Mathematical modelling of growth factor induced cell migration in 3D engineered matrices - Ahmed, Riham K I (Department of Human Biology, 2024)
Cells mechanically interact with their environment to sense, for example, topography, elasticity, mechanical cues from other cells, and chemical signals. Multi-signalling stimuli have profound effects on cellular behaviour, including migration. The current study aims to develop a mathematical model for chemo-mechanically induced migration of individual cells in a collective in three-dimensional engineered extracellular matrices governed by the mechanical properties of the matrix and a growth factor gradient. In the developed model, each cell is assumed to transmit a traction force that locally deforms a planar elastic substrate, resulting in spatially varying strain energy density gradients. The magnitude and direction of strain energy density gradients define cell migration. Cell-substrate adhesion and partial random motion are included. Further, the Green function and Duhamel principle are used to solve the diffusion equation to describe the presence of a growth factor and represent chemo-mechanically induced deterministic collective cell migration on planar elastic substrates. Finally, three-dimensional strain energy density gradients due to local matrix deformation by embedded cells are obtained using finite element methods and implemented in the model to describe chemo-mechanically induced collective cell migration in extracellular matrices. Deterministic and random migration of up to 50 cells on planar substrates and threedimensional extracellular matrices with spatially uniform and varying stiffness is predicted. The effect of varying growth factor productivity and diffusivity is explored for cell migration on a planar substrate induced by a growth factor only and combined with mechanical cues. The model predicts that the maximum velocity of a cell migrating towards the growth factor source increases with increasing productivity and decreasing diffusivity of the growth factor. Collective cell migration due to mechanical cell interactions in the extracellular matrix is studied with sequential and non-sequential changes in matrix stiffness. The overall migration is directed towards the stiffest region for the sequential stiffness change and the softest region for the non-sequential stiffness change in the matrix. The chemo-mechanically induced cell migration is presented in three sequential extracellular matrices with an overall migration direction towards the growth factor in the softest region. The mathematical models can adequately simulate the chemo-mechanically induced collective cell migration in elastic planar substrates and three-dimensional extracellular matrices. The models provide qualitative results demonstrating collective cell migration in complex environments with several cues increasing the potential and capabilities to replace in vitro and in vivo experiments with in silico simulations in, for example, wound healing, cancer treatment, and regenerative medicine.