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Thermodynamics 3: Amphiphile aggregation - critical micelle concentration
May 12, 2013
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
1 Consider the general result of Equation 11:
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
This can be substituted into the general form (Equation 16) to give:
Jones (2002) develops this case of the linear aggregate further, showing how the size distribution of aggregates, above the CMC, can be obtained.
About the author
Pietro Cicuta obtained his first degree in Physics in Milan, and has been at Cambridge University from his PhD studies onwards. His group, in collaboration with essential partners from the biological sciences, researches a spectrum of problems including understanding global gene regulation processes in bacteria, host-pathogen interaction mechanisms and proposing model systems for exploring the process of flow generation by ciliated tissues. A parallel activity on interfaces and colloidal systems also continues. Pietro gives a third year undergraduate course “Soft Condensed Matter” in which many problems and examples are taken from biology.