Grant: Canada Research Chairs

The aim of this CRC application is to formulate, analyse and simulate new mechanobiochemical models describing how single or collective cells migrate through complex non-isotropic two- and three dimensional environments. Understanding the complex mechanisms for cell migration through non-isotropic environments, such as during tissue building and regeneration, immune response, but also cancer, is of fundamental importance to health, experimental, material, and mathematical sciences. However, a framework that could enable theoreticians and experimentalists to capture most of the multiple processes and properties of cell migration does not yet exist. Hence, my research programme seeks to bring to health, experimental and material sciences novel mathematical models with forecasting and prediction capabilities similar to those in weather forecasting. I will derive new models that couple, in a natural way, biochemical processes and mechanical properties of three intrinsically linked time-evolving domains: the nucleus, cytoplasm and the extracellular matrix (ECM) to understand how living cells navigate through their native environments. I will formulate systems of nonlinear partial differential equations (PDEs), denoted as coupled bulk-surface PDEs, to couple biochemical interactions between molecular species resident on continuously involving domains (bulk represents the cell cytosol and ECM) and manifolds (manifolds represent the nuclear envelope and cell membrane) and the mechanical properties of the nucleus and cytoplasm which are treated as poro and visco-elastic materials, respectively. The energetic nuclear envelope and the plasma membrane, which enclose the nucleus and cytoplasm, respectively, are modelled as hyper and morphoelastic manifolds or surfaces. This ground-breaking theoretical and computational approach allows us to naturally encode the multi-physics and biochemistry of cell motility, morphology and pattern formation to unravel mechanisms for single and collective cell migration. By advancing knowledge of cutting-edge mathematical concepts, developing new data-driven mathematical formalisms, implementing new numerical and computational methods, designing open-source and commercial software packages, the proposed research and technology development provides numerous opportunities for training and mentoring of a new generation of mathematical and computational biologists (High Qualified Personnel) with theoretical and applied expertise.