Structural information content and Lyapunov exponent calculation in protein unfolding

Abstract

A lattice model with Monte Carlo dynamics is used to carry out computer simulations of protein dynamics on a four α-helix bundle. The interaction energies in the model can be set so that either the helix bundle structure remains relatively stable or changed so that it unfolds. The computer model produces output that simulates experimental measurements relating to the structure. We show how this output can be used with analytical techniques of nonlinear dynamics to obtain important information about the complex underlying protein dynamics. Time-delay reconstruction plots of structural parameters of unfolding bundles resemble strange attractors in a space of dimension 3–4. We calculate Lyapunov exponents for these unfolding runs and find positive Lyapunov exponents implying chaotic dynamics. For stable runs the Lyapunov exponents are close to zero. We use these Lyapunov exponents to calculate the rate of loss of structural information during the unfolding process and show how the approach may be useful for investigating the folding dynamics of proteins. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2761–2769, 1998