Modeling and Computational Approaches to Individual and Collective Cell Movement in Complex Environments (Online) (21w5225)


(University of Minnesota)

Thomas Hillen (University of Alberta)


The Casa Matemática Oaxaca (CMO) will host the "Modeling and Computational Approaches to Individual and Collective Cell Movement in Complex Environments" workshop in Oaxaca, from September 26 - October 1, 2021.

Locomotion of cells, both individually and collectively, plays an important role in development, the immune response, wound healing, and cancer metastasis. Movement requires force transmission to the environment, and motile cells are robustly-designed nanomachines that often can cope with a variety of environmental conditions by altering the mode of force transmission – which ranges from crawling to swimming. The shape and integrity of a cell is determined by its cytoskeleton, and thus the shape changes that may be required to move involve controlled remodeling of the cytoskeleton. Motion in vivo is often in response to extracellular signals, which requires the ability to detect such signals and transduce them into the shape changes and force generation needed for movement. Thus the nanomachine is complex, and while much is known about individual components involved in movement, an integrated understanding of single cell motility, even in simple cells such as bacteria, is not at hand. At the next level, collective movement requires coordination of these nanomachines, which introduces another level of complexity.

This complexity has stimulated mathematical modelling and computational simulations of cell and tissue movement at various levels, which has advanced our understanding of movement on multiple time and space scales. Exisiting mathematical models may be based on high-level macroscopic models or detailed mechanical descriptions, leading to transport equations for density distributions in position, velocity and internal state, or to macro- scopic continuum descriptions of spatio-temporal population densities. Computational models include continuum models, individual-based models, hybrid models, and stochastic models, and each type has led to new insights about movement and new mathematical and computational challenges.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT