What is it about?

The intervals between rare occurrences in molecules, for example gross structural changes in biological enzymes, are difficult to predict due to the very large time-scale differences between microscopic and macroscopic events. It is currently not feasible to simulate biological macromolecules for more than several milliseconds, yet much longer times are typically necessary to obtain accurate statistics of waiting times so that true rate constants can be compared to theoretical calculations. To address this problem of time scale we used a toy lattice model (the Ising model) whose dynamic simplicity allows thousands of barrier transitions to be simulated in short time. The measured rate constants were 50% greater than expected from theoretical predictions based on coarse-grained kinetic models. This was true for a range of temperatures and field strengths. The rate constant discrepancy could be accounted for by decomposing the diffusion constant at the energy barrier into its spectral components.

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Why is it important?

The study of toy models often provide insight into the workings of real systems. This has resoundingly been the case for the Ising model in the study of critical behavior in condensed systems. Our study of the kinetic Ising model is important for three reasons: (1) adequate statistics from "brute force" simulations allowed comparison with theoretical predictions, which is not currently possible with real molecules; (2) kinetic coarse-graining was performed in the microcanonical ensemble, allowing rate constant predictions to be made for all temperature and field strengths; (3) the spectral method accounting for the discrepancy between "brute force" and theoretical predictions may have utility for systems more complex than the Ising model.


The random opening and closing of the pore gate in ion channels has been a constant source of fascination to me, but the mechanism is too complex to fully explore using molecular dynamics. Thus, it is very satisfying to explore in great detail the kinetics of the "simple" Ising model, whose behavior as a function of temperature and field strength are in many respects similar to real ion channels. We hope to apply what we've learned from simple toy models such as the Ising model to progressively more complex systems in order to eventually better understand the kinetics of real biological proteins.

Daniel Sigg

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This page is a summary of: Microcanonical coarse-graining of the kinetic Ising model, The Journal of Chemical Physics, February 2020, American Institute of Physics, DOI: 10.1063/1.5139228.
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