Test of the Inverse Monte Carlo Method for the Calculation of Interatomic Potential Energies in Atomic Liquids

Abstract

The principle purpose of this paper is to demonstrate the use of the Inverse Monte Carlo technique for calculating pair interaction energies in monoatomic liquids from a given equilibrium property. This method is based on the mathematical relation between transition probability and pair potential given by the fundamental equation of the “importance sampling” Monte Carlo method. In order to have well defined conditions for the test of the Inverse Monte Carlo method a Metropolis Monte Carlo simulation of a Lennard Jones liquid is carried out to give the equilibrium pair correlation function determined by the assumed potential. Because an equilibrium configuration is prerequisite for an Inverse Monte Carlo simulation a model system is generated reproducing the pair correlation function, which has been calculated by the Metropolis Monte Carlo simulation and therefore representing the system in thermal equilibrium. This configuration is used to simulate virtual atom displacements. The resulting changes in atom distribution for each single simulation step are inserted in a set of non-linear equations defining the transition probability for the virtual change of configuration. The solution of the set of equations for pair interaction energies yields the Lennard Jones potential by which the equilibrium configuration has been determined.     

A Two-Ellipsoid Model Based Upon A Gaussian Overlap Potential

Abstract

The two-ellipsoid model (TEM) is proposed as a versatile single-site model which can be used in the study of liquid crystal phases. This TEM uses two ellipsoids to describe a molecule, one ellipsoid for the geometry and the other for the interaction strengths of the molecule. The present TEM can mimic asymmetric interactions of a liquid crystal molecule by separating the center of the interaction ellipsoid from that of the geometry ellipsoid. The potential energy surfaces of the present TEMs compare favorably with those of the corresponding Gay-Berne and the site–site models.

Monte Carlo simulations with 320 particles are performed for a symmetric interaction TEM and an asymmetric interaction TEM. The asymmetric interaction TEM displays a slightly higher transition temperature than the symmetric interaction TEM indicating that asymmetric interactions can be a driving force in a phase transition. Radial and cylindrical distribution functions of two models in the isotropic phase are similar, but those in the nematic phase are quite different.     

BACE-1 hydroxyethylamine inhibitors using novel edge-to-face interaction with Arg-296

Inhibition of the aspartyl protease BACE-1 has the potential to deliver a disease-modifying therapy for Alzheimer’s disease. Herein, is described a series of potent inhibitors based on an hydroxyethylamine (HEA) transition state mimetic template. These inhibitors interact with the non prime side of the enzyme using a novel edge-to-face interaction with Arg-296.     

Folding pathway dependence on energetic frustration and interaction heterogeneity for a three-dimensional hydrophobic protein model

Monte Carlo simulations of a hydrophobic protein model of 40 monomers in the cubic lattice are used to explore the effect of energetic frustration and interaction heterogeneity on its folding pathway. The folding pathway is described by the dependence of relevant conformational averages on an appropriate reaction coordinate, pfold, defined as the probability for a given conformation to reach the native structure before unfolding. We compare the energetically frustrated and heterogeneous hydrophobic potential, according to which individual monomers have a higher or lower tendency to form contacts unspecifically depending on their hydrophobicities, to an unfrustrated homogeneous Go-type potential with uniformly attractive native interactions and neutral non-native interactions (called Go1 in this study), and to an unfrustrated heterogeneous potential with neutral non-native interactions and native interactions having the same energy as the hydrophobic potential (called Go2 in this study). Folding kinetics are slowed down dramatically when energetic frustration increases, as expected and previously observed in a two-dimensional model. Contrary to our previous results in two dimensions, however, it appears that the folding pathway and transition state ensemble can be significantly dependent on the energy function used to stabilize the native structure. The sequence of events along the reaction coordinate, or the order along this coordinate in which different regions of the native conformation become structured, turns out to be similar for the hydrophobic and Go2 potentials, but with analogous events tending to occur at lower pfold values in the first case. In particular, the transition state obtained from the ensemble around pfold = 0.5 is more structured for the hydrophobic potential. For Go1, not only the transition state ensemble but the order of events itself is modified, suggesting that interaction heterogeneity, in addition to energetic frustration, can have significant effects on the folding mechanism, most likely by modifying the probability of different contacts in the unfolded state, the starting point for the folding reaction. Although based on a simple model, these results provide interesting insight into how sequence-dependent switching between folding pathways might occur in real proteins.     

Mechanism for the alpha-helix to beta-hairpin transition

The aggregation of alpha-helix-rich proteins into beta-sheet-rich amyloid fibrils is associated with fatal diseases, such as Alzheimer's disease and prion disease. During an aggregation process, protein secondary structure elements-alpha-helices-undergo conformational changes to beta-sheets. The fact that proteins with different sequences and structures undergo a similar transition on aggregation suggests that the sequence nonspecific hydrogen bond interaction among protein backbones is an important factor. We perform molecular dynamics simulations of a polyalanine model, which is an alpha-helix in its native state and observe a metastable beta-hairpin intermediate. Although a beta-hairpin has larger potential energy than an alpha-helix, the entropy of a beta-hairpin is larger because of fewer constraints imposed by the hydrogen bonds. In the vicinity of the transition temperature, we observe the interconversion of the alpha-helix and beta-sheet states via a random coil state. We also study the effect of the environment by varying the relative strength of side-chain interactions for a designed peptide-an alpha-helix in its native state. For a certain range of side-chain interaction strengths, we find that the intermediate beta-hairpin state is destabilized and even disappears, suggesting an important role of the environment in the aggregation propensity of a peptide.     

High pressure phase transition and elastic properties of covalent heavy rare-earth Antimonides

In the present paper, we report an investigation into the high-pressure structural phase transition of rare earth antimonides (DySb and ErSb). A modified interaction potential model (MIPM) (including the covalency effect) has been developed. Phase transition pressures are associated with a sudden collapse in volume, indicating the occurrence of a first order phase transition. At compressed volumes, these compounds are found in the CsCl phase. The phase transition pressures and associated volume collapses obtained from the potential model developed here show a generally better agreement with available experimental data than others available in the literature. The elastic constants and bulk modulus are also reported. Our results are, in general, in good agreement with experimental and theoretical data where available, and provide predictions where data are unavailable.     

A bioenergetic model of the mitochondrial population undergoing permeability transition

Mitochondrial permeability transition (MPT) is a highly regulated complex phenomenon that is a type of ischemia/reperfusion injury that can lead to cell death and ultimately organ dysfunction. A novel population transition and detailed permeability transition pore regulation model were integrated with an existing bioenergetics model to describe MPT induction under a variety of conditions. The framework of the MPT induction model includes the potential states of the mitochondria (aggregated, orthodox and post-transition), their transitions from one state to another as well as their interaction with the extra-mitochondrial environment. The model encodes the three basic necessary conditions for MPT: a high calcium load, alkaline matrix pH and circumstances which favor de-energization. The MPT induction model was able to reproduce the expected bioenergetic trends observed in a population of mitochondria subjected to conditions that favor MPT. The model was corroborated and used to predict that MPT in an acidic environment is mitigated by an increase in activity of the mitochondrial potassium/hydrogen exchanger. The model was also used to present the beneficial impact of reducing the duration mitochondria spend in the orthodox state on preserving the extra-mitochondrial ATP levels. The model serves as a tool for investigators to use to understand the MPT induction phenomenon, explore alternative hypotheses for PTP regulation, as well as identify endogenous pharmacological targets and evaluate potential therapeutics for MPT mitigation.     

Dual Process for Intentional and Reactive Decisions

Efficient cognitive decisions should be adjustable to incoming novel information. However, most current models of decision making have so far neglected any potential interaction between intentional and stimulus-driven decisions. We report here behavioral results and a new model on the interaction between a perceptual decision and non-predictable novel information. We asked participants to anticipate their response to an external stimulus and presented this stimulus with variable delay. Participants were clearly able to adjust their initial decision to the new stimulus if this latter appeared sufficiently early. To account for these results, we present a two-stage model in which two systems, an intentional and a stimulus-driven, interact only in the second stage. In the first stage of the model, the intentional and stimulus-driven processes race independently to reach a transition threshold between the two stages. The model can also account for results of a second experiment where a response bias is introduced. Our model is consistent with some physiological results that indicate that both parallel and interactive processing take place between intentional and stimulus-driven information. It emphasizes that in natural conditions, both types of processing are important and it helps pinpoint the transition between parallel and interactive processing.     

Effect of water potential on sol-gel transition and intermolecular interaction of gelatin near the transition temperature

The sol-gel transition of gelatin, measured by thermal analysis and viscosity measurement, was analyzed in terms of the change in hydration state of polymer molecules. A new thermodynamic model was proposed in which the effect of water potential is explicitly taken into account for the evaluation of the free energy change in the sol-gel transition process. Because of the large number of water molecules involved and the small free energy change in the transition process, the contribution of water activity, a(W), was proved to be not negligible in the sol-gel transition process in solutions containing such low-molecular cosolutes as sugars, glycerol, urea, and formamide. The gel-stabilization effect of sugars and glycerol was linear with a(W), which seemed consistent with the contribution of water potential in the proposed model. The different stabilization effect among sugars and glycerol was explained by the difference in solvent ordering, which affects hydrophobic interaction among protein molecules. The gel-destabilization effect of urea and formamide could be explained only by the direct binding of them to protein molecules through hydrogen bonding. On the contrary, the polymer-polymer interaction, measured by the viscosity analysis, in polyethyleneglycol and dextran solutions was not sensitive to the change in a(W), suggesting that no substantial change in hydration state with a(W) occurred in these polymer solutions.     

A dynamical model for phospholipid-calcium binding

A model for an isothermal gel-liquid crystalline transition induced by ionic binding is proposed. A Ginsburg-Landau functional was used to describe the long-range order that spontaneously arises during the transition. By calculation of the corresponding chemical potential we obtain the mass current of phospholipids in gel-phase described by an order parameter. In the conservation of mass equation the kinetics of the phospholipids-calcium interaction is introduced, together with the flux divergency. A circular membrane is considered for the analysis, so that the model can be studied in polar coordinates. A solution approximated to first order shows an heterogeneous distribution of domains of phospholipids in gel and liquid crystalline phases. These spatial domains have been detected experimentally by diverse methods in vesicles and cellular membranes. Spatial heterogeneities may cause destabilization of the membrane in the boundaries between domains. This may explain the enhanced vesicle fusion observed in the presence of Ca2+.     

An Approach to the Current-Voltage Characteristics of Nerve Membranbs Based on Adsorption Phenomena

Using Stern's double-layer adsorption model for the density of cations in the membrane pores, a quantitative approach to the stationary current-voltage characteristic of nerve membranes is developed. The interaction of mobile cations with the negative fixed charges, located inside the membrane, constitutes a resistance for the current through the membrane. The stepwise increase in the resistance for the hyperpolarization is ascribed to a stronger interaction accompanying a depletion of the adsorbed cations from the interior. Thermodynamic treatment of flows and forces is adapted to the situation, to give a current voltage relation amenable to experimental check. The value of the resting potential thus obtained gives a deviation from Nernst equation applied to the ion for which the membrane is mainly permeable. The effect of the membrane double-layer potential on the potential range in which the transition from low to high resistance takes place, is explicitly incorporated. Finally, a comparison of the theory with the experimental results for the squid axon and frog nerve fibers is made.     

Interaction of dipalmitoyl-phosphatidylcholine with calf thymus histone H1

The interaction between dipalmitoyl-phosphatidylcholine and calf thymus histone H1 has been studied. A protein-phospholipid complex, resulting from this interaction, has been isolated by centrifugation in a sucrose gradient. The phospholipid-histone interaction causes an increase in the alpha-helix content of the protein; the corresponding conformational transition is observed by CD studies in the far-u.v. region. The only tyrosine residue of the protein can be advantageously used as an intrinsic fluorescent probe; thus, fluorescence spectra indicate that protein folding induced by phospholipids is concomitant with the tyrosine transfer into a more hydrophobic environment. The trypsin-resistant core of the histone is also folded in the presence of the phospholipid but the conformational transition occurs at lower lipid concentration than for the intact protein. Fluorescence polarization of 1,6-diphenyl-1,3,5-hexatriene indicates that the protein shifts the transition temperature of the phospholipid from 41.5 to 44.0 degrees. Secondary structure prediction of the trypsin-resistant core of the histone indicates the existence of an amphipathic helix that could be responsible for the lipid-protein interaction.     

Optical spectroscopic investigation of the alkaline transition in umecyanin from horseradish root

Umecyanin (UMC) from horseradish root belongs to the stellacyanin subclass of the phytocyanins, a family of plant cupredoxins. The protein possesses the typical type-1 His(2)Cys equatorial ligand set at its mononuclear copper site but has an axial Gln ligand in place of the usual weakly coordinated Met of the plantacyanins, uclacyanins, and most other cupredoxins. UMC exhibits, like other phytocyanins, altered visible, EPR, and paramagnetic (1)H NMR spectra at elevated pH values and also a modified reduction potential. This alkaline transition occurs with a pK(a) of approximately 10 [Dennison, C., Lawler, A. T. (2001) Biochemistry 40, 3158-3166]. In this study, we investigate the alkaline transition by complementary optical spectroscopic techniques. The contemporary use of absorption, fluorescence, dynamic light scattering, and resonance Raman spectroscopy allows us to demonstrate that the alkaline transition induces a reorganization of the protein and that the overall size of UMC increases, but protein aggregation does not occur. The transition does not have a dramatic influence on the active-site environment of UMC, but there are subtle alterations in the Cu site geometry. Direct evidence for the strengthening of a Cu-N(His) bond is presented, which is in agreement with the hypothesis that the deprotonation of the N(epsilon2)H moiety of one of the His ligands is the cause of the alkaline transition. A weakening of the Cu-S(Cys) bond is also observed which, along with a weakened axial interaction, must be due to the enhanced Cu-N(His) interaction.     

The Middle/Later Stone Age transition and cultural dynamics of late Pleistocene East Africa

The Middle to Later Stone Age (MSA/LSA) transition is a prominent feature of the African archeological record that began in some places ~30,000–60,000 years ago, historically associated with the origin and/or dispersal of “modern” humans. Unlike the analogous Middle to Upper Paleolithic transition in Eurasia and associated Neanderthal extinction, the African MSA/LSA record remains poorly documented, with its potential role in explaining changes in the behavioral diversity and geographic range of Homo sapiens largely unexplored. I review archeological and biogeographic data from East Africa, show regionally diverse pathways to the MSA/LSA transition, and emphasize the need for analytical approaches that document potential ancestor‐descendent relationships visible in the archeological record, needed to assess independent invention, population interaction, dispersal, and other potential mechanisms for behavioral change. Diversity within East Africa underscores the need for regional, rather than continental‐scale narratives of the later evolutionary history of H. sapiens.     

The effect of protein stability on protein-monoglyceride interactions

We have previously shown that proteins such as beta-lactoglobulin and lysozyme insert into monoglyceride monolayers and are able to induce an L(beta) to coagel phase transition in monoglyceride bilayers. These studies gave a first indication that protein stability could be an important factor for these interactions. This study therefore aims at further investigating the potential role of protein stability on protein-monoglyceride interactions. To this end we studied the interaction of stable and destabilized alpha-lactalbumin with monostearoylglycerol. Our results show that protein stability is important for the insertion of proteins into a monostearoylglycerol monolayer, such that the lower the stability of the protein the better the protein inserts. In marked contrast to beta-lactoglobulin and lysozyme we found that destabilized alpha-lactalbumin does not induce the L(beta) to coagel phase transition in monoglyceride bilayers. We propose that this is due to an increased surface coverage by the protein which could result from the unfolding of the protein upon binding to the interface.     

An ionotropic phase transition in phosphatidylcholine: cation and anion cooperativity

Evidence is presented for cooperative interaction between cations and anions specifically bound to dimyristoylphosphatidylcholine (DMPC). The cooperativity is with regard to an ion-induced (ionotropic) phase transition for the lipid and is signalled by a change in the luminescence from bound Tb3+. The intrinsic binding of Tb3+ to DMPC was determined from equilibrium dialysis experiments, using conventional methods to correct for electrostatic contributions. Preliminary results demonstrate great potential for infrared spectroscopy as a means to relate these Tb3+ luminescence studies to experiments involving less tractable cations. This work provides insight into the role of bound ions in modifying lateral phase behavior in phospholipid membranes.     

A cooperative transition theory applied to the kinetics of ionic exchanges in cells

Manifestations of a cooperative interaction between ion-adsorbing sites in cells include steep, sigmoidal equilibrium adsorption isotherms of K+ and Na+, critical temperature transitions of net exchanges of Na+ for K+, and the allosteric nature of the effects of ligands on cellular K+ and Na+. Cooperative ionic adsorption is described by a one-dimensional Ising model. The experimentally-determined equilibrium parameters permit prediction of the kinetics of exchange of K+ for Na+ (the approach to equilibrium) by stochastic or hydrodynamic solutions of a time-dependent Ising model. Studies of the rates of self-exchange of adsorbed ions reveal properties of the cooperatively interacting adsorption sites and their dependence on temperature and chemical potential. High rates of isotopic exchanges of K+ and Na+ occur near the transition point. This is explained by the hypothesis of an increase in susceptibility of the ensemble to slight variations of microK or microNA near the phase transition, which leads to an increase in microscopic fluctuations within the ensemble. It is suggested that the isotopic ion exchange experiment may be a means to explore the microscopic states of the ensemble and their transition probabilities.     

Cluster buckling as a result of compression-bending balance in lipid bilayer.

A new approach supporting the possibility of cluster buckling during the main phase transition in the lipid bilayer is presented. The elastic energy is calculated via harmonic approximation which yields the potential minimum in the case of buckling cluster, if critical cluster size is achieved. The significance of this event for interbilayer interaction in multilamellar vesicles is discussed.     

分子马达定向运动的两态模型

采用非对称周期势来描述马达蛋白与具有周期性和极性的微丝轨道之间的相互作用,计算了马达蛋白两态模型的几率流和有效势之间的关系。计算结果表明：马达蛋白的定向运动不仅与有效势的整体倾斜密切相关,还与有效势的势垒高度有关。有效势倾斜等效于一个平均力的作用,而这一平均力的存在体现了两态跃迁细致平衡的破坏。同时将不同ATP浓度下力与速度的关系曲线与实验作了比较,这些曲线与实验定性吻合。