A synthetic peptide has Zimm-Bragg nucleation parameter and

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Macromolecules, membranes and cell architecture · Macromolecules, membranes and cell architecture

Forces, Machines and Signals, Ch Cooperativity: zippers, melting and allosteric binding

Problem

A synthetic peptide has Zimm-Bragg nucleation parameter σ=1.0×10−4\sigma = 1.0\times10^{-4} and, at a particular temperature, propagation parameter s=1.05s = 1.05. The transfer matrix is M=(s1σs1)\mathbf{M} = \begin{pmatrix} s & 1 \\ \sigma s & 1\end{pmatrix}. ((a)) Find the largest eigenvalue λ+\lambda_+ of M\mathbf{M}. ((b)) Hence find the helix fraction θ=∂ln⁡λ+/∂ln⁡s\theta = \partial \ln\lambda_+ / \partial \ln s for this long chain.

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