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.

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