Disentangling Folding from Energetic Traps in Simulationsof Disordered Proteins

Protein conformational heterogeneity plays an essential role in a myriad of different biological processes. Extensive conformational heterogeneity is especially characteristic of intrinsically disordered proteins and protein regions (collectively IDRs), which lack a well-defined three-dimensional structure and instead rapidly exchange between a diverse ensemble of configurations. An emerging paradigm recognizes that the conformational biases encoded in IDR ensembles can play a central role in their biological function, necessitating understanding these sequence–ensemble relations. All-atom simulations have provided critical insight into our modern understanding of the solution behavior of IDRs. However, effectively exploring the accessible conformational space associated with large, heterogeneous ensembles is challenging. In particular, identifying poorly sampled or energetically trapped regions of disordered proteins in simulations often relies on qualitative assessment based on visual inspection of simulations and/or analysis data. These approaches, while convenient, run the risk of masking poorly sampled simulations. In this work, we present an algorithm for quantifying per-residue local conformational heterogeneity in protein simulations. Our work builds on prior work and compares the similarity between backbone dihedral angle distributions generated from molecular simulations in a limiting polymer model and across independent all-atom simulations. In this regime, the polymer model serves as a statistical reference model for extensive conformational heterogeneity in a real chain. Quantitative comparisons of probability vectors generated from these simulations reveal the extent of conformational sampling in a simulation, enabling us to distinguish between situations in which protein regions are well-sampled, poorly sampled, or folded. To demonstrate the effectiveness of this approach, we apply our algorithm to several toy, synthetic, and biological systems. Accurately assessing local conformational sampling in simulations of IDRs will help better quantify new enhanced sampling methods, ensure force field comparisons are equivalent, and provide confidence that conclusions drawn from simulations are robust.