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We present the exact solution of a microscopic statistical mechanical modelfor the transformation of a long polypeptide between an unstructured coilconformation and an $\alpha$-helix conformation. The polypeptide is assumed tobe adsorbed to the interface between a polar and a non-polar environment suchas realized by water and the lipid bilayer of a membrane. The interfacialcoil-helix transformation is the first stage in the folding process of helicalmembrane proteins. Depending on the values of model parameters, theconformation changes as a crossover, a discontinuous transition, or acontinuous transition with helicity in the role of order parameter. Our modelis constructed as a system of statistically interacting quasiparticles that areactivated from the helix pseudo-vacuum. The particles represent links betweenadjacent residues in coil conformation that form a self-avoiding random walk intwo dimensions. Explicit results are presented for helicity, entropy, heatcapacity, and the average numbers and sizes of both coil and helix segments.

Coil-helix transition of polypeptide at water-lipid interface