Statistical thermodynamic analysis of peptide and protein insertion into lipid membranes.

A statistical thermodynamic approach is used to analyze the various contributions to the free energy change associated with the insertion of proteins and protein fragments into lipid bilayers. The partition coefficient that determines the equilibrium distribution of proteins between the membrane and the solution is expressed as the ratio between the partition functions of the protein in the two phases. It is shown that when all of the relevant degrees of freedom (i.e., those that change their character upon insertion into the membrane) can be treated classically, the partition coefficient is fully determined by the ratio of the configurational integrals and thus does not involve any mass-dependent factors, a conclusion that is also valid for related processes such as protein adsorption on a membrane surface or substrate binding to proteins. The partition coefficient, and hence the transfer free energy, depend only on the potential energy of the protein in the membrane. Expressing this potential as a sum of a "static" term, corresponding to the equilibrium (minimal free energy) configuration of the protein in the membrane, and a "dynamical" term representing fluctuations around the equilibrium configuration, we show that the static term contains the "solvation" and "lipid perturbation" contributions to the transfer free energy. The dynamical term is responsible for the "immobilization" free energy, reflecting the loss of translational and rotational entropy of the protein upon incorporation into the membrane. Based on a recent molecular theory of lipid-protein interactions, the lipid perturbation and immobilization contributions are then expressed in terms of the elastic deformation free energy resulting from the perturbation of the lipid environment by the foreign (protein) inclusion. The model is formulated for cylindrically shaped proteins, and numerical estimates are given for the insertion of an alpha-helical peptide into a lipid bilayer. The immobilization free energy is shown to be considerably smaller than in previous estimates of this quantity, and the origin of the difference is discussed in detail.     

Structure-based parallel medicinal chemistry approach to improve metabolic stability of benzopyran COX-2 inhibitors

Combination of the structure-based design and solid-phase parallel synthesis provided an integrated approach to rapidly develop the structure-activity relationship of benzopyran COX-2 inhibitors. Binding free energies predicted by free energy perturbation theory yielded good agreement with experimental results. New potent and selective lead compounds with improved metabolic properties were identified.     

Evaluation of catalytic free energies in genetically modified proteins

A combination of the empirical valence bond method and a free energy perturbation approach is used to simulate the activity of genetically modified enzymes. The simulations reproduce in a semiquantitative way the observed effects of mutations on the activity and binding free energies of trypsin and subtilisin. This suggests that we are approaching a stage of quantitative structure-function correlation of enzymes. The analysis of the calculations points towards the electrostatic energy of the reacting system as the key factor in enzyme catalysis. The changes in the charges of the reacting system and the corresponding changes in "solvation" free energy (generalized here as the interaction between the charges and the given microenvironment) are emphasized. It is argued that a reliable evaluation of these changes might be sufficient for correlating structure and catalysis. The use of free energy perturbation methods and thermodynamic cycles for evaluation of solvation energies and reactivity is discussed, pointing out our early contributions. The apparent elaborated nature of our treatment is clarified, explaining that such a treatment is essential for consistent calculations of chemical reactions in polar environments. The problems associated with seemingly more rigorous quantum mechanical methods are discussed, emphasizing the inconsistency associated with using gas phase charge distributions. The importance of dynamic aspects is examined by evaluating the autocorrelation of the protein "reaction field" on the reacting substrate. It is found that, at least in the present case, dynamic effects are not important. The nature of the catalytic free energy is considered, arguing that the protein provides preoriented dipoles (polarized to stabilize the transition state charge distribution) and small reorganization energy, thus reducing the activation free energy. The corresponding catalytic free energy is related to the folding free energy, which is being invested in aligning the active site dipoles.     

Dissipative surface waves in plasma

Debatable aspects of the theory of nonpotential surface waves propagating along the boundary of a dissipative medium with frequency dispersion are discussed. On the basis of the known theoretical results and theoretical analysis carried out in this work, a theory of surface waves that is valid for any dissipation of the perturbation energy in the medium is developed. It is shown that, if dissipation is sufficiently strong, there can be surface waves the physical nature and dispersion law of which differ radically from those of ordinary surface waves. The damping rate of such waves is low even at large dissipation in the medium, and their group and phase velocities exceed the speed of light. In particular, surface waves on the interface between vacuum and cold collisional electron plasma are considered. The existence of such surface waves for different media of laboratory and natural origin is discussed.     

Lysozyme-lysozyme and lysozyme-salt interactions in the aqueous saline solution: a new square-well potential

We investigate lysozyme-lysozyme and lysozyme-salt interactions in electrolyte solutions using a molecular-thermodynamic model. An equation of state based on the statistical mechanical perturbation theory is applied to describe the interactions. The perturbation term includes a new square-well potential of mean force, which implies the information about the lysozyme surface and salt type. The attractive energy of the potential of mean force is correlated with experimental cloud-point temperatures of lysozyme in various solution conditions. The same attractive energy is used to predict osmotic pressure of a given system with no additional parameters. The new potential shows a satisfactory improvement in understanding the interactions between lysozymes in aqueous salt solutions.     

Biased random walk models for chemotaxis and related diffusion approximations

Summary Stochastic models of biased random walk are discussed, which describe the behavior of chemosensitive cells like bacteria or leukocytes in the gradient of a chemotactic factor. In particular the turning frequency and turn angle distributions are derived from certain biological hypotheses on the background of related experimental observations. Under suitable assumptions it is shown that solutions of the underlying differential-integral equation approximately satisfy the well-known Patlak-Keller-Segel diffusion equation, whose coefficients can be expressed in terms of the microscopic parameters. By an appropriate energy functional a precise error estimation of the diffusion approximation is given within the framework of singular perturbation theory.     

The structure of ecosystems

Input-output theory is developed for an ecosystem in terms of production and respiration energy flows. The theory reveals a “structure” of the system by demonstrating the direct and indirect energy flow dependence of each member of the system upon the others. A method for tracing the direct and indirect element flows through the ecosystem is proposed.The structure is determined for two examples and a perturbation technique for the energy flow is suggested.     

Collective aspects of conformons and the electron transfer chain

A set of interacting harmonic oscillators is used as a model to define a low frequency collective mode in protein molecules. Such a mode may arise from electron-phonon interactions in second order perturbation theory. The mathematical scheme is analogous to those used in the theory of carcadian rhythms and in the theory of superconductivity. This collective mode may receive energy from electrons in the electron transfer chain (conformon) and pass the energy on to other similar modes. The low frequency of the mode leads to slow reactions, in agreement with experimental data. The model is compatible with some general characteristics of the electron transfer chain and its constituents: high thermodynamic efficiency, redox pools, redox switches, entatic states and conformational free energy transfer.     

Tryptophan-47 rotational isomerization in variant-3 scorpion neurotoxin. A combination thermodynamic perturbation and umbrella sampling study.

A combination thermodynamic perturbation and umbrella sampling study predicts two free energy wells for the rotational isomerization of the variant-3 scorpion neurotoxin tryptophan-47 indole side chain. One well has the indole side chain in the crystallographic orientation; the other has the indole rotated approximately 220 degrees to form a new conformation with a relative free energy of 3 +/- 2 kcal/mol. The activation barrier is 8.5 kcal/mol from the crystallographic well, from which transition state theory predicts a rate of escape of 2 x 10(5) s-1. Correlations in the displacements of side chains neighboring tryptophan-47 and the isomerization reaction coordinate last up to 20 ps. Favorable conditions of experimental verification are discussed.     

Extending the viability theory framework of resilience to uncertain dynamics,and application to lake eutrophication

Resilience, the capacity for a system to recover from a perturbation so as to keep its properties and functions, is of growing concern to a wide range of environmental systems. The challenge is often to render this concept operational without betraying it, nor diluting its content. The focus here is on building on the viability theory framework of resilience to extend it to discrete-time stochastic dynamical systems. The viability framework describes properties of the system as a subset of its state space. This property is resilient to a perturbation if it can be recovered and kept by the system after a perturbation: its trajectory can come back and stay in the subset. This is shown to reflect a general definition of resilience. With stochastic dynamics, the stochastic viability kernel describes the robust states, in which the system has a high probability of staying in the subset for a long time. Then, probability of resilience is defined as the maximal probability that the system reaches a robust state within a time horizon. Management strategies that maximize the probability of resilience can be found through dynamic programming. It is then possible to compute a range of statistics on the time for restoring the property. The approach is illustrated on the example of lake eutrophication and shown to foster the use of different indicators that are adapted to distinct situations. Its relevance for the management of ecological systems is also discussed.     

Interaction between inclusions embedded in membranes.

We calculate the membrane-induced interaction between inclusions, in terms of the membrane stretching and bending moduli and the spontaneous curvature. We find that the membrane-induced interaction between inclusions varies nonmonotonically as a function of the inclusion spacing. The location of the energy minimum depends on the spontaneous curvature and the membrane perturbation decay length, where the latter is set by the membrane moduli. The membrane perturbation energy increases with the inclusion radius. The Ornstein-Zernike theory, with the Percus-Yevick closure, is used to calculate the radial distribution function of inclusions. We find that when the spontaneous curvature is zero, the interaction between inclusions due to the membrane deformation is qualitatively similar to the hard-core interaction. However, in the case of finite spontaneous curvature, the effective interaction is dramatically modified.     

Molecular dynamics and free energy analysis of neuraminidase-ligand interactions

We report molecular dynamics calculations of neuraminidase in complex with an inhibitor, 4-amino-2-deoxy-2,3-didehydro-N-acetylneuraminic acid (N-DANA), with subsequent free energy analysis of binding by using a combined molecular mechanics/continuum solvent model approach. A dynamical model of the complex containing an ionized Glu119 amino acid residue is found to be consistent with experimental data. Computational analysis indicates a major van der Waals component to the inhibitor-neuraminidase binding free energy. Based on the N-DANA/neuraminidase molecular dynamics trajectory, a perturbation methodology was used to predict the binding affinity of related neuraminidase inhibitors by using a force field/Poisson-Boltzmann potential. This approach, incorporating conformational search/local minimization schemes with distance-dependent dielectric or generalized Born solvent models, correctly identifies the most potent neuraminidase inhibitor. Mutation of the key ligand four-substituent to a hydrogen atom indicates no favorable binding free energy contribution of a hydroxyl group; conversely, cationic substituents form favorable electrostatic interactions with neuraminidase. Prospects for further development of the method as an analysis and rational design tool are discussed.     

Random matrix theory in biological nuclear magnetic resonance spectroscopy

The statistical theory of energy levels or random matrix theory is presented in the context of the analysis of chemical shifts of nuclear magnetic resonance (NMR) spectra of large biological systems. Distribution functions for the spacing between nearest-neighbor energy levels are discussed for uncorrelated, correlated, and random superposition of correlated energy levels. Application of this approach to the NMR spectra of a vitamin, an antibiotic, and a protein demonstrates the state of correlation of an ensemble of energy levels that characterizes each system. The detection of coherent and dissipative structures in proteins becomes feasible with this statistical spectroscopic technique.     

Analysis of intermolecular interaction energy inputs in benzene-imidazole and imidazole-imidazole systems in parallel displaced and T-configuration

Intermolecular interactions in several dimer aromatic systems were analyzed to determine how various energy contributions (electrostatic, exchange, repulsion, and polarization) change depending on the value of monomers separation. Different contributions to the intermolecular energy interactions between imidazole-imidazole and benzene-imidazole dimers are studied using the aug-cc-pVDZ basis set in the framework of ab initio Hartree-Fock and second-order Møller-Plesset perturbation theory methods. Special attention is paid to the exchange and dispersion energy binding contributions.     

Theoretical investigation on the hypochromism of dinucleoside phosphates]

The hypochromism of stacked dimers of the nucleotide bases taken as models of the dinucleoside phosphates and dinucleotides was studied with the use of the configuration interaction and pertubation theory methods. General expression for the hypochromism of the polynucleotides is given in the first order perturbation theory with three different ways for approximation of the matrix elements of the perturbation operator. This expression was used for calculation of the dimer hypochromism in terms of theoretically calculated monomer characteristics. Dependence of the hypochromism on the dimer conformation was investigated. The results obtained so far demonstrate that it is important to take into account the electronic transitions in the vacuum UV region. This approach will enable one to elucidate the contribution of neighbouring bases into the DNA hypochromism.     

Optimal foraging in bumblebees: Calculation of net rate of energy intake and optimal patch choice

To test many predictions of “optimal foraging theory” it is necessary to calculate the rate of net energy intake of a foraging animal. Equations are derived for the calculation of the rate of net energy intake of a foraging bumblebee. The assumptions that form the basis of these energy equations are discussed. As examples, the rates of net energy intake are calculated for Bombus flavifrons workers foraging on neighboring patches of Aconitum columbianum and Delphinium barbeyi. If the bumblebees forage optimally, their net rates of energy intake in the two patches should be equal. The observed rates are consistent with this hypothesis. The application of an optimality approach to pollination biology is briefly discussed.     

The Spherical Expansion of H2 Dimer Interaction Energy by Double Symmetry-Adapted Perturbation Theory

Abstract

The weak interaction energy of H₂ dimer is studied by double symmetry-adapted perturbation theory (SAPT) within second-order of intermolecular and intramonomer perturbation for molecular simulations. The assumed orientations of H₂ dimer are linear, parallel, T type and X type. Among four orientations T orientation is the most stable, while linear orientation is the most repulsive. The second-order dispersion energy E _disp ⁽²⁾ is the most attractive contribution in all orientations. The interaction energy has the anisotropy, so we expressed our total interaction energy by the spherical expansion to compare with the experimental value. The isotropic interaction energy is about 85% of the experimental value.     

Optical activity of saccharides—the vacuum-uv origin of sodium-D rotation

A semiempirical theory of saccharide optical activity indicates that the dominant source of Na_D rotation is a vacuum-uv CD band near 150 nm, a band observed experimentally in polysaccharide film CD spectra. The model is a modification of polarizability theory in which high-energy electronic excitations are coupled by degenerate perturbation theory, giving rise to “molecular excitons.” The existence of an excitation mode well separated in energy from even higher energy modes arises from the local symmetry of tetrahedral carbon atoms in a puckered ring structure. Calculated Na_D rotations correlate well with experimental values.     

On the nature of stability of the nucleotide base associates in water solution

Expression for the long-range intermolecular interaction energy obtained by the perturbation theory method in atomic dipole approximation are used for the study of the nature of base interaction in stacked dimers formed of two neighbouring DNA base pairs. Base wave functions are computed by the CNDO-CI method. The inplane interactions are shown to give the dominant contribution into the DNA stabilization energy in vacuum. The estimations performed for the solvent effect on intermolecular interaction energy allowed us to draw conclusions about the decisive role of hydrophobic interactions in a base stacking.     

Biological power laws and Darwin's principle

Assuming that the repertoire of responses by living systems to perturbation gives a measure of their Darwinian fitness in a rapidly fluctuating environment, those that fulfill allometries (power laws) are described by means of catastrophes, whose variables and parameters are smooth functions of biological attributes. Using empirical allometries from a given system as input, a method is proposed to construct its associated catastrophe, allowing specific predictions on its susceptibility to perturbation and related properties, based on general results from catastrophe theory. The method is discussed within the macroecological context, and an example is provided by applying it to ecological systems that satisfy the self-thinning rule.