Multiscale modelling of cellular oscillators: applications to vertebrate segmentation and hair follicle cycling.

The dramatic advances made in genetic and molecular biology in recent years have resulted in detailed descriptions of a number of complex processes that arise on many different spatial and temporal scales. This unparalleled flood of data may well enable us to understand how genes and proteins work collectively in a cell and from this how multi-cellular organisms develop. However, therein lies one of the great challenges of modern science: all too often our knowledge remains in isolated pockets, lacking a conceptual framework tying the fragmented data together and allowing ideas and hypotheses to be generated and tested. This is where mathematical modelling and numerical simulation can play a fundamental role, comparable with any research tool; they allow us to combine the effects of multiple non-linear processes into a coherent structure that can be used for the generation of hypotheses and experimentally testable predictions. In particular we will be interested in modelling two paradigm systems of biological oscillators: a molecular clock involved in segmentation of the head-tail axis of vertebrate embryos and the hair follicle cycle. Somitogenesis, segmentation of the head-tail axis of vertebrate embryos into repeated units known as somites, results in formation of precursors of the vertebrae, ribs and associated musculature. The somites consist of tightly bound blocks of cells, one of each side of the spinal chord, and they form in a strict spatio-temporal order: from head to tail, at well-defined time intervals. Before becoming incorporated into somites, cells lying along the head-tail axis exhibit oscillations in a number of gene products. These oscillations are synchronised via cell-cell signalling, resulting in travelling bands of gene expression that begin in the tail and are stabilised in the newly forming somites. Disruption of cell-cell signalling results in segmental defects that are characterised by malformed ribs and vertebrae.The skin of many mammals is covered with hair follicles, each undergoing regenerative cycling. The reasons for this cycling are plentiful: to allow for expansion and growth, to control hair length, to adapt to changing environmental and social conditions and to protect against the malignant degeneration associated with rapidly dividing tissue. Each hair follicle goes through a series of stages with the transformations between cycle stages dependent on secretion, by the follicles, of chemicals into the local environment. Many hair growth defects can be characterised by incorrect rates of progression through the follicular cycle and give rise to disorders such as alopecia. The main aim of this project is to develop novel mathematical and computational techniques in order to model the systems of oscillating biological elements described previously. We will assume each individual element can display either sustained or excitable oscillations (requires a supra-threshold stimulus in order to exhibit an oscillation) and that it interacts with other elements in the field. Depending on the level of interaction the system may display synchronised oscillations on a tissue level. However, this synchronisation can be disturbed by, for example, external influence from the environment or variation in the oscillation frequency of individual elements. Mathematical techniques will be developed and numerical simulations employed to describe the behaviour of the individual oscillators and different forms for their interaction. The models will be constructed using currently available biological hypotheses, parametrised and tested against experimental observations. In turn, the models will be used to generate hypotheses and experimentally testable predictions which will further our understanding in the area.