Boundary conditions for ionotropic gelation of polyuronides

The determination of reagent concentrations sufficient for gelation in the course of a crosslinking reaction in solution enables characterization of macromolecular coil dimensions as a function of solvent quality and calculation of the apparent equilibrium constant and the reaction order with respect to polymer. Interactions of polyuronides with polycoordinative metal ions are discussed.     

Boundary conditions in the theory of the relaxation field

The perturbationf _ji ^' generated by an external field in the distribution function is derived by integration of the Onsager-Fuoss equation of continuity. The solution isf _ji ^' (r)=C(I+Ah₁+Bh₂) whereCI is a particular integral andh ₁ andh ₂ are solutions of the homogeneous equation. The physical significance of the boundary conditions which evaluate the constantsA andB is discussed. It is then shown that the conditionf _ji ^' () 0 requiresB=0 and that the condition lim(f _ji ^' /n²) 0 at zero concentration is satisfied if and only ifA=–1.     

Role of short-range electrostatics in torsional potentials

A force field needs to decide if it should contain a torsional potential or not. A helpful guide to this decision should come from a quantum mechanical energy partitioning. Here we analyze the energy profiles of eight simple molecules (ethane, hydrogen peroxide, hydrazine, methanol, acetaldehyde, formamide, acetamide and N-methylacetamide) subject to rotation around a torsion angle. Coulomb interaction energies between all atom pairs in a molecule are monitored during the rotation. Atoms are defined as finite electron density fragments by quantum chemical topology, a method that enables well-defined short-range interactions (1-2, 1-3 and 1-4). Energy profiles of Coulomb interaction energies mostly counteract the ab initio energy profiles. This and future work strives to settle ambiguities in current force field design.     

Multipole electrostatics in hydration free energy calculations

Hydration free energy (HFE) is generally used for evaluating molecular solubility, which is an important property for pharmaceutical and chemical engineering processes. Accurately predicting HFE is also recognized as one fundamental capability of molecular mechanics force field. Here, we present a systematic investigation on HFE calculations with AMOEBA polarizable force field at various parameterization and simulation conditions. The HFEs of seven small organic molecules have been obtained alchemically using the Bennett Acceptance Ratio method. We have compared two approaches to derive the atomic multipoles from quantum mechanical calculations: one directly from the new distributed multipole analysis and the other involving fitting to the electrostatic potential around the molecules. Wave functions solved at the MP2 level with four basis sets (6-311G*, 6-311++G(2d,2p), cc-pVTZ, and aug-cc-pVTZ) are used to derive the atomic multipoles. HFEs from all four basis sets show a reasonable agreement with experimental data (root mean square error 0.63 kcal/mol for aug-cc-pVTZ). We conclude that aug-cc-pVTZ gives the best performance when used with AMOEBA, and 6-311++G(2d,2p) is comparable but more efficient for larger systems. The results suggest that the inclusion of diffuse basis functions is important for capturing intermolecular interactions. The effect of long-range correction to van der Waals interaction on the hydration free energies is about 0.1 kcal/mol when the cutoff is 12?, and increases linearly with the number of atoms in the solute/ligand. In addition, we also discussed the results from a hybrid approach that combines polarizable solute with fixed-charge water in the HFE calculation.     

Limiting assumptions in molecular modeling: electrostatics

Molecular mechanics attempts to represent intermolecular interactions in terms of classical physics. Initial efforts assumed a point charge located at the atom center and coulombic interactions. It is been recognized over multiple decades that simply representing electrostatics with a charge on each atom failed to reproduce the electrostatic potential surrounding a molecule as estimated by quantum mechanics. Molecular orbitals are not spherically symmetrical, an implicit assumption of monopole electrostatics. This perspective reviews recent evidence that requires use of multipole electrostatics and polarizability in molecular modeling.     

Boundary conditions of liquid phase reactors with axial dispersion

Numerical calculations of concentration profiles in axially dispersed flow reactors with different properties from section to section show that the conversion may depend considerably on the kind of boundary conditions applied at the boundary surfaces between sections. The jump condition of Danckwerts and the non-jump condition of Wehner and Wilhelm yield different concentration profiles. An experimental study of an isothermal liquid phase reactor divided into sections with different properties reveals that no back effect can be found as would be predicted by the application of Wehner and Wilhelm's boundary conditions. This result and earlier experimental findings in the literature lead to the conclusion that the mechanism of effective turbulent diffusivity in liquids does not provide any back transport of mass. Therefore the application of the boundary conditions of Wehner and Wilhelm for flow reactors is not justified if mass dispersion is caused predominantly by effective turbulent diffusivity. From a macroscopic point of view, the jump condition of Danckwerts appears to be more appropriate as it predicts conversion profiles which agree well with experimental results.     

Generating inherent structures of liquids: comparison of local minimization algorithms

Properties of minima obtained by two different local minimization algorithms, the conjugate gradient and the limited-memory Broyden-Fletcher-Goldfarb-Shanno, are compared for a liquid whose particles interact via a modified Lennard-Jones pair interaction. The average properties of inherent structures obtained by the two minimization procedures are shown to agree within statistical error, though for a given starting configuration the two algorithms may not quench to identical minima.     

Atomic force algorithms in density functional theory electronic-structure techniques based on local orbitals

Electronic structure methods based on density-functional theory, pseudopotentials, and local-orbital basis sets offer a hierarchy of techniques for modeling complex condensed-matter systems with a wide range of precisions and computational speeds. We analyze the relationships between the algorithms for atomic forces in this hierarchy of techniques, going from empirical tight-binding through ab initio tight-binding to full ab initio. The analysis gives a unified overview of the force algorithms as applied within techniques based either on diagonalization or on linear-scaling approaches. The use of these force algorithms is illustrated by practical calculations with the CONQUEST code, in which different techniques in the hierarchy are applied in a concerted manner.     

Highly accurate biomolecular electrostatics in continuum dielectric environments

Implicit solvent models based on the Poisson-Boltzmann (PB) equation are frequently used to describe the interactions of a biomolecule with its dielectric continuum environment. A novel, highly accurate Poisson-Boltzmann solver is developed based on the matched interface and boundary (MIB) method, which rigorously enforces the continuity conditions of both the electrostatic potential and its flux at the molecular surface. The MIB based PB solver attains much better convergence rates as a function of mesh size compared to conventional finite difference and finite element based PB solvers. Consequently, highly accurate electrostatic potentials and solvation energies are obtained at coarse mesh sizes. In the context of biomolecular electrostatic calculations it is demonstrated that the MIB method generates substantially more accurate solutions of the PB equation than other established methods, thus providing a new level of reference values for such models. Initial results also indicate that the MIB method can significantly improve the quality of electrostatic surface potentials of biomolecules that are frequently used in the study of biomolecular interactions based on experimental structures.     

Multiple protonation equilibria in electrostatics of protein-protein binding

All proteins contain groups capable of exchanging protons with their environment. We present here an approach, based on a rigorous thermodynamic cycle and the partition functions for energy levels characterizing protonation states of the associating proteins and their complex, to compute the electrostatic pH-dependent contribution to the free energy of protein-protein binding. The computed electrostatic binding free energies include the pH of the solution as the variable of state, mutual "polarization" of associating proteins reflected as changes in the distribution of their protonation states upon binding and fluctuations between available protonation states. The only fixed property of both proteins is the conformation; the structure of the monomers is kept in the same conformation as they have in the complex structure. As a reference, we use the electrostatic binding free energies obtained from the traditional Poisson-Boltzmann model, computed for a single macromolecular conformation fixed in a given protonation state, appropriate for given solution conditions. The new approach was tested for 12 protein-protein complexes. It is shown that explicit inclusion of protonation degrees of freedom might lead to a substantially different estimation of the electrostatic contribution to the binding free energy than that based on the traditional Poisson-Boltzmann model. This has important implications for the balancing of different contributions to the energetics of protein-protein binding and other related problems, for example, the choice of protein models for Brownian dynamics simulations of their association. Our procedure can be generalized to include conformational degrees of freedom by combining it with molecular dynamics simulations at constant pH. Unfortunately, in practice, a prohibitive factor is an enormous requirement for computer time and power. However, there may be some hope for solving this problem by combining existing constant pH molecular dynamics algorithms with so-called accelerated molecular dynamics algorithms.     

Protein-water electrostatics and principles of bioenergetics

Despite its diversity, life universally relies on a simple basic mechanism of energy transfer in its energy chains-hopping electron transport between centers of electron localization on hydrated proteins and redox cofactors. Since many such hops connect the point of energy input with a catalytic site where energy is stored in chemical bonds, the question of energy losses in (nearly activationless) electron hops, i.e., energetic efficiency, becomes central for the understanding of the energetics of life. We show here that standard considerations based on rules of Gibbs thermodynamics are not sufficient, and the dynamics of the protein and the protein-water interface need to be involved. The rate of electronic transitions is primarily sensitive to the electrostatic potential at the center of electron localization. Numerical simulations show that the statistics of the electrostatic potential produced by hydration water are strongly non-Gaussian, with the breadth of the electrostatic noise far exceeding the expectations of the linear response. This phenomenon, which dramatically alters the energetic balance of a charge-transfer chain, is attributed to the formation of ferroelectric domains in the protein's hydration shell. These dynamically emerging and dissipating domains make the shell enveloping the protein highly polar, as gauged by the variance of the shell dipole which correlates with the variance of the protein dipole. The Stokes-shift dynamics of redox-active proteins are dominated by a slow component with the relaxation time of 100-500 ps. This slow relaxation mode is frozen on the time-scale of fast reactions, such as bacterial charge separation, resulting in a dramatically reduced reorganization free energy of fast electronic transitions. The electron transfer activation barrier becomes a function of the corresponding rate, self-consistently calculated from a non-ergodic version of the transition-state theory. The peculiar structure of the protein-water interface thus provides natural systems with two "non's"-non-Gaussian statistics and non-ergodic kinetics-to tune the efficiency of the redox energy transfer. Both act to reduce the amount of free energy released as heat in electronic transitions. These mechanisms are shown to increase the energetic efficiency of protein electron transfer by up to an order of magnitude compared to the "standard picture" based on canonical free energies and the linear response approximation. In other words, the protein-water tandem allows both the formation of a ferroelectric mesophase in the hydration shell and an efficient control of the energetics by manipulating the relaxation times.     

Boundary conditions on the partitioning of deaminatively generated benzyl cations

Nitrogenous entity-separated ion pairs (NESIPs) containing benzyl cations, nitrogen gas, and pivalate anions were generated via thermal deamination of N-benzyl-N-nitrosopivalamide. Some decompositions were performed in methanolic solutions saturated with selected nucleophiles: acetate, azide, or cyanide ions. Trace amounts of benzyl cyanide and tolunitriles were observed; no corresponding products were detected in the acetate and azide cases. Other decompositions were performed in the absence of traditional solvent but in the presence of the nucleophilic salts; again only poor cyanide interception of the cation was observed. The poor showing of the nucleophilic ions, when present, is discussed in the context of the lifetime of the cation, effective nucleophilicity, and cage effects in deamination.     

Effective multipoles and Yukawa electrostatics in dressed molecule theory

In this paper we derive the multipolar expansion of the screened Coulomb potential in electrolyte solutions with molecular solvent. The solute and solvent molecules can have arbitrary sizes, shapes, and internal charge distributions. We use the exact statistical mechanical definition of renormalized charge distributions coming from "dressed molecule theory" to determine the effective multipoles of a molecule immersed in an electrolyte. The effects of many-body correlations are fully included in our formally exact theory. We restrict ourselves to sufficiently dilute solutions so the screened Coulomb potential decays for large distances like a Yukawa function, exp(-kappa r)/r, where r is the distance and 1/kappa is the decay length (it is normally different from the Debye length). The resulting "Yukawa electrostatics" differ in many respects from ordinary, unscreened electrostatics. The "Yukawa charge" of a molecule (the lowest order moment in the multipolar expansion) is in general not equal to its Coulombic charge and it is not the integral of the renormalized charge distribution of the molecule. Moreover, as shown in this paper, the multipolar expansion of the Yukawa potential does not correspond, contrary to the case of the Coulomb potential, to its asymptotic expansion for large r. As a consequence, the charge term in the multipolar expansion is not the leading term in the asymptotic expansion. Instead, for large r values, multipoles of all orders contribute to the leading asymptotic term. Thus, the electrostatic potential from, for example, an electroneutral solvent molecule in an electrolyte solution has generally the same range as that from an ion. The proper asymptotic expansion for electrostatic interactions in electrolytes is derived. It is briefly shown how the multipole expansion formalism can also be applied in the Poisson-Boltzmann approximation for primitive model electrolytes.     

Role of electrostatics in the thermal stability of ubiquitin

The failure of the ubiquitin-proteasome system is involved in many diseases. Here, in order to assess the pH-induced changes in the physico-chemical properties of ubiquitin, DSC measurements have been carried out at 2.5 physico-chemical properties of ubiquitin, DSC measurements have been carried out at 2.5     

Aromatic molecules in anion recognition: electrostatics versus H-bonding

Mass-selected complexes A-.C6FnH(6-n) (A = Cl, I, SF6; n = 0-5) were studied by infrared photodissociation spectroscopy and computational chemistry methods to investigate the interaction of negative ions and aromatic molecules, in which the charge distribution can be tuned by fluorination. Surprisingly, we find that, despite positive partial charges on the carbon atoms at high levels of fluorination, all anions under study prefer hydrogen bonding to the remaining H atoms in the ligand rather than binding to the positively charged ring. Moreover, bifurcated hydrogen bonds to two neighboring CH groups are energetically favored over linear hydrogen bonds to a single CH group.