Quantifying the Long-Range Coupling of Electronic Properties in Proteins with Ab Initio Molecular Dynamics

Abstract

A delicate interplay of covalent and noncovalent interactions gives proteins their unique ability to flexibly play numerous roles in cellular processes. This interplay is inherently quantum mechanical and highly dynamic in nature. To directly interrogate the evolving nature of the electronic structure of proteins, we carry out 100-ps-scale <i>ab initio</i> molecular dynamics simulations of three representative small proteins with range-separated hybrid density functional theory. We quantify the nature and length-scale of the coupling of residue-specific charge probability distributions in these proteins. While some nonpolar residues exhibit expectedly narrow charge distributions, most polar and charged residues exhibit broad, multimodal distributions. Even for nonpolar residues, we observe sequence-specific deviations corresponding to charge accumulation or depletion that would be challenging to capture in a fixed charge force field. We quantify the effect of residue–residue interactions on charge distributions first with linear cross-correlations. We then show how additional insight can be gained from evaluating the mutual information of charge distributions. We show that a significant number of residues couple most strongly with residues that are distant in both sequence and space over a range of secondary structures including a-helical, b-sheet, disulfide bridging, and lasso motifs. The mutual information analysis is necessary to capture coupling between some polar and charged residues. These analyses are expected to be broadly useful in understanding the mechanisms of long-range charge transfer in proteins and for determining what interactions require a quantum mechanical description for predictive simulation of enzyme mechanism and protein function.

Harder, better, faster, stronger: Large-scale QM and QM/MM for predictive modeling in enzymes and proteins

“…Significant, long-range interactions were observed in pairs of residues that included at least one mobile, polar or charged residue. Consistent with observations from cross-correlation analysis in QM/MM MD on COMT [90,92], transient, non-covalent interactions result in significantly stronger coupling than is observed for shorter-range, covalently bound residue pairs (e.g., disulfide bridges [91] or Mg 2+ -carboxylate bonds [90,92]). Beyond small systems, analysis of charge coupling is not yet broadly tractable without resorting to lower-level theory (e.g., to semiempirical methods [89]) but could become a useful tool to provide guidance on how to select systematic or adaptive QM regions for robust QM/MM free energy simulations.…”

“…Machine learning will continue to play an increasing role in biological modeling. [93] Such advances will not be confined to further improvements to machine learning potentials [94] but will also involve systematic, statistical models to reveal modes of enzyme action [91,95,96] and to guide single-or multi-scale method selection [60,74,97,98], reducing the barriers to mechanistic study in the absence of a priori knowledge.…”

“…Systematic QM/MM methods that worked well for static calculations exhibit higher variability in free energy simulations due to greater differences in flexibility with change in QM region (Figure 4). Leveraging GPUaccelerated DFT, fully ab initio MD was very recently carried out with a range-separated hybrid functional [91] to evaluate the length-scales over which QM properties are coupled in proteins.…”

Convergence in Determining Enzyme Functional Descriptors across Kemp Eliminase Variants

“…The study informs the conditions under which different descriptors can be calculated with high fidelity for predicting the impact of mutations on catalytic functions. In addition, as the interplay between protein dynamics and electronic structures emerges as a new direction of study, 81,82 the convergence trend investigated in the current study might inspire the development of new strategies to predict computationally demanding QM properties using MM-derived properties.…”