1. Actin is a cytoskeletal protein that can polymerize into aggregates in solution to form linear aggregates, by the addition of successive monomers. Show that if kBT is the free energy of binding a monomer to the aggregate, and xN is the concentration of molecules in aggregates of number N, then

Problem Equation 1


1 Consider the general result of Equation 11:

Answer Equation 1

In this problem we are told that we deal with a linear aggregate. This is important information, because it tells us how many bonds we have in an aggregate of N monomers: we have (N – 1) . Therefore the interaction energy in our aggregates is

Answer Equation 2


Answer Equation 3

This can be substituted into the general form (Equation 16) to give:

Answer Equation 4

Jones (2002) develops this case of the linear aggregate further, showing how the size distribution of aggregates, above the CMC, can be obtained.