Stochastic cellular automata model of cell migration, proliferation and differentiation: validation with in vitro cultures of muscle satellite cells. (English) Zbl 1397.92093
Summary: Cell migration and proliferation has been modelled in the literature as a process similar to diffusion. However, using diffusion models to simulate the proliferation and migration of cells tends to create a homogeneous distribution in the cell density that does not correlate to empirical observations. In fact, the mechanism of cell dispersal is not diffusion. Cells disperse by crawling or proliferation, or are transported in a moving fluid. The use of cellular automata, particle models or cell-based models can overcome this limitation. This paper presents a stochastic cellular automata model to simulate the proliferation, migration and differentiation of cells. These processes are considered as completely stochastic as well as discrete. The model developed was applied to predict the behaviour of in vitro cell cultures performed with adult muscle satellite cells. Moreover, non homogeneous distribution of cells has been observed inside the culture well and, using the above mentioned stochastic cellular automata model, we have been able to predict this heterogeneous cell distribution and compute accurate quantitative results. Differentiation was also incorporated into the computational simulation. The results predicted the myotube formation that typically occurs with adult muscle satellite cells. In conclusion, we have shown how a stochastic cellular automata model can be implemented and is capable of reproducing the in vitro behaviour of adult muscle satellite cells.
MSC:
| 92C17 | Cell movement (chemotaxis, etc.) |
| 92C37 | Cell biology |
| 68Q80 | Cellular automata (computational aspects) |
| 92C15 | Developmental biology, pattern formation |
Keywords:
random-walk; muscle satellite cells; stochastic cellular automata model; proliferation-migration-differentiationReferences:
| [1] | Alarcón, T.; Byrne, H.M.; Maini, P.K., A cellular automaton model for tumour growth in inhomogeneous environment, J. theor. biol., 225, 257-274, (2003) · Zbl 1464.92060 |
| [2] | Ambrose, E.J., The movements of fibrocytes, Exp. cell res., 8, 54-73, (1961) |
| [3] | Bailón-Plaza, A.; van der Meulen, M.C.H., Beneficial effects of moderate, early loading and adverse effects of delayed or excessive loading on bone healing, J. biomech., 36, 1069-1077, (2003) |
| [4] | Bischoff, R.; Heintz, C., Enhancement of skeletal muscle regeneration, Dev. dyn., 201, 41-54, (1994) |
| [5] | Börner, U.; Deutsch, A.; Reichenback, H.; Bär, M., Rippling patterns in aggregates of myxobacteria arise from cell – cell collisions, Phys. rev. lett., 89, 7, 078101, (2002) |
| [6] | Boyle, C.J.; Lennon., A.B.; Early, M.; Kelly, D.J.; Lally, C.; Prendergast, P.J., Computational simulation methodologies for mechanobiological modeling: a cell-centred approach to neointima development in stents, Philos. trans. R. soc. A, 368, 2919-2935, (2010) |
| [7] | Byrne, D.P.; Lacroix, D.; Planell, J.A.; Kelly, D.J.; Prendergast, P.J., Simulation of tissue differentiation in a scaffold as a function of porosity, Young’s modulus and dissolution rate: application of mechanobiological models in tissue engineering, Biomaterials, 28, 5544-5554, (2007) |
| [8] | Byrne, H.; Drasdo, D., Individual-based and continuum models of growing cell populations: a comparison, J. math. biol., 58, 657-687, (2009) · Zbl 1311.92060 |
| [9] | Carter, S.B., “principles of cell motillity: the direction of cell movement and cancer invasion, Nature, 208, 16, 1183-1187, (1965) |
| [10] | Charge, S.B.; Rudnicki, M.A., Cellular and molecular regulation of muscle regeneration, Physiol. rev., 84, 1, 209-238, (2004) |
| [11] | Chakravarthy, M.V.; Davis, B.S.; Booth, F.W., IGF-I restores satellite cell proliferative potential in immobilized old skeletal muscle, J. appl. physiol., 89, 4, 1365-1379, (2000) |
| [12] | Checa, S.; Prendergast, P.J., Effect of cell seeding and mechanical loading on vascularisation and tissue formation inside a scaffold: a mechano-biological model using a lattice approach to simulate cell activity, J. biomech., 43, 961-968, (2010) |
| [13] | Chopard, B.; Ouared, R.; Deutsch, A.; Hatzikirou, H.; Wolf-Gladrow, D., Lattice-gas cellular automaton models for biology: from fluids to cells, Acta biotheor., 58, 4, 329-340, (2010) |
| [14] | Deutsch, A.; Dormann, S., Cellular automaton modeling of biological pattern formation, (2005), Birkhauser Boston · Zbl 1154.37007 |
| [15] | Drasdo, D.; Höhme, S., A single-cell-based model of tumor growth in vitro: monolayers and spheroids, Phys. biol., 2, 133-147, (2005) |
| [16] | Hatzikirou, H.; Deutsch, A., Cellular automata as microscopic models of cell migration in heterogeneous environments, Curr. top. dev. biol., 81, 401-434, (2008) |
| [17] | Hawke, T.J.; Garry, D.J., Myogenic satellite cells: physiology to molecular biology, J. appl. physiol., 91, 2, 534-551, (2001) |
| [18] | Henzé, M.L.; Collin, O.; Terrier, E.; Lennon-Doménil, A.M.; Piel, M., Cell migration in confinement: microchannel-based assay, Methods mol. biol., 769, 415-434, (2011) |
| [19] | Hoffmann, M.; Kuska, J.P.; Zscharnack, M.; Loeffler, M.; Galle, J., Spatial organization of mesenchymal stem cells in vitro-results from a new individual cell-based model with podia, Plos one, 6, 7, e21960, (2011) |
| [20] | Hwang, M.; Garbey, M.; Berceli, S.A.; Tran-Son-Tay, R., Rule-base simulation of multicellular biological systems—a review of modeling techniques, Cell. mol. bioeng., 2, 3, 285-294, (2009) |
| [21] | Kalhovde, J.M.; Jerkovic, R.; Sefland, I.; Cordonnier, C.; Calabria, E.; Schiaffino, S.; Lomo, T., “fast“ and “slow” muscle fibres in hindlimb muscles of adult rats regenerate from intrinsically different satellite cells, J. physiol., 562, 847-857, (2005) |
| [22] | Khayyeri, H.; Checa, S.; Tägil, M.; Aspenberg, P.; Prendergast, P.J., Variability observed in mechano-regulated in vivo tissue differentiation can be explained by variation in cell mechano-sensitivity, J. biomech., 44, 1051-1058, (2011) |
| [23] | Khayyeri., H.; Checa, S.; Tägil, M.; O’Brien, F.J.; Prendergast, P.J, Tissue differentiation in an in vivo bioreactor: in silico investigations of scaffold stiffness, J. mater. sci. mater. med., 21, 2331-2336, (2010) |
| [24] | Khayyeri, H.; Checa, S.; Tägil, M.; Prendergast, P.J., Corroboration of mechanobiological simulations of tissue differentiation in an in vivo bone chamber using a lattice-modeling approach, J. orthop. res., 27, 12, 1659-1666, (2009) |
| [25] | Lacroix, D.; Prendergast, P.J.; Li, G.; Marsh, D., Biomechanical model to simulate tissue differentiation and bone regeneration application to frature healing, Med. biol. eng. comput., 40, 14-21, (2002) |
| [26] | Landmann, K.A.; Fernando, A.E.; Zhang, D.; Newgreen, D.F., Building stable chains with motile agents: insights into the morphology of enteric neural crest cell migration, J. theor. biol., 276, 1, 250-268, (2011) · Zbl 1405.92048 |
| [27] | Lanza, R.; Thomas, E.D.; Thomson, J.; Pedersen, R., Essentials of stem cell biology, (2005), Academic Press New York |
| [28] | Longo, D.; Peirce, S.M.; Skalak, T.; Davidson, L.; Marsden, M.; Dzamba, B.; DeSimone, D.W., Multicellular computer simulation of morphogenesis: blastocoel roof thinning and matrix assembly in xenopus laevis, Dev. biol., 271, 210-222, (2004) |
| [29] | Manzano, R.; Toivonen, J.M.; Calvo, A.C.; Muñoz, M.J.; Zaragoza, P.; Osta, R., Housekeeping gene expression in myogenic cell cultures from neurodegeneration and denervation animal models, Biochem. biophys. res. commun., 407, 4, 758-763, (2011) |
| [30] | Manzano, R.; Toivonen, J.M.; Calvo, A.C.; Miana-Mena, F.J.; Zaragoza, P.; Muñoz, M.J.; Montarras, D.; Osta, R., Sex, Q1 fiber-type, and age dependent in vitro proliferation of mouse muscle satellite cells, J. cell. biochem., 112, 10, 2825-2836, (2011) |
| [31] | Palsson, B.O., Bhatia, S.N., 2004. Tissue Engineering, Pearson Prentice Hall Bioengineering, US.; Palsson, B.O., Bhatia, S.N., 2004. Tissue Engineering, Pearson Prentice Hall Bioengineering, US. |
| [32] | Patterson, M.F.; Stephenson, G.M.M.; Stephenson, D.G., Denervation produces different single fiber phenotypes in fast- and slow-twitch hindlimb muscles of the rat, Am. J. physiol. cell physiol., 291, 518-528, (2006) |
| [33] | Pradat, P.F.; Barani, A.; Wanschitz, J.; Dubourg, O.; Lombès, A.; Bigot, A.; Mouly, V.; Bruneteau, G.; Salachas, F.; Lenglet, T.; Meininger, V.; Butler-Browne, G., Abnormalities of satellite cells function in amyotrophic lateral sclerosis, Amyotroph. lateral scler., 12, 4, 264-271, (2011) |
| [34] | Pérez, M.A.; Prendergast, P.J., Random-walk models of cell dispersal included in mechanobiological simulations of tissue differentiation, J. biomech., 40, 2244-2253, (2007) |
| [35] | Peirce, S.M.; Van Gieson, E.J.; Skalak, T.C., Multicellular simulation predicts microvascular patterning and in silico tissue assembly, Faseb j., 18, 6, 731-733, (2004) |
| [36] | Sandino, C.; Checa, S.; Prendergast, P.J.; Lacroix, D., Simulation of angiogenesis and cell differentiation in cap scaffold subjected to compressive strains using a lattice modelling approach, Biomaterials, 31, 2446-2452, (2010) |
| [37] | Siegel, A.L.; Atchison, K.; Fisher, K.E.; Davis, G.D.; Cornelison, D.D.V., 3D timelaspse analysis of muscle satellite cell motility, Stem cell, 27, 2527-2538, (2009) |
| [38] | Simpson, M.J.; Merrifield, A.; Landman, K.A.; Hughes, B.D., Simulating invasion with cellular automata: connecting cell-scale and population-scale properties, Phys. rev. E stat. nonlinear soft matter phys., 76, 2 Pt 1, 021918, (2007) |
| [39] | Stokes, C.L.; Lauffenburger, D.A., Migration of individual microvessel endothelial cells: stochastic model and parameter measurement, J. cell sci., 99, 419-430, (1991) |
| [40] | Terranova, V.P.; Diflorio, R.; Lyall, R.M.; Hic, S.; Friesel, R.; Maciag, T., Human endothelial cells are chemotactic to endothelial cell growth factor and heparin, J. cell sci., 101, 2330-2334, (1985) |
| [41] | Turner, S.; Sherrat, J.A., Intercellular adhesion and cancer invasion: a discrete simulation using the extended Potts model, J. theor. biol., 216, 85-100, (2002) |
| [42] | Zahedmanesh, H.; Lally, C., A multiscale mechanobiological modeling framework using agent-based models and finite element analysis: application to vascular tissue engineering, Biomech. model. mechanobiol., 11, 3-4, 363-377, (2012) |
| [43] | Zierath, J.R.; Hawley, J.A., Skeletal muscle fiber type: influence on contractile and metabolic properties, Plos biol., 2, 10, e348, (2004) |
| [44] | Zohar, R.; Cheifetz, S.; McCulloch, C.A.G.; Sodek, J., Analysis of intracellular osteopontin as a marker of osteoblastic cell differentiation and mesenchymal cell migration, Eur. J. oral sci., 106, 401-407, (1998) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
