Some novel techniques of parameter estimation for the dynamical models in biological systems

Inverse problems based on using experimental data to estimate unknown parameters of a system often arise in biological and chaotic systems. In this paper, we consider parameter estimation in systems biology involving linear and non-linear complex dynamical models, including the Michaelis–Menten enzyme kinetic system, a dynamical model of competence induction in Bacillus subtilis bacteria and a model of feedback bypass in B. subtilis bacteria. We propose some novel techniques for inverse problems. Firstly, we establish an approximation of a non-linear differential algebraic equation that corresponds to the given biological systems. Secondly, we use the Picard contraction mapping, collage methods and numerical integration techniques to convert the parameter estimation into a minimization problem of the parameters. We propose two optimization techniques: a grid approximation method and a modified hybrid Nelder–Mead simplex search and particle swarm optimization (MH-NMSS-PSO) for non-linear parameter estimation. The two techniques are used for parameter estimation in a model of competence induction in B. subtilis bacteria with noisy data. The MH-NMSS-PSO scheme is applied to a dynamical model of competence induction in B. subtilis bacteria based on experimental data and the model for feedback bypass. Numerical results demonstrate the effectiveness of our approach.

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.

A Krylov-based finite state projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems

Biochemical reactions underlying genetic regulation are often modelled as a continuous-time, discrete-state, Markov process, and the evolution of the associated probability density is described by the so-called chemical master equation (CME). However the CME is typically difficult to solve, since the state-space involved can be very large or even countably infinite. Recently a finite state projection method (FSP) that truncates the state-space was suggested and shown to be effective in an example of a model of the Pap-pili epigenetic switch. However in this example, both the model and the final time at which the solution was computed, were relatively small. Presented here is a Krylov FSP algorithm based on a combination of state-space truncation and inexact matrix-vector product routines. This allows larger-scale models to be studied and solutions for larger final times to be computed in a realistic execution time. Additionally the new method computes the solution at intermediate times at virtually no extra cost, since it is derived from Krylov-type methods for computing matrix exponentials. For the purpose of comparison the new algorithm is applied to the model of the Pap-pili epigenetic switch, where the original FSP was first demonstrated. Also the method is applied to a more sophisticated model of regulated transcription. Numerical results indicate that the new approach is significantly faster and extendable to larger biological models.

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.