Pattern Formation in a Spatially Extended Model of Pacemaker Dynamics in Smooth Muscle Cells.

Spatiotemporal patterns are common in biological systems. For electrically coupled cells, previous studies of pattern formation have mainly used applied current as the primary bifurcation parameter. The purpose of this paper is to show that applied current is not needed to generate spatiotemporal patterns for smooth muscle cells. The patterns can be generated solely by external mechanical stimulation (transmural pressure). To do this we study a reaction-diffusion system involving the Morris-Lecar equations and observe a wide range of spatiotemporal patterns for different values of the model parameters. Some aspects of these patterns are explained via a bifurcation analysis of the system without coupling - in particular Type I and Type II excitability both occur. We show the patterns are not due to a Turing instability and that the spatially extended model exhibits spatiotemporal chaos. We also use travelling wave coordinates to analyse travelling waves.

Numerical Bifurcation Analysis of Pacemaker Dynamics in a Model of Smooth Muscle Cells.

Evidence from experimental studies shows that oscillations due to electro-mechanical coupling can be generated spontaneously in smooth muscle cells. Such cellular dynamics are known as pacemaker dynamics. In this article, we address pacemaker dynamics associated with the interaction of [Formula: see text] and [Formula: see text] fluxes in the cell membrane of a smooth muscle cell. First we reduce a pacemaker model to a two-dimensional system equivalent to the reduced Morris-Lecar model and then perform a detailed numerical bifurcation analysis of the reduced model. Existing bifurcation analyses of the Morris-Lecar model concentrate on external applied current, whereas we focus on parameters that model the response of the cell to changes in transmural pressure. We reveal a transition between Type I and Type II excitabilities with no external current required. We also compute a two-parameter bifurcation diagram and show how the transition is explained by the bifurcation structure.

Modelling thermodynamic feedback on the metabolism of hydrogenotrophic methanogens.

The magnitude of the Gibbs free energy change of the substrate transformation that supports the growth of a microbe is decreased when the concentrations of the substrates are decreased and when the concentrations of the products of metabolism are increased. Microbes require a supply of ATP for cell maintenance and growth, and coupling the transformation of substrates to products with the formation of ATP also decreases the magnitude of the Gibbs free energy change. Here we include these three thermodynamic controllers (substrate and product concentration, and ATP formation) in a model of substrate transformation by hydrogenotrophic methanogens that results in a number of realistic behaviours. First, a threshold for substrate use emerges, below which the methanogen cannot metabolise its substrate. Under this model, microbes that capture more of the Gibbs free energy change from substrate transformation in the form of ATP have greater thresholds for their substrate, in line with observations of actual microbes. Second, an apparent saturation constant emerges that is controlled by the thermodynamics of the reaction. This increases with increasing ATP synthesis per substrate, so that methanogens that conserve more ATP grow faster at higher substrate concentrations, but are less competitive at low substrate concentrations. As a result, simply changing the ATP yield (moles of ATP per mole of substrate) results in methanogens with differing ecological strategies through thermodynamic impacts on their metabolism. Third, end-product inhibition through thermodynamic feedback can limit the growth of microbes, and those that capture more ATP per substrate are limited by smaller product concentrations than those that capture less ATP.

Solutions to an advanced functional partial differential equation of the pantograph type.

A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained.

On a cell-growth model for plankton.

The frequency distribution of diatoms (microscopic unicellular alga with silicified cell-walls, found as plankton) is shown to evolve in time as a steady-size distribution with constant shape, scaled by time. This distribution is preserved when the division occurs at a fixed size into two daughter cells of half-size. In cases where the parameters for growth, division frequency, dispersion and mortality are constants, the frequency distributions can be found explicitly and thus provide a benchmark for computations in more complex cases.