Refining protein structures using enhanced sampling techniques with restraints derived from an ensemble-based model

CryoEM reveals oligomeric isomers of a multienzyme complex and assembly mechanics

Propionyl-CoA carboxylase (PCC) is a multienzyme complex consisting of up to six α-subunits and six β-subunits. Belonging to a metabolic pathway converging on the citric acid cycle, it is present in most forms of life and irregularities in its assembly lead to serious illness in humans, known as propionic acidemia. Here, we report the cryogenic electron microscopy (cryoEM) structures and assembly of different oligomeric isomers of endogenous PCC from the parasitic protozoan Leishmania tarentolae (LtPCC). These structures and their statistical distribution reveal the mechanics of PCC assembly and disassembly at equilibrium. We show that, in solution, endogenous LtPCC β-subunits form stable homohexamers, to which different numbers of α-subunits attach. Sorting LtPCC particles into seven classes (i.e., oligomeric formulae α0β6, α1β6, α2β6, α3β6, α4β6, α5β6, α6β6) enables formulation of a model for PCC assembly. Our results suggest how multimerization regulates PCC enzymatic activity and showcase the utility of cryoEM in revealing the statistical mechanics of reaction pathways.

A restrained locally enhanced sampling method (RLES) for finding free energy minima in complex systems

We present an extension of the locally enhanced sampling method. A restraint potential is introduced to drive the many-replica system to the canonical ensemble corresponding to the physical, single-replica system. Convergence properties are demonstrated using a model rugged two-dimensional potential, for which sampling by conventional equilibrium molecular dynamics is inefficient. Restrained locally enhanced sampling (RLES) is found to explore the space of configurations with an efficiency comparable to that of temperature replica exchange. To demonstrate the potential of RLES for realistic applications, the method is used to fold the 12-residue tryptophan zipper miniprotein in explicit solvent. The RLES algorithm can be incorporated into existing LES implementations with minor code modifications.

Forging tools for refining predicted protein structures

Refining predicted protein structures with all-atom molecular dynamics simulations is one route to producing, entirely by computational means, structural models of proteins that rival in quality those that are determined by X-ray diffraction experiments. Slow rearrangements within the compact folded state, however, make routine refinement of predicted structures by unrestrained simulations infeasible. In this work, we draw inspiration from the fields of metallurgy and blacksmithing, where practitioners have worked out practical means of controlling equilibration by mechanically deforming their samples. We describe a two-step refinement procedure that involves identifying collective variables for mechanical deformations using a coarse-grained model and then sampling along these deformation modes in all-atom simulations. Identifying those low-frequency collective modes that change the contact map the most proves to be an effective strategy for choosing which deformations to use for sampling. The method is tested on 20 refinement targets from the CASP12 competition and is found to induce large structural rearrangements that drive the structures closer to the experimentally determined structures during relatively short all-atom simulations of 50 ns. By examining the accuracy of side-chain rotamer states in subensembles of structures that have varying degrees of similarity to the experimental structure, we identified the reorientation of aromatic side chains as a step that remains slow even when encouraging global mechanical deformations in the all-atom simulations. Reducing the side-chain rotamer isomerization barriers in the all-atom force field is found to further speed up refinement.

A Hybrid Hamiltonian for the Accelerated Sampling along Experimental Restraints

In this article, we present an enhanced sampling method based on a hybrid Hamiltonian which combines experimental distance restraints with a bias dependent from multiple path-dependent variables. This simulation method determines the bias-coordinates on the fly and does not require a priori knowledge about reaction coordinates. The hybrid Hamiltonian accelerates the sampling of proteins, and, combined with experimental distance information, the technique considers the restraints adaptively and in dependency of the system's intrinsic dynamics. We validate the methodology on the dipole relaxation of two water models and the conformational landscape of dialanine. Using experimental NMR-restraint data, we explore the folding landscape of the TrpCage mini-protein and in a second example apply distance restraints from chemical crosslinking/mass spectrometry experiments for the sampling of the conformation space of the Killer Cell Lectin-like Receptor Subfamily B Member 1A (NKR-P1A). The new methodology has the potential to adaptively introduce experimental restraints without affecting the conformational space of the system along an ergodic trajectory. Since only a limited number of input- and no-order parameters are required for the setup of the simulation, the method is broadly applicable and has the potential to be combined with coarse-graining methods.