The Role of Molecular Dynamics Simulations for the Study of Slow Dynamics

Abstract

A two step strategy is proposed to study dynamical properties of a physical system much slower than the time scales accessible by molecular dynamics simulations. The strategy is applied to investigate the slow dynamics of supercooled liquids.     

Study on the β Peak of χ″ for a Two-Dimensional Supercooled Fluid State Via Molecular Dynamics Simulation

Abstract

We have computed the generalized susceptibility (imaginary part of χ) of two-dimensional supercooled fluid states through molecular dynamics simulations with different system sizes. It is found that when the temperature of the system is higher than T_c (critical temperature) there is no significant difference between the large (10,000-particle) and small (100-particle) systems in the χ obtained, but for much lower temperatures the spectra of the χ″ obtained reveal a remarkable system-size dependent behavior such as the β peak becomes much broader for the large system. This phenomenon is physically understood in terms of the strongly correlated motion of atoms extending over a wide range of space of the system. We will discuss in this work about the relaxations on two-dimensional supercooled fluids and their microscopic origins as well as their system-size dependence.     

Deep supercooling enabled by surface impregnation with lipophilic substances explains the survival of overwintering buds at extreme freezing

The frost survival mechanism of vegetative buds of angiosperms was suggested to be extracellular freezing causing dehydration, elevated osmotic potential to prevent freezing. However, extreme dehydration would be needed to avoid freezing at the temperatures down to ?45°C encountered by many trees. Buds of Alnus alnobetula, in common with other frost hardy angiosperms, excrete a lipophilic substance, whose functional role remains unclear. Freezing of buds was studied by infrared thermography, psychrometry, and cryomicroscopy. Buds of A. alnobetula did not survive by extracellular ice tolerance but by deep supercooling, down to ?45°C. An internal ice barrier prevented ice penetration from the frozen stem into the bud. Cryomicroscopy revealed a new freezing mechanism. Until now, supercooled buds lost water towards ice masses that form in the subtending stem and/or bud scales. In A. alnobetula, ice forms harmlessly inside the bud between the supercooled leaves. This would immediately trigger intracellular freezing and kill the supercooled bud in other species. In A. alnobetula, lipophilic substances (triterpenoids and flavonoid aglycones) impregnate the surface of bud leaves. These prevent extrinsic ice nucleation so allowing supercooling. This suggests a means to protect forestry and agricultural crops from extrinsic ice nucleation allowing transient supercooling during night frosts.     

Models for the length distributions of actin filaments: II. Polymerization and fragmentation by gelsolin acting together

In a previous paper, we studied elementary models for polymerization, depolymerization, and fragmentation of actin filaments (Edelstein-Keshet and Ermentrout, 1998, Bull. Math. Biol. 60, 449–475). When these processes act together, more complicated dynamics occur. We concentrate on a particular case study, using the actin-fragmenting protein gelsolin. A set of biological parameter values (drawn from the experimental literature) is used in computer simulations of the kinetics of gelsolin-mediated actin filament fragmentation.     

Nonlocal nature of the electron energy spectrum in a glow discharge in pure O2: I. Nonlocal character of the electron distribution function

Abstrac A study is made of the nonlocal nature of the electron energy distribution function in the positive column of a glow discharge in a tube filled with pure oxygen. The distribution function and the axial (E _z) and radial (E _r) electric fields as functions of radius are measured using an array of mobile probes. The experimentally obtained spatial profiles of the distribution function are used to test the applicability of the two-term approximation to the distribution function of the electrons with a nonlocal energy spectrum. The distribution function in a specified electric field E=E _z +E _r (where E _z ⊥ E _r) is calculated by solving the coordinate-dependent Boltzmann equation in the two-term approximation and by directly integrating the equations of electron motion using the Monte Carlo method. A comparison between the experimental data and the results of simulations carried out for a broad parameter range shows that, in the case of a highly nonlocal electron energy spectrum, the two-term approximation makes it possible to calculate the electron distribution function with a fairly good accuracy, in which case, however, in imposing the boundary conditions, the electron losses at the plasma surface should be treated in the kinetic approximation. It is shown that using the reflection coefficient of the plasma surface for electrons instead of the loss cone in space makes it possible to accurately calculate the electron energy distribution function over the entire parameter range under consideration, including the transient region in which the electron-energy relaxation length is comparable to the characteristic plasma dimension. __________ Translated from Fizika Plazmy, Vol. 26, No. 11, 2000, pp. 1038–1045. Original Russian Text Copyright ? 2000 by Ivanov, Klopovskii, Lopaev, Rakhimov, Rakhimova.     

A Derivative Matching Approach to Moment Closure for the Stochastic Logistic Model

Continuous-time birth-death Markov processes serve as useful models in population biology. When the birth-death rates are nonlinear, the time evolution of the first n order moments of the population is not closed, in the sense that it depends on moments of order higher than n. For analysis purposes, the time evolution of the first n order moments is often made to be closed by approximating these higher order moments as a nonlinear function of moments up to order n, which we refer to as the moment closure function. In this paper, a systematic procedure for constructing moment closure functions of arbitrary order is presented for the stochastic logistic model. We obtain the moment closure function by first assuming a certain separable form for it, and then matching time derivatives of the exact (not closed) moment equations with that of the approximate (closed) equations for some initial time and set of initial conditions. The separable structure ensures that the steady-state solutions for the approximate equations are unique, real and positive, while the derivative matching guarantees a good approximation, at least locally in time. Explicit formulas to construct these moment closure functions for arbitrary order of truncation n are provided with higher values of n leading to better approximations of the actual moment dynamics. A host of other moment closure functions previously proposed in the literature are also investigated. Among these we show that only the ones that achieve derivative matching provide a close approximation to the exact solution. Moreover, we improve the accuracy of several previously proposed moment closure functions by forcing derivative matching.     

Lipase-catalyzed transformations using poly(ethylene glycol) as solvent

Abstract

Candida antarctica lipase catalyzes a number of elementary reactions like alcoholysis, ammoniolysis and aminolysis in poly(ethylene glycol) (PEG) media. Reaction rates were comparable to or better than those observed in conventional organic reaction media and ionic liquids. It is envisaged that PEGs could have added benefits for performing biotransformations with highly polar substrates, which are sparingly soluble in common organic solvents.     

Sequence Structure of Hidden 10.4-base Repeat in the Nucleosomes of C. elegans

Abstract

By measuring prevailing distances between YY, YR, RR, and RY dinucleotides in the large database of the nucleosome DNA fragments from C. elegans, the consensus sequence structure of the nucleosome DNA repeat of C. elegans was reconstructed: (YYYYYRRRRR)_n. An actual period was estimated to be 10.4 bases. The pattern is fully consistent with the nucleosome DNA patterns of other eukaryotes, as established earlier, and, thus, the YYYYYRRRRR repeat can be considered as consensus nucleosome DNA sequence repeat across eukaryotic species. Similar distance analysis for [A, T] dinucleotides suggested the related pattern (TTTYTARAAA)_n where the TT and AA dinucleotides display rather out of phase behavior, contrary to the “AA or TT” in-phase periodicity, considered in some publications. A weak 5-base periodicity in the distribution of TA dinucleotides was detected.     

Rotation-Vibration Coupling in Liquid Water Investigated by Molecular Dynamics Simulation

Abstract

The standard rotation-vibration decoupling approximation for liquid water is tested using a method based on the split of the molecular dipole fluctuation correlation function into pure rotational, pure vibrational and crossed terms. Our results corroborate the total decoupling between vibrational and rotational motions in liquid water at ambient conditions and provide a tool able to test the reliability of this approximation for molecular liquids at different states.     

Chemical Potential,Partial Enthalpy and Partial Volume of Mixtures by NPT Molecular Dynamics

Abstract

Equilibrium NPT molecular dynamics computer simulations have been used to determine the chemical potential, partial enthalpy and partial volume of model Ar-Kr mixtures using newly devised non-intrusive particle insertion and particle swap techniques [P. Sindzingre et al. Chemical Physics, 129 (1989) 213]. In this report we examine, for the first time, in some detail the relative convergence statistics of the particle swap and particle insertion methods for these properties for binary Lennard-Jones (LJ) mixtures. Both species are represented by single-site Lennard-Jones pair potentials with Lorentz-Berthelot rules for the cross-species interactions. We show that, over the whole phase diagram and especially in the vicinity of the fluid-solid coexistence line, the particle swap method gives significantly better statistics than the particle insertion method for the difference in chemical potential of the two species, partial enthalpy and partial volume of each species. Also, we find that, using the particle swap method, the difference in the chemical potential converges more rapidly than the differences in the partial enthalpy and volume.     

Dynamical machinery of a biochemical clock

Closed positive feedback loops of catalytic reactions between macromolecules, or hypercycles, provide a kinetic mechanism whereby each Species serves to catalyze selfreproduction of its successor in the loop. Hypercycles of five members or more evolve into limit cycles characteristic of a biochemical clock. Computer study of the coupled non-linear differential equations which describe these systems shows that the periodT _n of then-species limit cycle is given byT _n=nτ_n, where τ_n is an elemental repeat period reflecting translational time invariance. Analytic solutions of the equations are developed so that the time evolution of elementaryn-hypercycles can be traced in dynamical detail. It is shown that the magnitude of τ_n is, to good approximation, a linear function ofn. For a givenn, τ_n is a very sensitive function of the relative concentration a given member of the loop has at the time its predecessor dominates the state of the hypercycle. These concentrations decrease with increasingn. Aroundn=15 they become so small that elementary hypercycles become unstable against disruptive concentration fluctuations. Species concentrations for more realistic hypercycles tend not to be as small, so that the present estimate of a maximum number of components is a lower bound.     

Slow dynamics in glass-forming materials

Dynamical properties of glass-formers such as glassy crystals, molecular liquids and model atomic liquids have been investigated in the pico–nanosecond (ps–ns) regime with dl_poly. The change in nature of translation and rotational dynamics are investigated in the supercooled state. Some predictions of the mode-coupling theory and the coupling model are checked. The microscopic origin of the fragility, i.e. the characteristic parameter involved in the liquid–glass transition, is also highlighted: the interaction potential, especially its anharmonicity and capacity for intermolecular coupling, is the key parameter controlling both the long time dynamics in supercooled systems and the short time dynamics in their glassy states.     

The gamma distribution as the true aerobiological probability density function (PDF)

Most statistical analyses are done under the premisethat the population distribution of the phenomenaunder study is normally distributed. In order to findthe best probability distribution (also called theprobability density function) that should be appliedto aerobiological data (in order to find the mostadequate error probability to apply in any hypothesistesting), the whole airborne pollen data set of 11years in Montréal (comprising 4070 days of mainpollination periods) was subjected to a distributionmodel analysis. When considered as a time-series(i.e. keeping successive days on the X-axis) the PDFthat best represents the aerobiological data set isindeed the Normal distribution. However, when onlythe frequency of different atmospheric concentrationsis used (i.e. having a number of occurrences on theY-axis), as would be done for a site-specific insteadof a time-specific distribution, the PDF is notnormally distributed. The resulting distributionappears log-normal to the eye, but the resultingfrequency distribution is in fact only asymptoticallylog-normal. It is in fact a Gamma distribution G(, a). The two parameters of the Gammadistribution are its shape parameter () and itsscale parameter (a). In our case, was 0.08and was 0.002. The PDF is right-skewed when definedover the positive axis 0 < X < . Althoughlog-normal distribution is the most used datatransformation for parametric statistical analyses inaerobiology, it seldom accurately describes the lowerend of the observations near the minimum detectablelimits. Better aerobiological inferences could beobtained by using a Gamma PDF for calculatingthreshold probabilities.     

Computer vision for LCA foreground modelling—an initial pipeline and proof of concept software,lcopt-cv

Purpose

The majority of LCA studies begin with the drawing of a process flow diagram, which then needs to be translated manually into an LCA model. This study presents an initial image processing pipeline, implemented in an open-source software package, called lcopt-cv, which can be used to identify the boxes and links in a photograph of a hand-drawn process flow diagram and automatically create an LCA foreground model.

Methods

The computer vision pipeline consists of a total of 15 steps, beginning with loading the image file and conversion to greyscale. The background is equalised, then the foreground of the image is extracted from the background using thresholding. The lines are then dilated and closed to account for drawing errors. Contours in the image are detected and simplified, and rectangles (contours with four corners) are identified from the simplified contours as ‘boxes’. Links between these boxes are identified using a flood-filling technique. Heuristic processing, based on knowledge of common practice in drawing of process flow diagrams, is then performed to more accurately identify the typology of the identified boxes and the direction of the links between them.

Results and discussion

The performance of the image processing pipeline was tested on four flow diagrams of increasing difficulty: one simple computer drawn diagram and three photographs of hand-drawn diagrams (a simple diagram, a complex diagram and a diagram with merged lines). A set of default values for the variables which define the pipeline was developed through trial and error. For the two simple flow charts, all boxes and links were identified using the default settings. The complex diagram required minor tweaks to the default values to detect all boxes and links. An ‘unstacking’ heuristic allowed the diagram with merged lines to be correctly processed. After some manual reclassification of link directions and process types, the diagrams were turned into LCA models and exported to open-source LCA software packages (lcopt and Brightway) to be verified and analysed.

Conclusions

This study demonstrates that it is possible to generate a fully functional LCA model from a picture of a flow chart. This has potentially important implications not only for LCA practitioners as a whole, but in particular for the teaching of LCA. Skipping the steep learning curve required by most LCA software packages allows teachers to focus on important LCA concepts, while participants maintain the benefits of experiential learning by doing a ‘real’ LCA.

     

On the Application of Widom's Test Particle Method to Homogeneous and Inhomogeneous Fluids

Abstract

Chemical potentials of a homogeneous and an inhomogeneous Lennard-Jones fluid have been determined by molecular dynamics simulations on the vector computer CYBER 205 by applying essentially the fictitious test particle method of Widom. For the homogeneous fluid we find, contrary to the previous result of Guillot and Guissani, that the simulated chemical potential is independent of the particle number. The crucial point, however, is a sufficiently large cut-off radius in the evaluation of the Boltzmann factor. Comparing with our WCA-type perturbation theory, we get agreement in the chemical potentials within 0.1 kT up to the density n[sgrave]³ = 0.80 and a difference of 0.2 kT at n[sgrave]³ = 0.85. For the inhomogeneous case we consider a fluid in a cylindrical pore and integrate Widom's equation over a certain probe volume as suggested earlier by us. Chemical potentials are then calculated independently in five different probe volumes, which are cylindrical shells. The results agree well from the second to the fourth shell. Inaccuracies in the innermost cylinder can be easily explained by bad statistics. In the shell close to the wall the extremely high local density is responsible for the inaccuracies. Extending the probe volume over all cylindrical shells besides the one closest to the wall is thought to yield rather reliable results for the chemical potential. As a by-product of the simulations we also obtained diffusion coefficients, which are given in an appendix.     

Oxidative stress and antioxidant capacity of a terrestrially hibernating hatchling turtle

Hatchlings of the painted turtle, Chrysemys picta, hibernate terrestrially and can survive subfreezing temperatures by supercooling or by tolerating the freezing of their tissues. Whether supercooled or frozen, an ischemic hypoxia develops because tissue perfusion is limited by low temperature and/or freezing. Oxidative stress can occur if hatchlings lack sufficient antioxidant defenses to minimize or prevent damage by reactive oxygen species. We examined the antioxidant capacity and indices of oxidative damage in hatchling C. picta following survivable, 48 h bouts of supercooling (−6°C), freezing (−2.5°C), or hypoxia (4°C). Samples of plasma, brain, and liver were collected after a 24 h period of recovery (4°C) and assayed for Trolox-equivalent antioxidant capacity (TEAC), thiobarbituric acid reactive substances (TBARS), and carbonyl proteins. Antioxidant capacity did not vary among treatments in any of the tissues studied. We found a significant increase in TBARS in plasma, but not in the brain or liver, of frozen/thawed hatchlings as compared to untreated controls. No changes were found in the concentration of TBARS or carbonyl proteins in supercooled or hypoxia-exposed hatchlings. Our results suggest that hatchling C. picta have a well-developed antioxidant defense system that minimizes oxidative damage during hibernation.     

Molecular dynamics simulation on the effect of transition metal binding to the N-terminal fragment of amyloid-β

Abstract

We report molecular dynamics simulations of three possible adducts of Fe(II) to the N-terminal 1–16 fragments of the amyloid-β peptide, along with analogous simulations of Cu(II) and Zn(II) adducts. We find that multiple simulations from different starting points reach pseudo-equilibration within 100–300?ns, leading to over 900?ns of equilibrated trajectory data for each system. The specifics of the coordination modes for Fe(II) have only a weak effect on peptide secondary and tertiary structures, and we therefore compare one of these with analogous models of Cu(II) and Zn(II) complexes. All share broadly similar structural features, with mixture of coil, turn and bend in the N-terminal region and helical structure for residues 11–16. Within this overall pattern, subtle effects due to changes in metal are evident: Fe(II) complexes are more compact and are more likely to occupy bridge and ribbon regions of Ramachandran maps, while Cu(II) coordination leads to greater occupancy of the poly-proline region. Analysis of representative clusters in terms of molecular mechanics energy and atoms-in-molecules properties indicates similarity of four-coordinate Cu and Zn complexes, compared to five-coordinate Fe complex that exhibits lower stability and weaker metal–ligand bonding.

Communicated by Ramaswamy H. Sarma     

Comparative analysis of overwintering physiology in nine species of semi‐aquatic bugs (Heteroptera: Gerromorpha)

In semi‐aquatic bugs (Heteroptera: Gerromorpha), the strategies of overwintering in a cryothermic state (i.e. at body temperatures below the equilibrium freezing point) remain largely unexplored. The present study provides an analysis of the ecophysiological aspects of overwintering in nine gerromorphan species. All nine species avoid ice formation by means of a more or less extensive supercooling of their body fluids. There is a tight correlation between the supercooling point (SCP) and the lower lethal temperature. Different species use different physiological adjustments to increase the likelihood of survival in a supercooled state. These include stabilization of the supercooled state by active antifreeze factors that cause thermal hysteresis between equilibrium melting and freezing points, the accumulation of low‐molecular weight sugars and polyols with putative cryoprotective functions, or by having a relatively high body fluid osmolality, combined with a low level of hydration. The majority of species under study overwinter only as adults, whereas Velia caprai Tamanini can overwinter either as an adult or in the egg stage. The supercooling capacity of V. caprai adults is insufficient to prevent the risk of lethal freezing. The adults therefore survive only opportunistically in suitable microhabitats, and/or during mild winters. The survival of V. caprai in winter is assured by extensive supercooling and having overwintering eggs that are highly cold tolerant.     

The Rheology of 6-Propyl Duodecane and 5-Dibutyl Nonane by Non-Equilibrium Molecular Dynamics Simulations

Abstract

In recent papers, we reported non-equilibrium molecular dynamics (NEMD) simulations of planar Couette flow for liquid n- and i-butane, and liquid n-decane and 4-propyl heptane, using two collapsed atom models and an atomistically detailed model. It was found that the collapsed atom models predict the viscosities of the n-butane and n-decane quite well, and that the atomistically detailed model does not yield quantitative agreement with the viscosity of the n-alkanes or the branched alkanes, but it does have the one positive feature that the calculated viscosities of the branched alkanes are higher than these of the n-alkanes. In the present paper, we report results of NEMD simulations of planar Couette flow for liquid 6-propyl duodecane and 5-dibutyl nonane at 296 K and 0.782 g/cc, using an expanded collapsed atom model for simplicity. The strain rate dependent viscosity shows three different regions—two shear thinning ones and a Newtonian one. The slopes of the log-log plot for the branched-chain alkanes at high strain rate are different from those at intermediate strain rate, which is characterized as a rheological behavior of branched-chain alkanes. The Newtonian viscosity of the branched-chain alkanes can be extrapolated from the plateau value of the strain rate dependent viscosity at low strain rate as for straight-chain alkanes [J. Chem. Phys., 105, 1214 (1996)]. The results indicate that more-branched alkanes have a larger viscosity than less-branched C₁₇ alkanes.