Folding Rate Optimization Promotes Frustrated Interactions in Entangled Protein Structures

TL;DR

This study uses a lattice model to show that optimized protein sequences tend to have frustrated interactions at entangled loops, aiding rapid folding despite topological complexity, aligning with experimental insights.

Contribution

It demonstrates that evolutionary pressure promotes frustrated interactions at entangled loops, facilitating faster folding in complex protein topologies.

Findings

Optimized sequences in entangled structures exhibit frustrated interactions at loop closures.

Folding times are longer for random sequences, but optimized sequences fold faster.

Frustration at entangled loops is less prominent in non-entangled controls.

Abstract

Many native structures of proteins accomodate complex topological motifs such as knots, lassos, and other geometrical entanglements. How proteins can fold quickly even in the presence of such topological obstacles is a debated question in structural biology. Recently, the hypothesis that energetic frustration might be a mechanism to avoid topological frustration has been put forward based on the empirical observation that loops involved in entanglements are stabilized by weak interactions between amino-acids at their extrema. To verify this idea, we use a toy lattice model for the folding of proteins into two almost identical structures, one entangled and one not. As expected, the folding time is longer when random sequences folds into the entangled structure. This holds also under an evolutionary pressure simulated by optimizing the folding time. It turns out that optmized protein sequences in the entangled structure are in fact characterized by frustrated interactions at the closures of entangled loops. This phenomenon is much less enhanced in the control case where the entanglement is not present. Our findings, which are in agreement with experimental observations, corroborate the idea that an evolutionary pressure shapes the folding funnel to avoid topological and kinetic traps.