In addition to experimental approaches we develop and use a range of computational and theoretical approaches. These include using tools from dynamical systems to construct and analyse mathematical models of biological processes and methods from computational statistics to analyse large datasets generated by genomic and imaging experiments.
Transcriptional Networks as Dynamical Systems
To analyse and understand how the complex transcriptional networks that control pattern formation in developing tissues we use mathematical models and techniques from the field of dynamical systems. Using these approaches we have analysed the transcriptional circuit that specifies the pattern of gene expression in progenitors of the ventral neural tube.
This network forms a circuit that acts as a multistate switch, patterning the tissue in response to a gradient of Sonic Hedgehog. Building a mathematical model that describes this network we found that the topology of the circuit allows either switch-like or oscillatory behaviour. The qualitative dynamics appear to be controlled by a simpler sub-circuit, which we termed the AC–DC motif.
This topology provides a natural way to implement a multistate gene expression switch that is readily extended to produce more distinct stripes of gene expression. Since the AC–DC motifs can be employed in tissues patterned by oscillatory mechanisms, it blurs the distinction between pattern-formation mechanisms relying on temporal oscillations or graded signals.
Visualising gene expression
Gene expression data generated by high-throughput approaches, such as next generation sequencing, play a central role in biological knowledge discovery. However, the size and complexity of these type of data make their analysis challenging. Clustering algorithms have proved a powerful and efficient way to analyse gene expression data, but they have limitations. They generally produce sharp delineations between clusters and do not reveal global patterns in the data.
To address this we have developed non-linear dimensionality reduction methods, t-statistic Stochastic Neighbor Embedding (t-SNE), for the display of gene expression data as interactive two-dimensional maps. This results in genes with similar expression patterns being located close together in the map.