Introduction to polymerization kinetics

To understand the cytoskeleton, it helps to also gain some background in simple polymer assembly, and the mathematics used to describe it. Here I review a succession of elementary models for polymers of various types starting from a mixture consisting only of subunits, called monomers. I point out that the accumulated polymer mass over time depends on the type of underlying assembly reaction. The idea of critical monomer concentration is introduced, and shown to arise as a consequence of scaling the models. We then consider the specific case of actin polymers and show that treadmilling (growth of one end and shrinkage of the other) can occur at a particular concentration. Growth of actin filaments at their tips in discussed in the context of a transcritical bifurcation. I introduce the Mogilner-Oster thermal ratchet and its relation to cell protrusion caused by actin filament polymerization against a load force.