HYPK: A marginally disordered protein sensitive to charge decoration.

Intrinsically disordered proteins (IDPs) that lie close to the empirical boundary separating IDPs and folded proteins in Uversky's charge-hydropathy plot may behave as "marginal IDPs" and sensitively switch conformation upon changes in environment (temperature, crowding, and charge screening), sequence, or both. In our search for such a marginal IDP, we selected Huntingtin-interacting protein K (HYPK) near that boundary as a candidate; PKIα, also near that boundary, has lower secondary structure propensity; and Crk1, just across the boundary on the folded side, has higher secondary structure propensity. We used a qualitative Förster resonance energy transfer-based assay together with circular dichroism to simultaneously probe global and local conformation. HYPK shows several unique features indicating marginality: a cooperative transition in end-to-end distance with temperature, like Crk1 and folded proteins, but unlike PKIα; enhanced secondary structure upon crowding, in contrast to Crk1 and PKIα; and a cross-over from salt-induced expansion to compaction at high temperature, likely due to a structure-to-disorder transition not seen in Crk1 and PKIα. We then tested HYPK's sensitivity to charge patterning by designing charge-flipped variants including two specific sequences with identical amino acid composition that markedly differ in their predicted size and response to salt. The experimentally observed trends, also including mutants of PKIα, verify the predictions from sequence charge decoration metrics. Marginal proteins like HYPK show features of both folded and disordered proteins that make them sensitive to physicochemical perturbations and structural control by charge patterning.

High Accuracy Protein Structures from Minimal Sparse Paramagnetic Solid-State NMR Restraints.

There is a pressing need for new computational tools to integrate data from diverse experimental approaches in structural biology. We present a strategy that combines sparse paramagnetic solid-state NMR restraints with physics-based atomistic simulations. Our approach explicitly accounts for uncertainty in the interpretation of experimental data through the use of a semi-quantitative mapping between the data and the restraint energy that is calibrated by extensive simulations. We apply our approach to solid-state NMR data for the model protein GB1 labeled with Cu2+ -EDTA at six different sites. We are able to determine the structure to 0.9 Šaccuracy within a single day of computation on a GPU cluster. We further show that in some cases, the data from only a single paramagnetic tag are sufficient for accurate folding.

Molecular modeling of biomolecules by paramagnetic NMR and computational hybrid methods.

The 3D atomic structures of biomolecules and their complexes are key to our understanding of biomolecular function, recognition, and mechanism. However, it is often difficult to obtain structures, particularly for systems that are complex, dynamic, disordered, or exist in environments like cell membranes. In such cases sparse data from a variety of paramagnetic NMR experiments offers one possible source of structural information. These restraints can be incorporated in computer modeling algorithms that can accurately translate the sparse experimental data into full 3D atomic structures. In this review, we discuss various types of paramagnetic NMR/computational hybrid modeling techniques that can be applied to successful modeling of not only the atomic structure of proteins but also their interacting partners. This article is part of a Special Issue entitled: Biophysics in Canada, edited by Lewis Kay, John Baenziger, Albert Berghuis and Peter Tieleman.

Critical Assessment of Self-Consistency Checks in the All-Atom Molecular Dynamics Simulation of Intrinsically Disordered Proteins.

All atom simulations can be used to quantify conformational properties of Intrinsically Disordered Proteins (IDP). However, simulations must satisfy convergence checks to ensure observables computed from simulation are reliable and reproducible. While absolute convergence is purely a theoretical concept requiring infinitely long simulation, a more practical, yet rigorous, approach is to impose Self Consistency Checks (SCCs) to gain confidence in the simulated data. Currently there is no study of SCCs in IDPs, unlike their folded counterparts. In this paper, we introduce different criteria for self-consistency checks for IDPs. Next, we impose these SCCs to critically assess the performance of different simulation protocols using the N terminal domain of HIV Integrase and the linker region of SARS-CoV-2 Nucleoprotein as two model IDPs. All simulation protocols begin with all-atom implicit solvent Monte Carlo (MC) simulation and subsequent clustering of MC generated conformations to create the representative structures of the IDPs. These representative structures serve as the initial structure for subsequent molecular dynamics (MD) runs with explicit solvent. We conclude that generating multiple short (∼3 µs) MD simulation trajectories─all starting from the most representative MC generated conformation─and merging them is the protocol of choice due to (i) its ability to satisfy multiple SCCs, (ii) consistently reproducing experimental data, and (iii) the efficiency of running independent trajectories in parallel by harnessing multiple cores available in modern GPU clusters. Running one long trajectory (greater than 20 µs) can also satisfy the first two criteria but is less desirable due to prohibitive computation time. These findings help resolve the challenge of identifying a usable starting configuration, provide an objective measure of SCC, and establish rigorous criteria to determine the minimum length (for one long simulation) or number of trajectories needed in all-atom simulation of IDPs.

An Integrative Approach to Determine 3D Protein Structures Using Sparse Paramagnetic NMR Data and Physical Modeling.

Paramagnetic nuclear magnetic resonance (NMR) methods have emerged as powerful tools for structure determination of large, sparsely protonated proteins. However traditional applications face several challenges, including a need for large datasets to offset the sparsity of restraints, the difficulty in accounting for the conformational heterogeneity of the spin-label, and noisy experimental data. Here we propose an integrative approach to structure determination combining sparse paramagnetic NMR with physical modelling to infer approximate protein structural ensembles. We use calmodulin in complex with the smooth muscle myosin light chain kinase peptide as a model system. Despite acquiring data from samples labeled only at the backbone amide positions, we are able to produce an ensemble with an average RMSD of ∼2.8 Å from a reference X-ray crystal structure. Our approach requires only backbone chemical shifts and measurements of the paramagnetic relaxation enhancement and residual dipolar couplings that can be obtained from sparsely labeled samples.

The emerging role of physical modeling in the future of structure determination.

Biomolecular structure determination has long relied on heuristics based on physical insight; however, recent efforts to model conformational ensembles and to make sense of sparse, ambiguous, and noisy data have revealed the value of detailed, quantitative physical models in structure determination. We review these two key challenges, describe different approaches to physical modeling in structure determination, and illustrate several successes and emerging technologies enabled by physical modeling.

Online Optimization of Total Acceptance in Hamiltonian Replica Exchange Simulations.

Replica exchange is a widely used sampling strategy in molecular simulation. While a variety of methods exist to optimize parameters for temperature replica exchange, less is known about how to optimize parameters for more general Hamiltonian replica exchange simulations. We present an algorithm for the online optimization of total acceptance for both temperature and Hamiltonian replica exchange simulations using stochastic gradient descent. We optimize the total acceptance, a heuristic objective function capturing the efficiency of replica exchange. Our approach is general and has several desirable properties, including: (1) it makes few assumptions about the system of interest, (2) optimization occurs online without the requirement of presimulation, and (3) most importantly, it readily generalizes to systems where there are multiple control parameters (e.g., temperatures, force constants, etc.) that determine the Hamiltonian of each replica. We explore some general properties of the algorithm on a simple harmonic oscillator system, and demonstrate its effectiveness on a more complex data-guided protein folding simulation.

An explicit-solvent conformation search method using open software.

Computer modeling is a popular tool to identify the most-probable conformers of a molecule. Although the solvent can have a large effect on the stability of a conformation, many popular conformational search methods are only capable of describing molecules in the gas phase or with an implicit solvent model. We have developed a work-flow for performing a conformation search on explicitly-solvated molecules using open source software. This method uses replica exchange molecular dynamics (REMD) to sample the conformational states of the molecule efficiently. Cluster analysis is used to identify the most probable conformations from the simulated trajectory. This work-flow was tested on drug molecules α-amanitin and cabergoline to illustrate its capabilities and effectiveness. The preferred conformations of these molecules in gas phase, implicit solvent, and explicit solvent are significantly different.

Generalized Langevin Methods for Calculating Transmembrane Diffusivity.

The membrane permeability coefficient of a solute can be estimated using the solubility-diffusion model. This model requires the diffusivity profile (D(z)) of the solute as it moves along the transmembrane axis, z. The generalized Langevin equation provides one strategy for calculating position-dependent diffusivity from straightforward molecular dynamics simulations where the solute is restrained to a series of positions on the z-coordinate by a harmonic potential. The diffusivity of the solute is calculated from its correlation functions, which are related to the friction experienced by the solute. Roux and Hummer have derived expressions for the diffusion coefficient from the velocity autocorrelation function (VACF) and position autocorrelation function (PACF), respectively. In this work, these methods are validated by calculating the diffusivity of H2O and O2 in homogeneous liquids. These methods are then used to calculate transmembrane diffusivity profiles. The VACF method is less sensitive to thermostat forces and has incrementally lower errors but is more sensitive to the spring constant of the harmonic restraint. For the permeation of a solute through a lipid bilayer, the diffusion coefficients calculated using these methods provided significantly different results. Long-lived correlations of the restrained solute due to inhomogeneities in the bilayer can result in spuriously low diffusivity when using the PACF method. The method based on the VACF does not have this issue and predicts higher rates of diffusion inside the bilayer.