Non-local models for the formation of hepatocyte–stellate cell aggregates

Green, J. E. F.; Waters, Sarah L.; Whiteley, Jonathan; Edelstein‐Keshet, Leah; Shakesheff, Kevin M.; Byrne, Helen M.

doi:10.1016/j.jtbi.2010.08.013

Cited by 43 publications

(40 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are several options for extending this work with an obvious extension being the consideration of other mechanisms, such as incorporating cell adhesion, cell death and cell processes within a developing tissue [3,7,21]. Similarly, this work has only considered cell populations composed of a single cell type; however, the formation of aggregates consisting of two or more cell types is also of interest [2,14,19,25]. A notable feature of these multispecies systems is that, depending upon the strengths of cell-to-cell attraction, different distributions of the various subpopulations are possible within the aggregates, e.g.…”

Section: Discussionmentioning

confidence: 99%

“…The formation of clusters or aggregates is a ubiquitous phenomenon in cell biology; examples include cultures of myxobacteria, the slime mould dictyostelium, and many other cell types grown in vitro for cancer research, studies in developmental biology, or applications in tissue engineering [1,6,14,16,18,19,25,26]. These aggregates can be produced by rapid cell proliferation [22] (as are, for example, those shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

“…1(a)), or by other mechanisms involving attractive cell-to-cell interactions, such as chemotaxis, or direct physical contact, as is the case for those shown in Fig. 1(b) [14,25]. Identifying the mechanism of aggregate formation in a particular case provides us with a fundamental understanding of the underlying processes, and can also be of practical importance in, for example, optimising culture conditions to promote cell viability and functionality.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Distinguishing between mechanisms of cell aggregation using pair-correlation functions

Agnew

Green

Brown

et al. 2014

Journal of Theoretical Biology

Self Cite

View full text Add to dashboard Cite

Many cell types form clumps or aggregates when cultured in vitro through a variety of mechanisms including rapid cell proliferation, chemotaxis, or direct cell-to-cell contact. In this paper we develop an agent-based model to explore the formation of aggregates in cultures where cells are initially distributed uniformly, at random, on a two-dimensional substrate. Our model includes unbiased random cell motion, together with two mechanisms which can produce cell aggregates: (i) rapid cell proliferation, and (ii) a biased cell motility mechanism where cells can sense other cells within a finite range, and will tend to move towards areas with higher numbers of cells. We then introduce a pair-correlation function which allows us to quantify aspects of the spatial patterns produced by our agent-based model. In particular, these pair-correlation functions are able to detect differences between domains populated uniformly at random (i.e. at the exclusion complete spatial randomness (ECSR) state) and those where the proliferation and biased motion rules have been employed -even when such differences are not obvious to the naked eye. The pair-correlation function can also detect the emergence of a characteristic inter-aggregate distance which occurs when the biased motion mechanism is dominant, and is not observed when cell proliferation is the main mechanism of aggregate formation. This suggests that applying the pair-correlation function to experimental images of cell aggregates may provide information about the mechanism associated with observed aggregates. As a proof of concept, we perform such analysis for images of cancer cell aggregates, which are known to be associated with rapid proliferation. The results of our analysis are consistent with the predictions of the proliferation-based simulations, which supports the potential usefulness of pair correlation functions for providing insight into the mechanisms of aggregate formation.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Distinguishing between mechanisms of cell aggregation using pair-correlation functions

Agnew

Green

Brown

et al. 2014

Journal of Theoretical Biology

Self Cite

View full text Add to dashboard Cite

show abstract

“…Cancer cells lose their ability to regulate genome stability which leads to further genetic changes and tumour development (Khalique et al, 2007). Over the last three decades it has been shown experimentally that tumours consist of heterogeneous populations of cells, which are the result of genetic instability (Stackpole, 1983; 3 of 36 new mathematical models of parabolic type have been derived to describe these cell-cell and cell-matrix adhesion processes (Armstrong et al, 2006;Dyson et al, 2016;Gerisch & Chaplain, 2008;Gerisch & Painter, 2010;Green et al, 2010;Painter et al, 2015). Since these models incorporate the assumption that cells at position x bind/unbind to/from other cells at position x ± s (for some s > 0 within cells sensing radius), they are generally nonlocal.…”

Section: Introductionmentioning

confidence: 99%

Lyapunov–Schmidt and Centre Manifold Reduction Methods for Nonlocal PDEs Modelling Animal Aggregations

Buono

Eftimie

2016

Springer Proceedings in Mathematics &Amp; Statistics

View full text Add to dashboard Cite

[Date] Cells adhere to each other and to the extracellular matrix (ECM) through protein molecules on the surface of the cells. The breaking and forming of adhesive bonds, a process critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this paper, we develop a nonlocal mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, for two cancer cell populations with different levels of mutation. The partial differential equations for cell dynamics are coupled with ordinary differential equations describing the extracellular matrix (ECM) degradation and the production and decay of integrins. We use this model to investigate the role of cancer mutation on the possibility of cancer clonal competition with alternating dominance, or even competitive exclusion (phenomena observed experimentally). We discuss different possible cell aggregation patterns, as well as travelling wave patterns. In regard to the travelling waves, we investigate the effect of cancer mutation rate on the speed of cancer invasion.

show abstract

“…In contrast, our framework allows fibres embedded within the ECM to affect both the collagen mechanics (through the transversely isotropic form of the stress tensor) and cell-ECM interactions (though the anisotropic drag and cell-ECM force terms). The cell-ECM force is modelled via a convolution integral term, an approach which is increasingly being used to represent cell-cell and cell-ECM interactions in continuum models (Gerisch and Chaplain, 2008;Green et al, 2010;Szymanska et al, 2009). For an isotropic ECM, recent work (Green et al, 2013) has shown that, if the 'sphere of influence' of each cell is small, the nonlocal term can be approximated by the gradient of a function of cell and ECM density.…”

Section: Discussionmentioning

confidence: 99%

An investigation of the influence of extracellular matrix anisotropy and cell–matrix interactions on tissue architecture

et al. 2015

View full text Add to dashboard Cite

Mechanical interactions between cells and the fibrous extracellular matrix (ECM) in which they reside play a key role in tissue development. Mechanical cues from the environment (such as stress, strain and fibre orientation) regulate a range of cell behaviours, including proliferation, differentiation and motility. In turn, the ECM structure is affected by cells exerting forces on the matrix which result in deformation and fibre realignment. In this paper we develop a mathematical model to investigate this mechanical feedback between cells and the ECM. We consider a three-phase mixture of collagen, culture medium and cells, and formulate a system of partial differential equations which represents conservation of mass and momentum for each phase. This modelling framework takes into account the anisotropic mechanical properties of the collagen gel arising from its fibrous microstructure. We also propose a cell-collagen interaction force which depends upon fibre orientation and collagen density. We use a combination of numerical and analytical techniques to study the influence of cell-ECM interactions on pattern formation in tissues. Our results illustrate the wide range of structures which may be formed, and how those that emerge depend upon the importance of cell-ECM interactions.

show abstract

Non-local models for the formation of hepatocyte–stellate cell aggregates

Cited by 43 publications

References 31 publications

Distinguishing between mechanisms of cell aggregation using pair-correlation functions

Distinguishing between mechanisms of cell aggregation using pair-correlation functions

Lyapunov–Schmidt and Centre Manifold Reduction Methods for Nonlocal PDEs Modelling Animal Aggregations

An investigation of the influence of extracellular matrix anisotropy and cell–matrix interactions on tissue architecture

Contact Info

Product

Resources

About