Spatial Turing-type Pattern Formation in a Model of Signal Transduction Involving Membrane-based Receptors Coupled by G Proteins

In this paper, a model of signaling pathways involving G proteins is investigated. The model incorporates reaction-diffusion mechanisms in which various reactants participate inside and on the extra-cellular surface membrane. The messenger molecules may diffuse over the surface of the cell membrane and signal transduction across the cell membrane is mediated by membrane receptor bound proteins which connect the genetically controlled biochemical intra-cellular reactions to the production of the second messenger, leading to desired functional responses. Dynamic and steady-state properties of the model are then investigated through weakly nonlinear stability analysis. Turing-type patterns are shown to form robustly under different delineating conditions on the system parameters. The theoretical predictions are then discussed in the context of some recently reported experimental evidence

Nonlinear stability analyses of vegetative pattern formation in an arid environment

The development of spontaneous stationary vegetative patterns in an arid isotropic homogeneous environment is investigated by means of various weakly nonlinear stability analyses applied to the appropriate governing equation for this phenomenon. In particular, that process can be represented by a fourth-order partial differential time-evolution logistic equation for the total plant biomass per unit area divided by the carrying capacity of its territory and defined on an unbounded flat spatial domain. Those patterns that consist of parallel stripes, labyrinth-like mazes, rhombic arrays of rectangular patches, and hexagonal distributions of spots or gaps are generated by the balance between the effects of short-range facilitation and long-range competition. Then those theoretical predictions are compared with both relevant observational evidence and existing numerical simulations as well as placed in the context of the results from some recent nonlinear pattern formation studies