Simple mathematical models have already provided remarkable insights into cell invasion; take, for example, the ubiquitous use of Fisher’s equation. However, modern developmental biology studies require more sophisticated models that incorporate driving processes on a range of spatial and temporal scales. These detailed, multi-scale models can provide vital insights where data alone cannot, but they require accurate data-driven calibration to do so. We are working to develop a range of tools that enable models to be calibrated using quantitative data.

We have two review papers that outline methods for simulation, inference and model selection in biology:

• D. J. Warne, R. E. Baker and M. J. Simpson (2019). Using experimental data and information criteria to guide model selection for reaction-diffusion problems in mathematical biology. Bull. Math. Biol. 81(6):1760–1804. DOI bioRxiv
• D. J. Warne, R. E. Baker and M. J. Simpson (2019). Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art. J. Roy. Soc. Interface 16. DOI arXiv

Theoretical projects, that focus on developing new methodologies, include:

• T. P. Prescott and R. E. Baker (2019). Multifidelity approximation Bayesian computation. To appear in SIAM / ASA J. Uncertainty Quantification. arXiv
• D. J. Warne, R. E. Baker and M. J. Simpson (2017). Multi-level rejection sampling for approximate Bayesian computation. arXiv
• J. U. Harrison and R. E. Baker (2017). An automatic adaptive method to combine summary statistics in approximate Bayesian computation. arXiv

Some applied projects in this area include:

• J. U. Harrison, R. M. Parton, I. Davis and R. E. Baker (2019). Testing models of mRNA localization reveals robustness regulated by reducing transport between cells. To appear in Biophys. J. bioRxiv
• O. M. Matsiaka, R. E. Baker. E. Shah and M. J. Simpson (2019). Mechanistic and experimental models of cell migration reveal the importance of intercellular interactions in cell invasion. Biomed. Phys. Eng. Express 5(4):045009. DOI bioRxiv
• J. U. Harrison and R. E. Baker (2018). The impact of temporal sampling resolution on parameter inference for biological transport models. PLoS Comp. Biol. 14(6): e1006235. DOI arXiv
• D. J. Warne, R. E. Baker and M. J. Simpson (2017). Optimal quantification of contact inhibition in cell populations. Biophys. J. 113(9):1920-1924. DOI arXiv
• J. Kursawe, R. E. Baker and A. G. Fletcher (2018). Approximate Bayesian computation reveals the importance of repeated measurements for parameterising cell-based models of growing tissues. J. Theor. Biol. 443:66-81. DOI bioRxiv
• R. J. H. Ross, R. E. Baker, A. Parker, M. J. Ford, R. L. Mort and C. A. Yates (2017). Using approximate Bayesian computation to quantify cell–cell adhesion parameters in a cell migratory process. npj Sys. Biol. Appl. 3:9. DOI bioRxiv

Bacterial motility

We have also developed approaches that combine mechanistic models with hidden Markov model approaches to better understand bacterial motility. Part of our work also considers how to design “optimal experiments” for the measurement of different model parameters.

• G. Rosser, R. E. Baker, J. P. Armitage and A. G. Fletcher (2014). Modelling and analysis of bacterial tracks suggest an active reorientation mechanism in Rhodobacter spheroides. J. Roy. Soc. Interface 11(97):20140320.  DOI bioRxiv
• G. Rosser, A. G. Fletcher, D. A. Wilkinson, J. A. de Beyer, C. A. Yates, J. P. Armitage, P. K. Maini and R. E. Baker (2013). Novel Methods for Analysing Bacterial Tracks Reveal Persistence in Rhodobacter sphaeroides. PLoS Comput. Biol. 9(10):e1003276. DOI
• G. Rosser, A. G. Fletcher, P. K. Maini and R. E. Baker (2013). The effect of sampling rate on observed statistics in a correlated random walk. J. Roy. Soc. Interface 10(85):20130273. DOI
• J. U. Harrison and R. E. Baker (2018). The impact of temporal sampling resolution on parameter inference for biological transport models. PLoS Comp. Biol. 14(6): e1006235. DOI arXiv