Optimal flexibility for conformational transitions in macromolecules

Conformational transitions in macromolecular complexes often involve the reorientation of lever-like structures. Using a simple theoretical model, we show that the rate of such transitions is drastically enhanced if the lever is bendable, e.g. at a localized “hinge’’. Surprisingly, the transition is fastest with an intermediate flexibility of the hinge. In this intermediate regime, the transition rate is also least sensitive to the amount of “cargo’’ attached to the lever arm, which could be exploited by molecular motors. To explain this effect, we generalize the Kramers-Langer theory for multi-dimensional barrier crossing to configuration dependent mobility matrices.

💡 Research Summary

The paper investigates how the flexibility of lever‑like elements within large macromolecular complexes influences the rate of conformational transitions that require reorientation of these structures. The authors construct a minimal theoretical model in which a lever consists of two rigid arms connected by a localized hinge whose stiffness can be tuned. By varying the hinge stiffness, the lever can range from completely rigid (infinite stiffness) to fully flexible (zero stiffness). The transition of interest is modeled as a multidimensional barrier‑crossing problem, where one coordinate describes motion along the reaction coordinate (the “gradient” direction) and a second coordinate describes hinge bending.

Traditional Kramers theory assumes a constant mobility (or friction) matrix, which is inadequate for a system whose internal degrees of freedom alter the effective friction. To address this, the authors extend the Kramers‑Langer framework to include a configuration‑dependent mobility matrix μ(q). Near the saddle point they simultaneously diagonalize the Hessian of the free‑energy surface and the mobility matrix, allowing them to compute the optimal escape pathway and the associated effective friction. This generalized expression for the escape rate reads

k_trans ≈ (|λ‡|/2π) √