Dynamic cellular finite-element method for modelling large-scale cell migration and proliferation under the control of mechanical and biochemical cues: a study of re-epithelialization

Abstract

Computational modelling of cells can reveal insight into the mechanisms of the important processes of tissue development. However, current cell models have limitations and are challenged to model detailed changes in cellular shapes and physical mechanics when thousands of migrating and interacting cells need to be modelled. Here we describe a novel dynamic cellular finite-element model (DyCelFEM), which accounts for changes in cellular shapes and mechanics. It also models the full range of cell motion, from movements of individual cells to collective cell migrations. The transmission of mechanical forces regulated by intercellular adhesions and their ruptures are also accounted for. Intra-cellular protein signalling networks controlling cell behaviours are embedded in individual cells. We employ DyCelFEM to examine specific effects of biochemical and mechanical cues in regulating cell migration and proliferation, and in controlling tissue patterning using a simplified re-epithelialization model of wound tissue. Our results suggest that biochemical cues are better at guiding cell migration with improved directionality and persistence, while mechanical cues are better at coordinating collective cell migration. Overall, DyCelFEM can be used to study developmental processes when a large population of migrating cells under mechanical and biochemical controls experience complex changes in cell shapes and mechanics.

Cell–substrate mechanics guide collective cell migration through intercellular adhesion: a dynamic finite element cellular model

“…In our model, a two-dimensional cell Ω ⊂ R 2 is represented as an oriented polygon connecting a set of boundary vertices V ∂Ω ≡ {v i ∈ ∂Ω ⊂ R 2 }, with the location of the vertex v i denoted as x i . The set of boundary vertices V ∂Ω , along with a set of internal vertices V Int and a set of triangular elements (Zhao et al, 2017). The E-cadhesion type of the intercellular junctions between two adherent cells are modeled as elastic springs (red bars in the blue box, a closer view in the enlarged dashed blue box).…”

“…Int } define the geometry of Ω (Fig. 1a, see more details of generating V Int and T Ω in (Zhao et al, 2017)). If two cells are in contact with each other, they are connected by adhesive springs between them ( Fig.…”

“…where K n+1 τ i, j, k , u n+1 τ i, j, k , and f n+1 τ i, j, k are the stiffness matrix, displacement vector, and integrated force vector of τ i, j, k at time step t n+1 (see more details of derivation of (Eqn 12) in (Zhao et al, 2017)).…”

How Computation Is Helping Unravel the Dynamics of Morphogenesis

“…These models have made contributions to our understanding various tissue behaviors: growth [115][116][117], cell division and packing [118], planar polarity [119] and the formation of compartments [120]. Dynamic cellular finiteelement models have been also proposed for individual and collective cell movements and mechanics [121].…”

Biomechanics of Collective Cell Migration in Cancer Progression: Experimental and Computational Methods

“…The Finite Element (FE) model has been extensively used in cell and tissue mechanics studies [177][178][179][180][181][182][183][184] . Recently, this model was used to investigate cell-substrate adhesion as well as cell migration [185][186][187][188] . Wong and Tang developed a FEA model to investigate the effects of focal adhesion mechanical properties, substrate stiffness and intracellular stress on cell-matrix interaction during cell migration.…”