Multiscale modelling of cellular oscillators: applications to vertebrate segmentation and hair follicle cycling.
Lead Research Organisation:
University of Oxford
Department Name: Mathematical Institute
Abstract
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.
Organisations
Publications
Scodras S
(2022)
Methodological approaches for identifying competencies for the physiotherapy profession: a scoping review.
in Discover education
Murray PJ
(2012)
Modelling hair follicle growth dynamics as an excitable medium.
in PLoS computational biology
Murray PJ
(2011)
The clock and wavefront model revisited.
in Journal of theoretical biology
Murray PJ
(2013)
Modelling Delta-Notch perturbations during zebrafish somitogenesis.
in Developmental biology
Baker RE
(2012)
Understanding hair follicle cycling: a systems approach.
in Current opinion in genetics & development
Description | The dramatic advances made in genetic and molecular biology in recent years have led to an unparalleled flood of experimental data that may one day enable us to understand how genes and proteins work collectively in a cell and from this how multi-cellular organisms arise. However, at the same time we are now faced with one of the great challenges of modern science. Much of 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. Mathematical modelling can play a fundamental role, comparable with any laboratory research tool, in investigating the effects of multiple non-linear processes interacting on many spatio-temporal scales. In trying to answer biological questions, new and exciting questions in mathematics are arising. The grand challenge is to generate systematic and consistent analytical and numerical methodologies for the accurate modelling of multiscale biological processes. The aim of this project was to use mathematical modelling and numerical simulation to better understand the role of biological oscillators in development. The main focus of our work is to understand (i) the cellular oscillators involved in segmentation of the head-tail axis of vertebrates and (ii) the behaviour of hair follicles as they transition through the follicle cycle. Each can be thought of as a paradigm for biological processes in which the cycling of individual units is coordinated to robustly produce behaviour at the tissue level. In the context of axis segmentation, a huge number of genes and proteins interact within the cell to give rise to oscillations in mRNA and protein levels. Model for this process can be unwieldy, particular when one wants to consider the interaction of a large number of cells via receptors on the cell surface. We developed a method to abstract the details of these underlying networks, so that one can consider each cell just in terms of its phase, the position within the oscillatory cycle. The resulting models contain only three parameters and these can be directly linked to experimentally measurable quantities, such as the length of a segment and the time taken between the formation of successive segments. We then used our model to examine long-held hypotheses by careful examination of a number of mutant zebrafish embryos. The second phase of our modelling in this area has been to couple the description of oscillation behaviour with tissue rearrangements that take places as the embryo develops. We have integrated experimentally gathered information on cell movements into a computational model and aim to use this model to test how cell density affects axis segmentation. In the second application, we developed a caricature model that describes the integrated behaviour of activators and inhibitors of hair follicle cycling and displays the excitable behaviour observed in experiments. Our model integrates the important observation that neighbouring follicle behaviours are coupled via the diffusion of these activators and inhibitors in the inter-follicular space, and shows the waves of follicle cycling that arise in species such as mouse and rabbit. A combination of mathematical and computational analysis of our model suggests the ability of the system to display a number of previously unexplained behaviours. We have made predictions that can be tested experimentally and used to further our understanding. For example, we are currently using our model to explain behaviours observed by our experimental collaborators on the hair waves that arise in ageing mice. |
Exploitation Route | * Used by researchers interested in understanding tissue / hair regeneration. * Methods for coarse-graining gene regulatory network models of biological oscillators could be used to understand a range of biological processes. * Models of the somitogenesis clock can be used to further interrogate our understanding of the segmentation process. |
Sectors | Healthcare,Pharmaceuticals and Medical Biotechnology |
URL | http://www.maths.ox.ac.uk/people/ruth.baker |
Description | A springboard for future research (e.g. collaboration with Professor Kim Dale at Dundee University and Professor Cheng-Ming Chuong at University of Southern California). Continued skin/hair regeneration studies by Assistant Professor Maksim Plikus at UC Irvine. |
First Year Of Impact | 2007 |
Sector | Healthcare,Pharmaceuticals and Medical Biotechnology |
Description | Applying mathematical models to biological systems: from embryo development to tumour growth |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Other audiences |
Results and Impact | Invited speaker at Mathematics seminar, University College Dublin, Ireland. |
Year(s) Of Engagement Activity | 2011 |
Description | Coarse-grained models of cellular oscillators |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Other audiences |
Results and Impact | Talk at EMBL Symposia "Biological Oscillators". |
Year(s) Of Engagement Activity | 2015 |
Description | Modelling pattern propagation in the PSM |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Other audiences |
Results and Impact | Invited seminar at Olivier Pourquie's laboratory, IGBMC, Strasbourg. |
Year(s) Of Engagement Activity | 2010 |
Description | Modelling pattern propagation in the PSM |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Other audiences |
Results and Impact | Invited seminar at Cheng-Ming Choung's laboratory, Keck School of Medicine, University of Southern California, Los Angeles. |
Year(s) Of Engagement Activity | 2010 |
Description | Somitogenesis: the clock and wavefront model revisited |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | Local |
Primary Audience | Other audiences |
Results and Impact | Invited speaker at the Computational Biology Group, Comlab, Oxford. |
Year(s) Of Engagement Activity | 2011 |
Description | Using Chaste to simulate a multiscale problem in developmental biology |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Other audiences |
Results and Impact | Contributed talk at the Society for Mathematical Biology Annual Meeting, Krakow, Poland. |
Year(s) Of Engagement Activity | 2011 |