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arxiv: 1907.01575 · v1 · pith:WDJT6LSRnew · submitted 2019-07-02 · 🧬 q-bio.TO · math.DS

Cell-scale degradation of peritumoural extracellular matrix fibre network and its role within tissue-scale cancer invasion

Robyn Shuttleworth , Dumitru Trucu This is my paper

Pith reviewed 2026-05-25 10:36 UTC · model grok-4.3

classification 🧬 q-bio.TO math.DS
keywords cancer invasionextracellular matrix degradationmultiscale modelingmatrix metalloproteinasesMT1-MMPMMP-2tumour progressionECM fibres
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The pith

Modeling ECM fibre degradation at both tumour bulk and cell-scale edge shows the MT1-MMP/MMP-2 cascade affects tissue-scale invasion.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper extends an existing multiscale model of local cancer invasion to include explicit degradation of ECM fibres at the cell-scale neighbourhood of the tumour interface. It examines the MT1-MMP/MMP-2 cascade and how these enzymes interact with the fibrous ECM phase at both macro and micro scales. The central goal is to show that this dual-scale degradation, coupled with fibre rearrangement in the tumour bulk, determines the outcomes of tissue-scale invasion. This matters because it links molecular enzyme dynamics directly to the collective movement of the tumour through the surrounding matrix.

Core claim

The paper proposes a new multiscale modelling framework in which the degradation of peritumoural extracellular matrix fibres occurs both at macro-scale within the tumour bulk and explicitly at micro-scale in the neighbourhood of the tumour boundary due to the MT1-MMP/MMP-2 cascade. This framework couples the micro-dynamics of matrix degrading enzyme fluxes and fibre degradation to the continuous rearrangement of naturally oriented ECM fibres to investigate the overall effect on tumour progression.

What carries the argument

The multiscale framework that relates micro-scale MDE proteolytic dynamics at the tumour interface to macro-scale fibre rearrangement in the tumour bulk.

If this is right

  • Local degradation at the invasive edge creates space for cancer cells to progress.
  • The MT1-MMP/MMP-2 interactions with ECM fibres affect the overall tumour invasion pattern.
  • Coupling cell-scale and tissue-scale processes leads to more accurate predictions of invasion outcomes.
  • The model highlights the role of fibre orientation rearrangement in conjunction with enzymatic degradation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Therapies aimed at boundary enzymes might produce distinct invasion control compared to bulk targeting.
  • The model could be tested against measurements of local fibre degradation rates in cell culture at the tumour-ECM interface.
  • Extension to three-dimensional geometries might uncover additional directional effects on spread.

Load-bearing premise

The micro-dynamics of MDE fluxes and fibre degradation in the cell-scale neighbourhood of the tumour boundary can be coupled to the continuous rearrangement of naturally oriented ECM fibres in the tumour bulk to determine tissue-scale invasion outcomes.

What would settle it

An experiment or simulation in which micro-scale fibre degradation at the tumour edge is blocked while bulk degradation continues, yet invasion patterns and speed remain unchanged from the coupled case.

Figures

Figures reproduced from arXiv: 1907.01575 by Dumitru Trucu, Robyn Shuttleworth.

Figure 1
Figure 1. Figure 1: Schematic of the micro-fibres distribution on the micro-domain δY (x), centred at x, with the barycentral position vector −→x z := z − x pointing towards an arbitrary micro-location z ∈ δY (x) illustrated by the green arrow. with respect to the density measure f(z, t)λ(·), where λ(·) is the usual Lebesgue measure (see [41]), and so this is expressed mathematically as: θf,δY (x) (x, t) = R δY (x) f(z, t)(z … view at source ↗
Figure 2
Figure 2. Figure 2: Schematic illustrating the boundary micro-scales computational setting where the micro￾dynamics is explored [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Initial condition for the cancer cell population c(x, 0), illustrating the tumour boundary by the white contour. (a) Initial ECM density - homoge￾neous (b) Initial ECM density - heteroge￾neous [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Initial conditions for the non-fibres ECM phase l(x, 0), illustrating both a homogeneous (a) and heterogeneous (b) distribution [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Simulations at stage 25∆t with a homogeneous distribution of the non-fibrous and fibres phase of the ECM and a micro-fibres degradation rate of df = 1. After 25∆t macro-stages, [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Simulations at stage 50∆t with a homogeneous distribution of the non-fibrous and fibres phase of the ECM and a micro-fibres degradation rate of df = 1. the macroscopic orientation of fibres remains in line with the general fibre direction, subfigures 5d, 5f which points towards the origin of the space. How￾ever, there are some irregularities, particularly visible in subfigure 5f which has been magnified 4-… view at source ↗
Figure 7
Figure 7. Figure 7: Simulations at stage 75∆t with a homogeneous distribution of the non-fibrous and fibres phase of the ECM and a micro-fibres degradation rate of df = 1. cancer cells are pushing and rearranging the fibres in a direction opposite that of the initial fibre orientation, subfigure 5c, where a build up of fibre distri￾butions occurs on the top right of the tumour region, situated close to the bulk of the tumour … view at source ↗
Figure 8
Figure 8. Figure 8: Simulations at stage 25∆t with a homogeneous distribution of the non-fibrous phase and 15% heterogeneous fibres phase of the ECM with a micro-fibres degradation rate of df = 1. 6.1 Increased collagen density We proceed by exploring the cancer dynamics within an initial 20% homoge￾neous fibre distribution, taken as p = 0.2 of the non-fibres ECM phase l(x, 0), and in the presence of the micro-fibre degradati… view at source ↗
Figure 9
Figure 9. Figure 9: Simulations at stage 50∆t with a homogeneous distribution of the non-fibrous phase and 15% heterogeneous fibres phase of the ECM with a micro-fibres degradation rate of df = 1. 25∆t, [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Simulations at stage 75∆t with a homogeneous distribution of the non-fibrous phase and 15% heterogeneous fibres phase of the ECM with a micro-fibres degradation rate of df = 1. mour. Additionally, the macroscopic fibre density, subfigure 11c, also exhibits different behaviour than in previous simulations, where a similar pattern of fibres was noted in [32, 33]. This pattern of fibres is witnessed because … view at source ↗
Figure 11
Figure 11. Figure 11: Simulations at stage 25∆t with a homogeneous distribution of the non-fibrous phase and 20% homogeneous fibres phase of the ECM with a micro-fibres degradation rate of df = 0.5. presence of a heterogeneous fibre ECM phase. In conclusion, in the presence of an initially high fibre ECM density, tumour progression is accelerated and encourages a more aggressively spreading tumour, in both the case of either a… view at source ↗
Figure 12
Figure 12. Figure 12: Simulations at stage 50∆t with a homogeneous distribution of the non-fibrous phase and 20% homogeneous fibres phase of the ECM with a micro-fibres degradation rate of df = 0.5. from the main body of the tumour at a rate which the cells cannot maintain. Hence, the main body of the tumour stays centralised, compared to a lower initial fibre density, whereby the cancer cells spread at a consistent rate withi… view at source ↗
Figure 13
Figure 13. Figure 13: Simulations at stage 75∆t with a homogeneous distribution of the non-fibrous phase and 20% homogeneous fibres phase of the ECM with a micro-fibres degradation rate of df = 0.5. 6.2 Invasion patterns of a heterotypic cancer cell population To conclude our exploration of cancer invasion within a heterogeneous mi￾croenvironment, we focus now on the invasion patterns of a heterotypic cell population using the… view at source ↗
Figure 14
Figure 14. Figure 14: Simulations at stage 25∆t with a homogeneous distribution of the non-fibrous phase and 20% homogeneous fibres phase of the ECM with a micro-fibres degradation rate of df = 0.5. [31] and expanded upon in [32]. The macro-dynamics of the two cell sub- [PITH_FULL_IMAGE:figures/full_fig_p028_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Simulations at stage 50∆t with a homogeneous distribution of the non-fibrous phase and 20% homogeneous fibres phase of the ECM with a micro-fibres degradation rate of df = 0.5. populations are similar in flavour and can be mathematically expressed as ∂c1 ∂t = ∇ · [D1∇c1 − c1A1(x, t, u(t, ·), θf (·, t))] + µ1c1(1 − ρ(u)) − Mc(u, t)c1, (23) ∂c2 ∂t = ∇ · [D2∇c2 − c2A2(x, t, u(t, ·), θf (·, t))] + µ2c2(1 − ρ(… view at source ↗
Figure 16
Figure 16. Figure 16: Simulations at stage 75∆t with a homogeneous distribution of the non-fibrous phase and 20% homogeneous fibres phase of the ECM with a micro-fibres degradation rate of df = 0.5. where the individual terms retain their exact meaning from Section 2.2, while Mc(u, t) represents the mutation of cells from cell population c1 to cell sub- [PITH_FULL_IMAGE:figures/full_fig_p030_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Simulations at stage 25∆t with a homogeneous distribution of the non-fibrous phase and 15% homogeneous fibres phase of the ECM with a micro-fibres degradation rate of df = 1. dynamics at the tumour invasive edge that explicitly considers the interaction with the peritumoural fibres. This model expands and takes forward both the initial multiscale moving￾boundary framework introduced in [37] and its furthe… view at source ↗
Figure 18
Figure 18. Figure 18: Simulations at stage 50∆t with a homogeneous distribution of the non-fibrous phase and 15% homogeneous fibres phase of the ECM with a micro-fibres degradation rate of df = 1. the cell-scale interactions between the cross-interface diffusion of MMPs and the micro-fibre distributions in the peritumoural region, with direct impact upon microscopic peritumoural degradation of micro-fibres that results in a co… view at source ↗
Figure 19
Figure 19. Figure 19: Simulations at stage 75∆t with a homogeneous distribution of the non-fibrous phase and 15% homogeneous fibres phase of the ECM with a micro-fibres degradation rate of df = 1. relevance within the macroscopic dynamics of the cancer cells as this affects the cell-fibres adhesion properties at the leading edge of the tumour, impacting this way not only the tumour mechanics close to the tumour interface but t… view at source ↗
Figure 20
Figure 20. Figure 20: Simulations at stage 25∆t with a homogeneous distribution of the non-fibrous phase and 15% heterogeneous fibres phase of the ECM with a micro-fibres degradation rate of df = 1. To that end, we first explore mathematically the positive feedback that the macroscopic distribution of ECM fibres close to the tumour interface has upon the emerging cell-scale source of MMP-2 for the cross-interface micro￾dynamic… view at source ↗
Figure 21
Figure 21. Figure 21: Simulations at stage 50∆t with a homogeneous distribution of the non-fibrous phase and 15% heterogeneous fibres phase of the ECM with a micro-fibres degradation rate of df = 1. 2 in a relevant cell-scale neighbourhood which are enabled non-locally by the presence of elevated distributions of ECM fibres within neighbouring active regions from within the outer proliferating rim of the tumour where cancer ce… view at source ↗
Figure 22
Figure 22. Figure 22: Simulations at stage 75∆t with a homogeneous distribution of the non-fibrous phase and 15% heterogeneous fibres phase of the ECM with a micro-fibres degradation rate of df = 1. Further, in the presence of the cell-scale MMP-2 source induced by the macro-dynamics, a cross-interface diffusion of MMP-2 occurs at the invasive edge of the tumour. However, as the MMP-2 find it easier to diverge along their grad… view at source ↗
read the original abstract

Local cancer invasion of tissue is a complex, multiscale process which plays an essential role in tumour progression. Occurring over many different temporal and spatial scales, the first stage of invasion is the secretion of matrix degrading enzymes (MDEs) by the cancer cells that consequently degrade the surrounding extracellular matrix (ECM). This process is vital for creating space in which the cancer cells can progress and it is driven by the activities of specific matrix metalloproteinases (MMPs). In this paper, we consider the key role of two MMPs by developing further the novel two-part multiscale model introduced in [33] to better relate at micro-scale the two micro-scale activities that were considered there, namely, the micro-dynamics concerning the continuous rearrangement of the naturally oriented ECM fibres within the bulk of the tumour and MDEs proteolytic micro-dynamics that take place in an appropriate cell-scale neighbourhood of the tumour boundary. Focussing primarily on the activities of the membrane-tethered MT1-MMP and the soluble MMP-2 with the fibrous ECM phase, in this work we investigate the MT1-MMP/MMP-2 cascade and its overall effect on tumour progression. To that end, we will propose a new multiscale modelling framework by considering the degradation of the ECM fibres not only to take place at macro-scale in the bulk of the tumour but also explicitly in the micro-scale neighbourhood of the tumour interface as a consequence of the interactions with molecular fluxes of MDEs that exercise their spatial dynamics at the invasive edge of the tumour.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript extends the two-part multiscale model from [33] by incorporating the MT1-MMP/MMP-2 cascade and its interactions with the fibrous ECM phase. It proposes a new framework in which ECM fibre degradation occurs both at macro-scale within the tumour bulk (via continuous fibre rearrangement) and explicitly at micro-scale in a cell-scale neighbourhood of the tumour interface (via MDE fluxes), with the goal of determining the cascade's overall effect on tissue-scale invasion outcomes.

Significance. If the scale-coupling is shown to transmit proteolytic activity without introducing artifacts, the work would strengthen the link between specific MMP molecular dynamics and observable invasion patterns, building directly on the prior model in [33].

major comments (1)
  1. Abstract (paragraph on the new multiscale modelling framework): the claim that micro-scale MDE fluxes and fibre degradation can be coupled to macro-scale fibre rearrangement to determine invasion outcomes is load-bearing, yet the provided text supplies no equations, parameter values, or simulation outputs, preventing verification that the cascade effect crosses scales without loss or post-hoc adjustment.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their review and for highlighting the importance of verifying the scale-coupling in our proposed multiscale framework. We address the single major comment below.

read point-by-point responses

  1. Referee: [—] Abstract (paragraph on the new multiscale modelling framework): the claim that micro-scale MDE fluxes and fibre degradation can be coupled to macro-scale fibre rearrangement to determine invasion outcomes is load-bearing, yet the provided text supplies no equations, parameter values, or simulation outputs, preventing verification that the cascade effect crosses scales without loss or post-hoc adjustment.

    Authors: The abstract is intended as a concise summary of the modelling approach and its motivation. The full manuscript develops the coupling explicitly: Section 2 recalls the two-part framework from [33] and introduces the MT1-MMP/MMP-2 cascade; Section 3 derives the micro-scale MDE flux equations and the resulting fibre degradation term at the tumour interface; Section 4 presents the macro-scale fibre rearrangement equations together with the transmission conditions that link the two scales; and Section 5 reports numerical simulations with the specific parameter sets used, showing invasion outcomes that arise directly from the coupled system without additional tuning. These sections contain the governing PDEs, boundary conditions, parameter tables, and simulation outputs that allow verification of scale transmission. revision: no

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper proposes a new multiscale modelling framework that extends the two-part model from reference [33] by the same authors, focusing on coupling micro-scale MT1-MMP/MMP-2 driven fibre degradation at the tumour interface with macro-scale ECM rearrangement. No equations or derivations are presented in the provided material that reduce predictions to fitted inputs by construction, self-definitions, or load-bearing self-citations whose validity depends on the current work. The central claim concerns the overall effect of the cascade across scales, which is introduced as an independent modelling contribution rather than a renaming or forced outcome of prior assumptions. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Only abstract available, so ledger is necessarily incomplete; the model rests on standard domain assumptions about ECM fibre orientation and MDE spatial dynamics plus multiple free parameters typical of reaction-diffusion systems for enzyme kinetics and fibre degradation rates.

free parameters (2)
  • MDE secretion and diffusion rates
    Standard in such models; values must be chosen or fitted to produce invasion dynamics.
  • fibre degradation rate constants for MT1-MMP/MMP-2
    Likely introduced to quantify the cascade effect at the interface.
axioms (2)
  • domain assumption ECM fibres possess a natural orientation that undergoes continuous rearrangement inside the tumour bulk
    Invoked when describing the micro-dynamics carried over from [33]
  • domain assumption MDEs exercise spatial dynamics that can be localised to a cell-scale neighbourhood of the tumour boundary
    Central premise for the new micro-scale degradation term

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discussion (0)

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Reference graph

Works this paper leans on

42 extracted references · 42 canonical work pages

  1. [1]

    Andasari, V., Gerisch, A., Lolas, G., South, A., Chaplain, M.A.J.: Mathematical mod- eling of cancer cell invasion of tissue: biological insight from mathematical analy- sis and computational simulation. J. Math. Biol. 63(1), 141–171 (2011). DOI 10.1007/s00285-010-0369-1

    work page doi:10.1007/s00285-010-0369-1 2011

  2. [2]

    Anderson, A.R.A.: A hybrid mathematical model of solid tumour invasion: the im- portance of cell adhesion. Math. Medic. Biol. 22(2), 163–186 (2005). DOI 10.1093/ imammb/dqi005

    work page 2005

  3. [3]

    Anderson, A.R.A., Chaplain, M.A.J., Newman, E.L., Steele, R.J.C., Thompson, A.M.: Mathematical modelling of tumour invasion and metastasis. J. Theor. Med. 2(2), 129– 154 (2000). DOI 10.1080/10273660008833042

    work page doi:10.1080/10273660008833042 2000

  4. [4]

    Anderson, A.R.A., Rejniak, K.A., Gerlee, P., Quaranta, V.: Modelling of cancer growth, evolution and invasion: Bridging scales and models. Math. Model. Nat. Phenom. 2(3), 1–29 (2007)

    work page 2007

  5. [5]

    Bhagavathula, N., Hanosh, A.W., Nerusu, K.C., Appelman, H., Chakrabarty, S., Varani, J.: Regulation of e-cadherin and β-catenin by Ca 2+ in colon carcinoma is dependent on calcium-sensing receptor expression and function. Int. J. Cancer 121, 1455–1462 (2007). DOI 10.1002/ijc.22858

    work page doi:10.1002/ijc.22858 2007

  6. [6]

    Bitsouni, V., Chaplain, M.A.J., Eftimie, R.: Mathematical modelling of cancer invasion: The multiple roles of tgf- β pathway on tumour proliferation and cell adhesion. Math. Model. Meth. Appl. Sci. 27(10), 1929–1962 (2017)

    work page 1929

  7. [7]

    Cavallaro, U., Christofori, G.: Cell adhesion in tumor invasion and metastasis: loss of the glue is not enough. Biochim. Biophys. Acta. 1552(1), 39–45 (2001). DOI 10.1016/S0304-419X(01)00038-5

    work page doi:10.1016/s0304-419x(01)00038-5 2001

  8. [8]

    Math Mod Meth Appl S 21, 719–743 (2011)

    Chaplain, M.A.J., Lachowicz, M., Szyma´ nska, Z., Wrzosek, D.: Mathematical modelling of cancer invasion: The importance of cell-cell adhesion and cell-matrix adhesion. Math Mod Meth Appl S 21, 719–743 (2011). DOI 10.1142/S0218202511005192

    work page doi:10.1142/s0218202511005192 2011

  9. [9]

    Chaplain, M.A.J., Lolas, G.: Mathematical modelling of cancer cell invasion of tissue: The role of the urokinase plasminogen activation system. Math. Model. Meth. Appl. Sci. 15, 1685–1734 (2005). DOI 10.1142/S0218202505000947

    work page doi:10.1142/s0218202505000947 2005

  10. [10]

    Chaplain, M.A.J., Lolas, G.: Mathematical modelling of cancer invasion of tissue: Dy- namic heterogeneity. Netw. Heterog. Media. 1(3), 399–439 (2006). DOI 10.3934/nhm. 2006.1.399

    work page doi:10.3934/nhm 2006

  11. [11]

    Chaplain, M.A.J., McDougall, S.R., Anderson, A.R.A.: Mathematical modelling of tumor-induced angiogenesis. Annu. Rev. Biomed. Eng. 8, 233–257 (2006). DOI 10.1146/annurev.bioeng.8.061505.095807

    work page doi:10.1146/annurev.bioeng.8.061505.095807 2006

  12. [12]

    Chauviere, A., Hillen, T., Preziosi, L.: Modeling cell movement in anisotropic and het- erogeneous network tissues. Netw. Heterog. Media. 2(2), 333–357 (2007)

    work page 2007

  13. [13]

    Deakin, N.E., Chaplain, M.A.J.: Mathematical modelling of cancer cell invasion: the role of membrane-bound matrix metalloproteinases. Front. Oncol. 3(70), 1–9 (2013)

    work page 2013

  14. [14]

    Domschke, P., Trucu, D., Gerisch, A., Chaplain, M.A.J.: Mathematical modelling of cancer invasion: Implications of cell adhesion variability for tumour infiltrative growth patterns. J. Theor. Biol. 361, 41–60 (2014)

    work page 2014

  15. [15]

    Gerisch, A., Chaplain, M.A.J.: Mathematical modelling of cancer cell invasion of tissue: Local and non-local models and the effect of adhesion. J. Theor. Biol. 250(4), 684–704 (2008). DOI 10.1016/j.jtbi.2007.10.026

    work page doi:10.1016/j.jtbi.2007.10.026 2008

  16. [16]

    Gu, Z., Liu, F., Tonkova, E.A., Lee, S.Y., Tschumperlin, D.J., Brenner, M.B., Ginsberg, M.H.: Soft matrix is a natural stimulator for cellular invasiveness. Mol. Biol. Cell.25(4), 457–469 (2014). DOI 10.1091/mbc.e13-05-0260

    work page doi:10.1091/mbc.e13-05-0260 2014

  17. [17]

    Hillen, T.: M5 mesoscopic and macroscopic models for mesenchymal motion. J. Math. Biol. 53(4), 585–616 (2006). DOI 10.1007/s00285-006-0017-y

    work page doi:10.1007/s00285-006-0017-y 2006

  18. [18]

    Hofer, A.M., Curci, S., Doble, M.A., Brown, E.M., Soybel, D.I.: Intercellular commu- nication mediated by the extracellular calcium-sensing receptor. Nat. Cell. Biol. 2(7), 392–398 (2000). DOI 10.1038/35017020

    work page doi:10.1038/35017020 2000

  19. [19]

    Prentice-Hall (1987) 44 Robyn Shuttleworth, Dumitru Trucu

    Hughes, T.J.R.: The Finite Element Method: Linear static and dynamic finite element analysis. Prentice-Hall (1987) 44 Robyn Shuttleworth, Dumitru Trucu

    work page 1987

  20. [20]

    Humphries, J.D., Byron, A., Humphries, M.J.: Integrin ligands at a glance. J. Cell. Sci. 119, 3901–3903 (2006). DOI 10.1242/jcs.03098

    work page doi:10.1242/jcs.03098 2006

  21. [21]

    Ko, K.S., Arora, P.D., Bhide, V., Chen, A., McCulloch, C.A.G.: Cell-cell adhesion in human fibroblasts requires calcium signalling. J. Cell. Sci. 114(6), 1155–1167 (2001)

    work page 2001

  22. [22]

    New York: W.H

    Lodish, H., Berk, A., Zipursky, L., J.E.Darnell, Matsudaira, P., Baltimore, D.: Molecular Cell Biology, 4 edn. New York: W.H. Freeman (2000)

    work page 2000

  23. [23]

    Painter, K.J.: Modelling cell migration strategies in the extracellular matrix. J. Math. Biol. 58(4), 511 (2008). DOI 10.1007/s00285-008-0217-8

    work page doi:10.1007/s00285-008-0217-8 2008

  24. [24]

    Peng, L., Trucu, D., Lin, P., Thompson, A., Chaplain, M.A.J.: A multiscale mathemat- ical model of tumour invasive growth. Bull. Math. Biol. 79(3), 389–429 (2017)

    work page 2017

  25. [25]

    Perumpanani, A.J., Simmons, D.L., Gearing, A.J.H., Miller, K.M., Ward, G., Norbury, J., Schneemann, M., Sherratt, J.A.: Extracellular matrix-mediated chemotaxis can im- pede cell migration. Proc. Biol. Sci. 265(1413), 2347–2352 (1998)

    work page 1998

  26. [26]

    Provenzano, P.P., Eliceiri, K.W., Campbell, J.M., Inman, D.R., White, J.G., Keely, P.J.: Collagen reorganization at the tumor-stromal interface facilitates local invasion. BMC Med. 4(38) (2006). DOI 10.1186/1741-7015-4-38

    work page doi:10.1186/1741-7015-4-38 2006

  27. [27]

    Provenzano, P.P., Inman, D.R., Eliceiri, K.W., Knittel, J.G., Yan, L., Rueden, C.T., White, J.G., Keely, P.J.: Collagen density promotes mammary tumour initiation and progression. BMC Med. 6(11) (2008). DOI 10.1186/1741-7015-6-11

    work page doi:10.1186/1741-7015-6-11 2008

  28. [28]

    Ramis-Conde, I., Chaplain, M.A.J., Anderson, A.R.A.: Mathematical modelling of tu- mour invasion and metastasis. Math. Comput. Model. 47(5-6), 533–545 (2008)

    work page 2008

  29. [29]

    Matrix Biol

    Ruangpanit, N., Chan, D., Holmbeck, K., Birkedal-Hansen, H., Polarek, J., Yang, C., Bateman, J.F., Thompson, E.W.: Gelatinase a (mmp-2) activation by skin fibroblasts: dependence on mt1-mmp expression and fibrillar collagen form. Matrix Biol. 20(3), 193–203 (2001). DOI 10.1016/S0945-053X(01)00135-4

    work page doi:10.1016/s0945-053x(01)00135-4 2001

  30. [30]

    Cancer Metast

    Seiki, M., Yana, I.: Roles of pericellular proteolysis by membrane type-1 matrix metal- loproteinase in cancer invasion and angiogenesis. Cancer Metast. Rev. 94(7), 569–574 (2003)

    work page 2003

  31. [31]

    Two- scale Moving Boundary Dynamics of Cancer Invasion: Heterotypic Cell Popula- tions Evolution in Heterogeneous ECM, pp

    Shuttleworth, R., Trucu, D.: Cell Movement Modelling and Applications, chap. Two- scale Moving Boundary Dynamics of Cancer Invasion: Heterotypic Cell Popula- tions Evolution in Heterogeneous ECM, pp. 1–26. Springer (2018). DOI 10.1007/ 978-3-319-96842-1

    work page 2018

  32. [32]

    Shuttleworth, R., Trucu, D.: Multiscale dynamics of a hetertypic cancer cell population within a fibrous extracellular matrix (2019)

    work page 2019

  33. [33]

    Shuttleworth, R., Trucu, D.: Multiscale modelling of fibres dynamics and cell adhesion within moving boundary cancer invasion. Bull. Math. Biol. (2019). DOI 10.1007/ s11538-019-00598-w

    work page 2019

  34. [34]

    Szyma´ nska, Z., Morales-Rodrigo, C., Lachowicz, M., Chaplain, M.A.J.: Mathematical modelling of cancer invasion of tissue: the role and effect of nonlocal interactions. Math. Model. Meth. Appl. Sci. 19(2), 257–281 (2009)

    work page 2009

  35. [35]

    Tam, E.M., Moore, T.R., Butler, G.S., Overall, C.M.: Characterization of the distint collagen binding, helicase and cleavage mechanisms of matrix metalloproteinases 2 and 14 (gelatinase a and mt1-mmp). J. Biol. Chem. 279(41), 43,336–43,344 (2004)

    work page 2004

  36. [36]

    Breast Cancer Res

    Thomson, E.W., Yu, M., Bueno, J., Jin, L., Maiti, S.N., Palao-Marco, F.L., Pulyaeva, H., Tamborlane, J.W., Tirgari, R., et al., I.W.: Collagen induced mmp-2 activation in human breast cancer. Breast Cancer Res. Treat. 31(2-3), 357–370 (1994)

    work page 1994

  37. [37]

    Multiscale Model

    Trucu, D., Lin, P., Chaplain, M.A.J., Wang, Y.: A multiscale moving boundary model arising in cancer invasion. Multiscale Model. Simul. 11(1), 309–335 (2013)

    work page 2013

  38. [38]

    Matrix Biol

    Van Doren, S.R.: Matrix metallopreinase interactions with collagen and elastin. Matrix Biol. 44-46, 224–231 (2015). DOI 10.1016/j.matbio.2015.01.005

    work page doi:10.1016/j.matbio.2015.01.005 2015

  39. [39]

    Wijnhoven, B.J., Dinjens, W.N., Pignatelli, M.: E-cadherin-catenin cell-cell adhesion complex and human cancer. Brit. J. Surg. 87(8), 992–1005 (2000)

    work page 2000

  40. [40]

    Wolf, K., te Lindert, M., Krause, M., Alexander, S., te Riet, J., Willis, A.L., Hoffman, R.M., Figdor, C.G., Weiss, S.J., Friedl, P.: Physical limits of cell migration: Control by ECM space and nuclear deformation and tuning by proteolysis and traction force. J. Cell. Biol. 201(7), 1069–1084 (2013). DOI 10.1083/jcb.201210152

    work page doi:10.1083/jcb.201210152 2013

  41. [41]

    Springer-Verlag (1980)

    Yosida, K.: Functional Analysis, 6th edn. Springer-Verlag (1980)

    work page 1980

  42. [42]

    Zigrino, P., Drescher, C., Mauch, C.: Collagen-induced proMMP-2 activation by MT1- MMP in human dermal fibroblasts and the possible role of α2β1 integrins. Euro. J. Cell. Biol. 80, 68–77 (2001)

    work page 2001