agent coast

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?: 

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: 

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: 

Model Implementation CELL COMMUNICATION For each cell in turn….

Cell cycle control – the model: 

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

Cell cycle control – the model: 

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

Cell cycle control – the model: 

Cell cycle control – the model M G2 S G1 G0 G1-G0 checkpoint General biological knowledge Ref: Nelson & Chen 2002, FEBS Letters 514 pp 238-242

Cell cycle control – the model: 

Cell cycle control – the model M G2 S G1 G0 G0 QUIESCENT PHASE

Cell cycle control – the model: 

Cell cycle control – the model M G2 S G1 G0 G1 GROWTH PHASE

Cell cycle control – the model: 

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

Cell cycle control – the model: 

Cell cycle control – the model M G2 S G1 G0 G2 PHASE – (HOUSEKEEPING)

Cell cycle control – the model: 

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

Bonding Rules: 

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.

Migration parameters: 

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

Physical model: 

Physical model F=ma  l

Ca2+ dependent behaviour - In Vitro vs. In Virtuo: 

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?

Model Simulations – urothelial monolayer growth: 

Model Simulations – urothelial monolayer growth Physiological Ca2+ (2mM) Low Ca2+ (0.09mM) ITERATION NUMBER NO. CELLS

Model Simulations – urothelial monolayer growth: 

Model Simulations – urothelial monolayer growth Physiological Ca2+ (2mM) Low Ca2+ (0.09mM) ITERATION NUMBER NO. CELLS

In virtuo wound healing (urothelium): 

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

In virtuo wound healing (urothelium): 

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

In Vitro wound healing (urothelium): 

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

In vitro vs. in virtuo population growth (urothelium): 

In vitro vs. in virtuo population growth (urothelium) In vitro model Computational model Day 1 Day 3 Day 5 Day 7 Day 9 Cell number / x10E4 per mL Low Calcium Physiological Calcium

Rule extension – cell contact and proliferation: 

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: 

Hypothesis (1) autocrine GF-mediated signalling Ratio of RT:CT Determines change in cell behaviour e.g. cell cycle progression, migration

Testing Hypothesis (1): 

Testing Hypothesis (1) [Ca2+]=0.05mM [Ca2+]=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): 

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

Summary: 

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)

Slide28: 

Thank you for listening Any Questions?