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Fig. 1 | Biology Direct

Fig. 1

From: Cell adhesion heterogeneity reinforces tumour cell dissemination: novel insights from a mathematical model

Fig. 1

Adhesive cell-cell interaction in the LGCA model. a Example configuration of the LGCA; additionally, momentum J(r) (framed arrow) of the central node and local adhesivity gradient G(r) (gray arrow) are indicated. State space: Cells are placed on a square lattice \(\mathcal {L}\) where each node has a substructure with four velocity channels c i ,i=0,...,3, and six rest channels (merged into one rest channel in the figure). Accordingly, nodes can host up to ten cells. Adhesive states a i (r) of single cells (indicated by filled dots) are determined by an adhesion receptor regulation model (see Fig. 2 and Additional file 1 for details). The momentum J(r) (framed arrow) at a given node r is the vector sum of all occupation states η i (r,k), weighted by the adhesive states a i (r) (dot size symbolises adhesivity strength). The local adhesivity gradient vector G(r) (gray arrow) at a given node r is the vector sum of the momenta in the next-neighbour neighbourhood, excluding r (see Additional file 1). b Adhesive interaction is characterised by a reorientation probability P that increases with the degree of alignment between local adhesivity gradient G(r) (left, gray arrow) and momentum J(r) of the reoriented configuration (right, framed arrow)

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