Fast numerical methods for simulating large-scale integrate-and-fire neuronal networks

We discuss numerical methods for simulating large-scale, integrate-and-fire (I&F) neuronal networks. Important elements in our numerical methods are (i) a neurophysiologically inspired integrating factor which casts the solution as a numerically tractable integral equation, and allows us to obtain stable and accurate individual neuronal trajectories (i.e., voltage and conductance time-courses) even when the I&F neuronal equations are stiff, such as in strongly fluctuating, high-conductance states; (ii) an iterated process of spike-spike corrections within groups of strongly coupled neurons to account for spike-spike interactions within a single large numerical time-step; and (iii) a clustering procedure of firing events in the network to take advantage of localized architectures, such as spatial scales of strong local interactions, which are often present in large-scale computational models—for example, those of the primary visual cortex. (We note that the spike-spike corrections in our methods are more involved than the correction of single neuron spike-time via a polynomial interpolation as in the modified Runge-Kutta methods commonly used in simulations of I&F neuronal networks.) Our methods can evolve networks with relatively strong local interactions in an asymptotically optimal way such that each neuron fires approximately once in operations, where N is the number of neurons in the system. We note that quantifications used in computational modeling are often statistical, since measurements in a real experiment to characterize physiological systems are typically statistical, such as firing rate, interspike interval distributions, and spike-triggered voltage distributions. We emphasize that it takes much less computational effort to resolve statistical properties of certain I&F neuronal networks than to fully resolve trajectories of each and every neuron within the system. For networks operating in realistic dynamical regimes, such as strongly fluctuating, high-conductance states, our methods are designed to achieve statistical accuracy when very large time-steps are used. Moreover, our methods can also achieve trajectory-wise accuracy when small time-steps are used. Action Editor: Nicolas Brunel     

Coordinates transformation and learning control for visually-guided voluntary movement with iteration: A Newton-like method in a function space

In order to control visually-guided voluntary movements, the central nervous system (CNS) must solve the following three computational problems at different levels: (1) determination of a desired trajectory in the visual coordinates, (2) transformation of the coordinates of the desired trajectory to the body coordinates and (3) generation of motor command. In this paper, the second and the third problems are treated at computational, representational and hardware levels of Marr. We first study the problems at the computational level, and then propose an iterative learning scheme as a possible algorithm. This is a trial and error type learning such as repetitive training of golf swing. The amount of motor command needed to coordinate activities of many muscles is not determined at once, but in a step-wise, trial and error fashion in the course of a set of repetitions. Actually, the motor command in the (n+1)-th iteration is a sum of the motor command in then-th iteration plus two modification terms which are, respectively, proportional to acceleration and speed errors between the desired trajectory and the realized trajectory in then-th iteration. We mathematically formulate this iterative learning control as a Newton-like method in functional spaces and prove its convergence under appropriate mathematical conditions with use of dynamical system theory and functional analysis. Computer simulations of this iterative learning control of a robotic manipulator in the body or visual coordinates are shown. Finally, we propose that areas 2, 5, and 7 of the sensory association cortex are possible sites of this learning control. Further we propose neural network model which acquires transformation matrices from acceleration or velocity to motor command, which are used in these schemes.     

Cutoff Errors in the Ewald Summation Formulae for Point Charge Systems

Abstract

Closed formulae for both real and reciprocal space parts of cutoff errors in the Ewald summation method in cubic periodic boundary conditions are derived. Such estimates are useful in tuning parameters in molecular simulations. Errors in both the electrostatic energy and forces are considered. The estimates apply to a disordered configuration of point charges and, with some limitations, also to point-charge molecular models. The accuracy of our estimates is tested and confirmed using simulated configurations of two systems (molten salt and diethylether) under a variety of conditions.     

Application of isotropic periodic sum method for 4-pentyl-4′-cyanobiphenyl liquid crystal

In future large-scale molecular dynamics (MD) simulations that will use parallel computing, the isotropic periodic sum (IPS) method is expected to effectively reduce the cost of interaction calculations while maintaining adequate accuracy. To assess the accuracy of this method in estimating low-charge-density polymer systems, we performed atomistic MD simulations of the bulk state of liquid crystal systems based on 4-pentyl-4′-cyanobiphenyl (5CB). In conditions of 270 K ≤ T ≤ 320 K and a normal pressure, the temperature dependence of the density, potential energy and order parameter was estimated using the IPS and Ewald sum method. The results of the IPS method and Ewald sum were consistent within the range of error. In conditions close to the phase transition point, however, the averaged values of potential energy and order parameter had a small difference. We concluded that the fundamental physical properties for the bulk state of 5CB systems are determined reasonably by using the IPS method, at least in conditions that are not close to the phase transition point.     

Mutation-selection equilibrium in games with mixed strategies

We develop a new method for studying stochastic evolutionary game dynamics of mixed strategies. We consider the general situation: there are n pure strategies whose interactions are described by an n×n payoff matrix. Players can use mixed strategies, which are given by the vector (p₁,…,p_n). Each entry specifies the probability to use the corresponding pure strategy. The sum over all entries is one. Therefore, a mixed strategy is a point in the simplex S_n. We study evolutionary dynamics in a well-mixed population of finite size. Individuals reproduce proportional to payoff. We consider the case of weak selection, which means the payoff from the game is only a small contribution to overall fitness. Reproduction can be subject to mutation; a mutant adopts a randomly chosen mixed strategy. We calculate the average abundance of every mixed strategy in the stationary distribution of the mutation-selection process. We find the crucial conditions that specify if a strategy is favored or opposed by selection. One condition holds for low mutation rate, another for high mutation rate. The result for any mutation rate is a linear combination of those two. As a specific example we study the Hawk-Dove game. We prove general statements about the relationship between games with pure and with mixed strategies.     

Molecular Dynamics Simulation Study of DNA Triplex Formed by Mixed Sequences in Solution

Abstract

The unrestrained molecular dynamics simulation of the triple helical DNA with mix sequences d(GACTGGTGAC)?d(CTGACCACTG)*d (GACTGGTGAC), using the particle mesh Ewald sum, is presented here. The Ewald summation method effectively eliminates the usual “cut-off” of the long—range interactions and allowed us to evaluate the full effect of the electrostatic forces. The AMBER5.0 force field has been used during the simulation in solvent. The MD results support a dynamically stable model of DNA triplex over the entire length of the trajectory. The duplex structure assumes the conformation, which is very close to B-DNA. In mixed sequences the purine bases occurs in both strand of DNA duplex. The bases of third strand do not favor the Hoogsteen or/and reverse Hoogsteen type of Hydrogen bonding but they form hydrogen bonds with the bases of both the strand of DNA duplex. The orientation of the third strand is parallel to one of the strand of duplex and all nucleotides (C, A, G & T) show isomorphic behavior with respect to the DNA duplex. The conformation of all the three strands is almost same except few exceptions. Due to interaction of third strand the conformational change in the duplex structure and a finite amount of displacement in the W-C base pairs have been observed. The conformational variation of the back bone torsion angles and helicoidal parameters, groove widths have been discussed. The sequence—dependent effects on local conformation, helicoidal and morphological structure, width of the grooves of DNA helix may have important implication for understanding the functional energetics and specificity of interactions of DNA and its triplexes with proteins, pharmaceutical agents and other legends.     

AGONISTIC BEHAVIOR IN HARBOR SEALS (PHOCA VITULINA) IN RELATION TO THE AVAILABILITY OF HAUL-OUT SPACE

The hypothesis that haul-out space is a contested resource among harbor seals (Phoca vitulina) was tested by comparing the number of agonistic interactions and the time devoted to them, at a haul-out with unlimited space and a haul-out with limited space, in Humboldt County, California. 798 agonistic interactions were recorded in 160 h of observation. The average number of agonistic interactions per seal per hour and the time spent on these interactions were significantly higher at the site with limited haul-our space (P < 0.05, n= 20). At this restricted site, the frequency of agonistic interactions was positively correlated with seal density (r= 0.61, P < 0.05, n= 20), as was time spent on agonistic interactions (r= 0.84, P < 0.05, n= 20). Size, sex, and age-class of individuals all influenced agonistic interactions. In 72.5% of displacements, smaller seals were displaced by larger ones. This may support claims that some harbor seal populations maintain a size-based dominance hierarchy. The results of this study support the hypothesis that there is competition among harbor seals for suitable haul-out space where this resource is limited. The outcome of these interactions may be predicted, at least in part, by theoretical models on pay-off asymmetries, resource holding power, and the prior residency effect.     

Combined use of periodic reaction field and coarse-grained molecular dynamics simulations. I. phospholipid monolayer systems

Abstract

A periodic reaction field based on a linear-combination-based isotropic periodic sum (LIPS) method was applied for coarse-grained molecular dynamics simulations of zwitterionic lipid systems. In phospholipid monolayer systems with various number of lipid molecules, the density profile, lipid orientation and surface tension were mainly calculated using the periodic reaction field and Ewald sum. The results from the periodic reaction field were almost equal to that from the Ewald sum. It is concluded that the periodic reaction field method has a great possibility to provide a high accuracy in determining coarse-grained zwitterionic lipid systems.     

Ewald Summation in the Molecular Dynamics Simulation of Large Ionic Systems

Abstract

The accuracy and efficiency of the direct Ewald summation are discussed in terms of the size of a Molecular Dynamics (MD) ionic system and the ranges of the r-space and q-space summations. The dependence of the convergence parameter α on the size of the system and on the choice of cut-off radius for the short-range potential is given. The possibility of neglecting the q-space term for large ionic systems is discussed in terms of the accuracy and efficiency of the simulation.     

Intermodulation components of the visual evoked potential: Responses to lateral and superimposed stimuli

Nonlinear interactions in the human visual system were studied using visual evoked potentials (VEPs). In one experiment (superimposed condition), all segments of a dartboard pattern were contrast reversed in time by a sum of two sinusoidal signals. In a second experiment (lateral condition), segments in some regions of the dartboard pattern were contrast reversed by a single sinusoid of one frequency, while segments in other (contiguous) regions of the pattern were contrast reversed by a single sinusoid of another frequency. An identical set of ten frequency pairs was used in each experiment. The frequency pairs were chosen such that the difference between frequencies in each pair was 2 Hz. Amplitudes and phases of the sum and difference frequency components of the VEP (intermodulation terms) were retrieved by Fourier analysis and served as measures of nonlinear interactions. The use of input pairs with a fixed separation in frequency enabled the estimation of the temporal characteristics of the visual pathways prior to a second linear stage. The use of superimposed and lateral conditions revealed antagonistic contributions to the VEP, possibly reflecting direct-through excitatory and lateral inhibitory pathways, respectively.Supported by grants from the U.S. National Eye Institute, the Esther A. and Joseph Klingenstein Fund, and the Harry Frank Guggenheim Foundation     

Comment on Barclay and Vreysen: Published dynamic population model for tsetse cannot fit field data

The structure, and assumed parameter values, of a recent dynamic population model for tsetse (Diptera: Glossinidae) render it unable to fit published data on tsetse control programs using odor-baited targets, insecticide-treated cattle and the sterile insect technique (SIT). The underlying problem is a mismatch between the small size of the mapped cells (1 ha) and the long time-step, which allows flies to move only once every 5 days, and then only to an adjacent cell. Assumed rates of tsetse dispersal and killing by odor-baited targets are consequently at least an order of magnitude lower than observed in the field. Suggestions that Glossina pallidipes could be eradicated more rapidly with SIT, than using hundreds of targets per km², is contradicted both by the field data and by three other independent modeling studies.     

Local adaptation of Ruellia nudiflora (Acanthaceae) to biotic counterparts: complex scenarios revealed when two herbivore guilds are considered

This study evaluated whether the herb Ruellia nudiflora is locally adapted to a specialist insect seed predator (SP) and insect folivores, and if plant local adaptation (LA) to the former is more likely. A reciprocal transplant experiment was conducted using three sites in Yucatan (Mexico) (n = 864 plants). A third of the plants of each origin were placed at each site, and we recorded the following during a 9‐month period: fruit number, leaf damage, and fruits attacked by SP. Results indicated lack of plant LA for all the variables measured. Instead, seed predation was c. 100% greater for native plants at one study site, suggesting insect LA or plant maladaptation; folivory was homogeneous across sites/origins. Based on these results, we discuss differences in the potential each herbivore guild has to promote plant LA, as well as divergent evolutionary outcomes of plant–herbivore interactions across sites.     

Modeling the succession of barnacles and mussels on a sandstone reef in Pernambuco State, Brazil

Settlement and recruitment rates, biological interactions, environmental parameters, and larval supply are factors that influence community structure in areas where barnacles and mussels are the dominant fauna. This study modeled the succession populations of two barnacle species, Tetraclita stalactifera (Lamarck, 1818) and Chthamalus bisinuatus (Pilsbry, 1916), and a bivalve, Brachidontes solisianus (d’Orbigny, 1846), on a sandstone reef at Piedade Beach, Pernambuco State, Brazil. The different stages of the life cycles of these invertebrates are represented by adult and immature forms in this model and are simulated as numbers of individuals per 100 cm². Recruitment rates are represented as forcing functions based on field recruitment experiments with time-steps of 1 day. In addition to intraspecific competition, the model takes into account interspecific competition based on reciprocal effects and carrying capacities. Field data from field succession experiments were used to calibrate the model. Recruitment and succession data were collected from random 10 × 10-cm plots within a 1-m transect on a Brachidontes bed from April to December 2007. Correlation coefficients between field data and simulation results were statistically significant for both populations; sensitivity analysis showed that increases and decreases in invertebrate population densities were always smaller than 10% compared to baseline model values. Patch closure by mussels population growth was one of the main succession processes observed during the rainy season. However, barnacles were the dominant species at the end of both field and simulation succession experiments, with an average density of close to 100 individuals per 100 cm². Cirripedia individuals may inhibit bivalve re-colonization by settling over shells and more efficiently occupying free space in addition to having higher recruitment rates than bivalves during the dry season.     

Semiempirical energy calculations on model compounds of polypeptides. Crystal structures of DL-acetylleucine N-methylamide and DL-acetyl-amino-n-butyric acid N-methylamide

The sum E of the packing and conformation energies of the crystals of DL -acetylleucine N-methylamide (ALNMA) and DL -acetyl-α-amino-n-butyric acid N-methylamide (ABAMA) is calculated as a function of the crystallographic parameters and the conformational angles. The intermolecular energy is assumed to be the pairwise sum of nonbonded and electrostatic atomic interactions, while both these terms and intrinsic terms describing barriers of internal rotation contribute to the intramolecular energy. For ALNMA E is minimized with respect to 18 parameters: the minimum found when starting from the experimental structure agrees with this within 0.07 Å and 3°, except for one angle which deviates by 6° the average deviations of the atomic coordinates are \documentclass{article}\pagestyle{empty}\begin{document}$ |\overline {\Delta x|} = 0.02,|\overline {\Delta y|} = 0.07,|\overline {\Delta z|} = 0.08 $\end{document} Å. Another minimum with about the same energy shows slightly worse agreement. A comparison between different sets of nonbonded functions is made. The prediction of conformation and intermolecular packing of ABAMA is attempted on the basis of the knowledge of the unit cell and the space group. In agreement with available experimental data it is found that only one-di-mensional arrays of molecules linked by pairs of hydrogen bonds are compatible with the unit cell. The more stable of two possible conformations of the main chain agrees approximately with the experimental conformation. The calculation is not conclusive with regard to the side-chain conformation and the packing of non-hydrogen-bonded molecules.     

A determination of liquid–vapour interfacial properties for methanol using a linear-combination-based isotropic periodic sum

We performed molecular dynamics simulations of the methanol liquid–vapour interfacial systems for a wide temperature range of 200–350 K. The linear-combination-based isotropic periodic sum (LIPS) method was used for estimating Coulombic interactions of the systems. The temperature dependence of the liquid and vapour phase densities, surface thickness and surface tension using the LIPS method was almost equal to that of the Ewald sum method. The temperature dependence of the electrostatic potential profile using the LIPS method was very similar to that of the Ewald sum method. We conclude that the LIPS method provides a reasonable accuracy in determining the liquid–vapour interfacial properties of polar molecules for many temperature conditions.     

A VERTEBRATE REPRODUCTIVE SYSTEM INVOLVING THREE PLOIDY LEVELS: HYBRID ORIGIN OF TRIPLOIDS IN A CONTACT ZONE OF DIPLOID AND TETRAPLOID PALEARCTIC GREEN TOADS (BUFO VIRIDIS SUBGROUP)*

The rise and consequences of polyploidy in vertebrates, whose origin was associated with genome duplications, may be best studied in natural diploid and polyploid populations. In a diploid/tetraploid (2n/4n) geographic contact zone of Palearctic green toads in northern Kyrgyzstan, we examine 4ns and triploids (3n) of unknown genetic composition and origins. Using mitochondrial and nuclear sequence, and nuclear microsatellite markers in 84 individuals, we show that 4n (Bufo pewzowi) are allopolyploids, with a geographically proximate 2n species (B. turanensis) being their maternal ancestor and their paternal ancestor as yet unidentified. Local 3n forms arise through hybridization. Adult 3n mature males (B. turanensis mtDNA) have 2n mothers and 4n fathers, but seem distinguishable by nuclear profiles from partly aneuploid 3n tadpoles (with B. pewzowi mtDNA). These observations suggest multiple pathways to the formation of triploids in the contact zone, involving both reciprocal origins. To explain the phenomena in the system, we favor a hypothesis where 3n males (with B. turanensis mtDNA) backcross with 4n and 2n females. Together with previous studies of a separately evolved, sexually reproducing 3n lineage, these observations reveal complex reproductive interactions among toads of different ploidy levels and multiple pathways to the evolution of polyploid lineages.     

Calculations of the circular dichroism of double-helical nucleic acids. II. Effects involving n leads to pi transitions

The circular dichroism of double-helical nucleic acids was calculated as a function of geometry, including terms involving n → π* transitions. The “nonbonding” n or σ orbitals were of the azine type, delocalized, but concentrated at the nitrogen atoms of the purines and pyrimidines. Dynamic coupling of the magnetic moments of the n → π* transitions with the electric moments of π → π* transitions generated important terms. Mixing of electric dipole character into n → π* transitions by the static electric field perturbation of the molecule is of lesser importance. The largest contributions of n → π* transitions to the circular dichroism of double-helical nucleic acids are comparable in magnitude to the sum of π → π* terms only for geometries where the circular dichroism is weak. Using both n → π* and π → π* contributions one is able to match experimental and calculated circular dichroism spectra for DNA's over a much wider range of conditions than was possible previously.     

Temperature dependence of single channel currents and the peptide libration mechanism for ion transport through the gramicidin A transmembrane channel

Summary A study of the temperature dependence of gramicidin A conductance of K⁺ in diphytanoyllecithin/n-decane membranes shows the plot of In (single channel conductance) as a function of reciprocal temperature to be nonlinear for the most probable set of conductance, states. These results are considered in terms of a series of barriers, of the dynamics of channel conformation,vis-a-vis the peptide libration mechanism, and of the effect of lipid viscosity on side chain motions again as affecting the energetics of peptide libration.     

The solvation of bromide anion in acetonitrile: a structural study based on the combination of theoretical calculations and X-ray absorption spectroscopy

This work studies the solvation of bromide in acetonitrile by combining quantum mechanics, computer simulations and X-ray absorption near edge structure (XANES) spectroscopy. Three different sets of interaction potentials were tested, one of them derived from literature and the other two are simple modifications of the previous one to include specificities of the bromide–acetonitrile interactions. Results for microsolvation of bromide were obtained by quantum mechanical optimization and classical minimization of small clusters [Br(ACN) _n ]^?  (n = 9, 20). Analysis of molecular dynamics (MD) simulations has provided structural, dynamic and energetic aspects of the solvation phenomenon. The theoretical computation of Br K-edge XANES spectrum in solution using the structural information obtained from the different simulations has allowed the comparison among the three different potentials, as well as the examination of the main structural and dynamic factors determining the shape of the experimental spectrum.