Quantifying the mechanical micro-environment during three-dimensional cell expansion on microbeads by means of individual cell-based modelling

Controlled in vitro three-dimensional cell expansion requires culture conditions that optimise the biophysical micro-environment of the cells during proliferation. In this study, we propose an individual cell-based modelling platform for simulating the mechanics of cell expansion on microcarriers. The lattice-free, particle-based method considers cells as individual interacting particles that deform and move over time. The model quantifies how the mechanical micro-environment of individual cells changes during the time of confluency. A sensitivity analysis is performed, which shows that changes in the cell-specific properties of cell–cell adhesion and cell stiffness cause the strongest change in the mechanical micro-environment of the cells. Furthermore, the influence of the mechanical properties of cells and microbead is characterised. The mechanical micro-environment is strongly influenced by the adhesive properties and the size of the microbead. Simulations show that even in the absence of strong biological heterogeneity, a large heterogeneity in mechanical stresses can be expected purely due to geometric properties of the culture system. Supplemental data for this article can be accessed online.

[1]  Ranjna C Dutta,et al.  Cell-interactive 3D-scaffold; advances and applications. , 2009, Biotechnology advances.

[2]  L. Feinendegen,et al.  Cellular and nuclear volume of human cells during the cell cycle , 1981, Radiation and environmental biophysics.

[3]  K. Rejniak,et al.  Current trends in mathematical modeling of tumor–microenvironment interactions: a survey of tools and applications , 2010, Experimental biology and medicine.

[4]  R. Hochmuth,et al.  Micropipette aspiration of living cells. , 2000, Journal of biomechanics.

[5]  Luigi Preziosi,et al.  Contact inhibition of growth described using a multiphase model and an individual cell based model , 2009, Appl. Math. Lett..

[6]  Jianping Fu,et al.  Cell shape and substrate rigidity both regulate cell stiffness. , 2011, Biophysical journal.

[7]  T. Meyer,et al.  A new method for the 3‐D in vitro growth of human RT112bladder carcinoma cells using the alginate culture technique , 1994, Biology of the cell.

[8]  G Mirams,et al.  A computational study of discrete mechanical tissue models , 2009, Physical biology.

[9]  Manuel Théry,et al.  The Universal Dynamics of Cell Spreading , 2007, Current Biology.

[10]  Richard T. Lee,et al.  Cell mechanics and mechanotransduction: pathways, probes, and physiology. , 2004, American journal of physiology. Cell physiology.

[11]  Petros Lenas,et al.  Developmental engineering: a new paradigm for the design and manufacturing of cell-based products. Part II: from genes to networks: tissue engineering from the viewpoint of systems biology and network science. , 2009, Tissue engineering. Part B, Reviews.

[12]  Jean Paul Thiery,et al.  Johnson-Kendall-Roberts theory applied to living cells. , 2005, Physical review letters.

[13]  J. De Baerdemaeker,et al.  Discrete element modelling for process simulation in agriculture , 2003 .

[14]  Elliot L. Botvinick,et al.  Visualizing the mechanical activation of Src , 2005, Nature.

[15]  Zhilin Qu,et al.  Coordination of cell growth and cell division: a mathematical modeling study , 2004, Journal of Cell Science.

[16]  W. Kruskal,et al.  Use of Ranks in One-Criterion Variance Analysis , 1952 .

[17]  D. Leckband,et al.  Intermolecular forces in biology , 2001, Quarterly Reviews of Biophysics.

[18]  Beth L. Pruitt,et al.  E-cadherin is under constitutive actomyosin-generated tension that is increased at cell–cell contacts upon externally applied stretch , 2012, Proceedings of the National Academy of Sciences.

[19]  D. Ingber,et al.  Cellular mechanotransduction: putting all the pieces together again , 2006, FASEB journal : official publication of the Federation of American Societies for Experimental Biology.

[20]  S. Hoehme,et al.  On the Role of Physics in the Growth and Pattern Formation of Multi-Cellular Systems: What can we Learn from Individual-Cell Based Models? , 2007 .

[21]  Martin Hoffmann,et al.  Individual fates of mesenchymal stem cells in vitro , 2010, BMC Systems Biology.

[22]  Y. Jiao,et al.  Adhesion energy of receptor-mediated interaction measured by elastic deformation. , 1999, Biophysical journal.

[23]  K. Kendall,et al.  Surface energy and the contact of elastic solids , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[24]  Johnson,et al.  An Adhesion Map for the Contact of Elastic Spheres , 1997, Journal of colloid and interface science.

[25]  David J. Mooney,et al.  Harnessing Traction-Mediated Manipulation of the Cell-Matrix Interface to Control Stem Cell Fate , 2010, Nature materials.

[26]  Smadar Cohen,et al.  Microenvironment design for stem cell fate determination. , 2012, Advances in biochemical engineering/biotechnology.

[27]  Wei-Shou Hu,et al.  Culture systems for pluripotent stem cells. , 2005, Journal of bioscience and bioengineering.

[28]  Zhibing Zhang,et al.  Strain-dependent viscoelastic behaviour and rupture force of single chondrocytes and chondrons under compression , 2009, Biotechnology Letters.

[29]  J. Fredberg,et al.  Mechanical waves during tissue expansion , 2012, Nature Physics.

[30]  D. Drasdo,et al.  Impact of oxygen environment on mesenchymal stem cell expansion and chondrogenic differentiation , 2009, Cell proliferation.

[31]  S. Sen,et al.  Matrix Elasticity Directs Stem Cell Lineage Specification , 2006, Cell.

[32]  P. Janmey,et al.  Tissue Cells Feel and Respond to the Stiffness of Their Substrate , 2005, Science.

[33]  Lang Li,et al.  Non-compartment model to compartment model pharmacokinetics transformation meta-analysis – a multivariate nonlinear mixed model , 2010, BMC Systems Biology.

[34]  Ning Wang,et al.  Rapid signal transduction in living cells is a unique feature of mechanotransduction , 2008, Proceedings of the National Academy of Sciences.

[35]  J. Fredberg,et al.  Collective cell guidance by cooperative intercellular forces , 2010, Nature materials.

[36]  S. Thrun,et al.  Substrate Elasticity Regulates Skeletal Muscle Stem Cell Self-Renewal in Culture , 2010, Science.

[37]  Liesbet Geris,et al.  Towards a quantitative understanding of oxygen tension and cell density evolution in fibrin hydrogels. , 2011, Biomaterials.

[38]  Pedro Moreo,et al.  Modeling mechanosensing and its effect on the migration and proliferation of adherent cells. , 2008, Acta biomaterialia.

[39]  J. Galle,et al.  From single cells to tissue architecture—a bottom-up approach to modelling the spatio-temporal organisation of complex multi-cellular systems , 2009, Journal of mathematical biology.

[40]  D. Mooney,et al.  Alginate: properties and biomedical applications. , 2012, Progress in polymer science.

[41]  John F. Brady,et al.  STOKESIAN DYNAMICS , 2006 .

[42]  Kejing He,et al.  Multigrid contact detection method. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  John W Haycock,et al.  3D cell culture: a review of current approaches and techniques. , 2011, Methods in molecular biology.

[44]  F. Sachs,et al.  Genetically encoded force sensors for measuring mechanical forces in proteins. , 2011, Communicative & integrative biology.

[45]  Liesbet Geris,et al.  Relating the Chondrocyte Gene Network to Growth Plate Morphology: From Genes to Phenotype , 2012, PloS one.

[46]  D. Stamenović,et al.  Cell prestress. I. Stiffness and prestress are closely associated in adherent contractile cells. , 2002, American journal of physiology. Cell physiology.

[47]  D. Ingber Tensegrity I. Cell structure and hierarchical systems biology , 2003, Journal of Cell Science.

[48]  Alexander R. A. Anderson,et al.  Single-Cell-Based Models in Biology and Medicine , 2007 .