of cytoskeletons by using a lattice model in two dimensions. The behavior of the length of a chain corresponding to one cytoskeleton immersed in a “gas” of the basic units of cytoskeletons is simulated for low and intermediate concentrations, which shows the characteristic behavior of dynamic instability. We calculate the mean long-time velocity for several low concentrations and find that the length dynamics is sensitive to the concentration, which suggests the existence of a critical concentration. We also calculate the mean velocity for several short time spans and the probability distribution functions (PDFs) of the length difference with different time lags Δt. We find that the PDFs have a shoulder at around zero and a peak in the positive velocity region and the central parts of the PDF are essentially independent of Δt