Is the free energy landscape informative about transition rates? Lessons from the kinetic Ising model

TL;DR

This study evaluates the effectiveness of the free energy landscape in predicting transition rates in a kinetic Ising model, revealing systematic overestimations and questioning its applicability to complex biological systems.

Contribution

It provides a critical comparison between experimental and coarse-grained rate constants, highlighting limitations in the diffusion coefficient calculation within the free energy landscape framework.

Findings

Coarse-grained rate constants were about 50% larger than experimental values.

Errors mainly stemmed from diffusion coefficient estimation, not landscape shape.

Fluctuation analysis did not significantly improve diffusion coefficient estimates.

Abstract

An oft-used concept in modeling macromolecules is the free energy landscape, obtained by coarse-graining a vast number of microstates into a low-dimensional mesh of mesostates. If the landscape contains two or more local minima (macrostates),one can compute global rate constants provided the dynamics of the dividing barrier regions are known. Here we compared experimental rate constants between ordered states in a kinetic Ising model with rates calculated from a coarse-grained master equation derived from the microcanonical ensemble. The coarse-grained macroscopic rate constants were roughly 50 % larger than experiment across a range of environmental constraints, suggesting a systematic impediment of configurational progress on the microscopic scale that is specific to the structure of the Ising model. The error in coarse-graining lay with the calculation of the diffusion coefficient rather than with the shape of the free energy landscape, as ensemble- and time-averaged estimates of the latter were indistinguishable. Fluctuation analysis in the form of Nyquist theorem also failed to substantially improve the value of the effective diffusion coefficient, suggesting a failure of the fluctuation-dissipation theorem. These findings from the Ising model raises doubts over the validity of the free energy landscape approach in calculating absolute transition rates for more complex systems such as proteins.