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The application of the particle–particle—particle–mesh (P3M) method for computing electrostatic interactions in molecular simulations relies on the use of a charge-shaping function to split the potential into two contributions, evaluated in real and reciprocal space, respectively. Although the charge-shaping function is traditionally taken to be a Gaussian, many other choices are possible. In the present study, we investigate the accuracy of the P3M method employing, as charge-shaping functions, polynomials truncated to a finite spacial range (TP functions). We first discuss and test analytical estimates of the P3M root-mean-square force error for both types of shaping functions. These estimates are then used to find the optimal values of the free parameters defining the two types of charge-shaping function (width of the Gaussian or coefficients of the TP function). Finally, we compare the accuracy properties of these optimized functions, using both analytical estimates and numerical results for a model ionic system. It is concluded that the use of specific TP functions instead of the traditional Gaussian function leads to improvements in terms of computational speed, simplicity of use, and accuracy of results.

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 ion–solvent and solvent–solvent 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. Additional...

We present the newest version of the GROningen MOlecular Simulation program package, GROMOS96. GROMOS96 has been developed for the dynamic modelling of (bio)molecules using the methods of molecular dynamics, stochastic dynamics, and energy minimization as well as the path-integral formalism. An overview of its functionality is given, highlighting methodology not present in the last major release, GROMOS87. The organization of the code is outlined, and reliability, testing, and efficiency issues involved in the design of this large (73 000 lines of FORTRAN77 code) and complex package are discussed. Finally, we present two applications illustrating new functionality: local elevation simulation and molecular dynamics in four spatial dimensions.

Protein kinases are essential for the regulation of cellular growth and metabolism. Since their dysfunction leads to debilitating diseases, they represent key targets for pharmaceutical research. The rational design of kinase inhibitors requires an understanding of the determinants of ligand binding to these proteins. In the present study, a theoretical model based on continuum electrostatics and a surface-area-dependent nonpolar term is used to calculate binding affinities of balanol derivatives, H-series inhibitors, and ATP analogues toward the catalytic subunit of cAMP-dependent protein kinase (cAPK or protein kinase A). The calculations reproduce most of the experimental trends and provide insight into the driving forces responsible for binding. Nonpolar interactions are found to govern protein-ligand affinity. Hydrogen bonds represent a negligible contribution, because hydrogen bond formation in the complex requires the desolvation of the interacting partners. However, the binding affinity is decreased if hydrogen-bonding groups of the ligand remain unsatisfied in the complex. The disposition of hydrogen-bonding groups in the ligand is therefore crucial for binding specificity. These observations should be valuable guides in the design of potent and specific kinase inhibitors.

The use of Ewald and related methods to handle electrostatic interactions in explicit-solvent simulations of solutions imposes an artificial periodicity on systems which are inherently nonperiodic. The consequences of this approximation should be assessed, since they may crucially affect the reliability of those computer simulations. In the present study, we propose a general method based on continuum electrostatics to investigate the nature and magnitude of periodicity-induced artifacts. As a first example, this scheme is applied to the solvation free-energy of a spherical ion. It is found that artificial periodicity reduces the magnitude of the ionic solvation free-energy, because the solvent in the periodic copies of the central unit cell is perturbed by the periodic copies of the ion, thus less available to solvate the central ion. In the limit of zero ionic radius and infinite solvent permittivity, this undersolvation can be corrected by adding the Wigner self-energy term to the solvation free-energy...

Hyperthermophilic proteins often possess an increased number of surface salt bridges compared with their mesophilic homologues. However, salt bridges are generally thought to be of minor importance in protein stability at room temperature. In an effort to understand why this may no longer be true at elevated temperatures, we performed molecular dynamics simulations of the hyperthermophilic protein Sac7d at 300 K, 360 K, and 550 K. The three trajectories are stable on the nanosecond timescale, as evidenced by the analysis of several time-resolved properties. The simulations at 300 K and (to a lesser extent) 360 K are also compatible with nuclear Overhauser effect-derived distances. Raising the temperature from 300 K to 360 K results in a less favourable protein-solvent interaction energy, and a more favourable intraprotein interaction energy. Both effects are almost exclusively electrostatic in nature and dominated by contributions due to charged side-chains. The reduced solvation is due to a loss of spatial and orientational structure of water around charged side-chains, which is a consequence of the increased thermal motion in the solvent. The favourable change in the intraprotein Coulombic interaction energy is essentially due to the tightening of salt bridges. Assuming that charged side-chains are on average more distant from one another in the unfolded state than in the folded state, it follows that salt bridges may contribute to protein stability at elevated temperatures because (i) the solvation free energy of charged side-chains is more adversely affected in the unfolded state than in the folded state by an increase in temperature, and (ii) due to the tightening of salt bridges, unfolding implies a larger unfavourable increase in the intraprotein Coulombic energy at higher temperature. Possible causes for the unexpected stability of the protein at 550 K are also discussed.

Different schemes for treating the electrostatic interactions in molecular dynamics simulations are investigated: charge-group truncation with or without reaction-field correction, atomic truncation with or without reaction-field correction, and Ewald summation. When a reaction-field correction is applied, the influence of the size of the radius selected for the spherical boundary to the continuum is also considered. The different schemes are applied to simple point charge water simulations, and simulated energetic, transport, structural, and dielectric properties are compared. It is concluded that (i) the inclusion of a reaction-field correction in a charge-group truncation scheme induces significant changes in different types of properties, and that a number of properties are not identical to those observed using the Ewald scheme, (ii) when the reaction-field correction is included in an atomic truncation scheme instead, the agreement with the Ewald results is in general improved, and (iii) the increase...

Binding affinities of (R,R)-1,2-cyclohexanediamine (R) to (R,R)-1,2-cyclopentanediol (R5) and (S,S)-1,2-cyclopentanediol (S5) and to the corresponding cyclohexanediols (R6 and S6) have been measure...

Experimentally determined water/chloroform partition coefficients for three indole derivatives (3- methylindole, N-acetyltryptamine, and 3-(3'-indolyl)propionic acid N-methylamide), models of the amino acid tryptophan, are compared to free-energy differences calculated using molecular dynamics simulations. The effect of the choice of force field, the choice of pathway along which the free-energy change is calculated, the inclusion of free-energy contributions from constraints, and the treatment of long-range interactions on the agreement with the experimental data for this system are investigated with an eye to understanding the importance of the different aspects of the molecular model and computational procedure. It is demonstrated that, although the compounds are neutral and do not differ much in dipole moment or charge distribution, the incorporation of a reaction field to treat long-range electrostatic interactions is necessary to reproduce the experimentally observed trends. The implications of these findings for free-energy calculations in general and for the estimation of partition coefficients in particular are discussed.

The application of molecular dynamics computer simulation methods to study the dynamics of proteins is reviewed with an eye to its possibilities and limitations. Examples are given, mainly using nanosecond trajectories of the proteins bovine pancreatic trypsin inhibitor and lysozyme, of the different protein properties, of which the dynamics can be or cannot be sampled on a nanosecond time scale. It is concluded that the major asset of the simulation technique is that the different factors contributing to the dynamics of a particular process can be analyzed at atomic detail, as long as one has sampled the appropriate time scale.

Four methods are compared to drive the unfolding of a protein: (1) high tem- perature (T-run), (2) high pressure (P-run), (3) by imposing a gradual increase in the mean ra- dius of the protein using a penalty function added to the physical interaction function (F- run, radial force driven unfolding), and (4) by weak coupling of the difference between the temperature of the radially outward moving at- oms and the radially inward moving atoms to an external temperature bath (K-run, kinetic energy driven unfolding). The characteristic features of the four unfolding pathways are an- alyzed in order to detect distortions due to the size or the type of the applied perturbation, as well as the features that are common to all of them. Hen egg white lysozyme is used as a test system. The simulations are analyzed and com- pared to experimental data like 'H-NMR amide proton exchange-folding competition, heat ca- pacity, and compressibility measurements. 0 1995 Wiley-Liss, Inc.

Since the most recent description of the functionalities of the GROMOS software for biomolecular simulation in 2005 many new functions have been implemented. In this article, the new functionalities that involve modified forces in a molecular dynamics (MD) simulation are described: the treatment of electronic polarizability, an implicit surface area and internal volume solvation term to calculate interatomic forces, functions for the GROMOS coarse-grained supramolecular force field, a multiplicative switching function for nonbonded interactions, adiabatic decoupling of a number of degrees of freedom with temperature or force scaling to enhance sampling, and nonequilibrium MD to calculate the dielectric permittivity or viscosity. Examples that illustrate the use of these functionalities are given. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2012

(1R,2R,4R)-2-exo-Cyano-7-oxabicyclo[2.2.1]hept-5-en-2-yl (1S')-camphanate [(+)-1, Diels-Alder adduct of furan to 1-cyanovinyl (1S)-camphanate] was transformed with high stereoselectivity into (1R,2R,6R,7R)-4-phenyl-3,10-dioxa-5-azatricyclo[5.2.1.0(2,6)]dec-4-en-9- one [(+)-10]. Bromination of the corresponding (tert-butyl)dimethylsilyl enol ether [(-)-11], followed by Baeyer-Villiger oxidation and then alkaline methanolysis provided methyl 3-amino-1,5-anhydro-2-O,3-N-benzoyl-3-deoxy-alpha-L-talofuranuronate [(-)-17], the reduction of which gave 3-amino-1,5-anhydro-2-O,3-N-benzoyl-3-deoxy-alpha-L-talofuranose [(-)-19]. Treatment with aqueous HCl furnished 3-amino-3-deoxy-L-talose hydrochloride [(-)-2].

The modulation of the properties of lipid membranes by polyhydroxylated cosolutes such as sugars is a phenomenon of considerable biological, technological and medicinal relevance. A few years ago, we proposed the sugar-like mechanism--binding driven by the release of water molecules--as an attempt to rationalize the preferential affinity of carbohydrate molecules compared to water molecules for the surface of lipid bilayers, which is presumably related to the bioprotective action of these compounds. The goal herein is to gain a better understanding of the driving force underlying this mechanism, in terms of specific interactions or effects, as well as in terms of the energy-entropy partitioning. This is done in the simplest possible context of an apolar rigid-wall model representing the membrane, and mixtures of closely related and possibly artificial species in solution, namely monomers or dimers of Lennard-Jones particles, water with physical or reduced charges, and hydroxymethyl groups. The results indicate that although the sugar-like mechanism seems phenomenologically reasonable, the main driving force underlying this mechanism is not the entropy gain upon releasing water molecules into the bulk, as originally suggested, but rather the hydrophobic effect. Note that the latter effect is a generic concept and may in principle involve both a solvent release and an interaction component, depending on the solute considered.

The problem of the experimental and theoretical determination of single-ion solvation free energies, as well as of corresponding derivative thermodynamic solvation properties, is relatively complex. However, it is often further complicated by imprecisions, alternatives or ambiguities in the definitions of a number of fundamental concepts. Chapter 4 aims at clarifying these concepts and definitions within thermodynamics and electrochemistry, in the context of: (i) thermodynamics (variables, basic relationships, ideal behaviors, standard states, processes and cycles relevant to ionic solvation); (ii) electrostatics (interfacial effects, electric potentials, chemical potentials, workfunctions, electrode potentials); (iii) electrochemistry (types of measurements, relationship to thermodynamic quantities and electric potentials); (iv) single-ion properties (conventional, real, and intrinsic scales). Great attention is paid here to the critical examination of the physics underlying key concepts, as well as to the clarity and consistency of the employed terminology and mathematical notation, new terms or symbols being introduced whenever necessary. Care is also taken here to precisely define and consistently apply a unique thermodynamic standard-state convention, referred to as the bbmeT convention (1 bar reference pressure for solids and liquids, 1 bar reference pressure for gases, 1 molal reference concentration for solutes, warm-electron convention with Fermi-Dirac statistics). Due to incomplete or ambiguous specification in many literature sources, alternative conventions represent an important source of complication and mistakes in the field, and can be encountered at no less than six different levels: (i) choice of a reference pressure and of a reference solution concentration; (ii) choice of a standard or density-corrected solute standard-state variant; (iii) choice of a warm- or cold-electron convention for the standard-state ideal electron gas; (iv) choice of Boltzmann or Fermi-Dirac statistics for calculating the properties of the standard-state electron and proton; (v) choice of a reference electric potential for the ideal electron gas in the definition of absolute electrode potentials; (vi) choice of a specific anchoring point for the conventional scale of single-ion solvation parameters. These include the presence of an ambiguity in the standard-state definition for solute species, namely the existence of standard and density-corrected variants. The natural variant in which a standard quantity is determined and reported depends on the type of measurement performed. However, to our knowledge, this issue is probably raised for the first time in this book, although the ambiguity affects all standard thermodynamic quantities reported in the literature concerning processes involving solute species. Note, finally, that the physics of the solvation process is most directly characterized by what is referred to as semi-standard point-to-point solvation parameters, which characterize the transfer of the ion from a fixed point in the gas phase to a fixed point in solution and are exempt of standard-state bias, besides the specification of a reference pressure and temperature for the solvent properties.

In Chapter 6, the approaches employed for the theoretical determination of thermodynamic parameters related to ionic solvation are reviewed, and illustrative results of these investigations are discussed, mainly in the restricted context of alkali and halide hydration. The relevant features of the basic physical models employed are presented in Chapter 3, and Chapter 6 is principally concerned with practical issues, improvements and corrections concerning these basic models. The most severe shortcomings of continuum-electrostatic calculations are to neglect the microscopic structure of the solvent molecules and the specific details of ion-solvent interactions, and to rely on the ill-defined concept of an ionic radius. Although numerous types of correction terms have been proposed in the past for various neglected effects, including semi-atomistic approaches, none of these arguably improved models can be considered to be at the same time quantitative and predictive. The most severe shortcomings of classical atomistic simulations are caused by finite-size effects, approximate electrostatics and ambiguity of the electric potential calculation. These issues have, up to recently, prevented the obtension of consistent results for single-ion thermodynamic solvation parameters and air-liquid interfacial potentials. Fortunately, the situation has changed in the past few years with the realization that the corresponding errors could be corrected ex post, so as to achieve methodological independence in the simulation results. Still, the outcome of these calculations remains, even after correction, affected by three major sources of error: the mean-field treatment of electronic polarizability (in most calculations), the approximate representation of van der Waals interactions (functional form and combination rules), and the dependence of the results on the choice of ion-solvent van der Waals interaction parameters, which suffer from a similar kind of ambiguity as the ionic radius of continuum-electrostatics calculations. It is nevertheless possible that the results of simulations concerning a large spectrum of ionic properties, including but extending beyond single-ion solvation free energies, provides in the near future a reliable approach for the accurate evaluation of the experimentally-elusive quantities H,svt, H,svt and χsvt. The corresponding extra-thermodynamic assumption is termed in this book the atomistic-consistency assumption. Finally, quantum-mechanical computations, including quasi-chemical theory, hybrid quantum-classical approaches and Car-Parrinello molecular dynamics simulations, have the major shortcoming of being computationally expensive, which results in practice nowadays in severe restrictions concerning the system size, configuration sampling, basis-set size and treatment of electron correlation. As a result, the computation of single-ion solvation free energies with a sufficient accuracy represents a considerable challenge. However, the steady increase in computing power along with recent methodology developments in the area suggest that the calculation of ionic solvation parameters may become feasible with a sufficient accuracy in the coming decades.

Chapter 7 provides concluding remarks, as well as a perspective on unsettled issues and expected progresses in the field. The authors are of the opinion that the experimentally-elusive nature of the quantities H,svt, H,svt and χsvt is not a mere consequence of a high level of technical difficulty involved in their measurement, although this difficulty certainly contributes to the challenge, but rather from a fundamental problem: bulk and surface effects are not unambiguously partitionable. Accepting that this ambiguity is a fundamental restriction imposed by the laws of physics, the concept of extra-thermodynamic assumption takes a different dimension, namely that of an arbitrary definition for this partitioning. The merit of theoretical approaches is to permit the formulation of this definition in the most fundamental context possible, i.e. as an ultimate extra-thermodynamic assumption. Adopting this line of thinking, an exact first-principles quantum-mechanical computation or a fully consistent application of the atomistic-consistency assumption in classical simulations cannot deliver assumption-free estimates for the experimentally-elusive quantities H,svt, H,svt and χsvt, i.e. there must still be some extra-thermodynamic assumption involved in the interpretation of the corresponding results. This assumption usually takes the form of a choice made concerning whether the electric potential is probed by a test charge without or with excluded volume or, equivalently, whether atoms or molecules are viewed as the source entities for this potential. The latter choice (test charge with excluded volume, molecules as sources of electric potential), referred to as the external definition, is recommended as the most “reasonable” one, because it corresponds to the assumption implicitly sustained by continuum-electrostatics calculations as well as intuitive chemical reasoning. Two other important and relatively intricate issues are also addressed in this chapter, namely whether: (i) the pressure or/and temperature derivatives of experimentally-elusive properties are also elusive; (ii) differences in experimentally-elusive properties between different solvents are also elusive. After a brief discussion of these two issues, the authors express the opinion that the answer to both questions is probably affirmative. The chapter closes on a discussion of the three main field-specific plagues of ionic thermodynamics, namely: (i) the incomplete or ambiguous definitions commonly adopted for some central concepts; (ii) the existence of numerous redundant parameters encompassing the same physical information in a different format; (iii) the plethora of alternative standard-state definitions.

The theoretical evalutation of single-ion solvation free energies, as well as of corresponding derivative thermodynamic solvation parameters, relies on models involving three different levels of resolution: (i) continuum-electrostatics calculations; (ii) classical atomistic simulations; (iii) quantum-mechanical computations. Chapter 3 introduces these three types of modeling approaches, and provides a summary of their strengths and shortcomings. On the low-resolution end, continuum-electrostatics calculations, inspired from the Born model, typically describe the ion as a rigid non-polarizable sphere and the solvent as a continuous medium of infinite extent, linear dielectric response, and homogeneous permittivity. These approaches have a long history and the merit of providing a simple and qualitatively correct framework for intuitive reasoning. However, they neglect the microscopic structure of the solvent molecules and the specific details of ion-solvent interactions, and rely on the ill-defined concept of an ionic radius. In the middle-resolution range, classical atomistic simulations describe the ion in solution as a system of classical point particles (atoms) interacting according to an empirically designed and calibrated potential energy function, called a force field. These methods should in principle be more accurate than continuum-electrostatics approaches, by accounting for the microscopic structure of the solvent molecules. However, in contrast to the latter methods, the averaging over solvent configurations must be carried out explicitly and the considered system is now of finite extent, e.g. liquid droplet or periodic computational box. The latter difference introduces serious methodological issues regarding the choice of boundary conditions, the approximate treatment of electrostatic interactions, and the evaluation of electric potentials based on the sampled configurations. The third issue appears in particular in the form of puzzling inconsistencies affecting the results of calculations involving slightly different potential-evaluation schemes. The origin of these inconsistencies is analyzed in more detail in Chapters 4, 6 and 7. The results of atomistic simulations also depend on the choice of ion-solvent van der Waals interaction parameters, which can be viewed as representing the atomistic analog of the ionic radius of continuum-electrostatics calculations, and suffer from a similar kind of ambiguity. Finally, on the high-resolution end, quantum-mechanical computations describe the ion in solution as a many-particle system characterized by a wavefunction obeying the Schrodinger equation, given a Hamiltonian encompassing Coulombic interactions between all the elementary particles involved. As first-principles approaches, these methods have a bright future and promise to enable the calculation of experimentally-elusive quantities H,svt, H,svt and χsvt based on the most accurate physical model available nowadays, without relying on the specification of ambiguous quantities such as ionic radii or ion-solvent van der Waals interaction parameters. Unfortunately, they have the major shortcoming of being computationally expensive, which results in practice nowadays in severe restrictions concerning the system size, configurational sampling, basis-set size, and treatment of electron correlation.

The experimental determination of single-ion solvation free energies, as well as of corresponding derivative thermodynamic solvation parameters, is complicated by two fundamental problems: (i) the local electroneutrality of macroscopic matter at equilibrium and its corollary, the absence of free gas-phase ions in equilibrium situations; (ii) the presence of a surface polarization at air-liquid interfaces. Chapter 2 discusses these two problems in sequence, and provides a summary of their practical implications. The local electroneutrality constraint implies that single-ion solvation parameters are only directly accessible, via calorimetry and gas-phase spectroscopy-based statistical mechanics, in the form of sums over neutral ion combinations or, equivalently, as conventional (relative) values, i.e. with the proton parameters set to zero by definition. Absolute single-ion solvation parameters can also be obtained via Voltaic cell experiments and workfunction measurements. However, the presence of surface polarization effects at air-liquid interfaces implies that these determinations lead to real values, i.e. including the reversible work of interface crossing. The absolute single-ion solvation parameters that are of greatest theoretical relevance are intrinsic, i.e. solely characterizing the interaction of the ion with its polarized solvent environment, without contamination from surface effects. They cannot be accessed on the sole basis of experimental data and require the introduction of some apparently reasonable but formally unprovable postulate or model, called in this context an extra-thermodynamic assumption. The introduction of a specific assumption permits to anchor the conventional scale by providing estimates for either of three equivalent experimentally-elusive solvent-dependent quantities, namely the intrinsic solvation free energy H,svt of the proton, the intrinsic absolute potential H,svt of the reference hydrogen electrode, or the air-liquid interfacial potential χsvt, along with their pressure or/and temperature derivatives. Unfortunately, considering the case of water, the use of different experimental approaches along with distinct extra-thermodynamic assumptions leads to a very large uncertainty range on the order of 0.5−1.0 V (potentials) or 50−100 kJ·mol−1 (free energy) in the estimated values for the three above quantities.

In Chapter 5, the approaches employed for the experimental determination of thermodynamic parameters related to ionic solvation are reviewed, and the results of investigations employing these methods are discussed in the restricted context of alkali and halide hydration in the infinitely-dilute regime. Closely related properties formally pertaining to the pure solvent (water), namely the absolute solvation parameters of the proton, the absolute potential of the reference hydrogen electrode and the air-liquid interfacial potential, are also considered in view of their central role in single-ion solvation thermodynamics, in both their real and intrinsic forms. The discussion proceeds roughly incrementally, from the most directly accessible quantities to the more elusive ones, namely: (i) molar thermodynamic parameters of the elements; (ii) structural and molar thermodynamic parameters of the salts (ionic crystals); (iii) gas-phase equilibrium ion-pair distances; (iv) effective ionic radii; (v) relative electrode (redox) potentials (anchored based on the reference hydrogen electrode); (vi) thermodynamic parameters of salt formation; (vii) thermodynamic parameters of dissolved salt formation; (viii) thermodynamic parameters of salt dissolution; (ix) thermodynamic parameters of atomization; (x) thermodynamic parameters of ionization; (xi) thermodynamic parameters of reticulation; (xii) thermodynamic parameters of salt solvation; (xiii) metal workfunctions; (xiv) real absolute potential of the reference hydrogen electrode; (xv) real single-ion solvation parameters; (xvi) conventional single-ion solvation parameters; (xvii) air-liquid interfacial potential of the pure solvent; (xviii) intrinsic proton solvation parameters. Three additional sections provide: (i) a summary of recommended data concerning alkali and halide hydration, along with relevant pure-solvent properties; (ii) a discussion of suggested intrinsic single-ion solvation parameters for the alkali and halide ions, in connection with the Hofmeister series; (iii) a brief discussion of the properties of the solvated electron. The recommended data is based on the careful investigation of experimental results from 221 literature sources over the past nearly hundred years. This data is presented in the form of a minimal (non-redundant) set of parameters concerning the gas-phase, salt and solution properties the alkali and halide ions, as well as of the proton, with reference to water as a solvent, converted to a unique standard-state convention (bbmeT convention).

The raw single-ion solvation free energies computed from atomistic (explicit-solvent) simulations are extremely sensitive to the boundary conditions (finite or periodic system, system or box size) and treatment of electrostatic interactions (Coulombic, lattice-sum, or cutoff-based) used during these simulations. However, as shown by Kastenholz and Hünenberger [J. Chem. Phys. 124, 224501 (2006)], correction terms can be derived for the effects of: (A) an incorrect solvent polarization around the ion and an incomplete or/and inexact interaction of the ion with the polarized solvent due to the use of an approximate (not strictly Coulombic) electrostatic scheme; (B) the finite-size or artificial periodicity of the simulated system; (C) an improper summation scheme to evaluate the potential at the ion site, and the possible presence of a polarized air-liquid interface or of a constraint of vanishing average electrostatic potential in the simulated system; and (D) an inaccurate dielectric permittivity of the employed solvent model. Comparison with standard experimental data also requires the inclusion of appropriate cavity-formation and standard-state correction terms. In the present study, this correction scheme is extended by: (i) providing simple approximate analytical expressions (empirically-fitted) for the correction terms that were evaluated numerically in the above scheme (continuum-electrostatics calculations); (ii) providing correction terms for derivative thermodynamic single-ion solvation properties (and corresponding partial molar variables in solution), namely, the enthalpy, entropy, isobaric heat capacity, volume, isothermal compressibility, and isobaric expansivity (including appropriate standard-state correction terms). The ability of the correction scheme to produce methodology-independent single-ion solvation free energies based on atomistic simulations is tested in the case of Na(+) hydration, and the nature and magnitude of the correction terms for derivative thermodynamic properties is assessed numerically.

A new parameter set (53A6OXY) is developed for the GROMOS force field, that combines reoptimized parameters for the oxygen-containing chemical functions (alcohols, ethers, aldehydes, ketones, carboxylic acids, and esters) with the current biomolecular force field version (53A6) for all other functions. In the context of oxygen-containing functions, the 53A6OXY parameter set is obtained by optimization of simulated pure-liquid properties, namely the density ρliq and enthalpy of vaporization ΔHvap, as well as solvation properties, namely the free energies of solvation in water ΔGwat and in cyclohexane ΔGche, against experimental data for 10 selected organic compounds, and further tested for 25 other compounds. The simultaneous refinement of atomic charges and Lennard-Jones interaction parameters against the four mentioned types of properties provides a single parameter set for the simulation of both liquid and biomolecular systems. Small changes in the covalent parameters controlling the geometry of the oxygen-containing chemical functions are also undertaken. The new 53A6OXY force-field parameters reproduce the mentioned experimental data within root-mean-square deviations of 22.4 kg m(-3) (ρliq), 3.1 kJ mol(-1) (ΔHvap), 3.0 kJ mol(-1) (ΔGwat), and 1.7 kJ mol(-1) (ΔGche) for the 35 compounds considered.

This article presents a reoptimization of the GROMOS 53A6 force field for hexopyranose-based carbohydrates (nearly equivalent to 45A4 for pure carbohydrate systems) into a new version 56A(CARBO) (nearly equivalent to 53A6 for non-carbohydrate systems). This reoptimization was found necessary to repair a number of shortcomings of the 53A6 (45A4) parameter set and to extend the scope of the force field to properties that had not been included previously into the parameterization procedure. The new 56A(CARBO) force field is characterized by: (i) the formulation of systematic build-up rules for the automatic generation of force-field topologies over a large class of compounds including (but not restricted to) unfunctionalized polyhexopyranoses with arbritrary connectivities; (ii) the systematic use of enhanced sampling methods for inclusion of experimental thermodynamic data concerning slow or unphysical processes into the parameterization procedure; and (iii) an extensive validation against available experimental data in solution and, to a limited extent, theoretical (quantum-mechanical) data in the gas phase. At present, the 56A(CARBO) force field is restricted to compounds of the elements C, O, and H presenting single bonds only, no oxygen functions other than alcohol, ether, hemiacetal, or acetal, and no cyclic segments other than six-membered rings (separated by at least one intermediate atom). After calibration, this force field is shown to reproduce well the relative free energies of ring conformers, anomers, epimers, hydroxymethyl rotamers, and glycosidic linkage conformers. As a result, the 56A(CARBO) force field should be suitable for: (i) the characterization of the dynamics of pyranose ring conformational transitions (in simulations on the microsecond timescale); (ii) the investigation of systems where alternative ring conformations become significantly populated; (iii) the investigation of anomerization or epimerization in terms of free-energy differences; and (iv) the design of simulation approaches accelerating the anomerization process along an unphysical pathway.

The relative stabilities of the alkali [M subset 222]+ cryptates (M = Na, K, Rb and Cs) in the gas phase and in solution (80:20 v/v methanol:water mixture) at 298 K, are computed using a combination of ab initio quantum-chemical calculations (HF/6-31G and MP2/6-31+G*//HF/6-31+G*) and explicit-solvent Monte Carlo free-energy simulations. The results suggest that the relative stabilities of the cryptates in solution are due to a combination of steric effects (compression of large ions within the cryptand cavity), electronic effects (delocalization of the ionic charge onto the cryptand atoms) and solvent effects (dominantly the ionic dessolvation penalty). Thus, the relative stabilities in solution cannot be rationalized solely on the basis of a simple match or mismatch between the ionic radius and the cryptand cavity size as has been suggested previously. For example, although the [K subset 222]+ cryptate is found to be the most stable in solution, in agreement with experimental data, it is the [Na subset 222]+ cryptate that is the most stable in the gas phase. The present results provide further support to the notion that the solvent in which supramolecules are dissolved plays a key role in modulating molecular recognition processes.

Estimating the relative stabilities of different conformational states of a (bio-)molecule using molecular dynamics simulations involves two challenging problems: the conceptual problem of how to define the states of interest and the technical problem of how to properly sample these states, along with achieving a sufficient number of interconversion transitions. In this study, the two issues are addressed in the context of a decaalanine peptide in water, by considering the 310-, α-, and π-helical states. The simulations rely on the ball-and-stick local-elevation umbrella-sampling (BS-LEUS) method. In this scheme, the states are defined as hyperspheres (balls) in a (possibly high dimensional) collective-coordinate space and connected by hypercylinders (sticks) to ensure transitions. A new object, the pipe, is also introduced here to handle curvilinear pathways. Optimal sampling within the so-defined space is ensured by confinement and (one-dimensional) memory-based biasing potentials associated with the three different kinds of objects. The simulation results are then analysed in terms of free energies using reweighting, possibly relying on two distinct sets of collective coordinates for the state definition and analysis. The four possible choices considered for these sets are Cartesian coordinates, hydrogen-bond distances, backbone dihedral angles, or pairwise sums of successive backbone dihedral angles. The results concerning decaalanine underline that the concept of conformational state may be extremely ambiguous, and that its tentative absolute definition as a free-energy basin remains subordinated to the choice of a specific analysis space. For example, within the force-field employed and depending on the analysis coordinates selected, the 310-helical state may refer to weakly overlapping collections of conformations, differing by as much as 25 kJ mol(-1) in terms of free energy. As another example, the π-helical state appears to correspond to a free-energy basin for three choices of analysis coordinates, but to be unstable with the fourth one. The problem of conformational-state definition may become even more intricate when comparison with experiment is involved, where the state definition relies on spectroscopic or functional observables.

Molecular dynamics simulations are used to investigate the interaction of the sugars trehalose, maltose, and glucose with a phospholipid bilayer at atomic resolution. Simulations of the bilayer in the absence or in the presence of sugar (2 molal concentration for the disaccharides, 4 molal for the monosaccharide) are carried out at 325 and 475 K. At 325 K, the three sugars are found to interact directly with the lipid headgroups through hydrogen bonds, replacing water at about one-fifth to one-quarter of the hydrogen-bonding sites provided by the membrane. Because of its small size and of the reduced topological constraints imposed on the hydroxyl group locations and orientations, glucose interacts more tightly (at identical effective hydroxyl group concentration) with the lipid headgroups when compared to the disaccharides. At high temperature, the three sugars are able to prevent the thermal disruption of the bilayer. This protective effect is correlated with a significant increase in the number of sugar-headgroups hydrogen bonds. For the disaccharides, this change is predominantly due to an increase in the number of sugar molecules bridging three or more lipid molecules. For glucose, it is primarily due to an increase in the number of sugar molecules bound to one or bridging two lipid molecules.

The present article reports long timescale (200 ns) simulations of four beta-D-hexopyranoses (beta-D-glucose, beta-D-mannose, beta-D-galactose and beta-D-talose) using explicit-solvent (water) molecular dynamics and vacuum stochastic dynamics simulations together with the GROMOS 45A4 force field. Free-energy and solvation free-energy differences between the four compounds are also calculated using thermodynamic integration. Along with previous experimental findings, the present results suggest that the formation of intramolecular hydrogen-bonds in water is an 'opportunistic' consequence of the close proximity of hydrogen-bonding groups, rather than a major conformational driving force promoting this proximity. In particular, the conformational preferences of the hydroxymethyl group in aqueous environment appear to be dominated by 1,3-syn-diaxial repulsion, with gauche and solvation effects being secondary, and intramolecular hydrogen-bonding essentially negligible. The rotational dynamics of the exocyclic hydroxyl groups, which cannot be probed experimentally, is found to be rapid (10-100 ps timescale) and correlated (flip-flop hydrogen-bonds interconverting preferentially through an asynchronous disrotatory pathway). Structured solvent environments are observed between the ring and lactol oxygen atoms, as well as between the 4-OH and hydroxymethyl groups. The calculated stability differences between the four compounds are dominated by intramolecular effects, while the corresponding differences in solvation free energies are small. An inversion of the stereochemistry at either C(2) or C(4) from equatorial to axial is associated with a raise in free energy. Finally, the particularly low hydrophilicity of beta-D-talose appears to be caused by the formation of a high-occurrence hydrogen-bonded bridge between the 1,3-syn-diaxial 2-OH and 4-OH groups. Overall, good agreement is found with available experimental and theoretical data on the structural, dynamical, solvation and energetic properties of these compounds. However, this detailed comparison also reveals some discrepancies, suggesting the need (and providing a solid basis) for further refinement.

This article investigates the convergence of structural and dynamical properties with system size and with time in molecular dynamics simulations of solvated phospholipid bilayers performed at constant volume under periodic boundary conditions using lattice-sum electrostatics. The electron density profile across the bilayer, the carbon-deuterium order parameters, and the surface tension are shown to be converged for a bilayer containing 36 lipids per leaflet and simulated over a period of 3-4 ns. Reasonable estimates for these properties can already be obtained from a system containing 16 lipids per leaflet. The convergence limit of 36 lipids per leaflet and the investigation of the correlation between lipid headgroup dipoles suggest a correlation length of about 3-5 nm in the lateral directions for a hydrated DPPC bilayer in the liquid-crystalline phase. Although these (relatively small) system sizes and (relatively short) time scales appear sufficient to obtain converged collective structural properties at constant volume, two restrictions should be kept in mind: (i) the relaxation times associated with the motion of individual lipids may be much longer and (ii) simulated properties converge significantly faster under constant volume conditions as compared to constant pressure conditions. Therefore, an accurate assessment of the dynamical properties of the system or of the relaxation of the bilayer under constant pressure conditions may require longer simulation time scales.

The raw ionic solvation free energies computed from atomistic (explicit-solvent) simulations are extremely sensitive to the boundary conditions (finite or periodic system, system shape, and size) and treatment of electrostatic interactions (Coulombic, lattice sum, or cutoff based) used during these simulations. In the present article, it is shown that correction terms can be derived for the effect of (A) an incorrect solvent polarization around the ion due to the use of an approximate (not strictly Coulombic) electrostatic scheme; (B) the finite size or artificial periodicity of the simulated system; (C) an improper summation scheme to evaluate the potential at the ion site and the possible presence of a liquid-vacuum interface in the simulated system. Taking the hydration free energy of the sodium cation as a test case, it is shown that the raw solvation free energies obtained using seven different types of boundary conditions and electrostatic schemes commonly used in explicit-solvent simulations (for a total of 72 simulations differing in the corresponding simulation parameters) can be corrected so as to obtain a consistent value for this quantity.

The computation of ionic solvation free energies from atomistic simulations is a surprisingly difficult problem that has found no satisfactory solution for more than 15 years. The reason is that the charging free energies evaluated from such simulations are affected by very large errors. One of these is related to the choice of a specific convention for summing up the contributions of solvent charges to the electrostatic potential in the ionic cavity, namely, on the basis of point charges within entire solvent molecules (M scheme) or on the basis of individual point charges (P scheme). The use of an inappropriate convention may lead to a charge-independent offset in the calculated potential, which depends on the details of the summation scheme, on the quadrupole-moment trace of the solvent molecule, and on the approximate form used to represent electrostatic interactions in the system. However, whether the M or P scheme (if any) represents the appropriate convention is still a matter of on-going debate. The goal of the present article is to settle this long-standing controversy by carefully analyzing (both analytically and numerically) the properties of the electrostatic potential in molecular liquids (and inside cavities within them). Restricting the discussion to real liquids of "spherical" solvent molecules (represented by a classical solvent model with a single van der Waals interaction site), it is concluded that (i) for Coulombic (or straight-cutoff truncated) electrostatic interactions, the M scheme is the appropriate way of calculating the electrostatic potential; (ii) for non-Coulombic interactions deriving from a continuously differentiable function, both M and P schemes generally deliver an incorrect result (for which an analytical correction must be applied); and (iii) finite-temperature effects, including intermolecular orientation correlations and a preferential orientational structure in the neighborhood of a liquid-vacuum interface, must be taken into account. Applications of these results to the computation methodology-independent ionic solvation free energies from molecular simulations will be the scope of a forthcoming article.

Artifacts induced by the application of periodic boundary conditions and lattice-sum methods in explicit-solvent simulations of (bio-)molecular systems are nowadays a major concern in the computer-simulation community. The present article reports a first step toward the design of a modified lattice-sum algorithm emulating nonperiodic boundary conditions, and therefore exempt of such periodicity-induced artifacts. This result is achieved here in the (more simple) context of continuum electrostatics. It is shown that an appropriate modification of the periodic Poisson equation and of its boundary conditions leads to a continuum-electrostatics scheme, which, although applied under periodic boundary conditions, exactly mimics the nonperiodic situation. The possible extension of this scheme to explicit-solvent simulations is outlined and its practical implementation will be described in more details in a forthcoming article.

Computation based on molecular models is playing an increasingly important role in biology, biological chemistry, and biophysics. Since only a very limited number of properties of biomolecular systems is actually accessible to measurement by experimental means, computer simulation can complement experiment by providing not only averages, but also distributions and time series of any definable quantity, for example, conformational distributions or interactions between parts of systems. Present day biomolecular modeling is limited in its application by four main problems: 1) the force-field problem, 2) the search (sampling) problem, 3) the ensemble (sampling) problem, and 4) the experimental problem. These four problems are discussed and illustrated by practical examples. Perspectives are also outlined for pushing forward the limitations of biomolecular modeling. © 2006 Wiley-VCH Verlag GmbH & Co. KGaA.

In a recent article [Bieler et al., J. Chem. Theory Comput. 10, 3006-3022 (2014)], we introduced a combination of the λ-dynamics (λD) approach for calculating alchemical free-energy differences and of the local-elevation umbrella-sampling (LEUS) memory-based biasing method to enhance the sampling along the alchemical coordinate. The combined scheme, referred to as λ-LEUS, was applied to the perturbation of hydroquinone to benzene in water as a test system, and found to represent an improvement over thermodynamic integration (TI) in terms of sampling efficiency at equivalent accuracy. However, the preoptimization of the biasing potential required in the λ-LEUS method requires "filling up" all the basins in the potential of mean force. This introduces a non-productive pre-sampling time that is system-dependent, and generally exceeds the corresponding equilibration time in a TI calculation. In this letter, a remedy is proposed to this problem, termed the slow growth memory guessing (SGMG) approach. Instead of initializing the biasing potential to zero at the start of the preoptimization, an approximate potential of mean force is estimated from a short slow growth calculation, and its negative used to construct the initial memory. Considering the same test system as in the preceding article, it is shown that of the application of SGMG in λ-LEUS permits to reduce the preoptimization time by about a factor of four.

A new scheme, the lattice-sum-emulated reaction-field (LSERF) method, is presented that combines the lattice-sum (LS) and reaction-field (RF) approaches for evaluating electrostatic interactions in molecular simulations. More precisely, the LSERF scheme emulates a RF calculation (based on an atomic cutoff) via the LS machinery. This is achieved by changing the form of the electrostatic interactions in a standard LS calculation (Coulombic) to the form corresponding to RF electrostatics (Coulombic plus quadratic reaction-field correction term, truncated at the cutoff distance). It is shown (both analytically and numerically) that in the limit of infinite reciprocal-space accuracy, (i) the LSERF scheme with a finite reaction-field cutoff and a given reaction-field permittivity is identical to the RF scheme with the same parameters (and an atomic cutoff), and (ii) the LSERF scheme is identical to the LS scheme in the limit of an infinite reaction-field cutoff, irrespective of the reaction-field permittivity. This new scheme offers two key advantages: (i) from a conceptual point of view, it shows that there is a continuity between the RF and LS schemes and unifies them into a common framework; (ii) from a practical point of view, it allows us to perform RF calculations with arbitrarily large reaction-field cutoff distances for the same computational costs as a corresponding LS calculation. The optimal choice for the cutoff will be the one that achieves the best compromise between artifacts arising from the dielectric heterogeneity of the system (short cutoff) and its artificial periodicity (long cutoff). The implementation of the LSERF method is extremely easy, requiring only very limited modifications of any standard LS code. For practical applications to biomolecular systems, the use of the LSERF scheme with large reaction-field cutoff distances is expected to represent a significant improvement over the current RF simulations involving comparatively much shorter cutoffs.

The study presented here consists of three parts. In the first, the ability of a set of differently substituted diazobenzene-based linkers to act as photoswitchable beta-turn building blocks was assessed. A 12-residue peptide known to form beta-hairpins was taken as the basis for the modeling process. The central (beta-turn) residue pair was successively replaced by six symmetrically ((o,o), (m,m), or (p,p)) substituted (aminomethyl/carboxymethyl or aminoethyl/carboxyethyl) diazobenzene derivatives leading to a set of peptides with a photoswitchable backbone conformation. The folding behavior of each peptide was then investigated by performing molecular dynamics simulations in water (4 ns) and in methanol (10 ns) at room temperature. The simulations suggest that (o,o)- and (m,m)-substituted linkers with a single methylene spacer are significantly better suited to act as photoswitchable beta-turn building blocks than the other linkers examined in this study. The peptide containing the (m,m)-substituted linker was synthesized and characterized by NMR in its cis configuration. In the second part of this study, the structure of this peptide was refined using explicit-solvent simulations and NOE distance restraints, employing a variety of refinement protocols (instantaneous and time-averaged restraining as well as unrestrained simulations). We show that for this type of systems, even short simulations provide a significant improvement in our understanding of their structure if physically meaningful force fields are employed. In the third part, unrestrained explicit-solvent simulations starting from either the NMR model structure (75 ns) or a fully extended structure (25 ns) are shown to converge to a stable beta-hairpin. The resulting ensemble is in good agreement with experimental data, indicating successful structure prediction of the investigated hairpin by classical explicit-solvent molecular dynamics simulations.

The optimization of coherence-transfer pulse-sequence elements (CTEs) is the most challenging step in the construction of heteronuclear correlation NMR experiments achieving sensitivity close to its theoretical maximum (in the absence of relaxation) in the shortest possible experimental time and featuring active suppression of undesired signals. As reported in the present article, this complex optimization problem in a space of high dimensionality turns out to be numerically tractable. Based on the application of molecular dynamics in the space of pulse-sequence variables, a general method is proposed for constructing optimized CTEs capable of transferring an arbitrary (generally non-Hermitian) spin operator encoding the chemical shift of heteronuclear spins to an arbitrary spin operator suitable for signal detection. The CTEs constructed in this way are evaluated against benchmarks provided by the theoretical unitary bound for coherence transfer and the minimal required transfer time (when available). This approach is used to design a set of NMR experiments enabling direct and selective observation of individual (1)H-transitions in (13)C-labeled methyl spin systems close to optimal sensitivity and using a minimal number of spectra. As an illustrative application of the method, optimized CTEs are used to quantitatively measure (1)H-(1)H and (1)H-(13)C residual dipolar couplings (RDCs) in a 17 kDa protein weakly aligned by means of Pf1 phages.

A variety of sugars are known to enhance the stability of biomaterials. Trehalose, a nonreducing disaccharide composed of two alpha, alpha(1 --> 1)-linked D-glucopyranose units, appears to be one of the most effective protectants. Both in vivo and in vitro, trehalose protects biostructures such as proteins and membranes from damage due to dehydration, heat, or cold. However, despite the significant amount of experimental data on this disaccharide, no clear picture of the molecular mechanism responsible for its stabilizing properties has emerged yet. Three major hypotheses (water-trehalose hydrogen-bond replacement, coating by a trapped water layer, and mechanical inhibition of the conformational fluctuations) have been proposed to explain the stabilizing effect of trehalose on proteins. To investigate the nature of protein-trehalose-water interactions in solution at the molecular level, two molecular dynamics simulations of the protein lysozyme in solution at room temperature have been carried out, one in the presence (about 0.5 M) and one in the absence of trehalose. The results show that the trehalose molecules cluster and move toward the protein, but neither completely expel water from the protein surface nor form hydrogen bonds with the protein. Furthermore, the coating by trehalose does not significantly reduce the conformational fluctuations of the protein compared to the trehalose-free system. Based on these observations, a model is proposed for the interaction of trehalose molecules with a protein in moderately concentrated solutions, at room temperature and on the nanosecond timescale.

An iterative algorithm based on fast-Fourier transforms is presented that solves the equations of continuum electrostatics for systems of heterogeneous dielectric permittivity (e.g., solute cavity in a solvent) under periodic boundary conditions. The method makes explicit use of the charge–dipole and dipole–dipole interaction tensors, and is thus applicable both to Coulombic interactions (Ewald scheme) and cutoff-based electrostatic interactions described by any polynomial function (including a Coulombic r−1 term), as commonly used in molecular dynamics simulations. The latter case includes, in particular, straight truncation of Coulombic interactions and truncation including a reaction-field correction. After testing and validation by comparison with existing methods, the algorithm is used to investigate the effect of cutoff truncation and artificial periodicity in explicit-solvent simulations of ionic solvation and ion–ion interactions. Both cutoff truncation and artificial periodicity are found to significantly affect the polarization around a spherical ion and its solvation free energy. The nature and magnitude of the two perturbations are analyzed in detail, and approximate analytical correction terms are derived to be applied to the results of explicit-solvent simulations. Cutoff truncation induces strong alterations in the potential of mean force for the interaction between two spherical ions. The present observations based on continuum electrostatics help to rationalize artifacts previously reported from explicit-solvent simulations involving cutoff truncation and, in particular, the unphysical attraction of like charges and repulsion of opposite charges, and the corresponding alterations in the relative stabilities of contact, solvent-separated, and free ion pairs. published

A new algorithm relying on finite integration is presented that solves the equations of continuum electrostatics for truncated (and possibly reaction-field corrected) solute–solvent and solvent–solvent interactions under either nonperiodic or periodic boundary conditions. After testing and validation by comparison with existing methods, the algorithm is applied to investigate the effect of cut-off truncation and artificial periodicity in explicit-solvent simulations of ionic solvation and ion–ion interactions. Both cut-off truncation and artificial periodicity significantly alter the polarization around a spherical ion and thus, its solvation free energy. The nature and magnitude of the two perturbations are analyzed in details, and correction terms are proposed for both effects. Cut-off truncation is also shown to induce strong alterations in the potential of mean force for ion–ion interaction. These observations help to rationalize artifacts previously observed in explicit–solvent simulations, namely spurious features in the radial distribution functions close to the cut-off distance and alterations in the relative stabilities of contact, solvent-separated and free ion pairs. published

Eight molecular dynamics simulations of a double crystal unit cell of ubiquitin were performed to investigate the effects of simulating at constant pressure and of simulating two unit cells compared to a single unit cell. To examine the influence of different simulation conditions, the constant-pressure and constant-volume simulations were each performed with and without counterions and using two different treatments of the long-range electrostatic interactions (lattice-sum and reaction-field methods). The constant-pressure simulations were analyzed in terms of unit cell deformation and accompanying protein deformations. Energetic and structural properties of the proteins in the simulations of the double unit cell were compared to the results of previously reported one-unit-cell simulations. Correlation between the two unit cells was also investigated based on relative translational and rotational movements of the proteins and on dipole fluctuations. The box in the constant-pressure simulations is found to deform slowly to reach convergence only after 5-10 ns. This deformation does not result from a distortion in the structure of the proteins but rather from changes in protein packing within the unit cell. The results of the double-unit-cell simulations are closely similar to the results of the single-unit-cell simulations, and little motional correlation is found between the two unit cells.

Protein kinases are important targets for designing therapeutic drugs. This paper illustrates a computational approach to extend the usefulness of a single protein-inhibitor structure in aiding the design of protein kinase inhibitors. Using the complex structure of the catalytic subunit of PKA (cPKA) and balanol as a guide, we have analyzed and compared the distribution of amino acid types near the protein-ligand interface for nearly 400 kinases. This analysis has identified a number of sites that are more variable in amino acid types among the kinases analyzed, and these are useful sites to consider in designing specific protein kinase inhibitors. On the other hand, we have found kinases whose protein-ligand interfaces are similar to that of the cPKA-balanol complex and balanol can be a useful lead compound for developing effective inhibitors for these kinases. Generally, this approach can help us discover new drug targets for an existing class of compounds that have already been well characterized pharmacologically. The relative significance of the charge/polarity of residues at the protein-ligand interface has been quantified by carrying out computational sensitivity analysis in which the charge/polarity of an atom or functional group was turned off/on, and the resulting effects on binding affinity have been examined. The binding affinity was estimated by using an implicit-solvent model in which the electrostatic contributions were obtained by solving the Poisson equation and the hydrophobic effects were accounted for by using surface-area dependent terms. The same sensitivity analysis approach was applied to the ligand balanol to develop a pharmacophoric model for searching new drug leads from small-molecule libraries. To help evaluate the binding affinity of designed inhibitors before they are made, we have developed a semiempirical approach to improve the predictive reliability of the implicit-solvent binding model.

Ewald and related methods are nowadays routinely used in explicit-solvent simulations of biomolecules, although they impose an artificial periodicity in systems which are inherently non-periodic. The consequences of this approximation should be assessed, since they may crucially affect the reliability of computer simulations under Ewald boundary conditions. In the present study we use a method based on continuum electrostatics to investigate the nature and magnitude of possible periodicity-induced artifacts on the potentials of mean force for conformational equilibria in biomolecules. Three model systems and pathways are considered: polyalanine oligopeptides (unfolding), a DNA tetranucleotide (separation of the strands), and the protein Sac7d (conformations from a molecular dynamics simulation). Artificial periodicity may significantly affect these conformational equilibria, in each case stabilizing the most compact conformation of the biomolecule. Three factors enhance periodicity-induced artifacts: (i) a solvent of low dielectric permittivity; (ii) a solute size which is non-negligible compared to the size of the unit cell; and (iii) a non-neutral solute. Neither the neutrality of the solute nor the absence of charge pairs at distances exceeding half the edge of the unit cell do guarantee the absence of artifacts.

Lattice-sum methods for computing electrostatic interactions are becoming increasingly popular in the area of molecular simulation. Although these methods are generally considered to be significantly more accurate than cutoff-based methods, there are two intrinsic difficulties linked with their application: (i) the relatively complicated mathematical formalism and somewhat non-intuitive physical picture associated with electrostatics under periodic boundary conditions makes the development of new algorithms a difficult task; (ii) the assumption of exact periodicity in simulations of liquids and solutions is an approximation and may lead to periodicity-induced artifacts, the nature and magnitude of which are still poorly characterized. The present text addresses these two issues by (i) providing a detailed and consistent derivation of the two main lattice-sum algorithms (Ewald and particle-particle–particle-mesh), and (ii) discussing the nature of periodicity-induced artifacts in the context of a few simple systems.

With the continuing increase of the power of computers, the past decades have seen a rapid increase in the number, performance and accuracy of theoretical computational methods in chemistry (van Gunsteren et al., 1989 ff, Lipkowitz & Boyd, 1990ff). One can distinguish three major classes of methods for the theoretical study of molecular properties, listed in order of decreasing computational expenses: (i) ab initio molecular-orbital methods (Hehre et al., 1986), (ii) semi-empirical molecular-orbital methods (Zerner, 1991), and (iii) empirical classical force-field methods. Since the available computing resources are most often the true limiting factor to numerical calculations, it has become clear that there is no universal method able to solve all possible problems, but that one should rather select the method that is the most suitable to a problem of interest. The properties of the observable (s) and system under consideration that will, together with the available computing power, largely determine which type of method can be used are (van Gunsteren & Berendsen, 1990): (i) the required system size, (ii) the required volume of conformational space that has to be searched or sampled (in terms of dynamics: the required time-scale), (iii) the required resolution in terms of particles (determined by the smallest entity, subatomic particle, atom, or group of atoms, treated explicitly in the model), and (iv) the required energetical accuracy of the interaction function. These requirements may be incompatible, in which case the observable cannot be computed adequately with the currently available computer resources (van Gunsteren et al., 1995b). When requirements (i) and (ii) are in conflict with requirement (iii), this conflict may be resolved by the design of hierarchical or hybrid models, where only the relevant degrees of freedom are treated with a more expensive, higher resolution method. This is often done, for example, in the study of acid- or base-catalysed, organic or enzymatic reactions in the bulk phase (Warshel, 1991, Field, 1993, Whitnell & Wilson, 1993, Liu et al., 1996a).

Nanosecond molecular dynamics simulations of bovine pancreatic trypsin inhibitor and lysozyme in water are analyzed in terms of backbone atomic positional fluctuations and dynamical cross-correlations. It is found that although the molecular systems are stable, B-factors calculated over a time period as long as 500 ps are not representative for the motions within the proteins. This is especially true for the most mobile residues. On a nanosecond time-scale, the B-factors calculated from the simulations of the proteins in solution are considerably larger than those obtained by structure refinement of the proteins in crystals, based on X-ray data. The time evolution of the atomic fluctuations shows that for large portions of the proteins under study, atomic positional fluctuations are not yet converged after a nanosecond. Cross-correlations do not converge faster than the fluctuations themselves. Most display very erratic behavior if the sampling covers less than about 200 ps. It is also shown that inclusion of mobile atoms into the procedure used to remove rigid-body motion from the simulation can lead to spurious correlations between the motions of the atoms at the surface of the protein.

The raw single-ion solvation free energies computed from atomistic (explicit-solvent) simulations are extremely sensitive to the boundary conditions and treatment of electrostatic interactions used during these simulations. However, as shown recently [M. A. Kastenholz and P. H. Hünenberger, J. Chem. Phys. 124, 224501 (2006); M. M. Reif and P. H. Hünenberger, J. Chem. Phys. 134, 144103 (2010)], the application of appropriate correction terms permits to obtain methodology-independent results. The corrected values are then exclusively characteristic of the underlying molecular model including in particular the ion-solvent van der Waals interaction parameters, determining the effective ion size and the magnitude of its dispersion interactions. In the present study, the comparison of calculated (corrected) hydration free energies with experimental data (along with the consideration of ionic polarizabilities) is used to calibrate new sets of ion-solvent van der Waals (Lennard-Jones) interaction parameters for the alkali (Li(+), Na(+), K(+), Rb(+), Cs(+)) and halide (F(-), Cl(-), Br(-), I(-)) ions along with either the SPC or the SPC/E water models. The experimental dataset is defined by conventional single-ion hydration free energies [Tissandier et al., J. Phys. Chem. A 102, 7787 (1998); Fawcett, J. Phys. Chem. B 103, 11181] along with three plausible choices for the (experimentally elusive) value of the absolute (intrinsic) hydration free energy of the proton, namely, ΔG(hyd)(⊖)[H(+)] = -1100, -1075 or -1050 kJ mol(-1), resulting in three sets L, M, and H for the SPC water model and three sets L(E), M(E), and H(E) for the SPC/E water model (alternative sets can easily be interpolated to intermediate ΔG(hyd)(⊖)[H(+)] values). The residual sensitivity of the calculated (corrected) hydration free energies on the volume-pressure boundary conditions and on the effective ionic radius entering into the calculation of the correction terms is also evaluated and found to be very limited. Ultimately, it is expected that comparison with other experimental ionic properties (e.g., derivative single-ion solvation properties, as well as data concerning ionic crystals, melts, solutions at finite concentrations, or nonaqueous solutions) will permit to validate one specific set and thus, the associated ΔG(hyd)(⊖)[H(+)] value (atomistic consistency assumption). Preliminary results (first-peak positions in the ion-water radial distribution functions, partial molar volumes of ionic salts in water, and structural properties of ionic crystals) support a value of ΔG(hyd)(⊖)[H(+)] close to -1100 kJ·mol(-1).

An error was made in the derivation of Eq. (25) for the integrated electric field. The error is corrected and the modified results reported. In general, the various truncation schemes show improved agreement with the Born model for solvent polarization.

The concept of high-resolution shapes (also referred to as folds or states, depending on the context) of a polymer chain plays a central role in polymer science, structural biology, bioinformatics, and biopolymer dynamics. However, although the idea of shape is intuitively very useful, there is no unambiguous mathematical definition for this concept. In the present work, the distributions of high-resolution shapes within the ideal random-walk ensembles with N=3, … , 6 beads (or up to N=10 for some properties) are investigated using a systematic (grid-based) approach based on a simple working definition of shapes relying on the root-mean-square atomic positional deviation as a metric (i.e., to define the distance between pairs of structures) and a single cutoff criterion for the shape assignment. Although the random-walk ensemble appears to represent the paramount of homogeneity and randomness, this analysis reveals that the distribution of shapes within this ensemble, i.e., in the total absence of interatomic interactions characteristic of a specific polymer (beyond the generic connectivity constraint), is significantly inhomogeneous. In particular, a specific (densest) shape occurs with a local probability that is 1.28, 1.79, 2.94, and 10.05 times (N=3, … , 6) higher than the corresponding average over all possible shapes (these results can tentatively be extrapolated to a factor as large as about 1028 for N=100). The qualitative results of this analysis lead to a few rather counterintuitive suggestions, namely, that, e.g., (i) a fold classification analysis applied to the random-walk ensemble would lead to the identification of random-walk “ folds ; ” (ii) a clustering analysis applied to the random-walk ensemble would also lead to the identification random-walk “ states” and associated relative free energies ; and (iii) a random-walk ensemble of polymer chains could lead to well-defined diffraction patterns in hypothetical fiber or crystal diffraction experiments. The inhomogeneous nature of the shape probability distribution identified here for random walks may represent a significant underlying baseline effect in the analysis of real polymer chain ensembles (i.e., in the presence of specific interatomic interactions). As a consequence, a part of what is called a polymer shape may actually reside just “ in the eye of the beholder” rather than in the nature of the interactions between the constituting atoms, and the corresponding observation-related bias should be taken into account when drawing conclusions from shape analyses as applied to real structural ensembles.