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 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.Comment: 5 figures, 2 table

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 co-ion 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 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 pairing 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. </p

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

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

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

<div><p>Type 1 Serine/Threonine Kinase Receptors (STKR1) transduce a wide spectrum of biological signals mediated by TGF-β 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.</p></div

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 membrane 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 multi-grid 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