Statistics, mathematical models and quantitative data as a tool to understand development & regeneration

ROST, FABIAN; BRUSCH, LUTZ; TANAKA, ELLY M; CHARA, OSVALDO

Nottingham

Conferencia; joint meeting of the European Society for Mathematical and Theoretical Biology and the Society for Mathematical Biology; 2016

ESMTB

Here, I?ll highlight the value of the interaction of mathematical modelling and quantitative data via statistics in the context of development and regeneration using the example of spinal cord regeneration in the axolotl (Mexican salamander). Quantitative mathematical modelling frameworks are a valuable tool to gain mechanistic insights and are suitable to estimate otherwise inaccessible parameters by fitting models to data. However, these data are often expensive to generate and hence sample sizes and spatiotemporal resolution are small. Here, I demonstrate that despite uncertainties in our data our quantitative mathematical modelling approach making substantial use of statistical tools leads to a deeper mechanistic understanding of axolotl spinal cord regeneration.We first used an empirical model of two spatial zones of differential cell behaviour to analyse spatiotemporal cell count data of 1 week of spinal cord regeneration. Using Bayesian inference we find a zone of upregulated proliferation close to the amputation site. Using cumulative cell labelling we estimated the proliferation rate time-course. We measured single cell clone velocities by time-lapse imaging.Using this results, we set up a mechanistic model of spinal cord growth during regeneration involving proliferation, differentiation and cell movements. This model correctly predicts the outgrowth time-course.We were able to integrate complex data into meaningful parameters of the system and we could infer that an upregulation of proliferation is the key cellular mechanism explaining axolotl spinal cord regeneration.Our example shows the power but also the workload of a fruitful interaction of mathematical modelling and quantitative data via statistics.