Download Mathematical Model of Cell Motility

Mathematical Model of Cell Motility
Nathan Willis and Olivia Dennis
May 8, 2016
Cell motility is a vital process in a wide array of biological contexts including immune response,
embryonic development, and wound healing, as well as the spread of cancer cells. Following previous
studies, we develop a one-dimensional partial differential equation which models a motile amoeboid
cell by balancing internal body forces with drag against the underlying substrate. We numerically
simulate this model using Finite Differences and the Forward Euler method. We investigate the
profile and coordination of adhesion between the cell and substrate.
(a) Shows the displacement for 25 cell body markers using a discretized version of our model. (b) The average displacement
of the whole cell (red). Blue indicates phases of contraction (blue ̸= 0) and relaxation (blue = 0) of the cell.
Through this mechanical model of cell motility we successfully simulate a cell that moves at reasonable speeds. Furthermore, we find that velocity of the cell is indifferent to the passive friction of
the substrate for many orders of magnitude. In addition, velocity scales with frequency of motility
cycles, as expected. In the future we would like to create a more mechanistic model of adhesion
between the cell and substrate.
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