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At least 973 records · Page 54Linked to original sources
PubMed2006

Efficient computation of the first passage time distribution of the generalized master equation by steady-state relaxation.

The generalized master equation or the equivalent continuous time random walk equations can be used to compute the macroscopic first passage time distribution (FPTD) of a complex stochastic system from short-term microscopic simulation data. The computation of the mean first passage time and additional low-order FPTD moments can be simplified by directly relating the FPTD moment generating function to the moments of the local FPTD matrix. This relationship can be physically interpreted in terms of steady-state relaxation, an extension of steady-state flow. Moreover, it is amenable to a statistical error analysis that can be used to significantly increase computational efficiency. The efficiency improvement can be extended to the FPTD itself by modelling it using a gamma distribution or rational function approximation to its Laplace transform.

Algorithms↗
PubMed2006

Theoretical studies of transition states by the multioverlap molecular dynamics methods.

The multioverlap molecular dynamics method gives a flat probability distribution in the multidimensional dihedral-angle-distance space, where the dihedral-angle distance of a configuration with respect to a reference state gives a measure for structural similarity. Hence, this method realizes a random walk among specific configurations in the multidimensional dihedral-angle-distance space at a constant temperature and explores widely in the configurational space. We applied the multioverlap molecular dynamics method to a pentapeptide, Met-enkephalin, in gas phase as a test system. Comparing the results of this method with those of the conventional canonical and multicanonical algorithms, we demonstrate its effectiveness. Furthermore, from the detailed free-energy landscape obtained from the results of the multioverlap molecular dynamics simulation, we obtain the transition state between two specific reference configurations of Met-enkephalin. We also deduce the transition pathway between the two specific reference configurations.

Algorithms↗
PubMed2006

Order-parameter-based Monte Carlo simulation of crystallization.

A Monte Carlo simulation method is presented for simulation of phase transitions, with emphasis on the study of crystallization. The method relies on a random walk in order parameter Phi(q(N)) space to calculate a free energy profile between the two coexisting phases. The energy and volume data generated over the course of the simulation are subsequently reweighed to identify the precise conditions for phase coexistence. The usefulness of the method is demonstrated in the context of crystallization of a purely repulsive Lennard-Jones system. A systematic analysis of precritical and critical nuclei as a function of supercooling reveals a gradual change from a bcc to a fcc structure inside the crystalline nucleus as it grows at large degrees of supercooling. The method is generally applicable and is expected to find applications in systems for which two or more coexisting phases can be distinguished through one or more order parameters.

Journal Article↗
PubMed2006

Facilitated diffusion of DNA-binding proteins: efficient simulation with the method of excess collisions.

In this paper, a new method to efficiently simulate diffusion controlled second order chemical reactions is derived and applied to site-specific DNA-binding proteins. The protein enters a spherical cell and propagates via two competing modes, a free diffusion and a DNA-sliding mode, to search for its specific binding site in the center of the cell. There is no need for a straightforward simulation of this process. Instead, an alternative and exact approach is shown to be essentially faster than explicit random walk simulations. The speed-up of this novel simulation technique is rapidly growing with system size.

Binding Sites↗
PubMed2006

Selectivity principle of the ligand escape process from a two-gate tunnel in myoglobin: molecular dynamics simulation.

We proposed a selectivity principle for the ligand escape process from two fluctuating bottlenecks in a cavity with a multigate inside a myoglobin pocket. Our previous analytical theory proposed a fluctuating bottleneck model for a Brownian particle passing through two gates on a cavity surface of an enzyme protein and has determined the escape rate in terms of the time-dependent gate function and the competition effect. It illustrated that with two (or more than two) gates on a cavity surface the gate modulation, which is controlled by protein fluctuation, dominates the ligand escape pathway. We have performed a molecular dynamics simulation to investigate the selectivity principle of the ligand escape process from two-gate tunnel in myoglobin. The simulation results confirm our theoretical conjecture. It indicates that the escape process is actually entropy driven, and the ligand escape pathway is chosen via the gate modulation. This suggests an interesting intrinsic property, that is, the oxymyoglobin tertiary structure is favorable to the departure of the ligand from one direction rather than through a biased random walk.

Computer Simulation↗
PubMed2006

An efficient sampling algorithm for variational Monte Carlo.

We propose a new algorithm for sampling the N-body density mid R:Psi(R)mid R:(2)R(3N)mid R:Psimid R:(2) in the variational Monte Carlo framework. This algorithm is based upon a modified Ricci-Ciccotti discretization of the Langevin dynamics in the phase space (R,P) improved by a Metropolis-Hastings accept/reject step. We show through some representative numerical examples (lithium, fluorine, and copper atoms and phenol molecule) that this algorithm is superior to the standard sampling algorithm based on the biased random walk (importance sampling).

Journal Article↗
PubMed2006

The effect of sequence correlation on bubble statistics in double-stranded DNA.

DNA exists stably in the double-stranded structure at physiological temperatures, but base pairs are observed to unbind locally, giving way to bubbles (i.e., locally denatured states) due to thermal fluctuation. In this study, we consider the effect of sequence on the bubble statistics. On the basis of the Edwards equation description [W. Sung and J.-H. Jeons, Phys. Rev. E 69, 031902 (2004) ], we develop a stochastic model incorporating the sequence randomness as a dichotomic noise, where the bubble and its size are identified as a returning random walk and its first passage time, respectively. By simulating the model Langevin equation, we obtain the bubble size distribution and show how it is affected by the sequence correlation. We find that the bubble size distribution of DNA with finite sequence correlation deviates from the Poland-Scheraga-type distribution. In particular, the formation of large bubbles is dramatically enhanced as sequence correlation length gets longer.

Base Sequence↗
PubMed2006

A Monte Carlo simulation study of branched polymers.

Monte Carlo simulations are presented for the static properties of highly branched polymer molecules. The molecules consist of a semiflexible backbone of hard-sphere monomers with semiflexible side chains, also composed of hard-sphere monomers, attached to either every backbone bead or every other backbone bead. The conformational properties and structure factor of this model are investigated as a function of the stiffness of the backbone and side chains. The average conformations of the side chains are similar to self-avoiding random walks. The simulations show that there is a stiffening of the backbone as degree of crowding is increased, for example, if the branch spacing is decreased or side chain length is increased. The persistence length of the backbone is relatively insensitive to the stiffness of the side chains over the range investigated. The simulations reproduce most of the qualitative features of the structure factor observed in experiment, although the magnitude of the stiffening of the backbone is smaller than in experiment.

Journal Article↗
PubMed1977

Stochastic models and fluctuations in reversal time of ambiguous figures.

Five probability distributions for the description of temporal fluctuations in the perception of ambiguous figures were fitted to previously obtained experimental results and classified according to their efficiency in describing the data. The gamma, Wiener, and Capocelli-Riciardi distributions showed the highest efficiency, while the chi2 and Taylor-Aldridge distributions showed a very low effiency. Therefore the underlying process may be described either by a simple Poisson model or by a random-walk model. For the gamma distribution there was a strong correlation between the parameters, while for the Wiener distribution this correlation was lower.

Humans↗
PubMed2002

Wavelet analysis of shoreline change on the Outer Banks of North Carolina: an example of complexity in the marine sciences.

The horizontal, shore-perpendicular change in shoreline position along the Outer Banks of North Carolina is found to be a self-affine signal. We measure shoreline change by determining the horizontal change in position of the 0.8-m contour sampled from shore-perpendicular profiles spaced at 20-m intervals along the coast. The profiles are obtained from two light detection and ranging surveys performed in September 1997 and September 1998. For six selected sections of coast, wavelet analysis of the shoreline change signal indicates the signal is self-affine with a scaling exponent that varies from 1.2 to 2.1. This self-affine behavior indicates that the shoreline change signal is nonstationary with long-range persistence. A stochastic diffusion model of sediment transport replicates the observed self-affine behavior observed south of Cape Hatteras (scaling exponent between 1.2 and 1.6) whereas a random walk model replicates the signal observed north of Cape Hatteras (scaling exponent approximately 2.0). Because of the finite nature of the data set, there are limits in space and time to the power law behavior of the system. Characteristics of such systems can be described by upper-truncated power laws, which yield the upper limits of power law behavior. Applying an upper-truncated power law to the data for one section of coast, we find an upper limit of 7 km for the maximum continuous alongshore distance eroding or accreting. For the same section of coast, we find upper limits of 25 m for the maximum shore-perpendicular erosion and 11 m for the maximum shore-perpendicular accretion during the study period.

Journal Article↗
PubMed2004

Irregularity, volatility, risk, and financial market time series.

The need to assess subtle, potentially exploitable changes in serial structure is paramount in the analysis of financial data. Herein, we demonstrate the utility of approximate entropy (ApEn), a model-independent measure of sequential irregularity, toward this goal, by several distinct applications. We consider both empirical data and models, including composite indices (Standard and Poor's 500 and Hang Seng), individual stock prices, the random-walk hypothesis, and the Black-Scholes and fractional Brownian motion models. Notably, ApEn appears to be a potentially useful marker of system stability, with rapid increases possibly foreshadowing significant changes in a financial variable.

Economics↗
PubMed2004

Win-stay, lose-shift in language learning from peers.

Traditional language learning theory explores an idealized interaction between a teacher and a learner. The teacher provides sentences from a language, while the learner has to infer the underlying grammar. Here, we study a new approach by considering a population of individuals that learn from each other. There is no designated teacher. We are inspired by the observation that children grow up to speak the language of their peers, not of their parents. Our goal is to characterize learning strategies that generate "linguistic coherence," which means that most individuals use the same language. We model the resulting learning dynamics as a random walk of a population on a graph. Each vertex represents a candidate language. We find that a simple strategy using a certain aspiration level with the principle of win-stay, lose-shift does extremely well: stay with your current language, if at least three others use that language; otherwise, shift to an adjacent language on the graph. This strategy guarantees linguistic coherence on all nearly regular graphs, in the relevant limit where the number of candidate languages is much greater than the population size. Moreover, for many graphs, it is sufficient to have an aspiration level demanding only two other individuals to use the same language.

Algorithms↗
PubMed2005

Protein folding pathways from replica exchange simulations and a kinetic network model.

We present an approach to the study of protein folding that uses the combined power of replica exchange simulations and a network model for the kinetics. We carry out replica exchange simulations to generate a large ( approximately 10(6)) set of states with an all-atom effective potential function and construct a kinetic model for folding, using an ansatz that allows kinetic transitions between states based on structural similarity. We use this network to perform random walks in the state space and examine the overall network structure. Results are presented for the C-terminal peptide from the B1 domain of protein G. The kinetics is two-state after small temperature perturbations. However, the coil-to-hairpin folding is dominated by pathways that visit metastable helical conformations. We propose possible mechanisms for the alpha-helix/beta-hairpin interconversion.

Biophysics↗
PubMed2005

Species lifetime distribution for simple models of ecologies.

Interpretation of empirical results based on a taxa's lifetime distribution shows apparently conflicting results. Species' lifetime is reported to be exponentially distributed, whereas higher-order taxa, such as families or genera, follow a broader distribution, compatible with power-law decay. We show that both forms of evidence are consistent with a simple evolutionary model that does not require specific assumptions on species interaction. The model provides a zero-order description of the dynamics of ecological communities, and its species lifetime distribution can be computed exactly. Different behaviors are found as follows: an initial t(-3/2) power law, emerging from a random walk type of dynamics, which crosses over to a steeper t(-2) branching process-like regime and finally is cut off by an exponential decay that becomes weaker and weaker as the total population increases. Sampling effects also can be taken into account and shown to be relevant. If species in the fossil record were sampled according to the Fisher log-series distribution, lifetime should be distributed according to a t(-1) power law. Such variability of behaviors in a simple model, combined with the scarcity of data available, casts serious doubt on the possibility of validating theories of evolution on the basis of species lifetime data.

Animals↗
PubMed2005

Electrochemical imaging of fusion pore openings by electrochemical detector arrays.

Opening of individual exocytotic fusion pores in chromaffin cells was imaged electrochemically with high time resolution. Electrochemical detector arrays that consist of four platinum microelectrodes were microfabricated on a glass coverslip. Exocytosis of single vesicles containing catecholamines from a cell positioned on top of the array is detected by the individual electrodes as a time-resolved oxidation current, reflecting the time course of arrival of catecholamine molecules at the electrode surfaces. The signals exhibit low noise and reveal foot signals indicating fusion pore formation and expansion. The position of individual release events is determined from the fraction of catecholamines recorded by the individual electrodes. Simultaneous fluorescence imaging of release of acridine orange from individual vesicles confirmed the electrochemical position assignments. This electrochemical camera provides very high time resolution, spatiotemporal localization of individual fusion pore openings and quantitative data on the flux of transmitter from individual vesicles. Analysis of the amperometric currents employing random walk simulations indicates that the time course of amperometric spikes measured near the cell surface is due to a low apparent diffusion coefficient of catecholamines near the cell surface and not due to slow dissociation from the granular matrix.

Acridine Orange↗
PubMed2006

Long-distance lateral diffusion of human Rad51 on double-stranded DNA.

Rad51 is the primary eukaryotic recombinase responsible for initiating DNA strand exchange during homologous recombination. Although the subject of intense study for over a decade, many molecular details of the reactions promoted by Rad51 and related recombinases remain unknown. Using total internal reflection fluorescence microscopy, we directly visualized the behavior of individual Rad51 complexes on double-stranded DNA (dsDNA) molecules suspended in an extended configuration above a lipid bilayer. Here we show that complexes of Rad51 can bind to and slide freely along the helical axis of dsDNA. Sliding is bidirectional, does not require ATP hydrolysis, and displays properties consistent with a 1D random walk driven solely by thermal diffusion. The proteins move freely on the DNA for long periods of time; however, sliding terminates and the proteins become immobile upon encountering the free end of a linear dsDNA molecule. This study provides previously uncharacterized insights into the behaviors of human Rad51, which may apply to other members of the RecA-like family of recombinases.

Adenosine Triphosphate↗
PubMed2006

On the dynamics of molecular conformation.

Understanding the mechanism of fast transitions between conformed states of large biomolecules is central to reconciling the dichotomy between the relatively high speed of metabolic processes and slow (random-walk based) estimates on the speed of biomolecular processes. Here we use the dynamical systems approach to suggest that the reduced time of transition between different conformations is due to features of the dynamics of molecules that are a consequence of their structural features. Long-range and local effects both play a role. Long-range molecular forces account for the robustness of final states and nonlinear processes that channel localized, bounded disturbances into collective, modal motions. Local interconnections provide fast transition dynamics. These properties are shared by a class of networked systems with strong local interconnections and long-range nonlinear forces that thus exhibit flexibility and robustness at the same time.

Macromolecular Substances↗
PubMed2002

Learning dynamics in social dilemmas.

The Nash equilibrium, the main solution concept in analytical game theory, cannot make precise predictions about the outcome of repeated mixed-motive games. Nor can it tell us much about the dynamics by which a population of players moves from one equilibrium to another. These limitations, along with concerns about the cognitive demands of forward-looking rationality, have motivated efforts to explore backward-looking alternatives to analytical game theory. Most of the effort has been invested in evolutionary models of population dynamics. We shift attention to a learning-theoretic alternative. Computational experiments with adaptive agents identify a fundamental solution concept for social dilemmas--stochastic collusion--based on a random walk from a self-limiting noncooperative equilibrium into a self-reinforcing cooperative equilibrium. However, we show that this solution is viable only within a narrow range of aspiration levels. Below the lower threshold, agents are pulled into a deficient equilibrium that is a stronger attractor than mutual cooperation. Above the upper threshold, agents are dissatisfied with mutual cooperation. Aspirations that adapt with experience (producing habituation to stimuli) do not gravitate into the window of viability; rather, they are the worst of both worlds. Habituation destabilizes cooperation and stabilizes defection. Results from the two-person problem suggest that applications to multiplex and embedded relationships will yield unexpected insights into the global dynamics of cooperation in social dilemmas.

Adaptation, Psychological↗