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Agent-based modelling of epithelial cells

Agent-based modelling of epithelial cells. An example of rule formulation and extension Dr Dawn Walker, University of Sheffield, UK. What determines cell behaviour?. Environmental factors Extracellular matrix Calcium concentration Growth medium. Other cells Intercellular bonds

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Agent-based modelling of epithelial cells

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  1. Agent-based modelling of epithelial cells An example of rule formulation and extension Dr Dawn Walker, University of Sheffield, UK

  2. What determines cell behaviour? • Environmental factors • Extracellular matrix • Calcium concentration • Growth medium • Other cells • Intercellular bonds • Intercellular signalling • Genetic ‘rules’ • Cell cycle • Differentiation

  3. Modelling strategy FOR EVERY CELL IN TURN Execute cell behaviour rules AGENT MODEL CLOCK Adjust position of all cells to ensure no overlap PHYSICAL MODEL Iterative coupled ‘agent – physics’ model

  4. CELL CYCLE RULES BONDING RULES SPREADING RULES APOPTOSIS RULES MOTILITY RULES EQUILIBRIATE CELL POSITIONS DUE TO GROWTH, MICRATION ETC. For all cells together…. Model Implementation For each cell in turn…. CELL COMMUNICATION

  5. Cell cycle control – the model G1GROWTH PHASE M G2 G0 Ref- general biological knowledge Publications of urothelial cell proliferation time G1 S

  6. Cell cycle control – the model G1GROWTH PHASE M G2 G0 Ref- general biological knowledge G1 S

  7. GROWTH FACTORS? CONTACT INHIBITION? (4 or more bonds) CELL SPREAD? Cell cycle control – the model G1-G0 checkpoint M G2 G0 G1 General biological knowledge Ref: Nelson & Chen 2002, FEBS Letters 514 pp 238-242 S

  8. GROWTH FACTORS? CONTACT INHIBITION? (4 or more bonds) QUIESCENCE CELL SPREAD? X Cell cycle control – the model G0QUIESCENT PHASE M G2 G0 G1 S

  9. GROWTH FACTORS? CONTACT INHIBITION? (4 or more bonds) x CELL SPREAD? Cell cycle control – the model G1GROWTH PHASE M G2 G0 G1 S

  10. Cell cycle control – the model S PHASE – (CHROMOSOME REPLICATION) M G2 G0 G1 S

  11. Cell cycle control – the model G2PHASE – (HOUSEKEEPING) M G2 G0 G1 S

  12. Cell cycle control – the model M M PHASE - DIVISION G2 G0 G1 S

  13. 1 Sep. = 0m 0.9 Sep. = 1m 0.8 Sep. = 5m 0.7 0.6 0.5 [Ca2+] Binding Probability 0.4 0.3 Sep 0.2 0.1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2.0 Ca2+ ion concentration Bonding Rules • Stochastic process governed by • Cell edge separation • Calcium ion concentration Ref: Baumgartner et al, 2000, Cadherin interaction probed by atomic force microscopy PNAS 97(8) 4005-4010.

  14. Migration parameters Urothelial cells in low Ca2+ (0.09mM)

  15. l Physical model F=ma  l

  16. Ca2+ dependent behaviour -In Vitro vs. In Virtuo • Intercellular bonds require the presence of Ca2+ ions • In Ca2+ conc.> 1mM many bonds are formed • Cells with several intercellular bonds become contact-inhibited (stop cycling) • WHAT IS THE EFFECT OF Ca2+ ON GROWTH AND PROLIFERATION?

  17. = STEM CELL = TRANSIT =MITOTIC CELL =QUIESCENT AMPLIFYING CELL (G0) CELL Ca2+ = 2mM Ca2+ = 0.09mM Model Simulations – urothelial monolayer growth Low Ca2+ (0.09mM) Physiological Ca2+ (2mM) NO. CELLS ITERATION NUMBER

  18. = STEM CELL = TRANSIT =MITOTIC CELL =QUIESCENT AMPLIFYING CELL (G0) CELL Ca2+ = 2mM Ca2+ = 0.09mM Model Simulations – urothelial monolayer growth Low Ca2+ (0.09mM) Physiological Ca2+ (2mM) NO. CELLS ITERATION NUMBER

  19. In virtuo wound healing (urothelium) Physiological Ca2+ (2mM) Low Ca2+ (0.09mM)

  20. In virtuo wound healing (urothelium) Physiological Ca2+ (2mM) Low Ca2+ (0.09mM)

  21. In Vitro wound healing (urothelium) Physiological Ca2+ Low Ca2+

  22. 2500 2000 120 Ca2+ conc.=2.0mM Ca2+ conc.=0.09mM 1500 100 80 1000 Total cell number 60 500 40 20 0 0 10 20 30 40 50 60 70 80 0 Simulation time in hours In vitro vs. in virtuo population growth (urothelium) Low Calcium Physiological Calcium Cell number / x10E4 per mL Day 1 Day 3 Day 5 Day 7 Day 9 In vitro model Computational model

  23. Rule extension – cell contact and proliferation Hypotheses: • 1. Short range growth factor diffusive signal • 2 Juxtacrine growth factor signal • 3 E-Cadherin - Catenin related signal

  24. Cell{x}…… Ligand released=Ls Free receptors=Rs Activated surface receptors= Cs Internalised complexes, Ce and receptors Re Hypothesis (1) autocrine GF-mediated signalling Ratio of RT:CT Determines change in cell behaviour e.g. cell cycle progression, migration

  25. Testing Hypothesis (1) Initial cell agent seeding density and distribution [Ca2+]=0.05mM [Ca2+]=2.5mM Conclusion: Diffusive growth factors – population growth is seeding density, but NOT distribution related

  26. Assembling rules to test hypothesis (2) EC_high Ca2+ EC_low Ca2+ Work in Progress! Thanks to Nik Georgopolous

  27. Summary • Initial rule formulation can be based on simplifications and abstractions of known biological behaviour • Iterative comparison with experimental data can improve the accuracy of the model and direct experimental investigation • The rule set can be extended to model additional aspects of cell behaviour (e.g. differentiation, stratification) • Rules can be replaced by more complex models (e.g. inter- and intra- cellular signalling)

  28. Thank you for listening Any Questions?

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