A Hybrid Model to Test the Importance of Mechanical Cues Driving Cell Migration in Angiogenesis

Abstract

Many studies are stressing the crucial importance of the mechanical component in angiogenesis, but still, very few models really integrate mechanics. In this paper, we propose to investigate the importance of mechanical cues for cell migration in the context of angiogenesis. We propose a hybrid continuous-discrete model that describes the individual migration of contracting cells on an elastic matrix of fibres. The matrix is described as a continuum whereas the cells are described as discrete elements. We also take into account the degradation of the matrix by proteases. The Young's modulus characterizing the matrix rigidity depends on the local and time-dependent density of matrix fibres. Our results show that acting on the mechanics, specifically on the cell traction force intensity and on the matrix rigidity, can significantly alter cell migration and angiogenesis. First, there is a limited range of traction force intensities for which a vascular network can be obtained. Second, the matrix rigidity plays a role, but only in a very specific range, compatible with the underlying biological process. Alteration of the matrix due to cell degradation appears too small to induce significant changes in cell migration trajectories.

Hybrid Modelling in Biology: a Classification Review

“…The paper by [33] is an illustration of a bi-directional coupling with the structure as in figure 3, case 2 (lower graph). It is a hybrid discrete-continuous model which describes the individual migration of contracting cells on a an elastic matrix of fibres in the context of tumour-induced angiogenesis.…”

Review on experiment-based two- and three-dimensional models for wound healing

“…Figure 3 shows a snapshot of a simulation of the development of angiogenic sprouts (see the topography of the top coloured surface). An alternative hybrid model, for angiogenesis under the influence of mechanical signals, was developed by Stephanou et al [63].…”

Hybrid modelling of mechanical cues in cell migration

“…Equations (2-3) form our hybrid model coupling cell migration and the cell deformable environment (figures 1.A), which we use to simulate tumour-induced angiogenesis and emphasize the importance of the mechanical coupling [10]. The comparison of simulations realized with and without the integration of the mechanical component (figures 1.B and 1.C) shows that i) the vessels are more rectilinear, ii) the density of the vascular network is lower and iii) matrix degradation is reduced when mechanics is included.…”

“…Our primary aim was to propose a more complete hybrid model of angiogenesis incorporating mechanical effects to be able to describe and investigate the anastomosis process [10]. This process, which is hypothesized to be mechanicsdependent, remains under-looked although it is known to be crucial for the formation of functional vascular networks [1].…”