Binding of Net-Fla,a Netropsin-Flavin Hybrid Molecule,to DNA: Molecular Mechanics and Dynamics Studies in vacuo and in Water Solution

Abstract

We have studied the binding of the hybrid netropsin-flavin (Net-Fla) molecule onto four sequences containing four A.T base pairs. Molecular mechanics minimizations in vacuo show numerous minimal conformations separated by one base pair. 400 ps molecular dynamics simulations in vacuo have been performed using the lowest minima as the starting conformations. During these simulations, the flavin moiety of the drug makes two hydrogen bonds with an amino group of a neighboring guanine. A 200 ps molecular dynamics simulation in explicit water solution suggests that the binding of Net-Fla upon the DNA substrate is enhanced by water bridges. A water molecule bridging the amidinium of Net-Fla to the N3 atom of an adenine seems to be stuck in the dmg-DNA complex during the whole simulation. The fluctuations of the DNA helical parameters and of the torsion angles of the sugar-phosphate backbone are very similar in the simulations in vacuo and in water. The time auto-correlation functions for the DNA helical parameters decrease rapidly in the picosecond range in vacuo. The same functions computed from the water solution molecular dynamics simulations seem to have two modes: the rapid mode is similar to the behavior in vacuo, and is followed by a slower mode in the 10 ps range.     

Grand Molecular Dynamics: A Method for Open Systems

We present a new molecular dynamics method for studying the dynamics of open systems. The method couples a classical system to a chemical potential reservior. In the formulation, following the extended system dynamics approach, we introduce a variable, v to represent the coupling to the chemical potential reservoir. The new variable governs the dynamics of the variation of number of particles in the system. The number of particles is determined by taking the integer part of v. The fractional part of the new variable is used to scale the potential energy and the kinetic energy of an additional particle: i.e., we introduce a fractional particle. We give the ansatz Lagrangians and equations of motion for both the isothermal and the adiabatic forms of grand molecular dynamics. The averages calculated over the trajectories generated by these equations of motion represent the classical grand canonical ensemble (μVT) and the constant chemical potential adiabatic ensemble (μVL) averages, respectively. The microcanonical phase space densities of the adiabatic and isothermal forms the molecular dynamics method are shown to be equivalent to adiabatic constant chemical potential ensemble, and grand canonical ensemble partition functions. We also discuss the extension to multi-component systems, molecular fluids, ionic solutions and the problems and solutions associated with the implementation of the method. The statistical expressions for thermodynamic functions such as specific heat; adiabatic bulk modulus, Grüneissen parameter and number fluctuations are derived. These expressions are used to analyse trajectories of constant chemical potential systems.     

Classical molecular dynamics simulation of the photoinduced electron transfer dynamics of plastocyanin.

Classical molecular dynamics simulations are used to investigate the nuclear motions associated with photoinduced electron transfer in plastocyanin. The blue copper protein is modeled using a molecular mechanics potential; potential parameters for the copper-protein interactions are determined using an x-ray crystallographic structure and absorption and resonance Raman spectra. Molecular dynamics simulations yield a variety of information about the ground (oxidized) and optically excited (charge-transfer) states: 1) The probability distribution of the potential difference between the states, which is used to determine the coordinate and energy displacements, places the states well within the Marcus inverted region. 2) The two-time autocorrelation function of the difference potential in the ground state and the average of the difference potential after instantaneous excitation to the excited state are very similar (confirming linear response in this system); their decay indicates that vibrational relaxation occurs in about 1 ps in both states. 3) The spectral densities of various internal coordinates begin to identify the vibrations that affect the optical transition; the spectral density of the difference potential correlation function should also prove useful in quantum simulations of the back electron transfer. 4) Correlation functions of the protein atomic motions with the difference potential show that the nuclear motions are correlated over a distance of more than 20 A, especially along proposed electron transport paths.     

Molecular Dynamics as a Mathematical Mapping. III. Efficient Evaluation of the Differentiable Force Functions and Their Derivatives

Abstract

The fully continuous and differentiable framework for performing molecular dynamics calculations introduced in parts I and II of this paper [1,2] requires the evaluation of rather complex force functions and their spatial partial derivatives. This paper presents an efficient interpolation scheme for the evaluation of these quantities over a finite spatial domain.

The modified force function is approximated by a linear combination of Hermite cubic basis functions such that both the interpolant of the force and its spatial derivatives are continuous across the grid boundaries. In order to achieve better accuracy for a given grid size, a nonuniform rectilinear grid is constructed via iterative refinement procedure. The latter guarantees the accuracy of the force computed by interpolation within any specified tolerance > ε O.

For many potential functions of practical interest, it is possible for polynomial interpolants to be constructed for parts of the force functions which are independent of the potential parameters and system density (the so-called “separable force functions”). In such cases, a single interpolation grid which is applicable for a wide range of potential parameters and system densities can be constructed a priori.     

Analyzing steady states of dynamics of bio-molecules from the structure of regulatory networks

Regulatory relations between biological molecules constitute complex network systems and realize diverse biological functions through the dynamics of molecular activities. However, we currently have very little understanding of the relationship between the structure of a regulatory network and its dynamical properties. In this paper we introduce a new method, named “linkage logic” to analyze the dynamics of network systems. By this method, we can restrict possible steady states of a given complex network system from the knowledge of regulatory linkages alone. The regulatory linkage simply specifies the list of variables that affect the dynamics of each variable. We formalize two aspects of the linkage logic: the “Principle of Compatibility” determines the upper limit of the diversity of possible steady states of the dynamics realized by a given network; the “Principle of Dependency” determines the possible combinations of states of the system. By combining these two aspects, (i) for a given network, we can identify a cluster of nodes that gives an alternative representation of the steady states of the whole system, (ii) we can reduce a given complex network into a simpler one without loss of the ability to generate the diversity of steady states, (iii) we can examine the consistency between the structure of network and observed set of steady states, and (iv) sometimes we can predict unknown states or unknown regulations from an observed set of steady states alone. We illustrate the method by several applications to an experimentally determined regulatory network for biological functions.     

Evidence of protein collective motions on the picosecond timescale

We investigate the presence of structural collective motions on a picosecond timescale for the heme protein, cytochrome c, as a function of oxidation and hydration, using terahertz (THz) time domain spectroscopy and molecular dynamics simulations. The THz response dramatically increases with oxidation, with the largest increase for lowest hydrations, and highest frequencies. For both oxidation states the THz response rapidly increases with hydration saturating above ∼25% (g H₂O/g protein). Quasiharmonic vibrational modes and dipole-dipole correlation functions were calculated from molecular dynamics trajectories. The collective mode density of states alone reproduces the measured hydration dependence, providing strong evidence of the existence of these motions. The large oxidation dependence is reproduced only by the dipole-dipole correlation function, indicating the contrast arises from diffusive motions consistent with structural changes occurring in the vicinity of buried internal water molecules. This source for the observed oxidation dependence is consistent with the lack of an oxidation dependence in nuclear resonant vibrational spectroscopy measurements.     

A model approach to the population dynamics of the rotifer Brachionus rubens in two-stage chemostat culture

Summary A model, based on energy-flow considerations, is presented which describes the population dynamics of Brachionus rubens in the second stage of a two-stage algalrotifer chemostat. The rotifers are foodlimited with substrate-inhibition occurring at high algal densities. The model shows two stable states: steady state with constant density of rotifers and washout of the animals. Which one of the stable states is reached depends on the initial conditions.Empirical data are in general agreement with the model. Deviations may be explained by the fact that the data underlying the model calculations are based on a different food alga (Chlorella vulgaris) than the one used in the experiments (Monoraphidium minutum).The observed population growth rate reaches a maximum value of 0.84 (1/day) at algal densities of 3–4. 10⁶ cells/ml. It decreases at higher algal densities. The egg ratio is related linearily to algal density without being reduced at high algal densities.This study is dedicated to the memory of Prof. Dr. Udo Halbach     

Microsecond simulations of the folding/unfolding thermodynamics of the Trp‐cage miniprotein

We study the unbiased folding/unfolding thermodynamics of the Trp‐cage miniprotein using detailed molecular dynamics simulations of an all‐atom model of the protein in explicit solvent using the Amberff99SB force field. Replica‐exchange molecular dynamics simulations are used to sample the protein ensembles over a broad range of temperatures covering the folded and unfolded states at two densities. The obtained ensembles are shown to reach equilibrium in the 1 μs/replica timescale. The total simulation time used in the calculations exceeds 100 μs. Ensemble averages of the fraction folded, pressure, and energy differences between the folded and unfolded states as a function of temperature are used to model the free energy of the folding transition, ΔG(P, T), over the whole region of temperatures and pressures sampled in the simulations. The ΔG(P, T) diagram describes an ellipse over the range of temperatures and pressures sampled, predicting that the system can undergo pressure‐induced unfolding and cold denaturation at low temperatures and high pressures, and unfolding at low pressures and high temperatures. The calculated free energy function exhibits remarkably good agreement with the experimental folding transition temperature (T_f = 321 K), free energy, and specific heat changes. However, changes in enthalpy and entropy are significantly different than the experimental values. We speculate that these differences may be due to the simplicity of the semiempirical force field used in the simulations and that more elaborate force fields may be required to describe appropriately the thermodynamics of proteins. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Molecular dynamics simulation of surfactin molecules at the water-hexane interface

The dynamics of surfactin, a lipopeptide surfactant from Bacillus subtilis, has been studied by molecular dynamics at different interfacial concentrations in a water-hexane medium reproducing a hydrophilic/hydrophobic biphasic system. The shapes and orientations of surfactin molecules, as hydrogen bonds and Ramachandran angles, have been recorded to investigate the environment effect on the molecular structure. We demonstrate that the peptidic backbone can exhibit a large flexibility and that conformational motions and structural fluctuations depend strongly on the interfacial concentration. Moreover, we have measured the surface activity of this biosurfactant by computing the interfacial tension and lateral and rotational diffusion coefficients.     

Density-dependent resistance of the gypsy moth <Emphasis Type="Italic">Lymantria dispar</Emphasis> to its nucleopolyhedrovirus,and the consequences for population dynamics

The processes controlling disease resistance can strongly influence the population dynamics of insect outbreaks. Evidence that disease resistance is density-dependent is accumulating, but the exact form of this relationship is highly variable from species to species. It has been hypothesized that insects experiencing high population densities might allocate more energy to disease resistance than those at lower densities, because they are more likely to encounter density-dependent pathogens. In contrast, the increased stress of high-density conditions might leave insects more vulnerable to disease. Both scenarios have been reported for various outbreak Lepidoptera in the literature. We tested the relationship between larval density and disease resistance with the gypsy moth (Lymantria dispar) and one of its most important density-dependent mortality factors, the nucleopolyhedrovirus (NPV) LdMNPV, in a series of bioassays. Larvae were reared in groups at different densities, fed the virus individually, and then reared individually to evaluate response to infection. In this system, resistance to the virus decreased with increasing larval density. Similarly, time to death was faster at high densities than at lower densities. Implications of density–resistance relationships for insect–pathogen population dynamics were explored in a mathematical model. In general, an inverse relationship between rearing density and disease resistance has a stabilizing effect on population dynamics.     

Simple models for complex systems: exploiting the relationship between local and global densities

Simple temporal models that ignore the spatial nature of interactions and track only changes in mean quantities, such as global densities, are typically used under the unrealistic assumption that individuals are well mixed. These so-called mean-field models are often considered overly simplified, given the ample evidence for distributed interactions and spatial heterogeneity over broad ranges of scales. Here, we present one reason why such simple population models may work even when mass-action assumptions do not hold: spatial structure is present but it relates to global densities in a special way. With an individual-based predator–prey model that is spatial and stochastic, and whose mean-field counterpart is the classic Lotka–Volterra model, we show that the global densities and densities of pairs (or spatial covariances) establish a bi-power law at the stationary state and also in their transient approach to this state. This relationship implies that the dynamics of global densities can be written simply as a function of those densities alone without invoking pairs (or higher order moments). The exponents of the bi-power law for the predation rate exhibit a remarkable robustness to changes in model parameters. Evidence is presented for a connection of our findings to the existence of a critical phase transition in the dynamics of the spatial system. We discuss the application of similar modified mean-field equations to other ecological systems for which similar transitions have been described, both in models and empirical data.     

A study of DNA denaturation in the ultracentrifuge

The melting transition of DNA in alkaline CsCl can be followed in the analytical ultracentrifuge. Equilibrium partially denatured states can be observed. These partially denatured DNA bands have bandwidths of up to several times those of native DNA. Less stable molecules melt early and are found at heavier densities in the melting region. An idealized ultracentrifuge melting transition is described. The melting transition of singly nicked PM-2 DNA resembles the idealized curve. The DNA profile is a Gaussian band at all points in the melt. DNA's from mouse, D. Melanogaster, M. lysodeikticus, T4, and T7 also show equilibrium bands at partially denatured densities, some of which are highly asymmetric. Simple sequence satellite DNA shows an all-or-none transition with no equilibrium bands at partially denatured densities. The temperature at which a DNA denatures is an increasing function of the (G + C) content of the DNA. The T_m does not show a molecular-weight dependence in the range 1.2 × 10⁶–1.5 × 10⁷ daltons (single strand) for mouse, M. lysodeikticus, or T4 DNA. The mouse DNA partially denatured bands do not change shape as a function of molecular weight. The T4 DNA intermediate band develops a late-melting tail at low molecular weight. M. lysodeikticus DNA bands at partially denatured densities become broader as the molecular weight is decreased. Mouse DNA is resolved into six Gaussian components at each point in the melting transition.     

Membrane-bound ARF1 peptide: interpretation of neutron diffraction data by molecular dynamics simulation methods

Adenosine diphosphate ribosylation factor-1 (ARF1) is activated by cell membrane binding of a self-folding N-terminal domain. We have previously presented four possible conformations of the membrane bound, human ARF1 N-terminal peptide in planar lipid bilayers of DOPC and DOPG (7:3 molar ratio), determined from lamellar neutron diffraction and circular dichroism data. In this paper we analyse the four possible conformations by molecular dynamics simulations. The aim of these simulations was to use MD to distinguish which of the four possible membrane bound structures was the most likely. The most likely conformation was determined according to the following criteria: (a) location of label positions on the peptide in relation to the bilayer, (b) lowest mean square displacement from the initial structure, (c) lowest system energy, (d) most peptide-lipid headgroup hydrogen bonding, (e) analysis of phi/psi angles of the peptide. These findings demonstrate the application of molecular dynamics simulations to explore neutron diffraction data.     

End-point targeted molecular dynamics: large-scale conformational changes in potassium channels

Large-scale conformational changes in proteins that happen often on biological time scales may be relatively rare events on the molecular dynamics time scale. We have implemented an approach to targeted molecular dynamics called end-point targeted molecular dynamics that transforms proteins between two specified conformational states through the use of nonharmonic “soft” restraints. A key feature of the method is that the protein is free to discover its own conformational pathway through the plethora of possible intermediate states. The method is applied to the Shaker K_v1.2 potassium channel in implicit solvent. The rate of cycling between the open and closed states was varied to explore how slow the cycling rate needed to be to ensure that microscopic reversibility along the transition pathways was well approximated. Results specific to the K⁺ channel include: 1), a variation in backbone torsion angles of residues near the Pro-Val-Pro motif in the inner helix during both opening and closing; 2), the identification of possible occlusion sites in the closed channel located among Pro-Val-Pro residues and downstream; 3), a difference in the opening and closing pathways of the channel; and 4), evidence of a transient intermediate structural substate. The results also show that likely intermediate conformations during the opening-closing process can be generated in computationally tractable simulation times.     

Microtubule Simulations Provide Insight into the Molecular Mechanism Underlying Dynamic Instability

The dynamic instability of microtubules (MTs), which refers to their ability to switch between polymerization and depolymerization states, is crucial for their function. It has been proposed that the growing MT ends are protected by a “GTP cap” that consists of GTP-bound tubulin dimers. When the speed of GTP hydrolysis is faster than dimer recruitment, the loss of this GTP cap will lead the MT to undergo rapid disassembly. However, the underlying atomistic mechanistic details of the dynamic instability remains unclear. In this study, we have performed long-time atomistic molecular dynamics simulations (1 μs for each system) for MT patches as well as a short segment of a closed MT in both GTP- and GDP-bound states. Our results confirmed that MTs in the GDP state generally have weaker lateral interactions between neighboring protofilaments (PFs) and less cooperative outward bending conformational change, where the difference between bending angles of neighboring PFs tends to be larger compared with GTP ones. As a result, when the GDP state tubulin dimer is exposed at the growing MT end, these factors will be more likely to cause the MT to undergo rapid disassembly. We also compared simulation results between the special MT seam region and the remaining material and found that the lateral interactions between MT PFs at the seam region were comparatively much weaker. This finding is consistent with the experimental suggestion that the seam region tends to separate during the disassembly process of an MT.     

Interrelationship between water film thicknesses and contact angles and a model for CO2 adhesion

Thermodynamics of contact angle phenomena is strongly affected by the presence of thin liquid films. However, at present, studies for CO₂/brine/mineral systems only consider the films apart from contact angles. In this paper, molecular dynamics (MD) simulations have been performed to simultaneously investigate the interrelationship between water film thicknesses and water contact angles. Two types of contact angles were considered namely Young’s contact angle (no water film is present) and contact angle with film (a stable film is present). The results showed that as Young’s contact angle increased, film thickness decreased which leading to increasing of contact angle with film. The effects of CO₂-mineral pre-contact have also been investigated and it has been found that on mediate hydrophilic surfaces (Q³), water films were present when CO₂ droplets were placed above the surfaces, however, water films were absent when CO₂ droplets directly contact with the surfaces. This phenomenon implies that water films on mineral surfaces have a possibility to rupture and a film rupture mechanism for CO₂ adhesion on hydrated mineral surfaces was proposed. These results may provide new information on interactions among CO₂, water/brine and mineral to better understand the behaviour of CO₂ during geologic sequestration.     

The role of Allee effects in gypsy moth, <Emphasis Type="Italic">Lymantria dispar</Emphasis> (L.), invasions

Allee effects have been applied historically in efforts to understand the low-density population dynamics of rare and endangered species. Many biological invasions likewise experience the phenomenon of decreasing population growth rates at low population densities because most founding populations of introduced nonnative species occur at low densities. In range expansion of established species, the initial colonizers of habitat beyond the organism’s current range are usually at low density, and thus could be subject to Allee dynamics. There has been consistent empirical and theoretical evidence demonstrating, and in some cases quantifying, the role of Allee dynamics in the gypsy moth, Lymantria dispar (L.), invasion of North America. In this review, we examine the potential causes of the Allee effect in the gypsy moth and highlight the importance of mate-finding failure as a primary mechanism behind an Allee effect, while the degree to which generalist predators induce an Allee effect remains unclear. We then explore the role of Allee effects in the establishment and spread dynamics of the gypsy moth system, which conceptually could serve as a model system for understanding how Allee effects manifest themselves in the dynamics of biological invasions.     

Neurochemical Oscillations in the Basal Ganglia

This work represents an attempt to elucidate the neurochemical processes in the basal ganglia by mathematical modelling. The correlation between neurochemistry and electrophysiology has been used to construct a dynamical system based on the basal ganglia’s network structure. Mathematical models were constructed for different physical scales to reformulate the neurochemical and electrophysiological behaviour from synapses up to multi-compartment systems. Transformation functions have been developed to transit between the different scales. We show through numerical simulations that this network produces oscillations in the electrical potentials as well as in neurotransmitter concentrations. In agreement with pharmacological experiments, a parameter sensitivity analysis reveals temporary changes in the neurochemical and electrophysiological systems after single exposure to antipsychotic drugs. This behaviour states the structural stability of the system. The correlation between the neurochemical dynamics and drug-induced behaviour provides the perspective for novel neurobiological hypotheses.     

A Molecular Dynamics Investigation of Compressed Aqueous Alkanoate Monolayers

Molecular dynamics are conducted on a dodecanoic acid monolayer/aqueous surface. Surface pressure is controlled by imposing constant-volume conditions for series of lengths of the square slab constituting the MD cell. The response of the alkanoate chains to the pressure is followed by examining various computed quantities that monitor their conformational order. These include atom-pair radial distribution functions, chain torsional angles, energies, atomic densities perpendicular to the interface, diffusivities and atomic plots. These quantities lead to chain separations which in the range 4-5 Å implying order when the alkanoate chains have a mean area of 0.18 nm 2.