Concepts, Practices, and Interactive Tutorial for Allosteric Network Analysis of Molecular Dynamics Simulations.

Over the past decade, concepts of network theory in combination with dynamical information from conformational ensembles have been widely applied to gain insights in understanding allosteric regulation in biomolecules. In this chapter, we introduce the basic theories and protocols used in protein dynamics network analysis through a series of interactive python Jupyter notebook scripts. While various network analysis methods exist in the literature, here we focus on the two popular methods based on correlated atomic motions and pairwise interaction energies. While the tutorial is based on a small prototypic protein, the workflow and protocol introduced here are optimized to handle large membrane proteins.

Ion Pairing and Dielectric Decrement in Glycosaminoglycan Brushes.

Cell-surface polysaccharides are essential to many aspects of physiology, serving as a highly conserved evolutionary feature of life and as an important part of the innate immune system in mammals. Here, as simplified biophysical models of these sugar coatings, we present results of molecular dynamics simulations of hyaluronic acid and heparin brushes that show important effects of ion pairing, water dielectric decrease, and coion exclusion. As in prior studies of macromolecular crowding under physiologically relevant salt concentrations, our results show equilibria with electroneutrality attained through screening and pairing of brush anionic charges by monovalent cations at the atomistic detail. Most surprising is the reversal of the Donnan potential obtained from both nonpolarizable and Drude polarizable force fields, in contrast to what would be expected based on electrostatic Boltzmann partitioning alone. Water dielectric decrement within the brush domain is also associated with Born hydration-driven cation exclusion from the brush. We observe that the primary partition energy attracting cations to attain brush electroneutrality is the ion pairing or salt-bridge energy. Potassium and sodium pairings to glycosaminoglycan carboxylates and sulfates show similar abundance of contact-pairing and solvent-separated pairing. We conclude that in these crowded macromolecular brushes, ion-pairing, Born-hydration, and electrostatic potential energies all contribute to attain electroneutrality and should therefore contribute in mean-field models to accurately represent brush electrostatics.

In silico prediction of ARB resistance: A first step in creating personalized ARB therapy.

Angiotensin II type 1 receptor (AT1R) blockers (ARBs) are among the most prescribed drugs. However, ARB effectiveness varies widely, which may be due to non-synonymous single nucleotide polymorphisms (nsSNPs) within the AT1R gene. The AT1R coding sequence contains over 100 nsSNPs; therefore, this study embarked on determining which nsSNPs may abrogate the binding of selective ARBs. The crystal structure of olmesartan-bound human AT1R (PDB:4ZUD) served as a template to create an inactive apo-AT1R via molecular dynamics simulation (n = 3). All simulations resulted in a water accessible ligand-binding pocket that lacked sodium ions. The model remained inactive displaying little movement in the receptor core; however, helix 8 showed considerable flexibility. A single frame representing the average stable AT1R was used as a template to dock Olmesartan via AutoDock 4.2, MOE, and AutoDock Vina to obtain predicted binding poses and mean Boltzmann weighted average affinity. The docking results did not match the known pose and affinity of Olmesartan. Thus, an optimization protocol was initiated using AutoDock 4.2 that provided more accurate poses and affinity for Olmesartan (n = 6). Atomic models of 103 of the known human AT1R polymorphisms were constructed using the molecular dynamics equilibrated apo-AT1R. Each of the eight ARBs was then docked, using ARB-optimized parameters, to each polymorphic AT1R (n = 6). Although each nsSNP has a negligible effect on the global AT1R structure, most nsSNPs drastically alter a sub-set of ARBs affinity to the AT1R. Alterations within N298 -L314 strongly effected predicted ARB affinity, which aligns with early mutagenesis studies. The current study demonstrates the potential of utilizing in silico approaches towards personalized ARB therapy. The results presented here will guide further biochemical studies and refinement of the model to increase the accuracy of the prediction of ARB resistance in order to increase overall ARB effectiveness.

Investigating Protein-Protein Allosteric Network using Current-Flow Scheme.

Protein dynamic network analysis provides a powerful tool for investigating protein allosteric regulation. We recently developed a current-flow betweenness scheme for protein network analysis and demonstrated that this method, that is, using current-flow betweenness as edge weights, is more appropriate and more robust for investigating the signal transmission between two predefined protein residues or domains as compared with direct usage of correlation scores as edge weights. Here we seek to expand the current-flow scheme to study allosteric regulations involving protein-protein binding. Specifically, we investigated three gain-of-function mutations located at the binding interface of ALK2 (also known as ACVR1) kinase and its inhibitory protein FKBP12. We first searched for the optimal smoothing function for contact network construction and then calculated the subnetwork between FKBP12 protein and the kinase ATP binding site using current-flow betweenness. By comparing the networks between the wild-type and three mutants, we have identified statistically significant changes in the protein-protein networks that are common among all three mutants that allosterically shift the kinase toward a catalytically competent configuration. © 2019 Wiley Periodicals, Inc.

A mechanism for the activation of the mechanosensitive Piezo1 channel by the small molecule Yoda1.

Mechanosensitive Piezo1 and Piezo2 channels transduce various forms of mechanical forces into cellular signals that play vital roles in many important biological processes in vertebrate organisms. Besides mechanical forces, Piezo1 is selectively activated by micromolar concentrations of the small molecule Yoda1 through an unknown mechanism. Here, using a combination of all-atom molecular dynamics simulations, calcium imaging and electrophysiology, we identify an allosteric Yoda1 binding pocket located in the putative mechanosensory domain, approximately 40 Å away from the central pore. Our simulations further indicate that the presence of the agonist correlates with increased tension-induced motions of the Yoda1-bound subunit. Our results suggest a model wherein Yoda1 acts as a molecular wedge, facilitating force-induced conformational changes, effectively lowering the channel's mechanical threshold for activation. The identification of an allosteric agonist binding site in Piezo1 channels will pave the way for the rational design of future Piezo modulators with clinical value.

Robust Determination of Protein Allosteric Signaling Pathways.

To understand how protein function changes upon an allosteric perturbation, such as ligand binding and mutation, significant progress in characterizing allosteric network from molecular dynamics (MD) simulations has been made. However, determining which amino acid(s) play an essential role in the propagation of signals may prove challenging, even when the location of the source and sink is known for a protein or protein complex. This challenge is mainly due to the large fluctuations in protein dynamics that cause instability of the network topology within a single trajectory or between multiple replicas. To solve this problem, we introduce the current-flow betweenness scheme, originated from electrical network theory, to protein dynamical network analysis. To demonstrate the benefit of this new method, we chose a prototypic allosteric enzyme (IGPS or HisH-HisF dimer) as our benchmark system. Using multiple replicas of simulations and multiple network topology comparison metrics (edge ranking, path length, and node frequency), we show that the current-flow betweenness provides a significant improvement in the convergence of the allosteric networks. The improved stability of the network topology allows us to generate a delta-network between the apo and holo forms of the protein. We illustrated that the delta-network is a more rigorous way to capture the subtle changes in the networks that would otherwise be neglected by comparing node usage frequencies alone. We have also investigated the use of a linear smoothing function to improve the stability of the contact map. The methodology presented here is general and may be applied to other topology and weighting schemes. We thus conclude that, for determining protein signaling pathways between the pair(s) of source and sink, multiple MD simulation replicas are necessary, and the current-flow betweenness scheme introduced here provides a more robust approach than the geodesic scheme based on correlation edge weighting.

The connexin26 human mutation N14K disrupts cytosolic intersubunit interactions and promotes channel opening.

A group of human mutations within the N-terminal (NT) domain of connexin 26 (Cx26) hemichannels produce aberrant channel activity, which gives rise to deafness and skin disorders, including keratitis-ichthyosis-deafness (KID) syndrome. Structural and functional studies indicate that the NT of connexin hemichannels is folded into the pore, where it plays important roles in permeability and gating. In this study, we explore the molecular basis by which N14K, an NT KID mutant, promotes gain of function. In macroscopic and single-channel recordings, we find that the N14K mutant favors the open conformation of hemichannels, shifts calcium and voltage sensitivity, and slows deactivation kinetics. Multiple copies of MD simulations of WT and N14K hemichannels, followed by the Kolmogorov-Smirnov significance test (KS test) of the distributions of interaction energies, reveal that the N14K mutation significantly disrupts pairwise interactions that occur in WT hemichannels between residue K15 of one subunit and residue E101 of the adjacent subunit (E101 being located at the transition between transmembrane segment 2 [TM2] and the cytoplasmic loop [CL]). Double mutant cycle analysis supports coupling between the NT and the TM2/CL transition in WT hemichannels, which is disrupted in N14K mutant hemichannels. KS tests of the α carbon correlation coefficients calculated over MD trajectories suggest that the effects of the N14K mutation are not confined to the K15-E101 pairs but extend to essentially all pairwise residue correlations between the NT and TM2/CL interface. Together, our data indicate that the N14K mutation increases hemichannel open probability by disrupting interactions between the NT and the TM2/CL region of the adjacent connexin subunit. This suggests that NT-TM2/CL interactions facilitate Cx26 hemichannel closure.

Alterations at Arg76 of human connexin 46, a residue associated with cataract formation, cause loss of gap junction formation but preserve hemichannel function.

The connexins are members of a family of integral membrane proteins that form gap junction channels between apposed cells and/or hemichannels across the plasma membranes. The importance of the arginine at position 76 (Arg76) in the structure and/or function of connexin 46 (Cx46) is highlighted by its conservation across the entire connexin family and the occurrence of pathogenic mutations at this (or the corresponding homologous) residue in a number of human diseases. Two mutations at Arg76 in Cx46 are associated with cataracts in humans, highlighting the importance of this residue. We examined the expression levels and macroscopic and single-channel properties of human Cx46 and compared them with those for two pathogenic mutants, namely R76H and R76G. To gain further insight into the role of charge at this position, we generated two additional nonnaturally occurring mutants, R76K (charge conserving) and R76E (charge inverting). We found that, when expressed exogenously in Neuro2a cells, all four mutants formed membrane hemichannels, inducing membrane permeability at levels comparable to those recorded in cells expressing the wild-type Cx46. In contrast, the number of gap-junction plaques and the magnitude of junctional coupling were reduced by all four mutations. To gain further insight into the role of Arg76 in the function of Cx46, we performed homology modeling of Cx46 and in silico mutagenesis of Arg76 to Gly, His, or Glu. Our studies suggest that the loss of interprotomeric interactions has a significant effect on the extracellular domain conformation and dynamics, thus affecting the hemichannel docking required for formation of cell-cell channels.

Probing the gating mechanism of the mechanosensitive channel Piezo1 with the small molecule Yoda1.

Piezo proteins are transmembrane ion channels which transduce many forms of mechanical stimuli into electrochemical signals. Their pore, formed by the assembly of three identical subunits, opens by an unknown mechanism. Here, to probe this mechanism, we investigate the interaction of Piezo1 with the small molecule agonist Yoda1. By engineering chimeras between mouse Piezo1 and its Yoda1-insensitive paralog Piezo2, we first identify a minimal protein region required for Yoda1 sensitivity. We next study the effect of Yoda1 on heterotrimeric Piezo1 channels harboring wild type subunits and Yoda1-insensitive mutant subunits. Using calcium imaging and patch-clamp electrophysiology, we show that hybrid channels harboring as few as one Yoda1-sensitive subunit exhibit Yoda1 sensitivity undistinguishable from homotrimeric wild type channels. Our results show that the Piezo1 pore remains fully open if only one subunit remains activated. This study sheds light on the gating and pharmacological mechanisms of a member of the Piezo channel family.

Molecular Mechanism of Resveratrol's Lipid Membrane Protection.

Resveratrol, a natural compound found in red wine and various vegetables, has drawn increasing interest due to its reported benefit in cardiovascular protection, neurodegenerative disorders, and cancer therapy. The mechanism by which resveratrol exerts such pleiotropic effects remains unclear. It remains as one of the most discussed polyphenol compounds in the debating "French Paradox". In this study, using molecular dynamics simulations of dipalmitoyl phosphatidylcholine (DPPC) bilayer with resveratrol, we generated a free energy map of resveratrol's location and orientation of inside the lipid bilayer. We found that resveratrol increases the surface area per lipid and decreases membrane thickness, which is the opposite effect of the well-studied cholesterol on liquid phase DPPC. Most importantly, based on the simulation observation that resveratrol has a high probability of forming hydrogen bonds with sn-1 and sn-2 ester groups, we discovered a new mechanism using experimental approach, in which resveratrol protects both sn-1 and sn-2 ester bonds of DPPC and distearoyl phosphatidylcholine (DSPC) from phospholipase A1 (PLA1) and phospholipase A2 (PLA2) cleavage. Our study elucidates the new molecular mechanism of potential health benefits of resveratrol and possibly other similar polyphenols and provides a new paradigm for drug design based on resveratrol and its analogs.

Can Relative Binding Free Energy Predict Selectivity of Reversible Covalent Inhibitors?

Reversible covalent inhibitors have many clinical advantages over noncovalent or irreversible covalent drugs. However, apart from selecting a warhead, substantial efforts in design and synthesis are needed to optimize noncovalent interactions to improve target-selective binding. Computational prediction of binding affinity for reversible covalent inhibitors presents a unique challenge since the binding process consists of multiple steps, which are not necessarily independent of each other. In this study, we lay out the relation between relative binding free energy and the overall reversible covalent binding affinity using a two-state binding model. To prove the concept, we employed free energy perturbation (FEP) coupled with λ-exchange molecular dynamics method to calculate the binding free energy of a series of α-ketoamide analogues relative to a common warhead scaffold, in both noncovalent and covalent binding states, and for two highly homologous proteases, calpain-1 and calpain-2. We conclude that covalent binding state alone, in general, can be used to predict reversible covalent binding selectivity. However, exceptions may exist. Therefore, we also discuss the conditions under which the noncovalent binding step is no longer negligible and propose to combine the relative FEP calculations with a single QM/MM calculation of warhead to predict the binding affinity and binding kinetics. Our FEP calculations also revealed that covalent and noncovalent binding states of an inhibitor do not necessarily exhibit the same selectivity. Thus, investigating both binding states, as well as the kinetics will provide extremely useful information for optimizing reversible covalent inhibitors.

Polymodal allosteric regulation of Type 1 Serine/Threonine Kinase Receptors via a conserved electrostatic lock.

Type 1 Serine/Threonine Kinase Receptors (STKR1) transduce a wide spectrum of biological signals mediated by TGF-ß superfamily members. The STKR1 activity is tightly controlled by their regulatory glycine-serine rich (GS) domain adjacent to the kinase domain. Despite decades of studies, it remains unknown how physiological or pathological GS domain modifications are coupled to STKR1 kinase activity. Here, by performing molecular dynamics simulations and free energy calculation of Activin-Like Kinase 2 (ALK2), we found that GS domain phosphorylation, FKBP12 dissociation, and disease mutations all destabilize a D354-R375 salt-bridge, which normally acts as an electrostatic lock to prevent coordination of adenosine triphosphate (ATP) to the catalytic site. We developed a WAFEX-guided principal analysis and unraveled how phosphorylation destabilizes this highly conserved salt-bridge in temporal and physical space. Using current-flow betweenness scores, we identified an allosteric network of residue-residue contacts between the GS domain and the catalytic site that controls the formation and disruption of this salt bridge. Importantly, our novel network analysis approach revealed how certain disease-causing mutations bypass FKBP12-mediated kinase inhibition to produce leaky signaling. We further provide experimental evidence that this salt-bridge lock exists in other STKR1s, and acts as a general safety mechanism in STKR1 to prevent pathological leaky signaling. In summary, our study provides a compelling and unifying allosteric activation mechanism in STKR1 kinases that reconciles a large number of experimental studies and sheds light on a novel therapeutic avenue to target disease-related STKR1 mutants.

Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.

Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.

Modeling Membrane Protein-Ligand Binding Interactions: The Human Purinergic Platelet Receptor.

Membrane proteins, due to their roles as cell receptors and signaling mediators, make prime candidates for drug targets. The computational analysis of protein-ligand binding affinities has been widely employed as a tool in rational drug design efforts. Although efficient implicit solvent-based methods for modeling globular protein-ligand binding have been around for many years, the extension of such methods to membrane protein-ligand binding is still in its infancy. In this study, we extended the widely used Amber/MMPBSA method to model membrane protein-ligand systems, and we used it to analyze protein-ligand binding for the human purinergic platelet receptor (P2Y12R), a prominent drug target in the inhibition of platelet aggregation for the prevention of myocardial infarction and stroke. The binding affinities, computed by the Amber/MMPBSA method using standard parameters, correlate well with experiment. A detailed investigation of these parameters was conducted to assess their impact on the accuracy of the method. These analyses show the importance of properly treating the nonpolar solvation interactions and the electrostatic polarization in the binding of nucleotide agonists and non-nucleotide antagonists to P2Y12R. On the basis of the crystal structures and the experimental conditions in the binding assay, we further hypothesized that the nucleotide agonists lose their bound magnesium ion upon binding to P2Y12R, and our computational study supports this hypothesis. Ultimately, this work illustrates the value of computational analysis in the interpretation of experimental binding reactions.

Applications of MMPBSA to Membrane Proteins I: Efficient Numerical Solutions of Periodic Poisson-Boltzmann Equation.

Continuum solvent models have been widely used in biomolecular modeling applications. Recently much attention has been given to inclusion of implicit membranes into existing continuum Poisson-Boltzmann solvent models to extend their applications to membrane systems. Inclusion of an implicit membrane complicates numerical solutions of the underlining Poisson-Boltzmann equation due to the dielectric inhomogeneity on the boundary surfaces of a computation grid. This can be alleviated by the use of the periodic boundary condition, a common practice in electrostatic computations in particle simulations. The conjugate gradient and successive over-relaxation methods are relatively straightforward to be adapted to periodic calculations, but their convergence rates are quite low, limiting their applications to free energy simulations that require a large number of conformations to be processed. To accelerate convergence, the Incomplete Cholesky preconditioning and the geometric multigrid methods have been extended to incorporate periodicity for biomolecular applications. Impressive convergence behaviors were found as in the previous applications of these numerical methods to tested biomolecules and MMPBSA calculations.

Numerical Poisson-Boltzmann Model for Continuum Membrane Systems.

Membrane protein systems are important computational research topics due to their roles in rational drug design. In this study, we developed a continuum membrane model utilizing a level set formulation under the numerical Poisson-Boltzmann framework within the AMBER molecular mechanics suite for applications such as protein-ligand binding affinity and docking pose predictions. Two numerical solvers were adapted for periodic systems to alleviate possible edge effects. Validation on systems ranging from organic molecules to membrane proteins up to 200 residues, demonstrated good numerical properties. This lays foundations for sophisticated models with variable dielectric treatments and second-order accurate modeling of solvation interactions.