Generalized binomial Tau-leap method for biochemical kinetics incorporating both delay and intrinsic noise

The delay stochastic simulation algorithm (DSSA) by Barrio et al. [Plos Comput. Biol.2, 117–E (2006)] was developed to simulate delayed processes in cell biology in the presence of intrinsic noise, that is, when there are small-to-moderate numbers of certain key molecules present in a chemical reaction system. These delayed processes can faithfully represent complex interactions and mechanisms that imply a number of spatiotemporal processes often not explicitly modeled such as transcription and translation, basic in the modeling of cell signaling pathways. However, for systems with widely varying reaction rate constants or large numbers of molecules, the simulation time steps of both the stochastic simulation algorithm (SSA) and the DSSA can become very small causing considerable computational overheads. In order to overcome the limit of small step sizes, various τ-leap strategies have been suggested for improving computational performance of the SSA. In this paper, we present a binomial τ- DSSA method that extends the τ-leap idea to the delay setting and avoids drawing insufficient numbers of reactions, a common shortcoming of existing binomial τ-leap methods that becomes evident when dealing with complex chemical interactions. The resulting inaccuracies are most evident in the delayed case, even when considering reaction products as potential reactants within the same time step in which they are produced. Moreover, we extend the framework to account for multicellular systems with different degrees of intercellular communication. We apply these ideas to two important genetic regulatory models, namely, the hes1 gene, implicated as a molecular clock, and a Her1/Her 7 model for coupled oscillating cells.

Modeling intrinsic noise and delays in chemical kinetics of coupled autoregulated oscillating cells

Delays are an important feature in temporal models of genetic regulation due to slow biochemical processes, such as transcription and translation. In this paper, we show how to model intrinsic noise effects in a delayed setting by either using a delay stochastic simulation algorithm (DSSA) or, for larger and more complex systems, a generalized Binomial τ-leap method (Bτ-DSSA). As a particular application, we apply these ideas to modeling somite segmentation in zebra fish across a number of cells in which two linked oscillatory genes (her1 and her7) are synchronized via Notch signaling between the cells.

Stochastic chemical kinetics and the quasi-steady-state assumption : application to the stochastic simulation algorithm and chemical master equation

Recently the application of the quasi-steady-state approximation (QSSA) to the stochastic simulation algorithm (SSA) was suggested for the purpose of speeding up stochastic simulations of chemical systems that involve both relatively fast and slow chemical reactions [Rao and Arkin, J. Chem. Phys. 118, 4999 (2003)] and further work has led to the nested and slow-scale SSA. Improved numerical efficiency is obtained by respecting the vastly different time scales characterizing the system and then by advancing only the slow reactions exactly, based on a suitable approximation to the fast reactions. We considerably extend these works by applying the QSSA to numerical methods for the direct solution of the chemical master equation (CME) and, in particular, to the finite state projection algorithm [Munsky and Khammash, J. Chem. Phys. 124, 044104 (2006)], in conjunction with Krylov methods. In addition, we point out some important connections to the literature on the (deterministic) total QSSA (tQSSA) and place the stochastic analogue of the QSSA within the more general framework of aggregation of Markov processes. We demonstrate the new methods on four examples: Michaelis–Menten enzyme kinetics, double phosphorylation, the Goldbeter–Koshland switch, and the mitogen activated protein kinase cascade. Overall, we report dramatic improvements by applying the tQSSA to the CME solver.

Novel corrosion sensor based on carbon nanotube composites for structural health monitoring

Bridges are important infrastructures of all nations and are required for transportation of goods as well as human. A catastrophic failure can result in loss of lives and enormous financial hardship to the nation. Hence, there is an urgent need to monitor our infrastructures to prolong their life span, at the same time catering for heavier and faster moving traffics. Although various kinds of sensors are now available to monitor the health of the structures due to corrosion, they do not provide permanent and long term measurements. This paper investigates the fabrication of Carbon Nanotube (CNT) based composite sensors for structural health monitoring. The CNTs, a key material in nanotechnology has aroused great interest in the research community due to their remarkable mechanical, electrochemical, piezoresistive and other physical properties. Multi-wall CNT (MWCNT)/Nafion composite sensors were fabricated to evaluate their electrical properties when subjected to chemical solutions, to simulate a chemical reaction due to corrosion and real life corrosion experimental tests. The electrical resistance of the sensor electrode was dramatically changed due to corrosion. The novel sensor is expected to effectively detect corrosion in structures based on the measurement of electrical impedances of the CNT composite.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

A software tool for simulating spatial separation and kinetics in biological membranes

Self-segregation and compartimentalisation are observed experimentally to occur spontaneously on live membranes as well as reconstructed model membranes. It is believed that many of these processes are caused or supported by anomalous diffusive behaviours of biomolecules on membranes due to the complex and heterogeneous nature of these environments. These phenomena are on the one hand of great interest in biology, since they may be an important way for biological systems to selectively localize receptors, regulate signaling or modulate kinetics; and on the other, they provide an inspiration for engineering designs that mimick natural systems. We present an interactive software package we are developing for the purpose of simulating such processes numerically using a fundamental Monte Carlo approach. This program includes the ability to simulate kinetics and mass transport in the presence of either mobile or immobile obstacles and other relevant structures such as liquid-ordered lipid microdomains. We also present preliminary simulation results regarding the selective spatial localization and chemical kinetics modulating power of immobile obstacles on the membrane, obtained using the program.

Kinetics of electron recombination of dye-senitized solar cells based on TiO2 nanorod arrays sensitized with different dyes

The performance and electron recombination kinetics of dye-sensitized solar cells based on TiO2 films consisting of one-dimensional nanorod arrays (NR-DSSCs) which are sensitized with dye N719, C218 and D205 respectively have been studied. It has been found that the best efficiency is obtained with the dye C218 based NR-DSSCs, benefiting from a 40% higher short-circuit photocurrent density. However, the open circuit photovoltage of the N719 based cell is 40 mV higher than that of the organic dye C218 and D205 based devices. Investigation of the electron recombination kinetics of the NR-DSSCs has revealed that the effective electron lifetime, τn, of the N719 based NR-DSSC is the lowest whereas the τn of the C218 based NR-DSSC is the highest among the three dyes. The higher Voc with the N719 based NR-DSSC is originated from the more negative energy level of the conduction band of the TiO2 film. In addition, in comparison to the DSSCs with conventional nanocrystalline particles based TiO2 films, the NR-DSSCs have shown over two orders of magnitude higher τn when employing N719 as the sensitizer. Nevertheless, the τn of the DSSCs with the C218 based nanorod arrays is only ten-fold higher than the that of the nanoparticles based devices. The remarkable characteristic of the dye C218 in suppressing the electron recombination of DSSCs is discussed.

Investigation of phenol degradation : True reaction kinetics on fixed film titanium dioxide photocatalyst

This study of photocatalytic oxidation of phenol over titanium dioxide films presents a method for the evaluation of true reaction kinetics. A flat plate reactor was designed for the specific purpose of investigating the influence of various reaction parameters, specifically photocatalytic film thickness, solution flow rate (1–8 l min−1), phenol concentration (20, 40 and 80 ppm), and irradiation intensity (70.6, 57.9, 37.1and 20.4 W m−2), in order to further understand their impact on the reaction kinetics. Special attention was given to the mass transfer phenomena and the influence of film thickness. The kinetics of phenol degradation were investigated with different irradiation levels and initial pollutant concentration. Photocatalytic degradation experiments were performed to evaluate the influence of mass transfer on the reaction and, in addition, the benzoic acid method was applied for the evaluation of mass transfer coefficient. For this study the reactor was modelled as a batch-recycle reactor. A system of equations that accounts for irradiation, mass transfer and reaction rate was developed to describe the photocatalytic process, to fit the experimental data and to obtain kinetic parameters. The rate of phenol photocatalytic oxidation was described by a Langmuir–Hinshelwood type law that included competitive adsorption and degradation of phenol and its by-products. The by-products were modelled through their additive effect on the solution total organic carbon.

A fibrocontractive mechanochemical model of dermal wound closure incorporating realistic growth factor kinetics

Fibroblasts and their activated phenotype, myofibroblasts, are the primary cell types involved in the contraction associated with dermal wound healing. Recent experimental evidence indicates that the transformation from fibroblasts to myofibroblasts involves two distinct processes: the cells are stimulated to change phenotype by the combined actions of transforming growth factor β (TGFβ) and mechanical tension. This observation indicates a need for a detailed exploration of the effect of the strong interactions between the mechanical changes and growth factors in dermal wound healing. We review the experimental findings in detail and develop a model of dermal wound healing that incorporates these phenomena. Our model includes the interactions between TGFβ and collagenase, providing a more biologically realistic form for the growth factor kinetics than those included in previous mechanochemical descriptions. A comparison is made between the model predictions and experimental data on human dermal wound healing and all the essential features are well matched.