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.

A genetic estimation algorithm for parameters of stochastic ordinary differential equations

A generic method for the estimation of parameters for Stochastic Ordinary Differential Equations (SODEs) is introduced and developed. This algorithm, called the GePERs method, utilises a genetic optimisation algorithm to minimise a stochastic objective function based on the Kolmogorov-Smirnov statistic. Numerical simulations are utilised to form the KS statistic. Further, the examination of some of the factors that improve the precision of the estimates is conducted. This method is used to estimate parameters of diffusion equations and jump-diffusion equations. It is also applied to the problem of model selection for the Queensland electricity market. (C) 2003 Elsevier B.V. All rights reserved.

Modelling the fate of chromated copper arsenate in a sandy soil

A pulse of chromated copper arsenate (CCA, a timber preservative) was applied in irrigation water to an undisturbed field soil in a laboratory column. Concentrations of various elements in the leachate from the column were measured during the experiment. Also, the remnants within the soil were measured at the end of the experiment. The geochemical modelling package, PHREEQC-2, was used to simulate the experimental data. Processes included in the CCA transport modelling were advection, dispersion, non-specific adsorption (cation exchange) and specific adsorption by clay minerals and organic matter, as well as other possible chemical reactions such as precipitation/dissolution. The modelling effort highlighted the possible complexities in CCA transport and reaction experiments. For example, the uneven dosing of CCA as well as incomplete knowledge of the soil properties resulted in simulations that gave only partial, although reasonable, agreement with the experimental data. Both the experimental data and simulations show that As and Cu are strongly adsorbed and therefore, will mostly remain at the top of the soil profile, with a small proportion appearing in leachate. On the other hand, Cr is more mobile and thus it is present in the soil column leachate. Further simulations show that both the quantity of CCA added to the soil and the pH of the irrigation water will influence CCA transport. Simulations suggest that application of larger doses of CCA to the soil will result in higher leachate concentrations, especially for Cu and As. Irrigation water with a lower pH will dramatically increase leaching of Cu. These results indicate that acidic rainfall or significant accidental spillage of CCA will increase the risk of groundwater pollution.

Simple microcavity for single-photon generation

A new design of an optical resonator for generation of single-photon pulses is proposed. The resonator is made of a cylindrical or spherical piece of a polymer squeezed between two flat dielectric mirrors. The mode characteristics of this resonator are calculated numerically. The numerical analysis is backed by a physical explanation. The decay time and the mode volume of the fundamental mode are sufficient for achieving more than 96% probability of generating a single-photon in a single-mode. The corresponding requirement for the reflectivity of the mirrors (similar to 99.9%) and the losses in the polymer ( 100 dB/m) are quite modest. The resonator is suitable for single-photon generation based on optical pumping of a single quantum system such as an organic molecule, a diamond nanocrystal, or a semiconductor quantum dot if they are imbedded in the polymer. (C) 2005 Optical Society of America.

Atmospheric boundary layer development over a narrow coastal plain during onshore flow

A study of the structure of the daytime atmospheric boundary layer during onshore flow over a narrow coastal plain is presented. The main emphasis of the study is on the nature and causes of heating and cooling observed in the boundary layer temperature profiles. Measurements included vertical temperature profiles above at least two sites derived from radiosondes and aircraft, as well as surface estimates of radiative and sensible heat fluxes. Surface meteorological and pilot balloon data were also available, providing further evidence of short-term changes in atmospheric boundary layer structure. The Manawatu case was representative of autumnal anticyclonic conditions with weak pressure gradients, and illustrated typical diurnal development of a convective boundary layer over a coastal plain bordered by mountain ranges, with a transition from a stable nocturnal situation to a well-mixed profile in the afternoon. The profiles show surface input of heat propagating upwards through the boundary layer during the day, as well as entrainment of heat at the top associated with shear induced turbulence and/or penetrative convection. Applying a one-dimensional model, estimates of boundary layer heat budget components were obtained for four time periods during the day. Later periods were affected by cumulus cloud development at the top of the boundary layer, resulting in significant changes in individual components. Input of sensible heat from the surface decreased, while the addition of heat to the boundary layer from both cloud condensation and advection increased.

A note on the Balanced method

Recently the Balanced method was introduced as a class of quasi-implicit methods for solving stiff stochastic differential equations. We examine asymptotic and mean-square stability for several implementations of the Balanced method and give a generalized result for the mean-square stability region of any Balanced method. We also investigate the optimal implementation of the Balanced method with respect to strong convergence.

Oscillatory regulation of hes1: Discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

Sigmoidal cosine series on the interval

We construct a set of functions, say, psi([r])(n) composed of a cosine function and a sigmoidal transformation gamma(r) of order r > 0. The present functions are orthonormal with respect to a proper weight function on the interval [-1, 1]. It is proven that if a function f is continuous and piecewise smooth on [-1, 1] then its series expansion based on psi([r])(n) converges uniformly to f so long as the order of the sigmoidal transformation employed is 0 < r

Stochastic models for regulatory networks of the genetic toggle switch

Bistability arises within a wide range of biological systems from the A phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. in this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

High-field magnetic resonance imaging with reduced field/tissue RF artefacts - A modeling study using hybrid MoM/FEM and FDTD technique

Due to complex field/tissue interactions, high-field magnetic resonance (MR) images suffer significant image distortions that result in compromised diagnostic quality. A new method that attempts to remove these distortions is proposed in this paper and is based on the use of transceiver-phased arrays. The proposed system uses, in the examples presented herein, a shielded four-element transceive-phased array head coil and involves performing two separate scans of the same slice with each scan using different excitations during transmission. By optimizing the amplitudes and phases for each scan, antipodal signal profiles can be obtained, and by combining both the images together, the image distortion can be reduced several fold. A combined hybrid method of moments (MoM)/finite element method (FEM) and finite-difference time-domain (FDTD) technique is proposed and used to elucidate the concept of the new method and to accurately evaluate the electromagnetic field (EMF) in a human head model. In addition, the proposed method is used in conjunction with the generalized auto-calibrating partially parallel acquisitions (GRAPPA) reconstruction technique to enable rapid imaging of the two scans. Simulation results reported herein for 11-T (470-MHz) brain imaging applications show that the new method with GRAPPA reconstruction theoretically results in improved image quality and that the proposed combined hybrid MoM/FEM and FDTD technique is. suitable for high-field magnetic resonance imaging (MRI) numerical analysis.