Mathematical Biology

DESCRIPTION/OBJECTIVES

Groups

CRM members

Tomás Alarcón (PI)
Isaac Salazar (PI)
Josep Sardanyés (PI)
Daria Stepanova (PhD)
Lourdes Menéndez-Moral (PhD)

Short description

The dynamics of biological systems is driven by interactions between many elements at a given level of biological organisation (e.g. molecular, cellular, organismc), but also by the couplings that exist between said levels (e.g. from molecules to cells to populations). Such couplings are highly non-linear and make the analysis of complex biological systems extremely challenging . The remit of the Computational & Mathematical Biology is the development of new models, techniques, and tools that are relevant to biologists and clinicians. For this pupose we use a plethora of mathematical techniques including stochastic multiscale models, dynamical systems theory, singular perturbation analysis, bifurcation analysis, morphometrics, dimensional reduction tools and efficient simulation methods, as well as statistics, machine learning or optimization. We tackle issues such as understanding how genetic variation leads to variation in the characteristics of organisms, the so-called genotype-phenotype map, formulate new models of virus evolution and therapies that account for intrinsic heterogeneity and noise, the design of new strategies to avoid drug resistance induced by cancer-cell heterogeneity, and the analysis of the mechanisms of ageing. Our research is collaborative in nature and we make an effort to keep close collaborations with both biologists and medical practitioners. Our research is articulated along three research lines:

Cancer Modelling

Mathematics of Development

Non-linear Dynamics and Evolution

CRM members

Marta Casanellas (PI)
Jesús Fernández (senior researcher)

Short description

Phylogenetics studies the ancestral relationships of living species and has implications in evolutionary biology, in ecology and in biomedicine (in descovering the origin of pathogens or tracing mutations of tumor cells). In this research line we deal with Markov processes on phylogenetic trees. These processes can be viewed as parametrizations of algebraic varieties, which allows the use of algebraic and geometric techniques to propose new successful phylogenetic reconstruction methods or improve the existing ones.