Modelling hair follicle growth dynamics as an excitable medium

The hair follicle system represents a tractable model for the study of stem cell behaviour in regenerative adult epithelial tissue. However, although there are numerous spatial scales of observation (molecular, cellular, follicle and multi follicle), it is not yet clear what mechanisms underpin the follicle growth cycle. In this study we seek to address this problem by describing how the growth dynamics of a large population of follicles can be treated as a classical excitable medium. Defining caricature interactions at the molecular scale and treating a single follicle as a functional unit, a minimal model is proposed in which the follicle growth cycle is an emergent phenomenon. Expressions are derived, in terms of parameters representing molecular regulation, for the time spent in the different functional phases of the cycle, a formalism that allows the model to be directly compared with a previous cellular automaton model and experimental measurements made at the single follicle scale. A multi follicle model is constructed and numerical simulations are used to demonstrate excellent qualitative agreement with a range of experimental observations. Notably, the excitable medium equations exhibit a wider family of solutions than the previous work and we demonstrate how parameter changes representing altered molecular regulation can explain perturbed patterns in Wnt over-expression and BMP down-regulation mouse models. Further experimental scenarios that could be used to test the fundamental premise of the model are suggested. The key conclusion from our work is that positive and negative regulatory interactions between activators and inhibitors can give rise to a range of experimentally observed phenomena at the follicle and multi follicle spatial scales and, as such, could represent a core mechanism underlying hair follicle growth

Controlling periodic long-range signalling to drive a morphogenetic transition

Cells use signal relay to transmit information across tissue scales. However, the production of information carried by signal relay remains poorly characterised. To determine how the coding features of signal relay are generated, we used the classic system for long-range signalling: the periodic cAMP waves that drive Dictyostelium collective migration. Combining imaging and optogenetic perturbation of cell signalling states, we find that migration is triggered by an increase in wave frequency generated at the signalling centre. Wave frequency is regulated by cAMP wave circulation, which organises the long-range signal. To determine the mechanisms modulating wave circulation, we combined mathematical modelling, the general theory of excitable media and mechanical perturbations to test competing models. Models in which cell density and spatial patterning modulate the wave frequency cannot explain the temporal evolution of signalling waves. Instead, our evidence leads to a model where wave circulation increases the ability for cells to relay the signal, causing further increase in the circulation rate. This positive feedback between cell state and signalling pattern regulates the long-range signal coding that drives morphogenesis

Receptors, sparks and waves in a fire-diffuse-fire framework for calcium release

Calcium ions are an important second messenger in living cells. Indeed calcium signals in the form of waves have been the subject of much recent experimental interest. It is now well established that these waves are composed of elementary stochastic release events (calcium puffs or sparks) from spatially localised calcium stores. The aim of this paper is to analyse how the stochastic nature of individual receptors within these stores combines to create stochastic behaviour on long timescales that may ultimately lead to waves of activity in a spatially extended cell model. Techniques from asymptotic analysis and stochastic phase-plane analysis are used to show that a large cluster of receptor channels leads to a release probability with a sigmoidal dependence on calcium density. This release probability is incorporated into a computationally inexpensive model of calcium release based upon a stochastic generalization of the Fire-Diffuse-Fire (FDF) threshold model. Numerical simulations of the model in one and two dimensions (with stores arranged on both regular and disordered lattices) illustrate that stochastic calcium release leads to the spontaneous production of calcium sparks that may merge to form saltatory waves. Illustrations of spreading circular waves, spirals and more irregular waves are presented. Furthermore, receptor noise is shown to generate a form of array enhanced coherence resonance whereby all calcium stores release periodically and simultaneously

Synchronization of spatiotemporal patterns and modeling disease spreading using excitable media

Studies of the photosensitive Belousov-Zhabotinsky (BZ) reaction are reviewed and the essential features of excitable media are described. The synchronization of two distributed Belousov-Zhabotinsky systems is experimentally and theoretically investigated. Symmetric local coupling of the systems is made possible with the use of a video camera-projector scheme. The spatial disorder of the coupled systems, with random initial configurations of spirals, gradually decreases until a final state is attained, which corresponds to a synchronized state with a single spiral in each system. The experimental observations are compared with numerical simulations of two identical Oregonator models with symmetric local coupling, and a systematic study reveals generalized synchronization of spiral waves. Modeling studies on disease spreading have been reviewed. The excitable medium of the photosensitive BZ reaction is used to model disease spreading, with static networks, dynamic networks, and a domain model. The spatiotemporal dynamics of disease spreading in these complex networks with diffusive and non-diffusive connections is characterized. The experimental and numerical studies reveal that disease spreading in these model systems is highly dependent on the non-diffusive connections