A multi-scaled approach for simulating chemical reaction systems

In this paper we give an overview of some very recent work, as well as presenting a new approach, on the stochastic simulation of multi-scaled systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge–Kutta methods and the balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and present a new approach which couples the three regimes mentioned above. We then apply this approach to a biologically inspired problem involving the expression and activity of LacZ and LacY proteins in E. coli, and conclude with a discussion on the significance of this work.

Evolution of stress deficit and changing rates of seismicity in cellular automaton models of earthquake faults

We investigate the internal dynamics of two cellular automaton models with heterogeneous strength fields and differing nearest neighbour laws. One model is a crack-like automaton, transferring ail stress from a rupture zone to the surroundings. The other automaton is a partial stress drop automaton, transferring only a fraction of the stress within a rupture zone to the surroundings. To study evolution of stress, the mean spectral density. f(k(r)) of a stress deficit held is: examined prior to, and immediately following ruptures in both models. Both models display a power-law relationship between f(k(r)) and spatial wavenumber (k(r)) of the form f(k(r)) similar tok(r)(-beta). In the crack model, the evolution of stress deficit is consistent with cyclic approach to, and retreat from a critical state in which large events occur. The approach to criticality is driven by tectonic loading. Short-range stress transfer in the model does not affect the approach to criticality of broad regions in the model. The evolution of stress deficit in the partial stress drop model is consistent with small fluctuations about a mean state of high stress, behaviour indicative of a self-organised critical system. Despite statistics similar to natural earthquakes these simplified models lack a physical basis. physically motivated models of earthquakes also display dynamical complexity similar to that of a critical point system. Studies of dynamical complexity in physical models of earthquakes may lead to advancement towards a physical theory for earthquakes.

FRAP analysis of nucleocytoplasmic dynamics of the vitamin D receptor splice variant VDRB1: preferential targeting to nuclear speckles

Although the key components of the cellular nuclear transport machinery have largely been characterized through extensive efforts in recent years, in vivo measurements of the kinetics of nuclear protein import/export are patently few. The present study applies the approach of FRAP (fluorescence recovery after photobleaching) to examine the nucleocytoplasmic flux of a novel human VDRB1 (vitamin D receptor B I) isoform in living cells. Through an N-terminal extension containing a consensus nuclear targeting sequence, VDRB1 is capable of localizing in nuclear speckles adjacent to SC-35 (35 kDa splicing component)containing speckles as well as in the nucleoplasm, dependent on ligand. Investigation of VDRB1 nucleocytoplasmic transport using FRAP indicates for the first time that the VDRB1 has a serum-modulated, active nuclear-import mechanism. There is no evidence of an efficient, active export mechanism for VDRB1, probably as a result of nuclear retention. VDRB1 nuclear import in the absence of serum occurred more rapidly and to a greater extent to nuclear speckles compared with import to other nuclear sites. This preferential transport from the cytoplasm to and accumulation within nuclear speckles is consistent with the idea that the latter represent dynamic centres of VDRB1 interaction with other nuclear proteins. The results are consistent with the existence of specialized pathways to target proteins to nuclear subdomains.

Transcriptional network dynamics in macrophage activation

Transcriptional regulatory networks govern cell differentiation and the cellular response to external stimuli. However, mammalian model systems have not yet been accessible for network analysis. Here, we present a genome-wide network analysis of the transcriptional regulation underlying the mouse macrophage response to bacterial lipopolysaccharide (LPS). Key to uncovering the network structure is our combination of time-series cap analysis of gene expression with in silico prediction of transcription factor binding sites. By integrating microarray and qPCR time-series expression data with a promoter analysis, we find dynamic subnetworks that describe how signaling pathways change dynamically during the progress of the macrophage LPS response, thus defining regulatory modules characteristic of the inflammatory response. In particular, our integrative analysis enabled us to suggest novel roles for the transcription factors ATF-3 and NRF-2 during the inflammatory response. We believe that our system approach presented here is applicable to understanding cellular differentiation in higher eukaryotes. (c) 2006 Elsevier Inc. All rights reserved.

Recurrence interval statistics of cellular automaton seismicity models

The recurrence interval statistics for regional seismicity follows a universal distribution function, independent of the tectonic setting or average rate of activity (Corral, 2004). The universal function is a modified gamma distribution with power-law scaling of recurrence intervals shorter than the average rate of activity and exponential decay for larger intervals. We employ the method of Corral (2004) to examine the recurrence statistics of a range of cellular automaton earthquake models. The majority of models has an exponential distribution of recurrence intervals, the same as that of a Poisson process. One model, the Olami-Feder-Christensen automaton, has recurrence statistics consistent with regional seismicity for a certain range of the conservation parameter of that model. For conservation parameters in this range, the event size statistics are also consistent with regional seismicity. Models whose dynamics are dominated by characteristic earthquakes do not appear to display universality of recurrence statistics.

Parallel implementation of stochastic simulation for large scale cellular processes

Experimental and theoretical studies have shown the importance of stochastic processes in genetic regulatory networks and cellular processes. Cellular networks and genetic circuits often involve small numbers of key proteins such as transcriptional factors and signaling proteins. In recent years stochastic models have been used successfully for studying noise in biological pathways, and stochastic modelling of biological systems has become a very important research field in computational biology. One of the challenge problems in this field is the reduction of the huge computing time in stochastic simulations. Based on the system of the mitogen-activated protein kinase cascade that is activated by epidermal growth factor, this work give a parallel implementation by using OpenMP and parallelism across the simulation. Special attention is paid to the independence of the generated random numbers in parallel computing, that is a key criterion for the success of stochastic simulations. Numerical results indicate that parallel computers can be used as an efficient tool for simulating the dynamics of large-scale genetic regulatory networks and cellular processes

Time-reversal test for stochastic quantum dynamics

The calculation of quantum dynamics is currently a central issue in theoretical physics, with diverse applications ranging from ultracold atomic Bose-Einstein condensates to condensed matter, biology, and even astrophysics. Here we demonstrate a conceptually simple method of determining the regime of validity of stochastic simulations of unitary quantum dynamics by employing a time-reversal test. We apply this test to a simulation of the evolution of a quantum anharmonic oscillator with up to 6.022×1023 (Avogadro's number) of particles. This system is realizable as a Bose-Einstein condensate in an optical lattice, for which the time-reversal procedure could be implemented experimentally.

Superchemistry: dynamics of coupled atomic and molecular Bose condensates

We analyze the dynamics of a dilute, trapped Bose-condensed atomic gas coupled to a diatomic molecular Bose gas by coherent Raman transitions. This system is shown to result in a new type of “superchemistry,” in which giant collective oscillations between the atomic and the molecular gas can occur. The phenomenon is caused by stimulated emission of bosonic atoms or molecules into their condensate phases.

Quantum dynamics of three coupled atomic Bose-Einstein condensates

The simplest model of three coupled Bose-Einstein condensates is investigated using a group theoretical method. The stationary solutions are determined using the SU(3) group under the mean-field approximation. This semiclassical analysis, using system symmetries, shows a transition in the dynamics of the system from self trapping to delocalization at a critical value for the coupling between the condensates. The global dynamics are investigated by examination of the stable points, and our analysis shows that the structure of the stable points depends on the ratio of the condensate coupling to the particle-particle interaction, and undergoes bifurcations as this ratio is varied. This semiclassical model is compared to a full quantum treatment, which also displays a dynamical transition. The quantum case has collapse and revival sequences superimposed on the semiclassical dynamics, reflecting the underlying discreteness of the spectrum. Nonzero circular current states are also demonstrated as one of the higher-dimensional effects displayed in this system.

Substructure and Dynamics of the Fornax Cluster

We present the first dynamical analysis of a galaxy cluster to include a large fraction of dwarf galaxies. Our sample of 108 Fornax Cluster members measured with the UK Schmidt Telescope FLAIR-II spectrograph contains 55 dwarf galaxies (15.5 > b(j) > 18.0 or -16 > M-B > -13.5). H alpha emission shows that of the dwarfs are star forming, twice the fraction implied by morphological classifications. The total sample has a mean velocity of 1493 +/- 36 kms s(-1) and a velocity dispersion of 374 +/- 26 km s(-1). The dwarf galaxies form a distinct population: their velocity dispersion (429 +/- 41 km s(-1)) is larger than that of the giants () at the 98% confidence level. This suggests that the dwarf population is dominated by infalling objects whereas the giants are virialized. The Fornax system has two components, the main Fornax Cluster centered on NGC 1399 with cz = 1478 km s(-1) and sigma (cz) = 370 km s(-1) and a subcluster centered 3 degrees to the southwest including NGC 1316 with cz = 1583 km s(-1) and sigma (cz) = 377 km s(-1). This partition is preferred over a single cluster at the 99% confidence level. The subcluster, a site of intense star formation, is bound to Fornax and probably infalling toward the cluster core for the first time. We discuss the implications of this substructure for distance estimates of the Fornax Cluster. We determine the cluster mass profile using the method of Diaferio, which does not assume a virialized sample. The mass within a projected radius of 1.4 Mpc is (7 +/- 2) x 10(13) M-., and the mass-to-light ratio is 300 +/- 100 M-./L-.. The mass is consistent with values derived from the projected mass virial estimator and X-ray measurements at smaller radii.

Evolution of Wolbachia pipientis transmission dynamics in insects

Wolbachia pipientis is an intracellular bacterial parasite of arthropods that enhances its transmission by manipulating host reproduction, most commonly by inducing cytoplasmic incompatibility. The discovery of isolates with modified cytoplasmic incompatibility phenotypes and others with novel virulence properties is an indication of the potential breadth of evolutionary strategies employed by Wolbachia.