Modeling Cell Migration in Extracellular Matrix: From Efficient Numerical Methods to Interpretable Mechanosensory Models

Speaker: Andreas Buttenschoen (UMass)

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.