\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

An agent-based model for elasto-plastic mechanical interactions between cells, basement membrane and extracellular matrix

Abstract Related Papers Cited by
  • The basement membrane (BM) and extracellular matrix (ECM) play critical roles in developmental and cancer biology, and are of great interest in biomathematics. We introduce a model of mechanical cell-BM-ECM interactions that extends current (visco)elastic models (e.g. [8,16]), and connects to recent agent-based cell models (e.g. [2,3,20,26]). We model the BM as a linked series of Hookean springs, each with time-varying length, thickness, and spring constant. Each BM spring node exchanges adhesive and repulsive forces with the cell agents using potential functions. We model elastic BM-ECM interactions with analogous ECM springs. We introduce a new model of plastic BM and ECM reorganization in response to prolonged strains, and new constitutive relations that incorporate molecular-scale effects of plasticity into the spring constants. We find that varying the balance of BM and ECM elasticity alters the node spacing along cell boundaries, yielding a nonuniform BM thickness. Uneven node spacing generates stresses that are relieved by plasticity over long times. We find that elasto-viscoplastic cell shape response is critical to relieving uneven stresses in the BM. Our modeling advances and results highlight the importance of rigorously modeling of cell-BM-ECM interactions in clinically important conditions with significant membrane deformations and time-varying membrane properties, such as aneurysms and progression from in situ to invasive carcinoma.
    Mathematics Subject Classification: 65C20, 74B99, 74C99, 74D99, 92C05, 92C10, 74L15.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    M. Aumailley, Structure and function of basement membrane components: laminin, nidogen, collagen IV, and BM-40, Advances in Molecular and Cell Biology, 6 (1993), 183-206.doi: 10.1016/S1569-2558(08)60202-7.

    [2]

    P. Buske, J. Galle, N. Barker, G. Aust, H. Clevers and M. Loeffler, A comprehensive model of the spatio-temporal stem cell and tissue organisation in the intestinal crypt, PLoS Comput. Biol., 7 (2011), e1001045.

    [3]

    P. Buske, J. Przybilla, M. Loeffler, N. Sachs, T. Sato, H. Clevers and J. GalleOn the biomechanics of stem cell niche formation in the gut: modelling growing organoids, FEBS J. (2012, in press). doi: 10.1111/j.1742-4658.2012.08646.x.

    [4]

    L. M. Coussens and Z. Werb, Matrix metalloproteinases and the development of cancer, Chemistry and Biology, 3 (1996), 895-904.

    [5]

    L. M. Coussens, C. L. Tinkle, D. Hanahan and Z. Werb, MMP-9 supplied by bone marrow-derived cells contributes to skin carcinogenesis, Cell, 103 (2000), 481-490.

    [6]

    J. C. Dallon and H. G. Othmer, How cellular movement determines the collective force generated by the dictyostelium discoideum slug, J. Theor. Biol., 231 (2004), 203-222.

    [7]

    G. D'Antonio, L. Preziosi and P. Macklin, A multiscale hybrid discrete-continuum model of matrix metalloproteinase transport and basement membrane-extracellular matrix degradation, in preparation (2012).

    [8]

    S. J. Dunn, A. G. Flethcer, S. J. Chapman, D. J. Gavaghan and J. M. Osborne, Modelling the role of the basement membrane beneath a growing epithelial monolayer, J. Theor. Biol., 298 (2012), 82-91.

    [9]

    S. J. Franks, H. M. Byrne, H. S. Mudhar, J. C. E. Underwood and C. E. Lewis, Mathematical modelling of comedo ductal carcinoma in situ of the breast, Math. Med. Biol., 20 (2003), 277-308.

    [10]

    S. J. Franks, H. M. Byrne, J. C. E. Underwood and C. E. Lewis, Biological inferences from a mathematical model of comedo ductal carcinoma in situ of the breast, J. Theor. Biol., 232 (2005), 523-543.

    [11]

    P. Ghysels, G. Samaey, B. Tijskens, P. Van Liedekerke H. Ramon and D. Roose, Multi-scale simulation of plant tissue deformation using a model for individual cell mechanics, Phys. Biol., 6 (2009).

    [12]

    J. Glazier and F. Graner, Simulation of the differential adhesion driven rearrangement of biological cells, Phys. Rev. E, 47 (1993), 2128-2154.doi: 10.1103/PhysRevE.47.2128.

    [13]

    F. Graner and J. Glazier, Simulation of biological cell sorting using a two-dimensional extended Potts model, Phys. Rev. Lett., 69 (1992), 2013-2016.doi: 10.1103/PhysRevLett.69.2013.

    [14]

    T. Hagemann, S. C. Robinson, M. Schulz, L. Trümper, F. R. Balkwill and C. Binder, Enhanced invasiveness of breast cancer cell lines upon co-cultivation with macrophages is due to TNF-$\alpha$ dependent up-regulation of matrix metalloproteinases, Carcinogenesis, 25 (2004), 1543-1549.

    [15]

    S. Jodele, L. Blavier, J. M. Yoon and Y. A. DeClerck, Modifying the soil to affect the seed: role of stromal-derived matrix metalloproteinases in cancer progression, Cancer and Metastasis Review, 25 (2006), 35-43.

    [16]

    Y. Kim, M. A. Stolarska and H.G . Othmer, The role of the microenvironment in tumor growth and invasion, Progress in Biophysics and Molecular Biology, 106 (2011), 353-379.doi: 10.1016/j.pbiomolbio.2011.06.006.

    [17]

    R. C. Liddington, Mapping out the basement membrane, Natural Structural Biology, 8 (2001), 573-574.

    [18]

    P. Macklin, Biological background, in "Multiscale Modeling of Cancer: An Integrated Experimental and Mathematical Modeling Approach'' (eds. V. Cristini and J. S. Lowengrub), Cambridge University Press (2010), 8-23.doi: 10.1017/CBO9780511781452.003.

    [19]

    P. Macklin, M. E. Edgerton, J. S. Lowengrub and V. Cristini, Discrete cell modeling, in "Multiscale Modeling of Cancer: An Integrated Experimental and Mathematical Modeling Approach'' (eds. V. Cristini and J. S. Lowengrub), Cambridge University Press (2010), 88-122.doi: 10.1017/CBO9780511781452.007.

    [20]

    P. Macklin, M. E. Edgerton, A. M. Thompson and V. Cristini, Patient-calibrated agent-based modelling of ductal carcinoma in situ (DCIS): From microscopic measurements to macroscopic predictions of clinical progression, J. Theor. Biol., 301 (2012), 122-140.doi: 10.1016/j.jtbi.2012.02.002.

    [21]

    P. Macklin, J. Kim, G. Tomaiuolo, M. E. Edgerton and V. Cristini, Agent-based modeling of ductal carcinoma in situ: application to patient-specific breast cancer modeling, in "Computational Biology: Issues and Applications in Oncology'' (ed. T. Pham), Springer (2009), 77-112.doi: 10.1007/978-1-4419-0811-7_4.

    [22]

    P. Macklin, S. Mumenthaler and J. Lowengrub, Modeling multiscale necrotic and calcified tissue biomechanics in cancer patients: application to ductal carcinoma in situ (DCIS), in "Multiscale Computer Modeling in Biomechanics and Biomedical Engineering'' (ed. A. Gefen), Springer (2013), in press.doi: 10.1007/8415_2012_150.

    [23]

    K. A. Norton, M. Wininger, G. Bhanot, S. Ganesan, N. Barnard and T. Shinbrot, A 2D mechanistic model of breast ductal carcinoma in situ (DCIS). Morphology and progression, J. Theor. Biol., 263 (2010), 393-406.

    [24]

    N. Poplawski, U. Agero, J. Gens, M. Swat, J. Glazier and A. Anderson, Front instabilities and invasiveness of simulated avascular tumors, Bull. Math. Biol., 71 (2009), 1189-1227.doi: 10.1007/s11538-009-9399-5.

    [25]

    L. Preziosi, D. Ambrosi and C. Verdier, An elasto-visco-plastic model of cell aggregates, J. Theor. Biol., 262 (2010), 35-47.doi: 10.1016/j.jtbi.2009.08.023.

    [26]

    I. Ramis-Conde, M. A. J. Chaplain and A. R. A. Anderson, Mathematical modelling of cancer cell invasion of tissue, Math. Comp. Model., 47 (2006), 533-545.

    [27]

    B. Ribba, O. Saut, T. Colin, D. Bresch, E. Grenier and J. P. Boissel, A multiscale mathematical model of avascular tumor growth to investigate the therapeutic benefit of anti-invasive agents, J. Theor. Biol., 243 (2006), 532-541.

    [28]

    S. A. Sandersius and T. J. Newman, Modeling cell rheology with the subcellular element model, Phys. Biol., 5 (2008), 015002.

    [29]

    S. A. Sandersius, C. J. Weijer and T. J. Newman, Emergent cell and tissue dynamics from subcellular modeling of active processes, Phys. Biol., 8 (2011), 045007.

    [30]

    M. Scianna and L. Preziosi, Multiscale developments of cellular Potts models, Multiscale Model. Sim., 10 (2012), 342-382.doi: \%2010.1137/100812951.

    [31]

    M. Scianna and L. Preziosi, "Cellular Potts Models: Multiscale Developments and Biological Applications,'' CRC/Academic Press, 2012.

    [32]

    M. Scianna, L. Preziosi and K. WolfA Cellular Potts Model simulating cell migration on and in matrix environments, Math. Biosci. Eng., (2013, in press).

    [33]

    C. Verdier, J. Etienne, A. Duperray and L. Preziosi, Review: rheological properties of biological materials, Comptes Rendus Physique, 10 (2009), 790-811.doi: 10.1016/j.crhy.2009.10.003.

    [34]

    Z. Zeng, A. M. Cohen and J. G. Guillem, Loss of basement membrane type IV collagen is associated with increased expression of metalloproteinases 2 and 9 (MMP-2 and MMP-9) during human colorectal tumorigenesis, Carcinogenesis, 20 (1999), 749-755.doi: 10.1093/carcin/20.5.749.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(51) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return