Novel druggable hot spots in avian influenza neuraminidase H5N1 revealed by computational solvent mapping of a reduced and representative receptor ensemble

The influenza virus subtype H5N1 has raised concerns of a possible human pandemic threat because of its high virulence and mutation rate. Although several approved anti-influenza drugs effectively target the neuraminidase, some strains have already acquired resistance to the currently available anti-influenza drugs. In this study, we present the synergistic application of extended explicit solvent molecular dynamics (MD) and computational solvent mapping (CS-Map) to identify putative 'hot spots' within flexible binding regions of N1 neuraminidase. Using representative conformations of the N1 binding region extracted from a clustering analysis of four concatenated 40-ns MD simulations, CS-Map was utilized to assess the ability of small, solvent-sized molecules to bind within close proximity to the sialic acid binding region. Mapping analyses of the dominant MD conformations reveal the presence of additional hot spot regions in the 150- and 430-loop regions. Our hot spot analysis provides further support for the feasibility of developing high-affinity inhibitors capable of binding these regions, which appear to be unique to the N1 strain.

Estimating kinetic rates from accelerated molecular dynamics simulations: alanine dipeptide in explicit solvent as a case study

Molecular dynamics (MD) simulation is the standard computational technique used to obtain information on the time evolution of the conformations of proteins and many other molecular systems. However, for most biological systems of interest, the time scale for slow conformational transitions is still inaccessible to standard MD simulations. Several sampling methods have been proposed to address this issue, including the accelerated molecular dynamics method. In this work, we study the extent of sampling of the phi/psi space of alanine dipeptide in explicit water using accelerated molecular dynamics and present a framework to recover the correct kinetic rate constant for the helix to beta-strand transition. We show that the accelerated MD can drastically enhance the sampling of the phi/psi conformational phase space when compared to normal MD. In addition, the free energy density plots of the phi/psi space show that all minima regions are accurately sampled and the canonical distribution is recovered. Moreover, the kinetic rate constant for the helix to beta-strand transition is accurately estimated from these simulations by relating the diffusion coefficient to the local energetic roughness of the energy landscape. Surprisingly, even for such a low barrier transition, it is difficult to obtain enough transitions to accurately estimate the rate constant when one uses normal MD.

Molecular surface-free continuum model for electrodiffusion processes

Incorporation of van der Waals interactions enables the continuum model of electrodiffusion in biomolecular system to avoid the artifacts of introducing a molecular surface and the painful task of the surface mesh generation. Calculation examples show that the electrostatics, diffusion-reaction kinetics, and molecular surface defined as an isosurface of a certain density distribution can be extracted from the solution of the Poisson-Nernst-Planck equations using this model. The molecular surface-free model enables a wider usage of some modern numerical methodologies such as finite element methods for biomolecular modeling, and sheds light on a new paradigm of continuum modeling for biomolecular systems.

Sampling of slow diffusive conformational transitions with accelerated molecular dynamics

Slow diffusive conformational transitions play key functional roles in biomolecular systems. Our ability to sample these motions with molecular dynamics simulation in explicit solvent is limited by the slow diffusion of the solvent molecules around the biomolecules. Previously, we proposed an accelerated molecular dynamics method that has been shown to efficiently sample the torsional degrees of freedom of biomolecules beyond the millisecond timescale. However, in our previous approach, large-amplitude displacements of biomolecules are still slowed by the diffusion of the solvent. Here we present a unified approach of efficiently sampling both the torsional degrees of freedom and the diffusive motions concurrently. We show that this approach samples the configuration space more efficiently than normal molecular dynamics and that ensemble averages converge faster to the correct values.

Accelerated entropy estimates with accelerated dynamics

Accelerated dynamics is applied to entropy calculations on a set of toy and molecular systems and is found to enhance the rate of convergence.

Solvent reaction field potential inside an uncharged globular protein: a bridge between implicit and explicit solvent models?

The solvent reaction field potential of an uncharged protein immersed in simple point charge/extended explicit solvent was computed over a series of molecular dynamics trajectories, in total 1560 ns of simulation time. A finite, positive potential of 13-24 kbTec(-1) (where T=300 K), dependent on the geometry of the solvent-accessible surface, was observed inside the biomolecule. The primary contribution to this potential arose from a layer of positive charge density 1.0 A from the solute surface, on average 0.008 ec/A3, which we found to be the product of a highly ordered first solvation shell. Significant second solvation shell effects, including additional layers of charge density and a slight decrease in the short-range solvent-solvent interaction strength, were also observed. The impact of these findings on implicit solvent models was assessed by running similar explicit solvent simulations on the fully charged protein system. When the energy due to the solvent reaction field in the uncharged system is accounted for, correlation between per-atom electrostatic energies for the explicit solvent model and a simple implicit (Poisson) calculation is 0.97, and correlation between per-atom energies for the explicit solvent model and a previously published, optimized Poisson model is 0.99.

Continuum simulations of acetylcholine consumption by acetylcholinesterase: a Poisson-Nernst-Planck approach

The Poisson-Nernst-Planck (PNP) equation provides a continuum description of electrostatic-driven diffusion and is used here to model the diffusion and reaction of acetylcholine (ACh) with acetylcholinesterase (AChE) enzymes. This study focuses on the effects of ion and substrate concentrations on the reaction rate and rate coefficient. To this end, the PNP equations are numerically solved with a hybrid finite element and boundary element method at a wide range of ion and substrate concentrations, and the results are compared with the partially coupled Smoluchowski-Poisson-Boltzmann model. The reaction rate is found to depend strongly on the concentrations of both the substrate and ions; this is explained by the competition between the intersubstrate repulsion and the ionic screening effects. The reaction rate coefficient is independent of the substrate concentration only at very high ion concentrations, whereas at low ion concentrations the behavior of the rate depends strongly on the substrate concentration. Moreover, at physiological ion concentrations, variations in substrate concentration significantly affect the transient behavior of the reaction. Our results offer a reliable estimate of reaction rates at various conditions and imply that the concentrations of charged substrates must be coupled with the electrostatic computation to provide a more realistic description of neurotransmission and other electrodiffusion and reaction processes.

Electrodiffusion: a continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution

A computational framework is presented for the continuum modeling of cellular biomolecular diffusion influenced by electrostatic driving forces. This framework is developed from a combination of state-of-the-art numerical methods, geometric meshing, and computer visualization tools. In particular, a hybrid of (adaptive) finite element and boundary element methods is adopted to solve the Smoluchowski equation (SE), the Poisson equation (PE), and the Poisson-Nernst-Planck equation (PNPE) in order to describe electrodiffusion processes. The finite element method is used because of its flexibility in modeling irregular geometries and complex boundary conditions. The boundary element method is used due to the convenience of treating the singularities in the source charge distribution and its accurate solution to electrostatic problems on molecular boundaries. Nonsteady-state diffusion can be studied using this framework, with the electric field computed using the densities of charged small molecules and mobile ions in the solvent. A solution for mesh generation for biomolecular systems is supplied, which is an essential component for the finite element and boundary element computations. The uncoupled Smoluchowski equation and Poisson-Boltzmann equation are considered as special cases of the PNPE in the numerical algorithm, and therefore can be solved in this framework as well. Two types of computations are reported in the results: stationary PNPE and time-dependent SE or Nernst-Planck equations solutions. A biological application of the first type is the ionic density distribution around a fragment of DNA determined by the equilibrium PNPE. The stationary PNPE with nonzero flux is also studied for a simple model system, and leads to an observation that the interference on electrostatic field of the substrate charges strongly affects the reaction rate coefficient. The second is a time-dependent diffusion process: the consumption of the neurotransmitter acetylcholine by acetylcholinesterase, determined by the SE and a single uncoupled solution of the Poisson-Boltzmann equation. The electrostatic effects, counterion compensation, spatiotemporal distribution, and diffusion-controlled reaction kinetics are analyzed and different methods are compared.

Limitations of atom-centered dielectric functions in implicit solvent models

Many recent advances in Poisson-Boltzmann and generalized Born implicit solvent models have used atom-centered polynomial or Gaussian functions to define the boundary separating low and high dielectric regions. In contrast to the Lee and Richards molecular surface, atom-centered surfaces result in interatomic crevices and buried pockets of high dielectric which are too small for a solvent molecule to occupy. We show that these interstitial high dielectric regions are of significant magnitude in globular proteins, that they artificially increase solvation energies, and that they distort the free energy surface of nonbonded interactions. These results suggest that implicit solvent dielectric functions must exclude interstitial high dielectric regions in order to yield physically meaningful results.

Functional and structural insights revealed by molecular dynamics simulations of an essential RNA editing ligase in Trypanosoma brucei

RNA editing ligase 1 (TbREL1) is required for the survival of both the insect and bloodstream forms of Trypanosoma brucei, the parasite responsible for the devastating tropical disease African sleeping sickness. The type of RNA editing that TbREL1 is involved in is unique to the trypanosomes, and no close human homolog is known to exist. In addition, the high-resolution crystal structure revealed several unique features of the active site, making this enzyme a promising target for structure-based drug design. In this work, two 20 ns atomistic molecular dynamics (MD) simulations are employed to investigate the dynamics of TbREL1, both with and without the ATP substrate present. The flexibility of the active site, dynamics of conserved residues and crystallized water molecules, and the interactions between TbREL1 and the ATP substrate are investigated and discussed in the context of TbREL1's function. Differences in local and global motion upon ATP binding suggest that two peripheral loops, unique to the trypanosomes, may be involved in interdomain signaling events. Notably, a significant structural rearrangement of the enzyme's active site occurs during the apo simulations, opening an additional cavity adjacent to the ATP binding site that could be exploited in the development of effective inhibitors directed against this protozoan parasite. Finally, ensemble averaged electrostatics calculations over the MD simulations reveal a novel putative RNA binding site, a discovery that has previously eluded scientists. Ultimately, we use the insights gained through the MD simulations to make several predictions and recommendations, which we anticipate will help direct future experimental studies and structure-based drug discovery efforts against this vital enzyme.

Generalized gradient-augmented harmonic Fourier beads method with multiple atomic and/or center-of-mass positional restraints

We describe a generalization of the gradient-augmented harmonic Fourier beads method for finding minimum free-energy transition path ensembles and similarly minimum potential energy paths to allow positional restraints on the centers of mass of selected atoms. The generalized gradient-augmented harmonic Fourier beads (ggaHFB) method further extends the scope of the HFB methodology to studying molecule transport across various mobile phases such as lipid membranes. Furthermore, the new implementation improves the applicability of the HFB method to studies of ligand binding, protein folding, and enzyme catalysis as well as modeling equilibrium pulling experiments. Like its predecessor, the ggaHFB method provides accurate energy profiles along the specified paths and in certain simple cases avoids the need for path optimization. The utility of the ggaHFB method is demonstrated with an application to the water permeation through a single-wall (5,5) carbon nanotube with a diameter of 6.78 A and length of 16.0 A. We provide a simple rationale as to why water enters the hydrophobic nanotube and why it does so in pulses and in wire assembly.

"New-version-fast-multipole-method" accelerated electrostatic interactions in biomolecular systems

In this paper, we present an efficient and accurate numerical algorithm for calculating the electrostatic interactions in biomolecular systems. In our scheme, a boundary integral equation (BIE) approach is applied to discretize the linearized Poisson-Boltzmann (PB) equation. The resulting integral formulas are well conditioned for single molecule cases as well as for systems with more than one macromolecule, and are solved efficiently using Krylov subspace based iterative methods such as generalized minimal residual (GMRES) or bi-conjugate gradients stabilized (BiCGStab) methods. In each iteration, the convolution type matrix-vector multiplications are accelerated by a new version of the fast multipole method (FMM). The implemented algorithm is asymptotically optimal O(N) both in CPU time and memory usage with optimized prefactors. Our approach enhances the present computational ability to treat electrostatics of large scale systems in protein-protein interactions and nano particle assembly processes. Applications including calculating the electrostatics of the nicotinic acetylcholine receptor (nAChR) and interactions between protein Sso7d and DNA are presented.

H-ras protein in a bilayer: interaction and structure perturbation

Ras GTPases become functionally active when anchored to membranes by inserting their lipid modified side chains. Their role in cell division, development, and cancer has made them targets of extensive research efforts, yet the mechanism of membrane insertion and the structure of the resulting complex remain elusive. Recently, the structure of the full-length H-ras protein in a DMPC bilayer has been computationally characterized. Here, the atomic interactions between the H-ras membrane anchor and the DMPC bilayer are investigated in detail. We find that the palmitoylated cysteines and Met182 have dual contributions to membrane affinity: hydrogen bonding by their amides and van der Waals interaction by their hydrophobic side chains. The polar side chains help maintain the orientation of the anchor. Although the overall structure of the bilayer is similar to that of a pure DMPC, there are localized perturbations. These perturbations depend on the insertion depth and backbone localization of the anchor, which in turn is modulated by the catalytic domain and the linker. The pattern of anchor amide-DMPC phosphate/carbonyl hydrogen bonds and the flexibility of Palm184 are important in discriminating between different modes of ras-DMPC interactions. The results provide structural arguments in support of the proposed participation of ras in the organization of membrane nanoclusters.

A proposed signaling motif for nuclear import in mRNA processing via the formation of arginine claw

Phosphorylation of proteins by kinases is the most commonly studied class of posttranslational modification, yet its structural consequences are not well understood. The human SR (serine-arginine) protein ASF/SF2 relies on the processive phosphorylation of the serine residues of eight consecutive arginine-serine (RS) dipeptide repeats at the C terminus by SRPK1 before it can be transported into the nucleus. This SR protein plays critical roles in spliceosome assembly, pre-mRNA splicing, and mRNA export, and the phosphorylation process of the RS repeats has been extensively studied experimentally. However, knowledge of the conformational changes associated with the phosphorylation of this simple sequence and how it triggers the importation of the SR protein is lacking. Here, we have carried out extensive molecular dynamics simulations to show that phosphorylation of the eight RS repeats significantly alters the peptide's conformation and leads to the formation of very stable structures that are likely to be involved in the recognition, binding, and transport of the SR protein. Specifically, we found an unusual symmetry-broken phase of conformations of the repetitive and quasi-symmetric phosphorylated peptide sequence. One of the main characteristics of these conformations is the exposed phosphate groups on the periphery, which possibly could serve as the recognition platform for the transport protein transportin-SR2.

Application of the level-set method to the implicit solvation of nonpolar molecules

A level-set method is developed for numerically capturing the equilibrium solute-solvent interface that is defined by the recently proposed variational implicit solvent model [Dzubiella, Swanson, and McCammon, Phys. Rev. Lett. 104, 527 (2006); J. Chem. Phys. 124, 084905 (2006)]. In the level-set method, a possible solute-solvent interface is represented by the zero level set (i.e., the zero level surface) of a level-set function and is eventually evolved into the equilibrium solute-solvent interface. The evolution law is determined by minimization of a solvation free energy functional that couples both the interfacial energy and the van der Waals type solute-solvent interaction energy. The surface evolution is thus an energy minimizing process, and the equilibrium solute-solvent interface is an output of this process. The method is implemented and applied to the solvation of nonpolar molecules such as two xenon atoms, two parallel paraffin plates, helical alkane chains, and a single fullerence C(60). The level-set solutions show good agreement for the solvation energies when compared to available molecular dynamics simulations. In particular, the method captures solvent dewetting (nanobubble formation) and quantitatively describes the interaction in the strongly hydrophobic plate system.

The influence of macromolecular crowding on HIV-1 protease internal dynamics

High macromolecular concentrations, or crowded conditions, have been shown to affect a wide variety of molecular processes, including diffusion, association and dissociation, and protein folding and stability. Here, we model the effect of macromolecular crowding on the internal dynamics of a protein, HIV-1 protease, using Brownian dynamics simulations. HIV-1 protease possesses a pair of flaps which are postulated to open in the early stages of its catalytic mechanism. Compared to low concentrations, close-packed concentrations of repulsive crowding agents are found to significantly reduce the fraction of time that the protease flaps are open. Macromolecular crowding is likely to have a major effect on in vivo enzyme activity, and may play an important regulatory role in the viral life cycle.

Dynamics, Hydration, and Motional Averaging of a Loop-Gated Artificial Protein Cavity: The W191G Mutant of Cytochrome c Peroxidase in Water as Revealed by Molecular Dynamics Simulations

Five molecular dynamics simulations of the W191G cavity mutant of cytochrome c peroxidase in explicit water reveal distinct dynamic and hydration behavior depending on the closed or open state of the flexible loop gating the cavity, the binding of (K+ or small molecule) cations, and the system temperature. The conformational spaces sampled by the loop region and by the cavity significantly reduce upon binding. The largest ordering factor on water dynamics is the presence of the K+ ion occupying the gated cavity. Considerable water exchange occurs for the open-gate cavity when no ligand or cation is bound. In all cases, good correspondence is found between the calculated (ensemble-averaged) location of water molecules and the water sites determined by X-ray crystallography experiments. However, our simulations suggest that these sites do not necessarily correspond to the presence of bound water molecules. In fact, individual water molecules may repeatedly exchange within the cavity volume yet occupy on average these water sites. Four major conclusions emerge. First, it seems misleading to interpret the conformation of protein loop regions in terms of single dominant structures. Second, our simulations support the general picture of Pro 190 cis-trans isomerization as a determinant of the loop-opening mechanism. Third, receptor flexibility is fundamental for ligand binding and molecular recognition, and our results suggest its importance for the docking of small compounds to the artificial cavity. Fourth, after validation against the available experimental data, molecular dynamics simulations can be used to characterize the dynamics and exchange of water molecules and ions, providing atomic level and time-dependent information otherwise inaccessible to experiments.

Comparative MD analysis of the stability of transthyretin providing insight into the fibrillation mechanism

Proteins can misfold and aggregate, which is believed to be the cause of a variety of diseases, affecting very diverse organs in the body. Many questions about the nature of aggregation and the proteins that are involved in these events are still left unanswered. One of the proteins that is known to form amyloids is transthyretin (TTR), the secondary transporter of thyroxine, and transporter of retinol-binding protein. Several experimental results have helped to explain this aberrant behavior of TTR; however, structural insights of the amyloidgenic process are still lacking. Therefore, we have used all-atom MD simulation and free energy calculations to study the initial phase of this process. We have calculated the free energy changes of the initial tetramer dissociation under different conditions and in the presence of thyroxine. We show that tetramer formation is indeed only thermodynamically favorable in neutral pH conditions. We find that binding of two thyroxine molecules stabilizes the complex, and that this occurs with negative cooperativity. In addition to the energetic calculations, we have also investigated the dominant motions of the TTR and found that only the dimeric form of the protein could undergo the initial fibril formation.

Insight into the role of hydration on protein dynamics

The potential energy surface of a protein is rough. This intrinsic energetic roughness affects diffusion, and hence the kinetics. The dynamics of a system undergoing Brownian motion on this surface in an implicit continuum solvent simulation can be tuned via the frictional drag or collision frequency to be comparable to that of experiments or explicit solvent simulations. We show that the kinetic rate constant for a local rotational isomerization in stochastic simulations with continuum solvent and a collision frequency of 2 ps(-1) is about 10(4) times faster than that in explicit water and experiments. A further increase in the collision frequency to 60 ps(-1) slows down the dynamics, but does not fully compensate for the lack of explicit water. We also show that the addition of explicit water does not only slow down the dynamics by increasing the frictional drag, but also increases the local energetic roughness of the energy landscape by as much as 1.0 kcal/mol.

Peptide insertion, positioning, and stabilization in a membrane: insight from an all-atom molecular dynamics simulation

Peptide insertion, positioning, and stabilization in a model membrane are probed via an all-atom molecular dynamics (MD) simulation. One peptide (WL5) is simulated in each leaflet of a solvated dimyristoylglycero-3-phosphate (DMPC) membrane. Within the first 5 ns, the peptides spontaneously insert into the membrane and then stabilize during the remaining 70 ns of simulation time. In both leaflets, the peptides localize to the membrane interface, and this localization is attributed to the formation of peptide-lipid hydrogen bonds. We show that the single tryptophan residue in each peptide contributes significantly to these hydrogen bonds; specifically, the nitrogen heteroatom of the indole ring plays a critical role. The tilt angles of the indole rings relative to the membrane normal in the upper and lower leaflets are approximately 26 degrees and 54 degrees , respectively. The tilt angles of the entire peptide chain are 62 degrees and 74 degrees . The membrane induces conformations of the peptide that are characteristic of beta-sheets, and the peptide enhances the lipid ordering in the membrane. Finally, the diffusion rate of the peptides in the membrane plane is calculated (based on experimental peptide concentrations) to be approximately 6 A(2)/ns, thus suggesting a 500 ns time scale for intermolecular interactions.

Calculation of the Maxwell stress tensor and the Poisson-Boltzmann force on a solvated molecular surface using hypersingular boundary integrals

The electrostatic interaction among molecules solvated in ionic solution is governed by the Poisson-Boltzmann equation (PBE). Here the hypersingular integral technique is used in a boundary element method (BEM) for the three-dimensional (3D) linear PBE to calculate the Maxwell stress tensor on the solvated molecular surface, and then the PB forces and torques can be obtained from the stress tensor. Compared with the variational method (also in a BEM frame) that we proposed recently, this method provides an even more efficient way to calculate the full intermolecular electrostatic interaction force, especially for macromolecular systems. Thus, it may be more suitable for the application of Brownian dynamics methods to study the dynamics of protein/protein docking as well as the assembly of large 3D architectures involving many diffusing subunits. The method has been tested on two simple cases to demonstrate its reliability and efficiency, and also compared with our previous variational method used in BEM.

Nanosecond-timescale conformational dynamics of the human alpha7 nicotinic acetylcholine receptor

We explore the conformational dynamics of a homology model of the human alpha7 nicotinic acetylcholine receptor using molecular dynamics simulation and analyses of root mean-square fluctuations, block partitioning of segmental motion, and principal component analysis. The results reveal flexible regions and concerted global motions of the subunits encompassing extracellular and transmembrane domains of the subunits. The most relevant motions comprise a bending, hinged at the beta10-M1 region, accompanied by concerted tilting of the M2 helices that widens the intracellular end of the channel. Despite the nanosecond timescale, the observations suggest that tilting of the M2 helices may initiate opening of the pore. The results also reveal direct coupling between a twisting motion of the extracellular domain and dynamic changes of M2. Covariance analysis of interresidue motions shows that this coupling arises through a network of residues within the Cys and M2-M3 loops where Phe135 is stabilized within a hydrophobic pocket formed by Leu270 and Ile271. The resulting concerted motion causes a downward shift of the M2 helices that disrupts a hydrophobic girdle formed by 9' and 13' residues.