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

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

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

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

Cell cycle control – the model M G2G2 S G1G1 G0G0 G 1 GROWTH PHASE Ref- general biological knowledge Publications of urothelial cell proliferation time

Cell cycle control – the model M G2G2 S G1G1 G0G0 G 1 GROWTH PHASE Ref- general biological knowledge

Cell cycle control – the model M G2G2 S G1G1 G0G0 CONTACT INHIBITION? (4 or more bonds) CELL SPREAD? G 1 -G 0 checkpoint GROWTH FACTORS? General biological knowledge Ref: Nelson & Chen 2002, FEBS Letters 514 pp

Cell cycle control – the model M G2G2 S G1G1 G0G0 CONTACT INHIBITION? (4 or more bonds) CELL SPREAD? X QUIESCENCE G 0 QUIESCENT PHASE GROWTH FACTORS?

Cell cycle control – the model M G2G2 S G1G1 G0G0 CONTACT INHIBITION? (4 or more bonds) x CELL SPREAD? G 1 GROWTH PHASE GROWTH FACTORS?

Cell cycle control – the model M G2G2 S G1G1 G0G0 S PHASE – (CHROMOSOME REPLICATION)

Cell cycle control – the model M G2G2 S G1G1 G0G0 G 2 PHASE – (HOUSEKEEPING)

Cell cycle control – the model M G2G2 S G1G1 G0G0 M PHASE - DIVISION

Bonding Rules Stochastic process governed by Cell edge separation Calcium ion concentration Sep [Ca 2+ ] Ref: Baumgartner et al, 2000, Cadherin interaction probed by atomic force microscopy PNAS 97(8)

Migration parameters Urothelial cells in low Ca 2+ (0.09mM)

Physical model l F=ma  l

Ca 2+ dependent behaviour - In Vitro vs. In Virtuo Intercellular bonds require the presence of Ca 2+ ions In Ca 2+ conc.> 1mM many bonds are formed Cells with several intercellular bonds become contact-inhibited (stop cycling) WHAT IS THE EFFECT OF Ca 2+ ON GROWTH AND PROLIFERATION?

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

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

In virtuo wound healing (urothelium) Physiological Ca 2+ (2mM)Low Ca 2+ (0.09mM)

In virtuo wound healing (urothelium) Physiological Ca 2+ (2mM)Low Ca 2+ (0.09mM)

In Vitro wound healing (urothelium) Low Ca 2+ Physiological Ca 2+

In vitro vs. in virtuo population growth (urothelium) In vitro model Computational model Simulation time in hours Total cell number Ca2+ conc.=2.0mM Ca2+ conc.=0.09mM Day 1Day 3Day 5Day 7Day 9Cell number / x10E4 per mL Low Calcium Physiological Calcium

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

Hypothesis (1) autocrine GF- mediated signalling Cell{x}…… Ligand released=L s Free receptors=R s Ratio of R T :C T Determines change in cell behaviour e.g. cell cycle progression, migration Internalised complexes, C e and receptors R e Activated surface receptors= C s

Testing Hypothesis (1) [Ca 2+ ]=0.05mM [Ca 2+ ]=2.5mM Initial cell agent seeding density and distribution Conclusion: Diffusive growth factors – population growth is seeding density, but NOT distribution related

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

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)

Thank you for listening Any Questions?