Strategic Research

Computational & Mathematical Biology

Most phenomena studied by the Natural Sciences, from Material Sciences to Astrophysics, are multi-scale processes, i.e. they involve the coupling of multiple different processes characterised by widely-ranging time and length scales, with the macroscopic behaviour emerging from the complex interactions between them. Whilst considerable progress has been done in dealing with such problems in the Physical Sciences, the success achieved so far in the Biological Sciences is rather more limited. This is partly due to the fact that the individual components of biological systems (e.g. cells) are much more complex than their counterparts in physical systems and, therefore, new methods and models are needed to analyse multi-scale processes in Biology. Such is the remit of the Computational & Mathematical Biology group at CRM: To propose new models relevant to experimental biologists and clinicians and develop the analytical and computational tools necessary for their analysis. We pay special attention to problems with clinical relevance, in particular those related to cancer.
The research activity of our group is developed along the following lines:

  • Multiscale modelling of tumour growth and tumour-induced angiogenesis
  • Evolutionary dynamics of populations with complex structure, in particular cell populations with hierarchical structure and genotype-phenotype map
  • Mathematical modelling of the cell-cycle
  • Stochastic modelling of receptor tyrosine kinases
  • Tumour dormancy

Main projects

  • 1.

    Multiscale modelling of tumour growth

    Cancer is (a set of) disease(s) which is characterised by disrupting the normal, homeostatic mechanisms at all levels of biological organisation, from abherrant structure of the vasculature all the way down to abnormalities in regulation of gene expression, with complex interactions between them. In this context, it is very clear that verbal models and traditional, lineal thinking are unlikely to produce a thorough understanding of tumour growth and its treatment. Instead, an integrative approach that includes within a unified framework phenomena occurring at different scales is needed. Together with some of my collaborators listed below, such framework has been developed to integrate processes as disparate, but at the same strongly interelated, as angiogenesis and delay of cell-cycle progression under oxygen starvation

  • 2.

    Hybrid methods for multiscale models

    Multiscale models of tumour growth and angiogenesis provide a wealth of detail on the state of the system which is not always needed. It often occurs that we only need such detailed information regarding a restricted part of the system (e.g. a limited spatial domain, a particular cell type, etc.) while a more coarse-grained description provides an accurate enough description of the rest of the system. We are working on developing methods for hybridisation of mean-field and stochastic descriptions of multiscale models of tumour growth. To this end, we are

  • 3.

    Stochastic modelling of somatic cell reprogramming

    The seminal work of Yamanaka and Gurdon on reprogramming somatic cells into induced pluripotent stem cells (IPSCs) was followed by a wealth of interesting results, applications and improvements of their initial technique. Yet, a lot needs to be learnt about mechanisms for improving the efficiency of the reprogramming process so it can become a viable biomedical technology. Our work within this area involves the stochastic modelling of the gene regulatory network involved in reprogramming and how it is affected by metabolic factors. We are also investigating the potential connections tof reprogramming to cancer stem cells



Bioinformatics expertise:

Group Leader:

Tomás Alarcón

Bioinformatics services offered

  • Expertise in mathematical modelling of complex biological phenomena