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.

Type III secretion contact-dependent model for the intracellular development of Chlamydia

The medically significant genus Chlamydia is a class of obligate intracellular bacterial pathogens that replicate within vacuoles in host eukaryotic cells termed inclusions. Chlamydia's developmental cycle involves two forms; an infectious extracellular form, known as an elementary body (EB), and a non-infectious form, known as the reticulate body (RB), that replicates inside the vacuoles of the host cells. The RB surface is covered in projections that are in intimate contact with the inclusion membrane. Late in the developmental cycle, these reticulate bodies differentiate into the elementary body form. In this paper, we present a hypothesis for the modulation of these developmental events involving the contact-dependent type III secretion (TTS) system. TTS surface projections mediate intimate contact between the RB and the inclusion membrane. Below a certain number of projections, detachment of the RB provides a signal for late differentiation of RB into EB. We use data and develop a mathematical model investigating this hypothesis. If the hypothesis proves to be accurate, then we have shown that increasing the number of inclusions per host cell will increase the number of infectious progeny EB until some optimal number of inclusions. For more inclusions than this optimum, the infectious yield is reduced because of spatial restrictions. We also predict that a reduction in the number of projections on the surface of the RB (and as early as possible during development) will significantly reduce the burst size of infectious EB particles. Many of the results predicted by the model can be tested experimentally and may lead to the identification of potential targets for drug design. © Society for Mathematical Biology 2006.

Direct numerical simulation of turbulent flow and mass transfer around a rotating circular cylinder

Turbulent flow around a rotating circular cylinder has numerous applications including wall shear stress and mass-transfer measurement related to the corrosion studies. It is also of interest in the context of flow over convex surfaces where standard turbulence models perform poorly. The main purpose of this paper is to elucidate the basic turbulence mechanism around a rotating cylinder at low Reynolds numbers to provide a better understanding of flow fundamentals. Direct numerical simulation (DNS) has been performed in a reference frame rotating at constant angular velocity with the cylinder. The governing equations are discretized by using a finite-volume method. As for fully developed channel, pipe, and boundary layer flows, a laminar sublayer, buffer layer, and logarithmic outer region were observed. The level of mean velocity is lower in the buffer and outer regions but the logarithmic region still has a slope equal to the inverse of the von Karman constant. Instantaneous flow visualization revealed that the turbulence length scale typically decreases as the Reynolds number increases. Wavelet analysis provided some insight into the dependence of structural characteristics on wave number. The budget of the turbulent kinetic energy was computed and found to be similar to that in plane channel flow as well as in pipe and zero pressure gradient boundary layer flows. Coriolis effects show as an equivalent production for the azimuthal and radial velocity fluctuations leading to their ratio being lowered relative to similar nonrotating boundary layer flows.