Elastic Energy and Phase Structure in a Continuous Spin Ising Chain with Applications to the Protein Folding Problem

Abstract

We present a numerical Monte Carlo analysis of a continuos spin Ising chain that can describe the statistical proterties of folded proteins. We find that depending on the value of the Metropolis temperature, the model displays the three known nontrivial phases of polymers: At low temperatures the model is in a collapsed phase, at medium temperatures it is in a random walk phase, and at high temperatures it enters the self-avoiding random walk phase. By investigating the temperature dependence of the specific energy we confirm that the transition between the collapsed phase and the random walk phase is a phase transition, while the random walk phase and self-avoiding random walk phase are separated from each other by a cross-over transition. We also compare the predictions of the model to a phenomenological elastic energy formula, proposed by Huang and Lei to describe folded proteins.

12 pages, 23 figures, RevTeX 4.1

References in corpus (2)

• Critical Exponents, Hyperscaling and Universal Amplitude Ratios for Two- and Three-Dimensional Self-Avoiding Walks
• Elastic energy of proteins and the stages of protein folding

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• Thermal unfolding of myoglobin in the Landau-Ginzburg-Wilson approach
• Thermodynamic properties of the one-dimensional Ising model with magnetoelastic interaction
• On the role of thermal backbone fluctuations in myoglobin ligand gate dynamics
• Multiple scales and phases in discrete chains with application to folded proteins
• Long range correlations and folding angle in polymers with applications to α-helical proteins