Continuum solvent model studies of the interactions of an anticonvulsant drug with a lipid bilayer

Valproic acid (VPA) is a short, branched fatty acid with broad-spectrum anticonvulsant activity. It has been suggested that VPA acts directly on the plasma membrane. We calculated the free energy of interaction of VPA with a model lipid bilayer using simulated annealing and the continuum solvent model. Our calculations indicate that VPA is likely to partition into the bilayer both in its neutral and charged forms, as expected from such an amphipathic molecule. The calculations also show that VPA may migrate (flip-flop) across the membrane; according to our (theoretical) study, the most likely flip-flop path at neutral pH involves protonation of VPA pending its insertion into the lipid bilayer and deprotonation upon departure from the other side of the bilayer. Recently, the flip-flop of long fatty acids across lipid bilayers was studied using fluorescence and NMR spectroscopies. However, the measured value of the flip-flop rate appears to depend on the method used in these studies. Our calculated value of the flip-flop rate constant, 20/s, agrees with some of these studies. The limitations of the model and the implications of the study for VPA and other fatty acids are discussed.     

A thermodynamic model for Nap1-histone interactions

The yeast nucleosome assembly protein 1 (yNap1) plays a role in chromatin maintenance by facilitating histone exchange as well as nucleosome assembly and disassembly. It has been suggested that yNap1 carries out these functions by regulating the concentration of free histones. Therefore, a quantitative understanding of yNap1-histone interactions also provides information on the thermodynamics of chromatin. We have developed quantitative methods to study the affinity of yNap1 for histones. We show that yNap1 binds H2A/H2B and H3/H4 histone complexes with low nm affinity, and that each yNap1 dimer binds two histone fold dimers. The yNap1 tails contribute synergistically to histone binding while the histone tails have a slightly repressive effect on binding. The (H3/H4)(2) tetramer binds DNA with higher affinity than it binds yNap1.     

Stability of an ion channel in lipid bilayers: implicit solvent model calculations with gramicidin

Gramicidin is a helical peptide, 15 residues in length, which dimerizes to form ion-conducting channels in lipid bilayers. Here we report calculations of its free energy of transfer from the aqueous phase into bilayers of different widths. The electrostatic and nonpolar contributions to the desolvation free energy were calculated using implicit solvent models, in which gramicidin was described in atomic detail and the hydrocarbon region of the membrane was described as a slab of hydrophobic medium embedded in water. The free energy penalties from the lipid perturbation and membrane deformation effects, and the entropy loss associated with gramicidin immobilization in the bilayer, were estimated from a statistical thermodynamic model of the bilayer. The calculations were carried out using two classes of experimentally observed conformations: a head-to-head dimer of two single-stranded (SS) beta-helices and a double-stranded (DS) intertwined double helix. The calculations showed that gramicidin is likely to partition into the bilayer in all of these conformations. However, the SS conformation was found to be significantly more stable than the DS in the bilayer, in agreement with most of the experimental data. We tested numerous transmembrane and surface orientations of gramicidin in bilayers of various widths. Our calculations indicate that the most favorable orientation is transmembrane, which is indeed to be expected from a channel-forming peptide. The calculations demonstrate that gramicidin insertion into the membrane is likely to involve a significant deformation of the bilayer to match the hydrophobic width of the peptide (22 A), again in good agreement with experimental data. Interestingly, deformation of the bilayer was induced by all of the gramicidin conformations.     

A fractional charge model for empirical calculations of peptide-water interactions.

The properties of an empirical model of interaction between a water molecule and polar groups of peptides or small peptides are explored. The H2O molecule is represented by a four-point charges distribution. In electron donor groups, a point charge is located on the axis of the lone pairs orbitals in order to introduce some directionality in hydrogen bonds. The effective potential is approximated by the sum of the coulombic interactions between point charges distribution and of a 6--12 atom-atom potential. The coefficients of this last potential are first adjusted by simulating the geometry of the water dimer. Equilibrium configurations of associated polar molecules and H2O predicted by the model are found to be in good agreement with those resulting from more sophisticated ab initio SCF calculations. Interactions between H2O and the side-chains of the cyclic dipeptide C(L-Thr-L-His) are then calculated. It is shown that internal bridging by water is an essential effect of the solvent. The experimental position of the H2O molecule is reproduced, stability of which depends also on intermolecular interactions.     

T-Pile--a package for thermodynamic calculations for biomolecules

Molecular dynamics and Monte Carlo, usually conducted in canonical ensemble, deliver a plethora of biomolecular conformations. Proper analysis of the simulation data is a crucial part of biophysical and bioinformatics studies. Sequence alignment problem can be also formulated in terms of Boltzmann distribution. Therefore tools for efficient analysis of canonical ensemble data become extremely valuable. T-Pile package, presented here provides a user-friendly implementation of most important algorithms such as multihistogram analysis and reweighting technique. The package can be used in studies of virtually any system governed by Boltzmann distribution. AVAILABILITY: T-Pile can be downloaded from: http://biocomp.chem.uw.edu.pl/services/tpile. These pages provide a comprehensive tutorial and documentation with illustrative examples of applications. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Structure and interactions of aggrecans: statistical thermodynamic approach

Weak polyelectrolytes tethered to cylindrical surfaces are investigated using a molecular theory. These polymers form a model system to describe the properties of aggrecan molecules, which is one of the main components of cartilage. We have studied the structural and thermodynamical properties of two interacting aggrecans with a molecular density functional theory that incorporates the acid-base equilibrium as well as the molecular properties: including conformations, size, shape, and charge distribution of all molecular species. The effect of acidity and salt concentration on the behavior is explored in detail. The repulsive interactions between two cylindrical-shaped aggrecans are strongly influenced by both the salt concentration and the pH. With increasing acidity, the polyelectrolytes of the aggrecan acquire charge and with decreasing salt concentration those charges become less screened. Consequently the interactions increase in size and range with increasing acidity and decreasing salt concentration. The size and range of the forces offers a possible explanation to the aggregation behavior of aggrecans and for their ability to resist compressive forces in cartilage. Likewise, the interdigitation of two aggrecan molecules is strongly affected by the salt concentration as well as the pH. With increasing pH, the number of charges increases, causing the repulsions between the polymers to increase, leading to a lower interdigitation of the two cylindrical polymer layers of the aggrecan molecules. The low interdigitation in charged polyelectrolytes layers provides an explanation for the good lubrication properties of polyelectrolyte layers in general and cartilage in particular.     

Continuum model of fibroblast-driven wound contraction: inflammation-mediation.

We propose a mathematical model to aid the understanding of how events in wound healing are orchestrated to result in wound contraction. Ultimately, a validated model could provide a predictive means for enhancing or mitigating contraction as is appropriate for managing a particular wound. The complex nature of wound healing and the lack of a modeling framework which can account for both the relevant cell biology and biomechanics are major reasons for the absence of models to date. Here we adapt a model originally proposed by Murray and co-workers to show how cell traction forces can result in spatial patterns of cell aggregates since it offers a framework for understanding how traction exerted by wound fibroblasts drives wound contraction. Since it is a continuum model based on conservation laws which reflect assumed cell and tissue properties, it is readily extended to account for emerging understanding of the cell biology of wound healing and its relationship to inflammation. We consider various sets of assumed properties, based on current knowledge, within a base model of dermal wound healing and compare predictions of the rate and extent of wound contraction to published experimental results.     

Radioimmunoassay of epitestosterone: methodology, thermodynamic aspects and applications

A radioimmunoassay system for 17 alpha-hydroxy-4-androstene-3-one (epitestosterone) was developed and evaluated using rabbit antisera against 17 alpha-hydroxy-4-androstene-3-one-3-(O-carboxymethyl)-oxime-bovine serum albumin conjugate, and radioiodinated homologous histaminyl derivative of epitestosterone as a tracer. Two antisera with different specificity were used for radioimmunological determination of epitestosterone in hydrolyzed urine and plasma, respectively. Apparent intrinsic association constants and derived thermodynamic variables for ligand-antibody interaction were measured under various conditions in order to set up an optimal assay protocol. The mean plasma epitestosterone levels for healthy subjects were 0.44 +/- 0.15 nmol.l-1 (means +/- SD) in males and 0.092 +/- 0.056 nmol.l-1 in females. The corresponding concentrations in urine were 320 +/- 70 nmol.l-1 (males) and 273 +/- 100 nmol.l-1 (females).     

水/乙醇溶剂中阿奇霉素的热力学及多晶型研究

在278.2~308.2 K温度范围内,测定阿奇霉素在水/乙醇混合溶剂中的溶解度,根据固液平衡理论建立了该体系的溶解度修正模型。采用X线粉末衍射法和差示扫描量热法,对阿奇霉素在不同温度、不同体积比的水/乙醇混合溶剂中得到的晶体进行鉴别。同时利用溶解度数据估算了阿奇霉素在水/乙醇体系中的溶解热(-25.26~-16.11 k J/mol)、混合热(-9.94~-3.25 k J/mol)。通过溶液化学理论推导了阿奇霉素溶剂化平衡常数K与活度系数γ2的方程:γ2=1/(1+K),建立了溶剂化焓与温度、水/乙醇两者体积比(φ)之间的关系式,为ΔH=RTln(17.86exp(3.4φ)-1)。采用溶析结晶方法得到的6种阿奇霉素晶体,均属单斜晶系,但具有不同的晶胞参数且其密度和熔点也不同。同时发现温度越高,水/乙醇体积比越大,得到的晶体稳定性越差(晶体的熔点和密度降低)。在水/乙醇混合溶剂的溶析结晶体系中,产生阿齐霉素多晶型的现象与溶剂化作用的强弱有关。     

Continuum solvent studies of the stability of RNA hairpin loops and helices

We apply continuum solvent models to investigate the relative stability of various conformational forms for two RNA sequences, GGAC(UUCG)GUCC and GGUG(UGAA)CACC. In the first part, we compare alternate hairpin conformations to explore the reliability of these models to discriminate between different local conformations. A second part looks at the hairpin-duplex conversion for the UUCG sequence, identifying major contributors to the thermodynamics of a much large scale transition. Structures were taken as snapshots from multi-nanosecond molecular dynamics simulations computed in a consistent fashion using explicit solvent and with long-range electrostatics accounted for using the Particle-Mesh Ewald procedure. The electrostatic contribution to solvation energies were computed using both a finite-difference Poisson-Boltzmann (PB) model and a pairwise Generalized Born model; non-electrostatic contributions were estimated with a surface-area dependent term. To these solvation free energies were added the mean solute internal energies (determined from a molecular mechanics potential) and estimates of the solute entropy (from a harmonic analysis). Consistent with experiment and with earlier solvated molecular dynamics simulations, the UUCG hairpin was found to prefer conformers close to a recent NMR structure determination in preference to those from an earlier NMR study. Similarly, results for the UGAA hairpin favored an NMR-derived structure over that to be expected for a generic GNRA hairpin loop. Experimental free energies are not known for the hairpin/duplex conversion, but must be close to zero since hairpins are seen in solution and duplexes in crystals; out calculations find a value near zero and illustrate the expected interplay of solvation, salt effects and entropy in affecting this equilibrium.     

Fundamental aspects in tumor photochemotherapy: interactions of porphyrins with membrane model systems and cells

Some molecular aspects underlying photochemotherapy and photodiagnosis of tumors with porphyrins are reviewed. The nature of the clinically used photosensitizer HpD is first presented along with structures of molecules found to be efficient in vitro. The possible role of pH in the preferential retention of dicarboxylic porphyrins by tumors is discussed in light of results obtained with membrane models. The uptake of dicarboxylic porphyrins by cells most likely involves passive mechanisms. Cell photoinactivation using a purified porphyrin does not depend upon the incubation time but only on the intracellular concentration of the dye. This likely reflects a poor specificity of the photoinactivation processes with regard to the cellular localization of the dye. The properties which should be presented by more efficient photosensitizers are discussed.     

Ab initio calculations on the thermodynamic properties of azaborospiropentanes

Following our recent studies of the thermodynamic properties of azaspiropentane and borospiropentane, in consideration of their usefulness as new potential high energy materials, we follow up with ab initio calculations on the thermodynamic properties of azaborospiropentanes. Properties reported in this study include optimized structural parameters, vibrational frequencies, enthalpies of formation, specific enthalpies of combustion, proton affinities, and hydride affinities. Our results indicate that azatriborospiropentane gives off most energy when combusted, as evidenced by its specific enthalpy of combustion of about −52 kJ per gram. Figure Optimized geometry for R-azatriborospiropentane (10) Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Enzyme peptide synthesis and semisynthesis: Kinetic and thermodynamic aspects

The hydrolysis/synthesis equilibrium of the peptide bond is governed by the relative magnitudes of the corresponding Gibbs' energies of hydrolysis to non-ionized products and of their ionization. The positive energy change in peptide hydrolysis to non-ionized products is the thermodynamic basis for the acyl and leaving group specificity of proteinases. With a proteinase of suitable specificity, some peptide bonds can be synthesized by a thermodynamically controlled enzyme aminolysis of specific acylamino or peptide acids; any peptide bond can be formed by a kinetically controlled enzyme aminolysis of the corresponding acylamino or peptide esters.     

Explicit solvent models in protein pKa calculations.

Continuum methods for calculation of protein electrostatics treat buried and ordered water molecules by one of two approximations; either the dielectric constant of regions containing ordered water molecules is equal to the bulk solvent dielectric constant, or it is equal to the protein dielectric constant though no fixed atoms are used to represent water molecules. A method for calculating the titration behavior of individual residues in proteins has been tested on models of hen egg white lysozyme containing various numbers of explicit water molecules. Water molecules were included based on hydrogen bonding, solvent accessibility, and/or proximity to titrating groups in the protein. Inclusion of water molecules significantly alters the calculated titration behavior of individual titrating sites, shifting calculated pKa values by up to 0.5 pH unit. Our results suggest that approximately one water molecule within hydrogen-bonding distance of each charged group should be included in protein electrostatics calculations.     

Free energy calculations of protein-ligand interactions

In the calculation of free energies of binding for protein-ligand complexes, we distinguish endpoint methods, methods involving alchemical modifications and methods that physically displace the ligand from the protein. Most methodological advances seem to come from a clever combination of multiple existing methods to enhance the sampling or to utilize specific advantages of various approaches. The coupling parameters common in thermodynamic integration and in Hamiltonian replica exchange are for instance combined to yield replica exchange thermodynamic integration. As new methods mostly aim to improve efficiency or to attain more complete sampling, there are good prospects to understand and tackle the sampling problem better and to shift the focus towards the scoring problem in the context of more robust and accurate force fields.     

General thermodynamic considerations of receptor interactions.

Assuming that the biological response is directly proportional to the fractional degree of receptor occupancy, the mathematical relationships between free ligand concentration, receptor occupation and biological activity are developed for a number of equilibrium models. The models considered include simple 1:1 binding with and without conformational changes in the receptor, the coupled binding of two distinct effectors to a single macromolecule, and a system involving indirect coupling between two effectors that bind to two distinct components of the receptor system. This latter model is elaborated into the concept of a domain of receptor-enzyme pairs such that occupation of a single receptor may activate the entire domain of enzymes. This model can explain discrepancies between activation and binding isotherms as has been found with some beta-adrenergic agonist-sensitive adenylate cyclase systems.     

Halogenation of aromatic compounds: thermodynamic, mechanistic and ecological aspects

Biological halogenation of aromatic compounds implies the generation of reducing equivalents in the form of e.g. NADH. Thermodynamic calculations show that coupling the halogenation step to a step in which the reducing equivalents are oxidized with a potent oxidant such as O₂ or N₂O makes the halogenation reaction thermodynamically feasible without the input of additional energy in the form of e.g. NADH. In a current model on the halogenation of tryptophan to 7-chloro-l-tryptophan NADH and O₂ are proposed as co-substrates in a reaction in which the aromatic compound is oxidized via an epoxide as intermediate. The thermodynamic calculations thus indicate that such a route hinges on mechanistic insights but has no thermodynamic necessity. Furthermore the calculations suggest that halogenation of tryptophan and other aromatic compounds should be possible with N₂O, and possibly even with nitrate replacing O₂ as the oxidant.     

Hydrophobicity scales: a thermodynamic looking glass into lipid-protein interactions

The partitioning of amino acid sidechains into the membrane is a key aspect of membrane protein folding. However, lipid bilayers exhibit rapidly changing physicochemical properties over their nanometer-scale thickness, which complicates understanding the thermodynamics and microscopic details of membrane partitioning. Recent data from diverse approaches, including protein insertion by the Sec translocon, folding of a small beta-barrel membrane protein and computer simulations of the exact distribution of a variety of small molecules and peptides, have joined older hydrophobicity scales for membrane protein prediction. We examine the correlations among the scales and find that they are remarkably correlated even though there are large differences in magnitude. We discuss the implications of these scales for understanding membrane protein structure and function.