Multiscale dynamics of a heterotypic cancer cell population within a fibrous extracellular matrix

Abstract

Local cancer cell invasion is a complex process involving many cellular and tissue interactions and is an important prerequisite for metastatic spread, the main cause of cancer related deaths. Occurring over many different temporal and spatial scales, the first stage of local invasion is the secretion of matrixdegrading enzymes (MDEs) and the resulting degradation of the extra-cellular matrix (ECM). This process creates space in which the cells can invade and thus enlarge the tumour. As a tumour increases in malignancy, the cancer cells adopt the ability to mutate into secondary cell subpopulations giving rise to a heterogeneous tumour. This new cell subpopulation often carries higher invasive qualities and permits a quicker spread of the tumour.Building upon the recent multiscale modelling framework for cancer invasion within a fibrous ECM introduced in Shuttleworth and Trucu (2019), in this paper we consider the process of local invasion by a heterotypic tumour consisting of two cancer cell populations mixed with a two-phase ECM. To that end, we address the double feedback link between the tissue-scale cancer dynamics and the cell-scale molecular processes through the development of a two-part modelling framework that crucially incorporates the multiscale dynamic redistribution of oriented fibres occurring within a two-phase extra-cellular matrix and combines this with the multiscale leading edge dynamics exploring key matrix-degrading enzymes molecular processes along the tumour interface that drive the movement of the cancer boundary. The modelling framework will be accompanied by computational results that explore the effects of the underlying fibre network on the overall pattern of cancer invasion.

Directionality of Macrophages Movement in Tumour Invasion: A Multiscale Moving-Boundary Approach

“…( 2013 ), Peng et al. ( 2017 ) and Shuttleworth and Trucu ( 2019 , 2020a , 2020b ) where aside from the tumour cells population c ( x , t ), the rest of the tumour micro-environment and surrounding tissue is represented here simply by a generic ECM. To that end, while we acknowledge that, besides the tumour cells, some of the tumour micro-environment components are not ECM constituents and are rather only supported by the usual ECM, in this framework we still regard all those constituents (such as VEGF, FGF, TGF-beta and ions such as ) as being part of and represented by this extended concept of ECM.…”

“…To that end, while we acknowledge that, besides the tumour cells, some of the tumour micro-environment components are not ECM constituents and are rather only supported by the usual ECM, in this framework we still regard all those constituents (such as VEGF, FGF, TGF-beta and ions such as ) as being part of and represented by this extended concept of ECM. Furthermore, due to the biologically established importance played within cell migration by the major ECM fibres, namely collagen and fibronectin, as considered also in Shuttleworth and Trucu ( 2019 , 2020a , 2020b ), we regard this ECM as two-phase matter, consisting of an ECM fibre phase and an ECM non-fibre phase.Specifically, on one hand the ECM fibres phase accounts exclusively for all major fibres components such as collagen and fibronectin (notably characterised by their insolubility properties (Hynes and Naba 2012 )), and its amount distributed at ( x , t ) is denoted here by F ( x , t ). On the other hand, besides the major fibres components, the ECM contains also an entire host of other soluble constituents, such as calcium ions Ca (Bhagavathula et al.…”

“…In this context, the spatio-temporal dynamics of the cancer cell population can therefore be expressed mathematically as: where is a constant diffusion coefficient, and describes the cell-adhesion processes that bias the cancer cell population movement in accordance with the spatial heterogeneous distribution of the surrounding cancer cells, macrophages, and ECM components including the oriented ECM fibres. Specifically, in addition to the situation considered in Shuttleworth and Trucu ( 2019 , 2020a , 2020b ) (exploring the adhesive interactions of the cells distributed at with the other cancer cells as well as with the distribution of non-fibres ECM phase (Ghosh et al. 2017 ; Gras 2009 ; Gras et al.…”

“… 2000 ) (revealing the positive correlation between the availability of the extracellular Ca ions within the ECM and the strength of the adhesion bonds that the cancer cells are able to establish between themselves) enables us to assume that the cell–cell adhesion strength depends on the non-fibre ECM density. Hence, proceeding here as in Shuttleworth and Trucu ( 2019 , 2020a , 2020b ), we take to be of the form which smoothly explores a full range of cell–cell cancer self-adhesion strengths, from its maximum level that corresponds to the Ca -saturation level to its minimum values that corresponds to the minimum level of Ca . Further, as on the sensing region the cell–cell cancer self-adhesion is complemented by an adhesion relationship between the cancer cells and macrophages, represents the combined strength of the cancer cell–macrophages adhesion.…”

Non-local multiscale approaches for tumour-oncolytic viruses interactions

“…Death rate of OV [9] ν e 1 The fraction of physical space occupied by the ECM [44] ν c 1 The fraction of physical space occupied by cancer cells [44] γ c 1 MDEs secretion rate by uninfected cancer cell [45] γ i 1.5 MDEs secretion rate by infected cancer cell [45] D m 0.0025 MDE diffusion coefficient [39] h 0.03125 spatial discretisation step size in both x and y directions [44] there is no difference in the spatial distribution of uninfected cancer cells between panels (a) and (b). However, the addition of haptotactic movement impacts the spatial distribution of infected cancer cells and OVs, leading to more localised viral infections.…”