Research
The central topic of my DPhil thesis is the modelling of cell migration with early embryo somitogenesis as a motivating biological context. I am also interested in collective behaviour of animal groups and in various aspects of bacterial chemotaxis.Modelling Cell Migration
A number of genetic diseases, including congenital scoliosis (characterised by lateral deviation and rotation of the spinal column) and Jarcho-Levin syndrome (characterised by distinctive malformations of the vertebrae and the ribs and respiratory insufficiency), result from problems caused by erroneous cell migration in somitogenesis and segmentation during embryogenesis (Pourquié and Kusumi, 2001). Later in life cell migration is essential to wound healing, tissue repair (Deng et al., 2006) and immune responses (Madri and Graesser, 2000). Defects in cell migration can undermine the effectiveness of these processes. Cell migration also contributes to tumour invasion and metastasis (Franz et al., 2002) making it all the more important that we have a full understanding of the processes that underlie it. Elucidation of the mechanisms of cell migration may lead to more effective cancer treatments, to the understanding of defects in wound healing and to the elimination of birth defects initiated in somitogenesis.
Somitogenesis is the phase in embryonic development of vertebrates during which the somites (segmented mesodermal tissue along each side of the neural tube) are successively generated in spatially aggregated pairs (see Fig. 1.1) along the head-tail axis. More precisely it is the embryogenetic process leading to the subdivision of the paraxial mesoderm through the progressive formation of metameric mesodermal units (somites) that are the precursor structures of dermis, skeletal muscles and the axial skeleton itself. Somite formation begins at the anterior end of the presomitic mesoderm (PSM) and proceeds posteriorly (from right to left on Fig. 1.1) as successive groups of cells bud off from the anterior end of the mesenchymal PSM. New cells enter the posterior PSM and move anteriorly (from left to 1 right on Fig. 1.1) as a result of continuing posterior gastrulation, maintaining the length of the PSM as it moves posteriorly along the antero-posterior (AP) axis, leaving behind the somites (Baker et al., 2006; Collier et al., 2000; Dubrulle et al., 2001).
It is clear from the above examples that cell movement plays a crucial role in many areas in biology. Furthermore, particularly in areas in developmental biology, domain growth is important and there has been extensive modelling of cell movement (in response to signalling cues) and domain growth. Cell movement is usually modelled either by continuum approaches or stochastically, while growth is usually modelled by simply imposing a growth function and determining the effects on patterning of this growth.
Despite this wide ranging research there are still a number of open questions. For example:
- When is it realistic to use a continuum approximation to cell density and what is the appropriate form of continuum approximation?
- How do cells respond to signalling cues?
- How do we "properly" model domain growth?
- For computationally-intensive stochastic simulations, can we speed up simulations?
To answer questions 1-4 fully is well beyond the scope of a D.Phil. project. However, for the remainder of my DPhil I will focus on aspects of each question with particular emphasis on the biological system I will be modelling: somitogenesis.
Modelling Collective Animal Movement
Amongst the most striking aspects of the movement of many animal groups are their sudden coherent changes in direction. Recent observations of locusts and starlings have shown that this directional switching is an intrinsic property of their motion. Similar direction switches are seen in self-propelled particle and other models of group motion. Comprehending the factors which determine such switches is key to understanding the movement of these groups.While recent years have seen an explosion in the number of simulation models of moving animal groups, there is little detailed comparison between these models and experimental data (Couzin and Krause 2003, Sumpter et al., 2008). The models usually produce motion that ‘looks like’ that of a swarm of locusts, a school of fish or a flock of birds, but the similarities are difficult to quantify (Parrish et al., 2003). Furthermore, the simulation models themselves are often difficult to understand from a mathematical viewpoint since, by their nature, they resist simple mean-field descriptions.
Our studies on locusts suggest that an individual’s response to a loss of alignment in the group is increased randomness of its motion, until an aligned state is again achieved. This alignment-dependent stochasticity, using randomness to keep the group ordered, appears counterintuitive. However, we have shown that noise induced alignment seems, in this case, to be an intrinsic characteristic of collective coherent motion (Yates et al., 2009).
Modelling Bacterial Chemotaxis
I am interested in Chemotaxis from two quite different angles: The first is from the point of view of tracking bacteria with regards to creating a model of bacteria acting as self propelled particles. Work on the tracking of bacteria by use of the Kalman filter is currently being undertaking in collaboration with Trevor Wood and Philip Bond.My other interest in bacterial chemotaxis is the study of the flagellar motor and specifically its action as a stochastic switch. In their paper, 'Conformational spread in a ring of Proteins: A Stochastic Ap- proach to Allostery', Duke et al. examine the consequences of a "Conformational Spread" mechanism for an idealised one-dimensional system comprising a closed ring of allosteric protomers. They also showed that an allosteric ring of protomers can exhibit a switch-like response to changes in ligand con- centration. They go on to show that this representation of a protomer ring can be used to model the switch complex of a bacterial flagellar motor based on a ring of 34 flim proteins.
References (In order)
Cell Migration References
O. Pourquié and K. Kusumi. When body segmentation goes wrong. Clin. Genet., 60(6): 409-416, 2001.M. Deng, W. L. Chen, A. Takatori, Z. Peng, L. Zhang, M. Mongan, R. Parthasarathy, M. Sartor, M. Miller, J. Yang, et al. A role for the mitogen-activated protein kinase kinase kinase 1 in epithelial wound healing. Mol. Biol. Cell., 17(8): 3446, 2006.
J. A. Madri and D. Graesser. Cell migration in the immune system: the evolving interrelated roles of adhesion molecules and proteinases. Dev. Immunol., 7(2-4): 103-116, 2000.
C. M. Franz, G. E. Jones, and A. J. Ridley. Cell migration in development and disease. Dev. Cell, 2(2): 153-158, 2002.
R. E. Baker, S. Schnell, and P. K. Maini. A clock and wavefront mechanism for somite formation. Dev. Biol., 293(1): 116-126, 2006.
J. R. Collier, D. McInerney, S. Schnell, P. K. Maini, D. J. Gavaghan, B. P. Houston, and C. D. Stern. A cell cycle model for somitogenesis: Mathematical formulation and numerical simulation. J. Theor. Biol., 207(3): 305, 2000.
J. Dubrulle, M. J. McGrew, and O. Pourquié. FGF signaling controls somite boundary position and regulates segmentation clock control of spatiotemporal Hox gene activation. Cell, 106(2):219-232, 2001.
Collective Animal Motion References
I. D. Couzin and J. Krause. Self-organization and collective behavior in vertebrates. Adv Stud Behav 32: 1-75, 2003.D. J. T. Sumpter, J. Buhl, D. Biro and I.D. Couzin. Information transfer in moving animal groups. Theor Biosci 127: 177-186, 2008
J.K. Parrish, S.V. Viscido and D. Grunbaum. Self-organized fish schools: An examination of emergent properties. Biol Bull 202(3) 296-305, 2002.
C. Yates, R. Erban, C. Escudero, I. Couzin, J. Buhl, I. Kevrekidis, P. Maini and D. Sumpter. Inherent noise can facilitate coherence in collective swarm motion. Proceedings of the National Academy of Sciences (PNAS), 106(14): 5464-5469, 2009.
Bacterial Chemotaxis References
T. A. J. Duke, N. Le Novere, and D. Bray. Conformational spread in a ring of proteins: a stochastic approach to allostery. Journal of Molecular Biology, 308(3): 541-553, 2001.