A cartoon illustrating cell migration.

Migration transition rate (Eq (7)) is illustrated for a cell coloured in green. Its nucleus is marked with a green star. The motility of this cell depends on the ECM density, c_i, in the voxel where its nucleus is situated (accounted for by the S(⋅) function (Eq (8)). The green cell forms cell-cell adhesions with other cells coloured in red. In this work, we assume a circular neighbourhood for cell-cell interactions within the so-called interaction radius, R_c, for the cellular scale (here it is drawn to have the same value as in our simulations, R_c = 1.5h, where h is the voxel width). This allows cells to interact beyond their immediate neighbours as, for example, the cell with the nucleus marked by a red star and the focal green cell. Other geometries (e.g. elliptical neighbourhood aligned with cell polarity vector) are unlikely to alter the model behaviour significantly since, in sprouting structures, lateral regions of the circular neighbourhood, which would be ignored by an elliptic neighbourhood, are typically empty. Cell-cell adhesion is accounted for by the neighbourhood function, F(⋅), Eq (9). The individual cell polarity, ϕ, is sampled from the von Mises distribution (Eq (12)) with the mean value given by the mean polarization direction, (calculated as a function of local ECM fibril alignment, l_i, Eq (13)). The distribution spread, κ, is assumed to depend on the focal cell phenotype and the concentration of the BM components, Eq (14).