Abstract
Single and collective cell dynamics, cell shape changes, and cell migration can be conveniently represented by the Cellular Potts Model, a computational platform based on minimization of a Hamiltonian. Using the fact that a force field is easily derived from a scalar energy (F = −∇H), we develop a simple algorithm to associate effective forces with cell shapes in the CPM. We predict the traction forces exerted by single cells of various shapes and sizes on a 2D substrate. While CPM forces are specified directly from the Hamiltonian on the cell perimeter, we approximate the force field inside the cell domain using interpolation, and refine the results with smoothing. Predicted forces compare favorably with experimentally measured cellular traction forces. We show that a CPM model with internal signaling (such as Rho-GTPase-related contractility) can be associated with retraction-protrusion forces that accompany cell shape changes and migration. We adapt the computations to multicellular systems, showing, for example, the forces that a pair of swirling cells exert on one another, demonstrating that our algorithm works equally well for interacting cells. Finally, we show forces exerted by cells on one another in classic cell-sorting experiments.
Highlights
From embryogenesis and throughout life, cells exert forces on one another and on their surroundings
We computed the force-fields associated with the Cellular Potts Model (CPM) Hamiltonians of single static cells with circular (A), elliptical (B), and irregular shapes (C,D)
We find forces directed approximately normal to the boundary, with magnitudes that decay towards the centroid, as a consequence of our interpolation
Summary
From embryogenesis and throughout life, cells exert forces on one another and on their surroundings. Computing forces in the Cellular Potts Model signaling and inducing remodeling of the cytoskeleton. Along with progress in experimental quantification of cellular forces, there has been much activity in modeling and developing computational platforms to explore cellular mechanobiology. Among them vertex-based and cell-center based simulations, the shape of a cell is depicted by convex polygons, ellipsoids or spheres. The Cellular Potts Model (CPM) is a convenient and relatively popular computational platform for modeling dynamic, irregular and highly fluctuating cell shapes [1,2,3]. An advantage of the CPM is its high resolution description of cell shapes compared with polygonal cells in vertex-based computations [4]. The CPM can accommodate cell detachment or reattachment from an aggregate, and a range of cell-cell adhesion, where vertex-based simulations are less suitable. For a detailed rebuttal of this issue, see the recent work of [5]
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