Answer Happy

(b) As a toy model for dimerisation of proteins on a membrane, consider a canonical ensemble of two proteins bound to the sites of a square lattice. The two proteins are a dimer if they occupy adjacent (nearest neighbour) sites on the lattice, and are monomers otherwise. The energies of the monomeric and dimeric states are 0 and €p, respectively. The lattice contains L x L = M sites, where you may assume that L » 1 and that the multiplicity of the dimeric state is small compared to that of the monomeric state. [3] i. What is the multiplicity of the monomeric state for these two proteins on the lattice? Explain your answer. [3] ii. What is the multiplicity of the dimeric state for these two proteins on the lattice? Explain your answer. [4] iii. Derive expressions for the Helmholtz free energy of the monomeric state and of the dimeric state. Show that the two proteins are more likely to form a dimer than to be monomers if M €D<-KBT In = €* . 4 iv. Explain why |e*| increases with T and with M. [2]