Performance of Nonlinear Finite-Difference Poisson-Boltzmann Solvers

Coupling finite and boundary element methods to solve the Poisson-Boltzmann equation for electrostatics in molecular solvation

The Poisson-Boltzmann equation is widely used to model electrostatics in molecular systems. Available software packages solve it using finite difference, finite element, and boundary element methods, where the latter is attractive due to the accurate representation of the molecular surface and partial charges, and exact enforcement of the boundary conditions at infinity. However, the boundary element method is limited to linear equations and piecewise constant variations of the material properties. In this work, we present a scheme that couples finite and boundary elements for the linearised Poisson-Boltzmann equation, where the finite element method is applied in a confined solute region and the boundary element method in the external solvent region. As a proof-of-concept exercise, we use the simplest methods available: Johnson-Nédélec coupling with mass matrix and diagonal preconditioning, implemented using the Bempp-cl and FEniCSx libraries via their Python interfaces. We showcase our implementation by computing the polar component of the solvation free energy of a set of molecules using a constant and a Gaussian-varying permittivity. As validation, we compare against well-established finite difference solvers for an extensive binding energy data set, and with the finite difference code APBS (to 0.5%) for Gaussian permittivities. We also show scaling results from protein G B1 (955 atoms) up to immunoglobulin G (20,148 atoms). For small problems, the coupled method was efficient, outperforming a purely boundary integral approach. For Gaussian-varying permittivities, which are beyond the applicability of boundary elements alone, we were able to run medium to large-sized problems on a single workstation. The development of better preconditioning techniques and the use of distributed memory parallelism for larger systems remains an area for future work. We hope this work will serve as inspiration for future developments that consider space-varying field parameters, and mixed linear-nonlinear schemes for molecular electrostatics with implicit solvent models.

Poisson-Boltzmann-based machine learning model for electrostatic analysis

Electrostatics is of paramount importance to chemistry, physics, biology, and medicine. The Poisson-Boltzmann (PB) theory is a primary model for electrostatic analysis. However, it is highly challenging to compute accurate PB electrostatic solvation free energies for macromolecules due to the nonlinearity, dielectric jumps, charge singularity, and geometric complexity associated with the PB equation. The present work introduces a PB-based machine learning (PBML) model for biomolecular electrostatic analysis. Trained with the second-order accurate MIBPB solver, the proposed PBML model is found to be more accurate and faster than several eminent PB solvers in electrostatic analysis. The proposed PBML model can provide highly accurate PB electrostatic solvation free energy of new biomolecules or new conformations generated by molecular dynamics with much reduced computational cost.

AmberTools

AmberTools is a free and open-source collection of programs used to set up, run, and analyze molecular simulations. The newer features contained within AmberTools23 are briefly described in this Application note.

Optimal Scheme to Achieve Energy Conservation in Induced Dipole Models

Induced dipole models have proven to be effective tools for simulating electronic polarization effects in biochemical processes, yet their potential has been constrained by energy conservation issue, particularly when historical data is utilized for dipole prediction. This study identifies error outliers as the primary factor causing this failure of energy conservation and proposes a comprehensive scheme to overcome this limitation. Leveraging maximum relative errors as a convergence metric, our data demonstrates that energy conservation can be upheld even when using historical information for dipole predictions. Our study introduces the multi-order extrapolation method to quicken induction iteration and optimize the use of historical data, while also developing the preconditioned conjugate gradient with local iterations to refine the iteration process and effectively remove error outliers. This scheme further incorporates a "peek" step via Jacobi under-relaxation for optimal performance. Simulation evidence suggests that our proposed scheme can achieve energy convergence akin to that of point-charge models within a limited number of iterations, thus promising significant improvements in efficiency and accuracy.

Comprehensive evaluation of end-point free energy techniques in carboxylated-pillar[6]arene host-guest binding: I. Standard procedure

Despite the massive application of end-point free energy methods in protein-ligand and protein-protein interactions, computational understandings about their performance in relatively simple and prototypical host-guest systems are limited. In this work, we present a comprehensive benchmark calculation with standard end-point free energy techniques in a recent host-guest dataset containing 13 host-guest pairs involving the carboxylated-pillar[6]arene host. We first assess the charge schemes for solutes by comparing the charge-produced electrostatics with many ab initio references, in order to obtain a preliminary albeit detailed view of the charge quality. Then, we focus on four modelling details of end-point free energy calculations, including the docking procedure for the generation of initial condition, the charge scheme for host and guest molecules, the water model used in explicit-solvent sampling, and the end-point methods for free energy estimation. The binding thermodynamics obtained with different modelling schemes are compared with experimental references, and some practical guidelines on maximizing the performance of end-point methods in practical host-guest systems are summarized. Further, we compare our simulation outcome with predictions in the grand challenge and discuss further developments to improve the prediction quality of end-point free energy methods. Overall, unlike the widely acknowledged applicability in protein-ligand binding, the standard end-point calculations cannot produce useful outcomes in host-guest binding and thus are not recommended unless alterations are performed.

RNA Electrostatics: How Ribozymes Engineer Active Sites to Enable Catalysis

Electrostatic interactions are fundamental to RNA structure and function, and intimately influenced by solvation and the ion atmosphere. RNA enzymes, or ribozymes, are catalytic RNAs that are able to enhance reaction rates over a million-fold, despite having only a limited repertoire of building blocks and available set of chemical functional groups. Ribozyme active sites usually occur at junctions where negatively charged helices come together, and in many cases leverage this strained electrostatic environment to recruit metal ions in solution that can assist in catalysis. Similar strategies have been implicated in related artificially engineered DNA enzymes. Herein, we apply Poisson-Boltzmann, 3D-RISM, and molecular simulations to study a set of metal-dependent small self-cleaving ribozymes (hammerhead, pistol, and Varkud satellite) as well as an artificially engineered DNAzyme (8-17) to examine electrostatic features and their relation to the recruitment of monovalent and divalent metal ions important for activity. We examine several fundamental roles for these ions that include: (1) structural integrity of the catalytically active state, (2) pKa tuning of residues involved in acid-base catalysis, and (3) direct electrostatic stabilization of the transition state via Lewis acid catalysis. Taken together, these examples demonstrate how RNA electrostatics orchestrates the site-specific and territorial binding of metal ions to play important roles in catalysis.

QM/MM Energy Decomposition Using the Interacting Quantum Atoms Approach

The interacting quantum atoms (IQA) method decomposes the quantum mechanical (QM) energy of a molecular system in terms of one- and two-center (atomic) contributions within the context of the quantum theory of atoms in molecules. Here, we demonstrate that IQA, enhanced with molecular mechanics (MM) and Poisson-Boltzmann surface-area (PBSA) solvation methods, is naturally extended to the realm of hybrid QM/MM methodologies, yielding intra- and inter-residue energy terms that characterize all kinds of covalent and noncovalent bonding interactions. To test the robustness of this approach, both metal-water interactions and QM/MM boundary artifacts are characterized in terms of the IQA descriptors derived from QM regions of varying size in Zn(II)- and Mg(II)-water clusters. In addition, we analyze a homologous series of inhibitors in complex with a matrix metalloproteinase (MMP-12) by carrying out QM/MM-PBSA calculations on their crystallographic structures followed by IQA energy decomposition. Overall, these applications not only show the advantages of the IQA QM/MM approach but also address some of the challenges lying ahead for expanding the QM/MM methodology.

Computational investigation of the impact of core sequence on immobile DNA four-way junction structure and dynamics

Immobile four-way junctions (4WJs) are core structural motifs employed in the design of programmed DNA assemblies. Understanding the impact of sequence on their equilibrium structure and flexibility is important to informing the design of complex DNA architectures. While core junction sequence is known to impact the preferences for the two possible isomeric states that junctions reside in, previous investigations have not quantified these preferences based on molecular-level interactions. Here, we use all-atom molecular dynamics simulations to investigate base-pair level structure and dynamics of four-way junctions, using the canonical Seeman J1 junction as a reference. Comparison of J1 with equivalent single-crossover topologies and isolated nicked duplexes reveal conformational impact of the double-crossover motif. We additionally contrast J1 with a second junction core sequence termed J24, with equal thermodynamic preference for each isomeric configuration. Analyses of the base-pair degrees of freedom for each system, free energy calculations, and reduced-coordinate sampling of the 4WJ isomers reveal the significant impact base sequence has on local structure, isomer bias, and global junction dynamics.

gmx_MMPBSA: A New Tool to Perform End-State Free Energy Calculations with GROMACS

Molecular mechanics/Poisson-Boltzmann (Generalized-Born) surface area is one of the most popular methods to estimate binding free energies. This method has been proven to balance accuracy and computational efficiency, especially when dealing with large systems. As a result of its popularity, several programs have been developed for performing MM/PB(GB)SA calculations within the GROMACS community. These programs, however, present several limitations. Here we present gmx_MMPBSA, a new tool to perform end-state free energy calculations from GROMACS molecular dynamics trajectories. gmx_MMPBSA provides the user with several options, including binding free energy calculations with different solvation models (PB, GB, or 3D-RISM), stability calculations, computational alanine scanning, entropy corrections, and binding free energy decomposition. Noteworthy, several promising methodologies to calculate relative binding free energies such as alanine scanning with variable dielectric constant and interaction entropy have also been implemented in gmx_MMPBSA. Two additional tools-gmx_MMPBSA_test and gmx_MMPBSA_ana-have been integrated within gmx_MMPBSA to improve its usability. Multiple illustrating examples can be accessed through gmx_MMPBSA_test, while gmx_MMPBSA_ana provides fast, easy, and efficient access to different graphics plotted from gmx_MMPBSA output files. The latest version (v1.4.3, 26/05/2021) is available free of charge (documentation, test files, and tutorials included) at https://github.com/Valdes-Tresanco-MS/gmx_MMPBSA.

Machine-Learned Molecular Surface and Its Application to Implicit Solvent Simulations

Implicit solvent models, such as Poisson-Boltzmann models, play important roles in computational studies of biomolecules. A vital step in almost all implicit solvent models is to determine the solvent-solute interface, and the solvent excluded surface (SES) is the most widely used interface definition in these models. However, classical algorithms used for computing SES are geometry-based, so that they are neither suitable for parallel implementations nor convenient for obtaining surface derivatives. To address the limitations, we explored a machine learning strategy to obtain a level set formulation for the SES. The training process was conducted in three steps, eventually leading to a model with over 95% agreement with the classical SES. Visualization of tested molecular surfaces shows that the machine-learned SES overlaps with the classical SES in almost all situations. Further analyses show that the machine-learned SES is incredibly stable in terms of rotational variation of tested molecules. Our timing analysis shows that the machine-learned SES is roughly 2.5 times as efficient as the classical SES routine implemented in Amber/PBSA on a tested central processing unit (CPU) platform. We expect further performance gain on massively parallel platforms such as graphics processing units (GPUs) given the ease in converting the machine-learned SES to a parallel procedure. We also implemented the machine-learned SES into the Amber/PBSA program to study its performance on reaction field energy calculation. The analysis shows that the two sets of reaction field energies are highly consistent with a 1% deviation on average. Given its level set formulation, we expect the machine-learned SES to be applied in molecular simulations that require either surface derivatives or high efficiency on parallel computing platforms.

Recent Developments in Free Energy Calculations for Drug Discovery

The grand challenge in structure-based drug design is achieving accurate prediction of binding free energies. Molecular dynamics (MD) simulations enable modeling of conformational changes critical to the binding process, leading to calculation of thermodynamic quantities involved in estimation of binding affinities. With recent advancements in computing capability and predictive accuracy, MD based virtual screening has progressed from the domain of theoretical attempts to real application in drug development. Approaches including the Molecular Mechanics Poisson Boltzmann Surface Area (MM-PBSA), Linear Interaction Energy (LIE), and alchemical methods have been broadly applied to model molecular recognition for drug discovery and lead optimization. Here we review the varied methodology of these approaches, developments enhancing simulation efficiency and reliability, remaining challenges hindering predictive performance, and applications to problems in the fields of medicine and biochemistry.

Estimating the Roles of Protonation and Electronic Polarization in Absolute Binding Affinity Simulations

Accurate prediction of binding free energies is critical to streamlining the drug development and protein design process. With the advent of GPU acceleration, absolute alchemical methods, which simulate the removal of ligand electrostatics and van der Waals interactions with the protein, have become routinely accessible and provide a physically rigorous approach that enables full consideration of flexibility and solvent interaction. However, standard explicit solvent simulations are unable to model protonation or electronic polarization changes upon ligand transfer from water to the protein interior, leading to inaccurate prediction of binding affinities for charged molecules. Here, we perform extensive simulation totaling ∼540 μs to benchmark the impact of modeling conditions on predictive accuracy for absolute alchemical simulations. Binding to urokinase plasminogen activator (UPA), a protein frequently overexpressed in metastatic tumors, is evaluated for a set of 10 inhibitors with extended flexibility, highly charged character, and titratable properties. We demonstrate that the alchemical simulations can be adapted to utilize the MBAR/PBSA method to improve the accuracy upon incorporating electronic polarization, highlighting the importance of polarization in alchemical simulations of binding affinities. Comparison of binding energy prediction at various protonation states indicates that proper electrostatic setup is also crucial in binding affinity prediction of charged systems, prompting us to propose an alternative binding mode with protonated ligand phenol and Hid-46 at the binding site, a testable hypothesis for future experimental validation.

Understanding the Conformational Properties of Fluorinated Polypeptides: Molecular Modelling of Unguisin A

In this work, we investigate the conformational properties of unguisin A, a natural macrocyclic heptapeptide that incorporates a γ-aminobutyric acid (Gaba), and four of its difluorinated stereoisomers at the Gaba residue. According to nuclear magnetic resonance (NMR) experiments, their secondary structure depends dramatically on the stereochemistry of the fluorinated carbon atoms. However, many molecular details of the structure and flexibility of these systems remain unknown, so that a rationale of the conformational changes induced by the fluorine atoms in the macrocycle is still missing. To fill this gap, we apply enhanced molecular dynamics (MD) techniques to explore the peptide conformational space in dimethyl sulfoxide solution followed by 4-8 μs of conventional MD simulations that provide extensive equilibrium sampling. The simulations, which compare reasonably well with the NMR-based observations, show that the secondary structure of the macrocycle is altered substantially upon fluorination, except for the (S,S) diastereomer. It also turns out that the conformations of the fluorinated peptides are visited during the enhanced MD simulation of natural unguisin A, suggesting thus that conformations accessible to the unsubstituted macrocyclic peptide may be selected by fluorination. Therefore, computational characterization of the macrocyclic peptides could be helpful in the rational design of stereoselective fluorinated peptides with fine-tuned conformation and activity.

A Newton-like iterative method implemented in the DelPhi for solving the nonlinear Poisson-Boltzmann equation

DelPhi is a popular scientific program which numerically solves the Poisson-Boltzmann equation (PBE) for electrostatic potentials and energies of biomolecules immersed in water via finite difference method. It is well known for its accuracy, reliability, flexibility, and efficiency. In this work, a new edition of DelPhi that uses a novel Newton-like method to solve the nonlinear PBE, in addition to the already implemented Successive Over Relaxation (SOR) algorithm, is introduced. Our tests on various examples have shown that this new method is superior to the SOR method in terms of stability when solving the nonlinear PBE, being able to converge even for problems involving very strong nonlinearity.

dUMP/F-dUMP Binding to Thymidylate Synthase: Human Versus Mycobacterium tuberculosis

Thymidylate synthase is an enzyme that catalyzes deoxythymidine monophosphate (dTMP) synthesis from substrate deoxyuridine monophosphate (dUMP). Thymidylate synthase of Mycobacterium tuberculosis (MtbThyX) is structurally distinct from its human analogue human thymidylate synthase (hThyA), thus drawing attention as an attractive drug target for combating tuberculosis. Fluorodeoxyuridylate (F-dUMP) is a successful inhibitor of both MtbThyX and hThyA, thus limited by poor selectivity. Understanding the dynamics and energetics associated with substrate/inhibitor binding to thymidylate synthase in atomic details remains a fundamental unsolved problem, which is necessary for a new selective inhibitor design. Structural studies of MtbThyX and hThyA bound substrate/inhibitor complexes not only revealed the extensive specific interaction network between protein and ligands but also opened up the possibility of directly computing the energetics of the substrate versus inhibitor recognition. Using experimentally determined structures as a template, we report extensive computer simulations (∼4.5 μs) that allow us to quantitatively estimate ligand selectivity (dUMP vs F-dUMP) by MtbThyX and hThyA. We show that MtbThyX prefers deprotonated dUMP (enolate form) as the substrate, whereas hThyA binds to the keto form of dUMP. Computed energetics clearly show that MtbThyX is less selective between dUMP and F-dUMP, favoring the latter, relative to hThyA. The simulations reveal the role of tyrosine at position 135 (Y135) of hThyA in amplifying the selectivity. The protonation state of the pyrimidine base of the ligand (i.e., keto or enolate) seems to have no role in MtbThyX ligand selectivity. A molecular gate (consists of Y108, K165, H203, and a water molecule) restricts water accessibility and offers a desolvated dry ligand-binding pocket for MtbThyX. The ligand-binding pocket of hThyA is relatively wet and exposed to bulk water.

Elucidation of WW domain ligand binding specificities in the Hippo pathway reveals STXBP4 as YAP inhibitor

The Hippo pathway, which plays a critical role in organ size control and cancer, features numerous WW domain-based protein-protein interactions. However, ~100 WW domains and 2,000 PY motif-containing peptide ligands are found in the human proteome, raising a "WW-PY" binding specificity issue in the Hippo pathway. In this study, we have established the WW domain binding specificity for Hippo pathway components and uncovered a unique amino acid sequence required for it. By using this criterion, we have identified a WW domain-containing protein, STXBP4, as a negative regulator of YAP. Mechanistically, STXBP4 assembles a protein complex comprising α-catenin and a group of Hippo PY motif-containing components/regulators to inhibit YAP, a process that is regulated by actin cytoskeleton tension. Interestingly, STXBP4 is a potential tumor suppressor for human kidney cancer, whose downregulation is correlated with YAP activation in clear cell renal cell carcinoma. Taken together, our study not only elucidates the WW domain binding specificity for the Hippo pathway, but also reveals STXBP4 as a player in actin cytoskeleton tension-mediated Hippo pathway regulation.

Improved Poisson-Boltzmann Methods for High-Performance Computing

Implicit solvent models based on the Poisson-Boltzmann equation (PBE) have been widely used to study electrostatic interactions in biophysical processes. These models often treat the solvent and solute regions as high and low dielectric continua, leading to a large jump in dielectrics across the molecular surface which is difficult to handle. Higher order interface schemes are often needed to seek higher accuracy for PBE applications. However, these methods are usually very liberal in the use of grid points nearby the molecular surface, making them difficult to use on high-performance computing platforms. Alternatively, the harmonic average (HA) method has been used to approximate dielectric interface conditions near the molecular surface with surprisingly good convergence and is well suited for high-performance computing. By adopting a 7-point stencil, the HA method is advantageous in generating simple 7-banded coefficient matrices, which greatly facilitate linear system solution with dense data parallelism, on high-performance computing platforms such as a graphics processing unit (GPU). However, the HA method is limited due to its lower accuracy. Therefore, it would be of great interest for high-performance applications to develop more accurate methods while retaining the simplicity and effectiveness of the 7-point stencil discretization scheme. In this study, we have developed two new algorithms based on the spirit of the HA method by introducing more physical interface relations and imposing the discretized Poisson's equation to the second order, respectively. Our testing shows that, for typical biomolecules, the new methods significantly improve the numerical accuracy to that comparable to the second-order solvers and with ∼65% overall efficiency gain on widely available high-performance GPU platforms.

Heterogeneous Dielectric Implicit Membrane Model for the Calculation of MMPBSA Binding Free Energies

Membrane-bound protein receptors are a primary biological drug target, but the computational analysis of membrane proteins has been limited. In order to improve molecular mechanics Poisson-Boltzmann surface area (MMPBSA) binding free energy calculations for membrane protein-ligand systems, we have optimized a new heterogeneous dielectric implicit membrane model, with respect to free energy simulations in explicit membrane and explicit water, and implemented it into the Amber software suite. This new model supersedes our previous uniform, single dielectric implicit membrane model by allowing the dielectric constant to vary with depth within the membrane. We calculated MMPBSA binding free energies for the human purinergic platelet receptor (P2Y₁₂R) and two of the muscarinic acetylcholine receptors (M2R and M3R) bound to various antagonist ligands using both membrane models, and we found that the heterogeneous dielectric membrane model has a stronger correlation with experimental binding affinities compared to the older model under otherwise identical conditions. This improved membrane model increases the utility of MMPBSA calculations for the rational design and improvement of future drug candidates.

An efficient second-order poisson-boltzmann method

Immersed interface method (IIM) is a promising high-accuracy numerical scheme for the Poisson-Boltzmann model that has been widely used to study electrostatic interactions in biomolecules. However, the IIM suffers from instability and slow convergence for typical applications. In this study, we introduced both analytical interface and surface regulation into IIM to address these issues. The analytical interface setup leads to better accuracy and its convergence closely follows a quadratic manner as predicted by theory. The surface regulation further speeds up the convergence for nontrivial biomolecules. In addition, uncertainties of the numerical energies for tested systems are also reduced by about half. More interestingly, the analytical setup significantly improves the linear solver efficiency and stability by generating more precise and better-conditioned linear systems. Finally, we implemented the bottleneck linear system solver on GPUs to further improve the efficiency of the method, so it can be widely used for practical biomolecular applications. © 2019 Wiley Periodicals, Inc.

Affinity Calculations of Cyclodextrin Host-Guest Complexes: Assessment of Strengths and Weaknesses of End-Point Free Energy Methods

The end-point methods like MM/PBSA or MM/GBSA estimate the free energy of a biomolecule by combining its molecular mechanics energy with solvation free energy and entropy terms. On the one hand, their performance largely depends on the particular system of interest, and despite numerous attempts to improve their reliability that have resulted in many variants, there is still no clear alternative to improve their accuracy. On the other hand, the relatively small cyclodextrin host-guest complexes, for which high-quality binding calorimetric data are usually available, are becoming reference models for testing the accuracy of free energy methods. In this work, we further assess the performance of various MM/PBSA-like approaches as applied to cyclodextrin complexes. To this end, we select a set of complexes between β-cyclodextrin and 57 small organic molecules that has been previously studied with the binding energy distribution analysis method in combination with an implicit solvent model ( Wickstrom, L.; He, P.; Gallicchio, E.; Levy, R. M. J. Chem. Theory Comput. 2013 , 9 , 3136 - 3150 ). For each complex, a conventional 1.0 μs molecular dynamics simulation in explicit solvent is performed. Then we employ semiempirical quantum chemical calculations, several variants of the MM-PB(GB)SA methods, entropy estimations, etc., to assess the reliability of the end-point affinity calculations. The best end-point protocol in this study, which combines DFTB3 energies with entropy corrections, yields estimations of the binding free energies that still have substantial errors (RMSE = 2.2 kcal/mol), but it exhibits a good prediction capacity in terms of ligand ranking ( R² = 0.66) that is close to or even better than that of rigorous free energy methodologies. Our results can be helpful to discriminate between the intrinsic limitations of the end-point methods and other sources of error, such as the underlying energy and continuum solvation methods.

Robustness and Efficiency of Poisson-Boltzmann Modeling on Graphics Processing Units

Poisson-Boltzmann equation (PBE) based continuum electrostatics models have been widely used in modeling electrostatic interactions in biochemical processes, particularly in estimating protein-ligand binding affinities. Fast convergence of PBE solvers is crucial in binding affinity computations as numerous snapshots need to be processed. Efforts have been reported to develop PBE solvers on graphics processing units (GPUs) for efficient modeling of biomolecules, though only relatively simple successive over-relaxation and conjugate gradient methods were implemented. However, neither convergence nor scaling properties of the two methods are optimal for large biomolecules. On the other hand, geometric multigrid (MG) has been shown to be an optimal solver on CPUs, though no MG have been reported for biomolecular applications on GPUs. This is not a surprise as it is a more complex method and depends on simpler but limited iterative methods such as Gauss-Seidel in its core relaxation procedure. The robustness and efficiency of MG on GPUs are also unclear. Here we present an implementation and a thorough analysis of MG on GPUs. Our analysis shows that robustness is a more pronounced issue than efficiency for both MG and other tested solvers when the single precision is used for complex biomolecules. We further show how to balance robustness and efficiency utilizing MG's overall efficiency and conjugate gradient's robustness, pointing to a hybrid GPU solver with a good balance of efficiency and accuracy. The new PBE solver will significantly improve the computational throughput for a range of biomolecular applications on the GPU platforms.

Discovery of CDK8/CycC Ligands with a New Virtual Screening Tool

Selective inhibition of cyclin-dependent kinase 8 and cyclin C (CDK8/CycC) has been suggested as a promising strategy for decreasing mitogenic signals in cancer cells with reduced toxicity toward normal cells. We developed a novel virtual screening protocol for drug development and applied it to the discovery of new CDK8/CycC type II ligands, which is likely to achieve long residence time and specificity. We first analyzed the binding thermodynamics of 11 published pyrazolourea ligands using molecular dynamics simulations and a free-energy calculation method, VM2, and extracted the key binding information to assist virtual screening. The urea moiety was found to be the critical structural contributor of the reference ligands. Starting with the urea moiety, we conducted substructure-based searches with our newly developed superposition and single-point energy evaluation method, followed by free-energy calculations, and singled out three purchasable compounds for bioassay testing. The ranking from the experimental results is completely consistent with the predicted rankings. A potent drug-like compound was found to have a K_d value of 42.5 nm, which is similar to those of the most potent reference ligands; this provided a good starting point for further improvement. This study shows that our novel virtual screening protocol is an accurate and efficient tool for drug development.

Implicit Solvation Using a Generalized Finite-Difference Approach in CRYSTAL: Implementation and Results for Molecules, Polymers, and Surfaces

We present the implementation of an implicit solvation model in the CRYSTAL code. The solvation energy is separated into two components: the electrostatic contribution arising from a self-consistent reaction field treatment obtained within a generalized finite-difference Poisson model, augmented by a nonelectrostatic contribution proportional to the solvent-accessible surface area of the solute. A discontinuous dielectric boundary is used, along with a solvent-excluded surface built from interlocking atom-centered spheres on which apparent surface point charges are mapped. The procedure is general and can be performed at both the Hartree-Fock and density functional theory levels, with pure or hybrid functionals, for systems periodic in 0, 1, and 2 directions, that is, for isolated molecules and extended polymers and surfaces. The Poisson equation resolution and apparent surface charge formalism is first validated on model analytical test cases. The good agreement obtained on solvation free energies is further confirmed by calculations performed on a large test set of 501 neutral molecules, for which a mean unsigned error of 1.3 kcal/mol is obtained when compared to the available experimental data. Importantly, the self-consistent reaction field procedure converges well for all molecules tested. This is further verified for all polymers and surfaces considered. In particular, for periodic systems, results obtained on an infinite glycine chain and on the wettability parameters of SiO₂ surfaces are in good agreement with previously published data. The size extensivity of the energetic terms involved in the electrostatic contribution to the solvation energy is also well verified. These encouraging results constitute a first step to take into account complex environments in the CRYSTAL code, potentially allowing for a more accurate modeling of complex processes for both periodic and nonperiodic systems.

Exploring a multi-scale method for molecular simulation in continuum solvent model: Explicit simulation of continuum solvent as an incompressible fluid

We explored a multi-scale algorithm for the Poisson-Boltzmann continuum solvent model for more robust simulations of biomolecules. In this method, the continuum solvent/solute interface is explicitly simulated with a numerical fluid dynamics procedure, which is tightly coupled to the solute molecular dynamics simulation. There are multiple benefits to adopt such a strategy as presented below. At this stage of the development, only nonelectrostatic interactions, i.e., van der Waals and hydrophobic interactions, are included in the algorithm to assess the quality of the solvent-solute interface generated by the new method. Nevertheless, numerical challenges exist in accurately interpolating the highly nonlinear van der Waals term when solving the finite-difference fluid dynamics equations. We were able to bypass the challenge rigorously by merging the van der Waals potential and pressure together when solving the fluid dynamics equations and by considering its contribution in the free-boundary condition analytically. The multi-scale simulation method was first validated by reproducing the solute-solvent interface of a single atom with analytical solution. Next, we performed the relaxation simulation of a restrained symmetrical monomer and observed a symmetrical solvent interface at equilibrium with detailed surface features resembling those found on the solvent excluded surface. Four typical small molecular complexes were then tested, both volume and force balancing analyses showing that these simple complexes can reach equilibrium within the simulation time window. Finally, we studied the quality of the multi-scale solute-solvent interfaces for the four tested dimer complexes and found that they agree well with the boundaries as sampled in the explicit water simulations.

Computational Analysis for the Rational Design of Anti-Amyloid Beta (Aβ) Antibodies

Alzheimer's disease (AD) is a neurodegenerative disorder that lacks effective treatment options. Anti-amyloid beta (Aβ) antibodies are the leading drug candidates to treat AD, but the results of clinical trials have been disappointing. Introducing rational mutations into anti-Aβ antibodies to increase their effectiveness is a way forward, but the path to take is unclear. In this study, we demonstrate the use of computational fragment-based docking and MMPBSA binding free energy calculations in the analysis of anti-Aβ antibodies for rational drug design efforts. Our fragment-based docking method successfully predicts the emergence of the common EFRH epitope. MD simulations coupled with MMPBSA binding free energy calculations are used to analyze scenarios described in prior studies, and we computationally introduce rational mutations into PFA1 to predict mutations that can improve its binding affinity toward the pE3-Aβ_3-8 form of Aβ. Two out of our four proposed mutations are predicted to stabilize binding. Our study demonstrates that a computational approach may lead to an improved drug candidate for AD in the future.

Synergistic regulation mechanism of iperoxo and LY2119620 for muscarinic acetylcholine M2 receptor

Muscarinic acetylcholine receptors are GPCRs that regulate the activity of a diverse array of central and peripheral functions in the human body, including the parasympathetic actions of acetylcholine. The M2 muscarinic receptor subtype plays a key role in modulating cardiac function and many important central processes. The orthosteric agonist and allosteric modulator can bind the pocket of M2. However, the detailed relationship between orthosteric agonist and allosteric modulator of M2 is still unclear. In this study, we intend to elucidate the residue-level regulation mechanism and pathway via a combined approach of dynamical correlation network and molecular dynamics simulation. Specifically computational residue-level fluctuation correlation data was analyzed to reveal detailed dynamics signatures in the regulation process. A hypothesis of "synergistic regulation" is proposed to reveal the cooperation affection between the orthosteric agonist and allosteric modulator, which is subsequently validated by perturbation and mutation analyses. Two possible synergistic regulation pathways of 2CU-I178-Y403-W400-F396-L114-Y440-Nb9 and IXO-V111-F396-L114-Y440-Nb9 were identified by the shortest path algorithm and were confirmed by the mutation of junction node. Furthermore, the efficiency of information transfer of bound M2 is significant higher than any single binding system. Our study shows that targeting the synergistic regulation pathways may better regulate the calcium channel of M2. The knowledge gained in this study may help develop drugs for diseases of the central nervous system and metabolic disorders.

The role of conserved QXG and binding affinity of S23G & S26G receptors on avian H5, swine H1 and human H1 of influenza A virus hemagglutinin

Outbreaks of avian, human and swine influenza are a serious concern for public health. In the reproductive cycle of the influenza virus, hemagglutinin (HA) is the primary protein responsible for binding to glycan receptor sites on the host cell surface. MD simulations of avian H5, swine H1 and human H1 complexed with S23G and S26G receptors were performed to study the role of key residues on the receptor conformational behaviors, hydrogen bond formation, binding free energy and residue-wise energy contribution. The obtained results indicated that the relative energies of swH1_S23G and swH1_S26G were found to be close to each other (3.1 kcal/mol) while the relative energies of AvH5 and HuH1 were found to be significantly different (11.1 ± 6.8 and 29.0 ± 8.2 kcal/mol for AvH5 and HuH1, respectively).

Molecular insights into substrate binding mechanism of undecaprenyl pyrophosphate with membrane integrated phosphatidyl glycerophosphate phosphatase B (PgpB) using molecular dynamics simulation approach

Undecaprenyl phosphate (C55-P) acts as carrier lipid in the synthesis of peptidoglycan, which is de novo synthesized from dephosphorylation of undecaprenyl pyrophosphate (C55-PP). The phosphatidylglycerol phosphate phosphatase B (PgpB) catalyzes the dephosphorylation of C55-PP and forms C55-P. As no structural study has been made regarding the binding of C55-PP to PgpB, in the current study, in silico molecular docking, followed by 150 ns molecular dynamics simulation of the putative binding complex in membrane/solvent environment has been performed to understand conformational dynamics. Results are compared with simulated apo form and PE inhibitor-bound form. Analysis of correlated residual fluctuation network in apo form, C55-PP bound and PE inhibitor-bound form suggests that difference in dynamic coupling between TM domain and α2 and α3 helix of periplasmic domain provides ligand binding to facilitate catalysis or to show inhibitory activity. Distance distribution in catalytic residual pair, H207-R104; H207-R201 and H207-D211 which stabilizes phosphate-enzyme intermediate shows a narrow peak in 2.4-3.6 Å in substrate-bound compared to apo form. Binding interactions and binding free energy analyses complement the partial inhibition of PE where PE has less binding free energy compared to the C55-PP substrate as well as the difference in binding interaction with catalytic pocket. Thus, the present study provides how substrate binding couples the movement in TM domain and periplasmic domain which might help in the understanding of active site communication in PgpB. C55-PP phosphatase interactions with a catalytic pocket of PgpB provide new insight for designing drugs against bacterial infection.

Recent Developments and Applications of the MMPBSA Method

The Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) approach has been widely applied as an efficient and reliable free energy simulation method to model molecular recognition, such as for protein-ligand binding interactions. In this review, we focus on recent developments and applications of the MMPBSA method. The methodology review covers solvation terms, the entropy term, extensions to membrane proteins and high-speed screening, and new automation toolkits. Recent applications in various important biomedical and chemical fields are also reviewed. We conclude with a few future directions aimed at making MMPBSA a more robust and efficient method.

Ionic Solution: What Goes Right and Wrong with Continuum Solvation Modeling

Solvent-mediated electrostatic interactions were well recognized to be important in the structure and function of molecular systems. Ionic interaction is an important component in electrostatic interactions, especially in highly charged molecules, such as nucleic acids. Here, we focus on the quality of the widely used Poisson-Boltzmann surface area (PBSA) continuum models in modeling ionic interactions by comparing with both explicit solvent simulations and the experiment. In this work, the molality-dependent chemical potentials for sodium chloride (NaCl) electrolyte were first simulated in the SPC/E explicit solvent. Our high-quality simulation agrees well with both the previous study and the experiment. Given the free-energy simulations in SPC/E as the benchmark, we used the same sets of snapshots collected in the SPC/E solvent model for PBSA free-energy calculations in the hope to achieve the maximum consistency between the two solvent models. Our comparative analysis shows that the molality-dependent chemical potentials of NaCl were reproduced well with both linear PB and nonlinear PB methods, although nonlinear PB agrees better with SPC/E and the experiment. Our free-energy simulations also show that the presence of salt increases the hydrophobic effect in a nonlinear fashion, in qualitative agreement with previous theoretical studies of Onsager and Samaras. However, the lack of molality-dependency in the nonelectrostatics continuum models dramatically reduces the overall quality of PBSA methods in modeling salt-dependent energetics. These analyses point to further improvements needed for more robust modeling of solvent-mediated interactions by the continuum solvation frameworks.

Electrostatics Explains the Position-Dependent Effect of G⋅U Wobble Base Pairs on the Affinity of RNA Kissing Complexes

In the RNA realm, non-Watson-Crick base pairs are abundant and can affect both the RNA 3D structure and its function. Here, we investigated the formation of RNA kissing complexes in which the loop-loop interaction is modulated by non-Watson-Crick pairs. Mass spectrometry, surface plasmon resonance, and UV-melting experiments show that the G⋅U wobble base pair favors kissing complex formation only when placed at specific positions. We tried to rationalize this effect by molecular modeling, including molecular mechanics Poisson-Boltzmann surface area (MMPBSA) thermodynamics calculations and PBSA calculations of the electrostatic potential surfaces. Modeling reveals that the G⋅U stabilization is due to a specific electrostatic environment defined by the base pairs of the entire loop-loop region. The loop is not symmetric, and therefore the identity and position of each base pair matters. Predicting and visualizing the electrostatic environment created by a given sequence can help to design specific kissing complexes with high affinity, for potential therapeutic, nanotechnology or analytical applications.

Ligand Strain and Entropic Effects on the Binding of Macrocyclic and Linear Inhibitors: Molecular Modeling of Penicillopepsin Complexes

Using extensive molecular dynamics simulations, we investigate the structure and dynamics of the complexes formed between penicillopepsin and two peptidomimetic inhibitors: a linear compound, isovaleryl(P₄)-valine(P₃)-asparagine(P₂)-leucine(P₁)-phosphonate-phenylalanine(P₁'), and its macrocylic analog that includes a methylene bridge between the Asn(P₂) and Phe(P₁') side chains. The macrocyclic inhibitor, which has a 420-fold stronger affinity than that of the acyclic one, has been considered to lower the entropic penalty for binding. To better understand this binding preference, the solution structure of the inhibitors is studied by molecular dynamics simulations. Subsequently, we assess the influence of the enzyme/inhibitor contacts, the enzyme-induced inhibitor strain, the variation of the ligand configurational entropy and the enzyme reorganization by combining molecular-mechanics Poisson-Boltzmann surface area and normal mode calculations with conformational entropy calculations. We find that there is no relevant entropic stabilization on the binding of the cyclic inhibitor with respect to the acyclic analog because the methylene bridge does not reduce appreciably the conformational flexibility of the free inhibitor. The most important factors explaining the stronger affinity of the macrocyclic inhibitor are the conformational filtering and the lower ligand strain induced by the methylene bridge.

A Continuum Poisson-Boltzmann Model for Membrane Channel Proteins

Membrane proteins constitute a large portion of the human proteome and perform a variety of important functions as membrane receptors, transport proteins, enzymes, signaling proteins, and more. Computational studies of membrane proteins are usually much more complicated than those of globular proteins. Here, we propose a new continuum model for Poisson-Boltzmann calculations of membrane channel proteins. Major improvements over the existing continuum slab model are as follows: (1) The location and thickness of the slab model are fine-tuned based on explicit-solvent MD simulations. (2) The highly different accessibilities in the membrane and water regions are addressed with a two-step, two-probe grid-labeling procedure. (3) The water pores/channels are automatically identified. The new continuum membrane model is optimized (by adjusting the membrane probe, as well as the slab thickness and center) to best reproduce the distributions of buried water molecules in the membrane region as sampled in explicit water simulations. Our optimization also shows that the widely adopted water probe of 1.4 Å for globular proteins is a very reasonable default value for membrane protein simulations. It gives the best compromise in reproducing the explicit water distributions in membrane channel proteins, at least in the water accessible pore/channel regions. Finally, we validate the new membrane model by carrying out binding affinity calculations for a potassium channel, and we observe good agreement with the experimental results.

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.

Numerical interpretation of molecular surface field in dielectric modeling of solvation

Continuum solvent models, particularly those based on the Poisson-Boltzmann equation (PBE), are widely used in the studies of biomolecular structures and functions. Existing PBE developments have been mainly focused on how to obtain more accurate and/or more efficient numerical potentials and energies. However to adopt the PBE models for molecular dynamics simulations, a difficulty is how to interpret dielectric boundary forces accurately and efficiently for robust dynamics simulations. This study documents the implementation and analysis of a range of standard fitting schemes, including both one-sided and two-sided methods with both first-order and second-order Taylor expansions, to calculate molecular surface electric fields to facilitate the numerical calculation of dielectric boundary forces. These efforts prompted us to develop an efficient approximated one-dimensional method, which is to fit the surface field one dimension at a time, for biomolecular applications without much compromise in accuracy. We also developed a surface-to-atom force partition scheme given a level set representation of analytical molecular surfaces to facilitate their applications to molecular simulations. Testing of these fitting methods in the dielectric boundary force calculations shows that the second-order methods, including the one-dimensional method, consistently perform among the best in the molecular test cases. Finally, the timing analysis shows the approximated one-dimensional method is far more efficient than standard second-order methods in the PBE force calculations. © 2017 Wiley Periodicals, Inc.

Accurate, robust, and reliable calculations of Poisson-Boltzmann binding energies

Poisson-Boltzmann (PB) model is one of the most popular implicit solvent models in biophysical modeling and computation. The ability of providing accurate and reliable PB estimation of electrostatic solvation free energy, ΔGel, and binding free energy, ΔΔGel, is important to computational biophysics and biochemistry. In this work, we investigate the grid dependence of our PB solver (MIBPB) with solvent excluded surfaces for estimating both electrostatic solvation free energies and electrostatic binding free energies. It is found that the relative absolute error of ΔGel obtained at the grid spacing of 1.0 Å compared to ΔGel at 0.2 Å averaged over 153 molecules is less than 0.2%. Our results indicate that the use of grid spacing 0.6 Å ensures accuracy and reliability in ΔΔGel calculation. In fact, the grid spacing of 1.1 Å appears to deliver adequate accuracy for high throughput screening. © 2017 Wiley Periodicals, Inc.

Crystal Structure of StnA for the Biosynthesis of Antitumor Drug Streptonigrin Reveals a Unique Substrate Binding Mode

Streptonigrin methylesterase A (StnA) is one of the tailoring enzymes that modify the aminoquinone skeleton in the biosynthesis pathway of Streptomyces species. Although StnA has no significant sequence homology with the reported α/β-fold hydrolases, it shows typical hydrolytic activity in vivo and in vitro. In order to reveal its functional characteristics, the crystal structures of the selenomethionine substituted StnA (SeMet-StnA) and the complex (S185A mutant) with its substrate were resolved to the resolution of 2.71 Å and 2.90 Å, respectively. The overall structure of StnA can be described as an α-helix cap domain on top of a common α/β hydrolase domain. The substrate methyl ester of 10'-demethoxystreptonigrin binds in a hydrophobic pocket that mainly consists of cap domain residues and is close to the catalytic triad Ser185-His349-Asp308. The transition state is stabilized by an oxyanion hole formed by the backbone amides of Ala102 and Leu186. The substrate binding appears to be dominated by interactions with several specific hydrophobic contacts and hydrogen bonds in the cap domain. The molecular dynamics simulation and site-directed mutagenesis confirmed the important roles of the key interacting residues in the cap domain. Structural alignment and phylogenetic tree analysis indicate that StnA represents a new subfamily of lipolytic enzymes with the specific binding pocket located at the cap domain instead of the interface between the two domains.

Stereoisomers of oseltamivir – synthesis, in silico prediction and biological evaluation

Three diastereoisomers of oseltamivir were synthesized, their properties predicted by quantum-chemical calculations and their antiviral activities evaluated.

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.

Susceptibility of inhibitors against 3C protease of coxsackievirus A16 and enterovirus A71 causing hand, foot and mouth disease: A molecular dynamics study

Hand foot and mouth disease (HFMD) epidemic has occurred in many countries. Coxsackievirus A16 (CV-A16) and Enterovirus A71 (EV-A71) are the main causes of HFMD. Up to now, there are no anti-HFMD drugs available. Rupintrivir, a broad-spectrum inhibitor, is a drug candidate for HFMD treatment, while other HFMD inhibitors designed from several studies have a relatively low efficiency. Therefore, in this work we aim to study the binding mechanisms of rupintrivir and a peptidic α,β-unsaturated ethyl ester (SG85) against both CV-A16 and EV-A71 3C proteases (3Cpro) using all-atoms molecular dynamics simulation. The obtained results indicate that SG85 shows a stronger binding affinity than rupintrivir against CV-A16. Both inhibitors exhibit a comparable affinity against EV-A71 3Cpro. The molecular information of the binding of the two inhibitors to the proteases will be elucidated. Thus, it is implied that these two compounds may be used as leads for further anti-HFMD drug design and development.

Calculating protein-ligand binding affinities with MMPBSA: Method and error analysis

Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) methods have become widely adopted in estimating protein-ligand binding affinities due to their efficiency and high correlation with experiment. Here different computational alternatives were investigated to assess their impact to the agreement of MMPBSA calculations with experiment. Seven receptor families with both high-quality crystal structures and binding affinities were selected. First the performance of nonpolar solvation models was studied and it was found that the modern approach that separately models hydrophobic and dispersion interactions dramatically reduces RMSD's of computed relative binding affinities. The numerical setup of the Poisson-Boltzmann methods was analyzed next. The data shows that the impact of grid spacing to the quality of MMPBSA calculations is small: the numerical error at the grid spacing of 0.5 Å is already small enough to be negligible. The impact of different atomic radius sets and different molecular surface definitions was further analyzed and weak influences were found on the agreement with experiment. The influence of solute dielectric constant was also analyzed: a higher dielectric constant generally improves the overall agreement with experiment, especially for highly charged binding pockets. The data also showed that the converged simulations caused slight reduction in the agreement with experiment. Finally the direction of estimating absolute binding free energies was briefly explored. Upon correction of the binding-induced rearrangement free energy and the binding entropy lost, the errors in absolute binding affinities were also reduced dramatically when the modern nonpolar solvent model was used, although further developments were apparently necessary to further improve the MMPBSA methods. © 2016 Wiley Periodicals, Inc.

Dynamics Correlation Network for Allosteric Switching of PreQ1 Riboswitch

Riboswitches are a class of metabolism control elements mostly found in bacteria. Due to their fundamental importance in bacteria gene regulation, riboswitches have been proposed as antibacterial drug targets. Prequeuosine (preQ₁) is the last free precursor in the biosynthetic pathway of queuosine that is crucial for translation efficiency and fidelity. However, the regulation mechanism for the preQ₁ riboswitch remains unclear. Here we constructed fluctuation correlation network based on all-atom molecular dynamics simulations to reveal the regulation mechanism. The results suggest that the correlation network in the bound riboswitch is distinctly different from that in the apo riboswitch. The community network indicates that the information freely transfers from the binding site of preQ₁ to the expression platform of the P3 helix in the bound riboswitch and the P3 helix is a bottleneck in the apo riboswitch. Thus, a hypothesis of “preQ₁-binding induced allosteric switching” is proposed to link riboswitch and translation regulation. The community networks of mutants support this hypothesis. Finally, a possible allosteric pathway of A50-A51-A52-U10-A11-G12-G56 was also identified based on the shortest path algorithm and confirmed by mutations and network perturbation. The novel fluctuation network analysis method can be used as a general strategy in studies of riboswitch structure-function relationship.

Synergistic Allosteric Mechanism of Fructose-1,6-bisphosphate and Serine for Pyruvate Kinase M2 via Dynamics Fluctuation Network Analysis

Pyruvate kinase M2 (PKM2) plays a key role in tumor metabolism and regulates the rate-limiting final step of glycolysis. In tumor cells, there are two allosteric effectors for PKM2: fructose-1,6-bisphosphate (FBP) and serine. However, the relationship between FBP and serine for allosteric regulation of PKM2 is unknown. Here we constructed residue/residue fluctuation correlation network based on all-atom molecular dynamics simulations to reveal the regulation mechanism. The results suggest that the correlation network in bound PKM2 is distinctly different from that in the free state, FBP/PKM2, or Ser/PKM2. The community network analysis indicates that the information can freely transfer from the allosteric sites of FBP and serine to the substrate site in bound PKM2, while there exists a bottleneck for information transfer in the network of the free state. Furthermore, the binding free energy between the substrate and PKM2 for bound PKM2 is significantly lower than either of FBP/PKM2 or Ser/PKM2. Thus, a hypothesis of "synergistic allosteric mechanism" is proposed for the allosteric regulation of FBP and serine. This hypothesis was further confirmed by the perturbational and mutational analyses of community networks and binding free energies. Finally, two possible synergistic allosteric pathways of FBP-K433-T459-R461-A109-V71-R73-MG2-OXL and Ser-I47-C49-R73-MG2-OXL were identified based on the shortest path algorithm and were confirmed by the network perturbation analysis. Interestingly, no similar pathways could be found in the free state. The process targeting on the allosteric pathways can better regulate the glycolysis of PKM2 and significantly inhibit the progression of tumor.

Charge Central Interpretation of the Full Nonlinear PB Equation: Implications for Accurate and Scalable Modeling of Solvation Interactions

Continuum solvation modeling based upon the Poisson-Boltzmann equation (PBE) is widely used in structural and functional analysis of biomolecules. In this work, we propose a charge-central interpretation of the full nonlinear PBE electrostatic interactions. The validity of the charge-central view or simply charge view, as formulated as a vacuum Poisson equation with effective charges, was first demonstrated by reproducing both electrostatic potentials and energies from the original solvated full nonlinear PBE. There are at least two benefits when the charge-central framework is applied. First the convergence analyses show that the use of polarization charges allows a much faster converging numerical procedure for electrostatic energy and forces calculation for the full nonlinear PBE. Second, the formulation of the solvated electrostatic interactions as effective charges in vacuum allows scalable algorithms to be deployed for large biomolecular systems. Here, we exploited the charge-view interpretation and developed a particle-particle particle-mesh (P3M) strategy for the full nonlinear PBE systems. We also studied the accuracy and convergence of solvation forces with the charge-view and the P3M methods. It is interesting to note that the convergence of both the charge-view and the P3M methods is more rapid than the original full nonlinear PBE method. Given the developments and validations documented here, we are working to adapt the P3M treatment of the full nonlinear PBE model to molecular dynamics simulations.

Synergistic Modification Induced Specific Recognition between Histone and TRIM24 via Fluctuation Correlation Network Analysis

Histone modification plays a key role in gene regulation and gene expression. TRIM24 as a histone reader can recognize histone modification. However the specific recognition mechanism between TRIM24 and histone modification is unsolved. Here, systems biology method of dynamics correlation network based on molecular dynamics simulation was used to answer the question. Our network analysis shows that the dynamics correlation network of H3K23ac is distinctly different from that of wild type and other modifications. A hypothesis of “synergistic modification induced recognition” is then proposed to link histone modification and TRIM24 binding. These observations were further confirmed from community analysis of networks with mutation and network perturbation. Finally, a possible recognition pathway is also identified based on the shortest path search for H3K23ac. Significant difference of recognition pathway was found among different systems due to methylation and acetylation modifications. The analysis presented here and other studies show that the dynamic network-based analysis might be a useful general strategy to study the biology of protein post-translational modification and associated recognition.

Multiscale method for modeling binding phenomena involving large objects: application to kinesin motor domains motion along microtubules

Many biological phenomena involve the binding of proteins to a large object. Because the electrostatic forces that guide binding act over large distances, truncating the size of the system to facilitate computational modeling frequently yields inaccurate results. Our multiscale approach implements a computational focusing method that permits computation of large systems without truncating the electrostatic potential and achieves the high resolution required for modeling macromolecular interactions, all while keeping the computational time reasonable. We tested our approach on the motility of various kinesin motor domains. We found that electrostatics help guide kinesins as they walk: N-kinesins towards the plus-end, and C-kinesins towards the minus-end of microtubules. Our methodology enables computation in similar, large systems including protein binding to DNA, viruses, and membranes.