NEEDS REWORKING SO THAT ISN'T NOT ALL 'I'...

This is a relatively new area for me but I have always been interested in it. My current work arises from my interactions with Eric Siggia and my research student Elena Camacho Aguilar. There are three main areas:

I. Morphogenetic modelling

In groundbreaking work Corson and Siggia (Corson & Siggia, (2012) PNAS, 109(15):5568-5575) introduced a new approach to the modelling of a a much-studied system, vulval development in the nematode Caenorhabditis elegans. Elena Camacho Aguilar and I have developed this approach further by using the classification theorems of catastrophe theory to select these models from robust universal unfoldings so reducing the ad hoc nature of the Corson and Siggia model and providing a rigorous basis for the reduction in both parameters and state variables enabled by this approach. We have also developed new statistical methods based on ABC MCMC to fit the model to experimental data.

II. From stochastic cells to ''deterministic'' populations and patterns.

The key question I am working on is how does a population of cells which are so highly stochastic interact so as to produce an almost deterministic developmental pattern. An obvious hypothesis is that a key component of any answer is that the role of signals from other cells play a crucial role in taming this stochasticity. However, how this works is far from clear. One key task for this part of the grant is \emph{the development of a proper stochastic approach to the characterisation of stochastic development states and the effectiveness of regulatory and signalling networks in enforcing them}. This will involve the introduction of an information theoretic approach. As part of this we will also need to develop a more analytical approach to stochastic models as in Minas & Rand (2017) PLoS Comput Biol 13(7): e1005676.

The consideration of approaches like this requires the \emph{development of a combined dynamical systems and information theoretic approach} to development in which one understands the dependence of the cell state distributions $P(xs)$ upon not only the signals $s$ but also network structure, noise level, and the dynamic range of mRNA and protein concentrations used by the cell. Moreover, it is crucial that any stochastic theory handles dynamics and bifurcations because differentiation is characterised by dynamical transitions between different stable or metastable states as the signalling environment of cells change. All this requires the further development of stochastic approaches as described below (and above) for both modelling and statistical analysis.