Overview
Title: Modeling Cell Migration in Extracellular Matrix: From Efficient Numerical Methods to Interpretable Mechanosensory Models
Abstract: Cell migration through extracellular matrix (ECM) is central to development, immune response, and cancer metastasis. Cells pull on ECM fibers to move, yet dense matrix simultaneously acts as a physical barrier. To navigate, cells squeeze through pores by adapting their shape, mechanically deform the elastic ECM, and degrade it via matrix metalloproteinases. How these space negotiation strategies interact to produce observed migration behaviors remains poorly understood.
We develop an off-lattice agent-based model in which deformable capsule-shaped cells interact with an explicit elastic ECM through discrete protrusions. Simulating such systems at scale requires solving large friction-dominated equations of motion, yielding sparse, symmetric, positive definite linear systems. We present a graph-based preconditioning strategy that extends support graph preconditioners to the block-structured matrices arising from cell-based models, with proved asymptotic bounds on the condition number.
To gain mechanistic insight beyond large-scale simulations, we complement the full model with low-dimensional toy models of protrusion-mediated mechanosensing and cell steering. These interpretable models isolate key biophysical trade-offs, and yield analytical criteria (e.g., constraints on motor velocity, ECM stiffness ratios) that inform parameter choices in the full simulation. Together, the efficient numerical framework and the interpretable reduced models enable us to connect subcellular mechanosensory mechanisms to emergent migration behaviors in complex ECM architectures.
Bio: I am an applied mathematician, building bridges between the mathematical, computational, and biological sciences. My strong foundations in each allow me to identify key biological problems, draw on and contribute to theoretical mathematical foundations, and develop advanced computational tools.
Swarms, flocks, and human societies all exhibit complex collective behaviours. I am interested in collective cell behaviours, which I view as swarms with a twist:
• Cells are not simply point-like particles but have spatial extent;
• Interactions between cells go beyond simple attraction-repulsion; and
• Cells “live” in a regime where friction dominates over inertia.
These principles guide my work on wound healing, embryogenesis, immune response, and cancer metastasis. I use mathematical modelling and computational biology to uncover the universal principles how biological, physical, and chemical factors shape biological tissues.
The NSF-Simons National Institute for Theory and Mathematics in Biology Seminar Series aims to bring together a mix of mathematicians and biologists to foster discussion and collaboration between the two fields. The seminar series will take place on Fridays from 10am – 11am at the NITMB in the John Hancock Center in downtown Chicago. There will be both an in-person and virtual component.
Learn more – https://www.nitmb.org/nitmb-seminar-series