Implicit solvation models are popular alternatives to explicit solvent methods due to their ability to "pre-average" solvent behavior and thus reduce the need for computationally-expensive sampling. Previously, we have demonstrated that Poisson-Boltzmann models for polar solvation and integral-based models for nonpolar solvation can reproduce explicit solvation forces in a low-charge density protein system. In the present work, we examine the ability of these continuum models to describe solvation forces at the surface of a RNA hairpin. While these models do not completely describe all of the details of solvent behavior at this highly-charged biomolecular interface, they do provide a reasonable description of average solvation forces and therefore show significant promise for developing more robust implicit descriptions of solvent around nucleic acid systems for use in biomolecular simulation and modeling. Additionally, we observe fairly good transferability in the nonpolar model parameters optimized for protein systems, suggesting its robustness for modeling general nonpolar solvation phenomena in biomolecular systems.
Link:
http://dx.doi.org/10.1039/b807384h
Digital object identifier:
10.1039/b807384h
E. coli NikR is a homotetrameric Ni2+- and DNA-binding protein that functions as a transcriptional repressor of the NikABCDE nickel permease. The protein is composed of 2 distinct domains. The Nterminal fifty amino acids of each chain forms part of the dimeric ribbon-helix-helix (RHH) domains, a wellstudied DNA-binding fold. The eighty-three residue C-terminal nickel-binding domain forms an ACT-fold and contains the tetrameric interface. In this study, we have utilized an equilibrium molecular dynamics (MD) simulation in order to explore the conformational dynamics of the NikR tetramer and determine important residue interactions within and between the RHH and ACT domains to gain insight into the effects of Ni on DNA-binding activity. The molecular simulation data was analyzed using two different correlation measures based on fluctuations in atomic position and non-covalent contacts, together with a clustering algorithm to define groups of residues with similar correlation patterns for both types of correlation measure. Based on these analyses, we have defined a series of residue interrelationships that describe an allosteric communication pathway between the Ni2+ and DNA binding sites, which are separated by 40 A. Several of the residues identified by our analyses have been previously shown experimentally to be important for NikR function. An additional subset of the identified residues structurally connects the experimentally implicated residues and may help coordinate the allosteric communication between the ACT and RHH domains.
Link:
http://dx.doi.org/10.1016/j.jmb.2008.03.010
Digital object identifier:
10.1016/j.jmb.2008.03.010
PubMed ID:
18433769
Differences of ionic concentrations across lipid bilayers are some of the primary energetic driving forces for cellular electrophysiology. While macroscopic models of asymmetric ionic solutions are well-developed, their connection to ion, water, and lipid interactions at the atomic scale are much more poorly understood. In this study, we used molec ular dynamics to examine a system of two chambers of equal ionic strength, but differing amounts of NaCl and KCl, separated by a lipid bilayer. Our expectation was that the net electrostatic potential difference between the two chambers should be small or zero. Contrary to our expectation, a large potential difference (-70 mV) slowly evolved across the two water chambers over the course of our 172 ns simulation. This potential primarily originated from strong Na+ binding to the carbonyls of the phosphatidylcholine lipids. This ion adsorption also led to significant structural and mechanical changes in the lipid bilayer. We discuss this surprising result in the context of indirect experimental evidence for Na+ interaction with bilayers as well as potential caveats in current biomembrane simulation methodology, including force field parameters and finite size effects.
Link:
http://dx.doi.org/10.1529/biophysj.107.116335
Digital object identifier:
10.1529/biophysj.107.116335
PubMed ID:
18222999
The solvent reaction field potential of an uncharged protein immersed in Simple Point Charge / Extended (SPC/E) explicit solvent was computed over a series of molecular dynamics trajectories, in total 1560 ns of simulation time. A finite, positive potential of 13 to 24 k_B T/e_c (where T = 300K), 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 e_c/A^3, 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.
Link:
http://dx.doi.org/10.1063/1.2771171
Digital object identifier:
dx.doi.org/10.1063/1.2771171
PubMed ID:
17949217
This article describes the numerical solution of the time-dependent Smoluchowski equation to study diffusion in biomolecular systems. Specifically, finite element methods have been developed to calculate ligand binding rate constants for large biomolecules. The resulting software has been validated and applied to the mouse acetylcholinesterase monomer and several tetramers. Rates for inhibitor binding to mAChE were calculated at various ionic strengths with several different time steps. Calculated rates show very good agreement with experimental and the- oretical steady-state studies. Furthermore, these finite element methods require significantly fewer computational resources than existing particle-based Brownian dynamics methods and are robust for complicated geometries. The key finding of biological importance is that the rate accelerations of the monomeric and tetrameric mAChE that result from electrostatic steering are preserved under the non-steady- state conditions that are expected to occur in physiological circumstances.
Link:
http://dx.doi.org/10.1529/biophysj.106.102533
Digital object identifier:
10.1529/biophysj.106.102533
PubMed ID:
17307827
Real-world observable physical and chemical characteristics are increasingly being calculated from the 3D structures of biomolecules. Methods for calculating pKa values, binding constants of ligands, changes in protein stability are readily available, but often the limiting step in computational biology is the conversion of PDB structures into formats ready for use with biomolecular simulation software. The continued sophistication and integration of biomolecular simulation methods for systems- and genome-wide studies requires a fast, robust, physically realistic and standardized protocol for preparing macromolecular structures for biophysical algorithms. As described previously, the PDB2PQR web server addresses this need for electrostatic field calculations (Dolinsky et al, NAR, 2004). Here we report the significantly-expanded PDB2PQR that includes the following features: robust standalone command line support, improved pKa estimation via the PROPKA framework, ligand parameterization via PEOE_PB charge methodology, expanded set of force fields and easily-incorporated user-defined parameters via XML input files, and improvement of atom addition and optimization code. These features are available through a new web interface (http://pdb2pqr.sourceforge.net/) which offers users a wide range of options for PDB file conversion, modification, and parameterization.
Link:
http://dx.doi.org/10.1093/nar/gkm276
Digital object identifier:
10.1093/nar/gkm276
PubMed ID:
17488841
PubMed Central (free preprint) ID:
PMC1933214
Modeling the change in the electrostatics of organic molecules upon moving from vacuum into solvent, due to polarization, has long been an interesting problem. In vacuum, experimental values for the dipole moments and polarizabilities of small, rigid molecules are known to high accuracy; however, it has generally been difficult to determine these quantities for a polar molecule in water. A theoretical approach introduced by Onsager used vacuum properties of small molecules, including polarizability, dipole moment and size, to predict experimentally known permittivities of neat liquids via the Poisson equation. Since this important advance in understanding the condensed phase, a large number of computational methods have been developed to study solutes embedded in a continuum via numerical solutions to the Poisson- Boltzmann equation (PBE). Only recently have the classical force fields used for studying biomolecules begun to include explicit polarization in their functional forms. Here we describe the theory underlying a newly developed Polarizable Multipole Poisson-Boltzmann (PMPB) continuum electrostatics model, which builds on the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field. As an application of the PMPB methodology, results are presented for several small folded proteins studied by molecular dynamics in explicit water as well as embedded in the PMPB continuum. The dipole moment of each protein increased on average by a factor of 1.27 in explicit water and 1.26 in continuum solvent. The essentially identical electrostatic response in both models suggests that PMPB electrostatics offers an efficient alternative to sampling explicit solvent molecules for a variety of interesting applications, including binding energies, conformational analysis, and pKa prediction. Introduction of 150 mM salt lowered the electrostatic solvation energy between 2-13 kcal/mole, depending on the formal charge of the protein, but had only a small influence on dipole moments.
Link:
http://dx.doi.org/10.1063/1.2714528
Digital object identifier:
10.1063/1.2714528
PubMed ID:
17411115
PubMed Central (free preprint) ID:
PMC2430168
Accurate implicit solvent models require parameters that have been optimized in a system- and/or atom-specific manner based on experimental data or more rigorous explicit solvent simulations. Models based on the Poisson or Poisson-Boltzmann equation are particularly sensitive to the nature and location of the boundary which separates the low dielectric solute from the high dielectric solvent. Here we present a novel method for optimizing the solute radii, which define the dielectric boundary, based on forces and energies from explicit solvent simulations. We use this method to optimize radii for protein systems defined by AMBER ff99 partial charges and a spline-smoothed solute surface. The spline-smoothed surface is an atom-centered dielectric function that enables stable and efficient force calculations. We explore the relative performance of radii optimized with forces alone and those optimized with forces and energies. We show that our radii reproduce the explicit solvent forces and energies more accurately than four other parameter sets commonly used in conjunction with the AMBER force field, each of which has been appropriately scaled for spline-smoothed surfaces. Finally, we demonstrate that spline-smoothed surfaces show surprising accuracy for small, compact systems, but may have limitations for highly-solvated protein systems. The optimization method presented here is efficient and applicable to any system with explicit solvent parameters. It can be used to determine the optimal continuum parameters when experimental solvation energies are unavailable and the computational costs of explicit solvent charging free energies are prohibitive.
Link:
http://dx.doi.org/10.1021/ct600216k
Digital object identifier:
10.1021/ct600216k
Electrostatic properties of cowpea chlorotic mottle virus (CCMV) and cucumber mosaic virus (CMV) were investigated using numerical solutions to the Poisson-Boltzmann equation. Experimentally, it has been shown that CCMV particles swell in the absence of divalent cations when the pH is raised from 5 to 7. CMV, although structurally homologous, does not undergo this transition. An analysis of the calculated electrostatic potential confirms that a strong electrostatic repulsion at the calcium binding sites in the CCMV capsid is most likely the driving force for the capsid swelling process during the release of calcium. The binding interaction between the encapsulated genome material (RNA) inside of the capsid and the inner capsid shell is weakened during the swelling transition. This probably aids in the RNA release process, but it is unlikely that the RNA is released through capsid openings due to unfavorable electrostatic interaction between the RNA and capsid inner shell residues at these openings. Calculations of the calcium binding energies show that Ca2+ can bind both to the native and swollen forms of the CCMV virion. Favorable binding to the swollen form suggests that Ca2+ ions can induce the capsid contraction and stabilize the native form.
Link:
http://dx.doi.org/10.1002/bip.20409
Digital object identifier:
10.1002/bip.20409
PubMed ID:
16278831
PubMed Central (free preprint) ID:
PMC2440512
Continuum solvation models provide appealing alternatives to explicit solvent methods due to their ability to reproduce solvation effects while alleviating the need for expensive sampling. Our previous work has demonstrated that Poisson-Boltzmann methods are capable of faithfully reproducing polar explicit solvent forces for dilute protein systems; however, the popular solvent-accessible surface area (SASA) model was shown to be incapable of accurately describing nonpolar solvation forces at atomic length scales. Therefore, alternate continuum methods are neeeded to reproduce nonpolar interactions at the atomic scale. In the present work, we address this issue by supplementing the SASA model with additional volume and dispersion integral terms suggested by scaled particle models and Weeks-Chandler-Andersen theory, respectively. This more complete nonpolar implicit solvent model shows very good agreement with explicit solvent results and suggests that, although often overlooked, the inclusion of appropriate dispersion and volume terms are essential for an accurate implicit solvent description of atomic-scale nonpolar forces.
Link:
http://dx.doi.org/10.1073/pnas.0600118103
Digital object identifier:
10.1073/pnas.0600118103
PubMed ID:
16709675
PubMed Central (free preprint) ID:
PMC1482494
The equilibrium binding of E. coli RecBC and RecBCD helicases to duplex DNA ends containing varying lengths of polyethylene glycol (PEG) spacers within pre-formed 3'-single-stranded (ss) DNA ((dT)_n) tails were studied. These studies were designed to test a previous proposal that the 3'-(dT)_n tail can be looped out upon binding RecBC and RecBCD for 3'-ssDNA tails with n \geq 6 nucleotides. Equilibrium binding of protein to unlabeled DNA substrates with ends containing PEG-substituted 3'-ssDNA tails was examined by competition with a Cy3-labeled reference DNA which undergoes a Cy3 fluorescence enhancement upon protein binding. We find that the binding affinities of both RecBC and RecBCD for a DNA end are unaffected upon substituting PEG for the ssDNA between the sixth and the final two nucleotides of the 3'-(dT)_n tail. However, placing PEG at the end of the 3'-(dT)_n tail increases the binding affinities to their maximum values (i.e. the same as binding constants for RecBC or RecBCD to a DNA end with only a 3'-(dT)_6 tail). Equilibrium binding studies of a RecBC mutant containing a nuclease domain deletion, RecB^{\Delta nuc}C^1 suggest that looping of the 3'-tail (when n \geq 6 nucleotides) occurs even in the absence of the RecB nuclease domain, the nuclease domain stabilizes such loop formation. Computer modeling of the RecBCD-DNA complexes suggests that the loop in the 3'-ssDNA tail may form at the RecB/RecC interface. Based on these results we suggest a model for how a loop in the 3'-ssDNA tail might form upon encounter of a "Chi" recognition sequence during unwinding of DNA by the RecBCD helicase.
Link:
http://dx.doi.org/10.1016/j.jmb.2006.07.016
Digital object identifier:
10.1016/j.jmb.2006.07.016
PubMed ID:
16901504
In this paper we present a method for the multi-resolution comparison of biomolecular electrostatic potentials without the need for global structural alignment of the biomolecules. The underlying computational geometry algorithm uses multi-resolution attributed contour trees (MACTs) to compare the topological features of volumetric scalar fields. We apply the MACTs to compute electrostatic similarity metrics for a large set of protein chains with varying degrees of sequence, structure, and function similarity. For calibration, we also compute similarity metrics for these chains by a more traditional approach based upon 3D structural alignment and analysis of Carbo similarity indices. Moreover, because the MACT approach does not rely upon pairwise structural alignment, its accuracy and efficiency may make it particularly well-suited to large-scale, structural genomics-type efforts. The MACT method discriminates between protein chains at a level comparable to the Carbo similarity index method; i.e., it is able to accurately cluster proteins into functionally-relevant groups which demonstrate strong dependence on ligand binding sitesw. The results of the analyses are available from the linked web databases http://ccvweb.cres.utexas.edu/MolSignature/ and http://agave.wustl.edu/similarity/. The MACT analysis tools are available as part of the public domain library of the Topological Analysis and Quantitative Tools (TAQT) from the Center of Computational Visualization, at the University of Texas at Austin (http://ccvweb.csres.utexas.edu/software). The Carbo software is available for download with the open-source APBS software package at http://apbs.sf.net/.
Link:
http://dx.doi.org/10.1137/050647670
Digital object identifier:
10.1137/050647670
The first example of the application of reorientational eigenmode dynamics (RED) to RNA is shown here for the small and floppy Iron Responsive Element (IRE) RNA hairpin. Order parameters calculated for bases and riboses from a 12 ns molecular dynamics trajectory are compared to experimentally determined order parameters from 13C-1H NMR relaxation experiments, and shown to be in qualitative agreement. Given the small size of the IRE hairpin and its very flexible loop, isotropic RED (iRED) was also used to analyze the trajectory in order to describe its dynamic motions. iRED analysis shows that the global and internal dynamics of the IRE are not rigorously separable, which will result in inaccurate experimental order parameters. In addition, the iRED analysis described the many correlated motions that comprise the dynamics of the IRE RNA. The combined use of NMR relaxation, RED, and iRED provide a uniquely detailed description of IRE RNA dynamics.
Link:
http://dx.doi.org/10.1007/s10858-005-7948-2
Digital object identifier:
10.1007/s10858-005-7948-2
PubMed ID:
16132819
Salicylate, an amphiphilic molecule and a popular member of non-steroidal anti-inflammatory drug family, is known to affect hearing through reduction of the electromechanical coupling in the outer hair cells of the ear. This reduction of electromotility by salicylate has been widely studied but the molecular mechanism of the phenomenon is still unknown. In this study, we investigated one aspect of salicylate's action; namely, the perturbation of electrical and mechanical membrane properties by salicylate in the absence of cytoskeletal or membrane-bound motor proteins such as prestin. In particular, we simulated the interaction of salicylate with a dipalmitoylphosphatidylcholine (DPPC) bilayer via atomically-detailed molecular dynamics simulations to observe the effect of salicylate on the microscopic and mesoscopic properties of the bilayer. The results demonstrate that salicylate interacts with the bilayer by associating at the water-DPPC interface in a nearly perpendicular orientation and penetrating more deeply into the bilayer than either sodium or chloride. This association has several affects on the membrane properties. First, binding of salicylate to the membrane displaces chloride from the bilayer-water interface. Second, salicylate influences the electrostatic potential and dielectric properties of the bilayer, with significant changes at the water-lipid bilayer interface. Third, salicylate association results in structural changes including decreased head group area per lipid and increased lipid tail order. However, salicylate does not significantly alter the mechanical properties of the DPPC bilayer; bulk compressibility, area compressibility, and bending modulus were only perturbed by small, statistically-insignificant amounts, by the presence of salicylate. The observations from these simulations are in qualitative agreement with experimental data and support the conclusion that salicylate influences the electrical but not the mechanical properties of DPPC membranes.
Link:
http://dx.doi.org/10.1021/bi0506829
Digital object identifier:
10.1021/bi0506829
PubMed ID:
16216066
PubMed Central (free preprint) ID:
PMC2435121
The tetramer is the most important form for acetylcholinesterase in physiological conditions, i.e., in the neuromuscular junction and the nervous system. It is important to study the diffusion of acetylcholine to the active sites of the tetrameric enzyme to understand the overall signal transduction process in these cellular components. Crystallographic studies revealed two different forms of tetramers, suggesting a flexible tetramer model for acetylcholinesterase. Using a recently developed finite element solver for the steady-state Smoluchowski equation, we have calculated the reaction rate for three mouse acetylcholinesterase tetramers using these two crystal structures and an intermediate structure as templates. Our results show that the reaction rates differ for different individual active sites in the compact tetramer crystal structure, and the rates are similar for different individual active sites in the other crystal structure and the intermediate structure. In the limit of zero salt, the reaction rates per active site for the tetramers are the same as that for the monomer, whereas at higher ionic strength, the rates per active site for the tetramers are ~67%-75% of the rate for the monomer. By analyzing the effect of electrostatic forces on ACh diffusion, we find that electrostatic forces play an even more important role for the tetramers than for the monomer. This study also shows that the finite element solver is well suited for solving the diffusion problem within complicated geometries.
Link:
http://dx.doi.org/10.1529/biophysj.104.053850
Digital object identifier:
10.1529/biophysj.104.053850
PubMed ID:
15626705
PubMed Central (free preprint) ID:
PMC1305222
Continuum solvation models, such as Poisson-Boltzmann and Generalized Born methods, have become increasingly popular tools for investigating the influence of electrostatics on biomolecular structure, energetics and dynamics. However, the use of such methods requires accurate and complete structural data as well as force field parameters such as atomic charges and radii. Unfortunately, the limiting step in continuum electrostatics calculations is often the addition of missing atomic coordinates to molecular structures from the Protein Data Bank and the assignment of parameters to biomolecular structures. To address this problem, we have developed the PDB2PQR web service (http://agave.wustl.edu/pdb2pqr/). This server automates many of the common tasks of preparing structures for continuum electrostatics calculations, including adding a limited number of missing heavy atoms to biomolecular structures, estimating titration states and protonating biomolecules in a manner consistent with favorable hydrogen bonding, assigning charge and radius parameters from a variety of force fields, and finally generating PQR output compatible with several popular computational biology packages. This service is intended to facilitate the setup and execution of electrostatics calculations for both experts and non-experts and thereby broaden the accessibility to the biological community of continuum electrostatics analyses of biomolecular systems.
Link:
http://tinyurl.com/4kcyc
Digital object identifier:
10.1093/nar/gkh381
PubMed ID:
15215472
PubMed Central (free preprint) ID:
PMC441519
Summary: SPrCY is a web-accessible database which provides comparison of structure prediction results for the Saccharomyces cerevisiae genome. This web service offers the ability to search, analyze and compare the yeast structural predictions from sequence-only (Superfamily, PDBAA BLAST and Pfam) and sequence-structure-based (SAM-T02, 3D-PSSM, mGenTHREADER) methods. Availability: The service is freely available via web at http://agave.wustl.edu/yeast/ Contact: baker@biochem.wustl.edu
Link:
http://dx.doi.org/10.1093/bioinformatics/bth223
Digital object identifier:
10.1093/bioinformatics/bth223
PubMed ID:
15059824
This article describes the development and implementation of algorithms to study diffusion in biomolecular systems using continuum mechanics equations. Specifically, finite element methods have been developed to solve the steady-state Smoluchowski equation to calculate ligand binding rate constants for large biomolecules. The resulting software has been validated and applied to mouse acetylcholinesterase. Rates for inhibitor binding to mAChE were calculated at various ionic strengths with several different reaction criteria. The calculated rates were compared with experimental data and show very good agreement when the correct reaction criterion is used. Additionally, these finite element methods require significantly less computational resources than existing particle-based Brownian dynamics methods.
Link:
http://www.biophysj.org/cgi/content/abstract/86/4/2017
PubMed ID:
15041644
PubMed Central (free preprint) ID:
PMC1304055
As described previously, continuum models, such as the Smoluchowski equation, offer a scalable framework for studying diffusion in biomolecular systems. This work presents new developments in the efficient solution of the continuum diffusion equation. Specifically, we present methods for adaptively refining finite element solutions of the Smoluchowski equation based on a posteriori error estimates. We also describe new, molecular-surface-based models, for diffusional reaction boundary criteria and compare results obtained from these models with the traditional spherical criteria. The new methods are validated by comparison of the calculated reaction rates with experimental values for wild-type and mutant forms of mouse acetylcholinesterase. The results show good agreement with experiment and help to define optimal reactive boundary conditions.
Link:
http://www.biophysj.org/cgi/content/abstract/87/3/1558
PubMed ID:
15345536
PubMed Central (free preprint) ID:
PMC1304562
In this work we present a new software package (ISIM), which represents a flexible, computational tool for simulations of electrolyte solutions via a grand canonical Monte Carlo procedure (GCMC) with a specific capability of treating biomolecules in solution. The GCMC method provides a powerful tool for studying the ionic environments of highly charged macromolecules with attention to the atomic detail of both the solute and the mobile counterions. The ISIM software differs from previous schemes mainly by treating different ion types independently and offering a new parameterization procedure for calibrating excess chemical potentials and bulk ion concentrations. Additionally, ISIM leverages the APBS software package to provide accurate descriptions of the biomolecular electrostatic potential through the efficient solution of Poisson's equation. ISIM has been validated on a variety of test systems; we successfully reproduce elementary properties of electrolyte solutions as well as theoretical and experimental results for challenging test systems like Calmodulin and DNA.
Link:
http://tinyurl.com/5986l
Digital object identifier:
10.1080/08927020310001597862
Continuum electrostatics methods have become increasingly popular due to their ability to provide approximate descriptions of solvation energies and forces without expensive sampling required by explicit solvent models. In particular, the Poisson-Boltzmann equation (PBE) provides electrostatic potentials, solvation energies, and forces by modeling the solvent as a featureless, dielectric material, and the mobile ions as a continuous distribution of charge. Polar solvation forces and energies obtained from the PBE are often supplemented with simple solvent-accessible surface area (SASA) models of nonpolar solvation. Given the recent development of methods that enable the use of PBE and SASA forces in molecular dynamics simulations, it is important to determine the ability of these implicit solvent models to accurately reproduce the solvation forces of more detailed explicit solvent simulations. In this article, we compare PBE and SASA solvation forces with explicit solvent forces for several snapshots from eight trajectories of static conformations of intestinal fatty acid binding protein. The results from this comparison show that current implementations of the PBE are capable of generating polar solvation forces that correlate well with explicit solvent forces but systematically overestimate the magnitude of the interaction. However, SASA-based nonpolar forces are found to have no significant correlation with nonpolar explicit solvent forces. Nevertheless, due to the small magnitude of the nonpolar forces in the current system, a good correlation is still obtained for total solvation forces. The good correlation of implicit solvent forces with more detailed explicit solvent models is encouraging and implies that the systematic errors identified in these models could be corrected by appropriate parameterization of the force fields.
Link:
http://dx.doi.org/10.1002/jcc.20089
Digital object identifier:
dx.doi.org/10.1002/jcc.20089
PubMed ID:
15264256
Although many viruses have been crystallized and the protein capsid structures have been determined by x-ray crystallography, the nucleic acids often cannot be resolved. This is especially true for RNA viruses. The lack of information about the conformation of DNA/RNA greatly hinders our understanding of the assembly mechanism of various viruses. Here we combine a coarse-grain model and a Monte Carlo method to simulate the distribution of viral RNA inside the capsid of cowpea chlorotic mottle virus. Our results show that there is very strong interaction between the N-terminal residues of the capsid proteins, which are highly positive charged, and the viral RNA. Without these residues, the binding energy disfavors the binding of RNA by the capsid. The RNA forms a shell close to the capsid with the highest densities associated with the capsid dimers. These high-density regions are connected to each other in the shape of a continuous net of triangles. The overall icosahedral shape of the net overlaps with the capsid subunit icosahedral organization. Medium density of RNA is found under the pentamers of the capsid. These findings are consistent with experimental observations.
Link:
http://dx.doi.org/10.1002/bip.20120
Digital object identifier:
10.1002/bip.20120
PubMed ID:
15386271
PubMed Central (free preprint) ID:
PMC2426774
Microtubules are cylindrical polymers found in every eukaryotic cell. They have a unique helical structure that has implications at both the cellular level, in terms of the functions they perform, and at the multicellular level, such as determining the leftright symmetry in plants. Through the combination of an atomically detailed model for a microtubule and large-scale computational techniques for computing electrostatic interactions, we are able to explain the observed microtubule structure. On the basis of the lateral interactions between protofilaments, we have determined that B lattice is the most favorable configuration. Further, we find that these lateral bonds are significantly weaker than the longitudinal bonds along protofilaments. This explains observations of microtubule disassembly and may serve as another step toward understanding the basis for dynamic instability.
Link:
http://www.proteinscience.org/cgi/content/abstract/12/10/2257
Digital object identifier:
10.1110/ps.03187503
PubMed ID:
14500883
PubMed Central (free preprint) ID:
PMC2366909
A robust infrastructure for solving time-dependent diffusion using the finite element package FEtk has been developed to simulate synaptic transmission in a neuromuscular junction with realistic postsynaptic folds. Simplified rectilinear synapse models serve as benchmarks in initial numerical studies of how variations in geometry and kinetics relate to endplate currents associated with fast-twitch, slow-twitch, and dystrophic muscles. The flexibility and scalability of FEtk affords increasingly realistic and complex models that can be formed in concert with expanding experimental understanding from electron microscopy. Ultimately, such models may provide useful insight on the functional implications of controlled changes in processes, suggesting therapies for neuromuscular diseases.
Link:
http://www.biophysj.org/cgi/content/abstract/84/4/2234
PubMed ID:
12668432
PubMed Central (free preprint) ID:
PMC1302790
Conformations of a zwitterionic bilayer were sampled from a molecular dynamics simulation and their electrostatic properties analyzed by solution of the Poisson equation. These traditionally implicit electrostatic calculations were performed in the presence of varying amounts of explicit solvent to assess the magnitude of error introduced by a uniform dielectric description of water surrounding the bilayer. It was observed that membrane dipole potential calculations in the presence of explicit water were significantly different than wholly implicit solvent calculations with the calculated dipole potential converging to a reasonable value when four or more hydration layers were included explicitly.
Link:
http://www.biophysj.org/cgi/content/abstract/83/3/1374
PubMed ID:
12202363
PubMed Central (free preprint) ID:
PMC1302236
The binding of paromomycin and similar antibiotics to the small (30S) ribosomal subunit has been studied using continuum electrostatics methods. Crystallographic information from a complex of paromomycin with the 30S subunit was used as a framework to develop structures of similar antibiotics in the same ribosomal binding site. Total binding energies were calculated from electrostatic properties obtained by solution of the Poisson-Boltzmann equation combined with a surface area-dependent apolar term. These computed results showed good correlation with experimental data. Additionally, calculation of the ribosomal electrostatic potential in the paromomycin binding site provided insight into the electrostatic mechanisms for aminoglycoside binding and clues for the rational design of more effective antibiotics.
Link:
http://tinyurl.com/48l3bp
Digital object identifier:
10.1021/ja016830+
PubMed ID:
11841313
By using new methods for the parallel solution of elliptic partial differential equations, the teraflops computing power of massively parallel computers can be leveraged to perform electrostatic calculations on large biological systems. This paper describes the adaptive multilevel finite element solution of the Poisson-Boltzmann equation for a microtubule on the NPACI Blue Horizon -- a massively parallel IBM RS/6000 SP with eight POWER3 SMP nodes. The microtubule system is 40 nm in length and 24 nm in diameters, consists of roughly 600000 atoms, and has a net charge of -1800 e. Poisson-Boltzmann calculations are performed for several processor configurations, and the algorithm used shows excellent parallel scaling.
Link:
http://dx.doi.org/10.1147/rd.453.0427
Digital object identifier:
10.1147/rd.453.0427
Evaluation of the electrostatic properties of biomolecules has become a standard practice in molecular biophysics. Foremost among the models used to elucidate the electrostatic potential is the Poisson-Boltzmann equation; however, existing methods for solving this equation have limited the scope of accurate electrostatic calculations to relatively small biomolecular systems. Here we present the application of numerical methods to enable the trivially parallel solution of the Poisson-Boltzmann equation for supramolecular structures that are orders of magnitude larger in size. As a demonstration of this methodology, electrostatic potentials have been calculated for large microtubule and ribosome structures. The results point to the likely role of electrostatics in a variety of activities of these structures.
Link:
http://dx.doi.org/10.1073/pnas.181342398
Digital object identifier:
10.1073/pnas.181342398
PubMed ID:
11517324
PubMed Central (free preprint) ID:
PMC56910
This article is the first of two articles on the adaptive multilevel finite element treatment of the nonlinear Poisson-Boltzmann equation (PBE), a nonlinear eliptic equation arising in biomolecular modeling. Fast and accurate numerical solution of the PBE is usually difficult to accomplish, due to the presence of discontinuous coefficients, delta functions, three spatial dimensions, unbounded domain, and rapid (exponential) nonlinearity. In this first article, we explain how adaptive multilevel finite element methods can be used to obtain extremely accurate solutions to the PBE with very modest computational resources, and we present some illustrative examples using two well-known test problems. The PBE is first discretized with piece-wise linear finite elements over a very coarse simplex triangulation of the domain. The resulting nonlinear algebraic equations are solved with global inexact Newton methods, which we have described in an article appearing previously in this journal. A posteriori error estimates are then computed from this discrete solution, which then drives a simplex subdivision algorithm for performing adaptive mesh refinement. The discretize-solve-estimate-refine procedure is then repeated, until a nearly uniform solution quality is obtained. The sequence of unstructured meshes is used to apply multilevel methods in conjunction with global inexact Newton methods, so that the cost of solving the nonlinear algebraic equations at each step approaches optimal O(N) linear complexity. All of the numerical procedures are implemented in MANIFOLD CODE (MC), a computer program designed and built by the first author over several years at Caltech and UC San Diego. MC is designed to solve a very general class of nonlinear elliptic equations on complicated domains in two and three dimensions. We describe some of the key features of MC, and give a detailed analysis of its performance for two model PBE problems, with comparisons to the alternative methods. It is shown that the best available uniform mesh-based finite difference or box-method algorithms, including multilevel methods, require substantially more time to reach a target PBE solution accuracy than the adaptive multilevel methods in MC. In the second article, we develop an error estimator based on geometric solvent accessibility, and present a series of detailed numerical experiments for several complex biomolecules.
Link:
http://tinyurl.com/3n92c
Digital object identifier:
10.1002/1096-987X(20001130)21:15<1343::AID-JCC2>3.0.CO;2-K
We apply the adaptive multilevel finite element techniques (Holst, Baker, and Wang [21]) to the nonlinear Poisson-Boltzmann equation (PBE) in the context of biomolecules. Fast and accurate numerical solution of the PBE in this setting is usually difficult to accomplish due to presence of discontinuous coefficients, delta functions, three spatial dimensions, unbounded domains, and rapid (exponential) nonlinearity. However, these adaptive techniques have shown substantial improvement in solution time over conventional uniform-mesh finite difference methods. One important aspect of the adaptive multilevel finite element method is the robust a posteriori error estimators necessary to drive the adaptive refinement routines. This article discusses the choice of solvent accessibility for a posteriori error estimation of PBE solutions and the implementation of such routines in the Adaptive Poisson-Boltzmann Solver (APBS) software package based on the Manifold Code (MC) libraries. Results are shown for the application of this method to several biomolecular systems.
Link:
http://tinyurl.com/3uzq4
Digital object identifier:
10.1002/1096-987X(20001130)21:15<1319::AID-JCC1>3.0.CO;2-8
The quaternary ammonium binding locus in the active site of mammalian acetylcholinesterase is subtended by the side chains of Trp86, Tyr133, Glu202, and Tyr337. Linear free-energy relationships define the interactions involved in molecular recognition by mouse acetylcholinesterase of the quaternary ammonium moiety of ligands. For substrates CH3C(=O)XCH2CH2Y [X = O, Y = CHMe2, or CH2CH3; X = S, Y = H, NH+Me2, or N+Me3 ] and trifluoroacetophenone transition state analogue inhibitors m-YC6H4C(=O)CF3 [Y = H, Me, Et, iPr, tBu, CF3, NH2, NO2, NMe2, or N+Me3], log(kcat/Km) and pKi depend linearly on the molar refractivity, but not the hydrophobicity, of the substituents Y. These correlations indicate that, in the acylation stage of catalysis, interactions in the quaternary ammonium binding locus stabilize the tetrahedral intermediate (as modeled by transition state analogue affinity) by (5 × 105)-fold (ddGTI = -32.5 kJ mol-1) and the transition state by (2 × 104)-fold (ddGt = -24.5 kJ mol-1). To evaluate the contribution of cation- interactions, Trp86 was converted into Tyr, Phe, and Ala by site-specific mutagenesis. For this set of enzymes, a linear free-energy relationship is observed between the pKi values for inhibitions by the respective neutral and cationic transition state analogue inhibitors, m-tert-butyltrifluoroacetophenone and m-(N,N,N-trimethylammonio)trifluoroacetophenone, which indicates that the free energy released on interaction of the quaternary ammonium moiety with Trp86 arises about equally from cation- and charge-independent interactions.
Link:
http://dx.doi.org/10.1021/ja9933588
Digital object identifier:
10.1021/ja9933588
Recently, a new mechanism for reaction selectivity, arising from conformational gating of the reactions, has been reported in the acetylcholinesterase system. Fluctuations in the enzyme are thought to greatly slow the access of molecules larger than the normal substrate to the active-site region. By assuming the gate fluctuations occur as a Brownian process in a harmonic well, it is possible to approximate the reaction rates for various limiting cases of substrate size. However, it is not possible to simplify the rates into a ratio which is equivalent to the Boltzmann distribution of states for the gate fluctuations.
Link:
http://dx.doi.org/10.1021/jp984151o
Digital object identifier:
10.1021/jp984151o
Fasciculin-2 (FAS2) is a potent protein inhibitor of the hydrolytic enzyme acetylcholinesterase. A 2-ns isobaric-isothermal ensemble molecular dynamics simulation of this toxin was performed to examine the dynamic structural properties which may play a role in this inhibition. Conformational fluctuations of the FAS2 protein were examined by a variety of techniques to identify flexible residues and determine their characteristic motion. The tips of the toxin finger loops and the turn connecting loops I and II were found to fluctuate, while the rest of the protein remained fairly rigid throughout the simulation. Finally, the structural fluctuations were compared to NMR data of fluctuations on a similar timescale in a related three-finger toxin. The molecular dynamics results were in good qualitative agreement with the experimental measurements.
Link:
http://tinyurl.com/3vtyh
Digital object identifier:
10.1002/1096-987X(20001130)21:15<1319::AID-JCC1>3.0.CO;2-8
PubMed ID:
10450086
In order to reduce computational effort and to allow for the use of periodic boundary conditions, electrostatic interactions in explicit solvent simulations of molecular systems do not obey Coulomb's law. Instead, a number of "effective potentials" have been proposed, including truncated Coulomb, shifted, switched, reaction-field corrected, or Ewald potentials. The present study compares the performance of these schemes in the context of ionic solvation. To this purpose, a generalized form of the Born continuum model for ion solvation is developed, where ionsolvent and solventsolvent interactions are determined by these effective potentials instead of Coulomb's law. An integral equation is formulated for calculating the polarization around a spherical ion from which the solvation free energy can be extracted. Comparison of the polarizations and free energies calculated for specific effective potentials and the exact Born result permits an assessment of the accuracy of these different schemes. Additionally, the present formalism can be used to develop corrections to the ionic solvation free energies calculated by molecular simulations implementing such effective potentials. Finally, an arbitrary effective potential is optimized to reproduce the Born polarization.
Link:
http://dx.doi.org/10.1063/1.479013
Digital object identifier:
10.1063/1.479013
The role of electrostatics in the function of acetylcholinesterase (AChE) has been investigated by both theoretical and experimental approaches. Second-order rate constants (kE = k(cat)/Km) for acetylthiocholine (ATCh) turnover have been measured as a function of ionic strength of the reaction medium for wild-type and mutant AChEs. Also, binding and dissociation rate constants have been measured as a function of ionic strength for the respective charged and neutral transition state analog inhibitors m-(N,N,N-trimethylammonio)trifluoroacetophenone (TMTFA) and m-(t-butyl)trifluoroacetophenone (TBTFA). Linear free-energy correlations between catalytic rate constants and inhibition constants indicate that kE for ATCh turnover is rate limited by terminal binding events. Comparison of binding rate constants for TMTFA and TBTFA attests to the sizable electrostatic discrimination of AChE. Free energy profiles for cationic ligand release from the active sites of wild-type and mutant AChEs have been calculated via a model that utilizes the structure of T. californica AChE, a spherical ligand, and energy terms that account for electrostatic and van der Waals interactions and chemical potential. These calculations indicate that EA and EI complexes are not bound with respect to electrostatic interactions, which obviates the need for a 'back door' for cationic ligand release. Moreover, the computed energy barriers for ligand release give linear free-energy correlations with log(kE) for substrate turnover, which supports the general correctness of the computational model.
Link:
http://dx.doi.org/10.1016/S0009-2797(99)00018-6
Digital object identifier:
10.1016/S0009-2797(99)00018-6
PubMed ID:
10421443
Interactions of mammalian pancreatic cholesterol esterases from pig and rat with a family of aryl carbamates CnH2n+1NHCOOAr [n = 4-9; Ar = phenyl, p-X-phenyl (X = acetamido, bromo, fluoro, nitro, trifluoromethyl), 2-naphthyl, 2-tetrahydronaphthyl, estronyl] have been investigated, with an aim of delineating the ligand structural features which lead to effective molecular recognition by the active site of the enzyme. These carbamates inhibit the catalytic activity of CEase by rapid carbamylation of the active site, a process that shows saturation kinetics. Subsequent slow decarbamylation usually leads to full restoration of activity, and therefore aryl carbamates are transient inhibitors, or pseudo-substrates, of CEase. Structural variation of carbamate inhibitors allowed molecular recognition in the fatty acid binding and steroid binding loci of the extended active site to be probed, and the electronic nature of the carbamylation transition state to be characterized. Optimal inhibitory activity is observed when the length of the carbamyl function is n = 6 and n = 7 for porcine and rat cholesterol esterases, respectively, equivalent to eight- and nine-carbon fatty acyl chains. In contrast, inhibitory activity increases progressively as the partial molecular volume of the aromatic fragment increases. Hammett plots for p-substituted phenyl-N-hexyl carbamates indicate that the rate-determining step for carbamate inhibition is phenolate anion expulsion. Effects of the bile salt activator taurocholate on the kinetically resolved phases of the pseudo-substrate turnover of aryl carbamates were also studied. Taurocholate increases the affinity of the carbamate for the active site of cholesterol esterase in the reversible, noncovalent complex that precedes carbamylation and increases the rate constants of the serial carbamylation and decarbamylation steps. Structural variation of the N-alkyl chain and of the aryl fused-ring system provides an accounting of bile salt modulation of the fatty acid and steroid binding sites, respectively. In that pseudo-substrate turnover of aryl carbamates proceeds by a three-step mechanism that is analogous to that for rapid turnover of lipid ester substrates, these investigations illuminate details of ligand recognition by the extended active site of cholesterol esterase that are prominent determinants of the substrate specificity and catalytic power of the enzyme.
Link:
http://dx.doi.org/10.1021/bi961677v
Digital object identifier:
10.1021/bi961677v
PubMed ID:
8988009
An understanding of intermolecular interactions is essential for insight into how cells develop, operate, communicate, and control their activities. Such interactions include several components: contributions from linear, angular, and torsional forces in covalent bonds, van der waals forces, as well as electrostatics. Among the various components of molecular interactions, electrostatics are of special importance because of their long range and their influence on polar or charged molecules, including water, aqueous ions, and amino or nucleic acids, which are some of the primary components of living systems. Electrostatics, therefore, play important roles in determining the structure, motion, and function of a wide range of biological molecules. This chapter presents a brief overview of electrostatic interactions in cellular systems, with a particular focus on how computational tools can be used to investigate these types of interactions.
Link:
http://dx.doi.org/10.1016/S0091-679X(07)84026-X
Digital object identifier:
10.1016/S0091-679X(07)84026-X
PubMed ID:
17964951
PubMed Central (free preprint) ID:
PMC2423940
Recent developments in implicit solvent models may be compared in terms of accuracy and computational efficiency. Based on improvements in the accuracy of generalized Born methods and the speed of Poisson-Boltzmann solvers, it appears that the two techniques are converging to a point at which both will be suitable for simulating certain types of biomolecular systems over sizable time and length scales.
Link:
http://dx.doi.org/10.1016/j.sbi.2005.02.001
Digital object identifier:
10.1016/j.sbi.2005.02.001
PubMed ID:
15837170
Link:
http://dx.doi.org/10.1016/S0076-6879(04)83005-2
Digital object identifier:
10.1016/S0076-6879(04)83005-2
PubMed ID:
15063648