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From pathway to population--a multiscale model of juxtacrine EGFR-MAPK signalling.

Walker DC, Georgopoulos NT, Southgate J - BMC Syst Biol (2008)

Bottom Line: A model consisting of a single pair of interacting agents predicted very different Erk activation (phosphorylation) profiles, depending on the formation rate and stability of intercellular contacts, with the slow formation of stable contacts resulting in low but sustained activation of Erk, and transient contacts resulting in a transient Erk signal.These results illustrate that mean experimental data obtained from analysing entire cell populations is an oversimplification, and should not be extrapolated to deduce the signal:response paradigm of individual cells.This multi-scale, multi-paradigm approach to biological simulation provides an important conceptual tool in addressing how information may be integrated over multiple scales to predict the behaviour of a biological system.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Computer Science, University of Sheffield, Kroto Research Institute, North Campus, Broad Lane, Sheffield, S3 7HQ, UK. d.c.walker@sheffield.ac.uk

ABSTRACT

Background: Most mathematical models of biochemical pathways consider either signalling events that take place within a single cell in isolation, or an 'average' cell which is considered to be representative of a cell population. Likewise, experimental measurements are often averaged over populations consisting of hundreds of thousands of cells. This approach ignores the fact that even within a genetically-homogeneous population, local conditions may influence cell signalling and result in phenotypic heterogeneity. We have developed a multi-scale computational model that accounts for emergent heterogeneity arising from the influences of intercellular signalling on individual cells within a population. Our approach was to develop an ODE model of juxtacrine EGFR-ligand activation of the MAPK intracellular pathway and to couple this to an agent-based representation of individual cells in an expanding epithelial cell culture population. This multi-scale, multi-paradigm approach has enabled us to simulate Extracellular signal-regulated kinase (Erk) activation in a population of cells and to examine the consequences of interpretation at a single cell or population-based level using virtual assays.

Results: A model consisting of a single pair of interacting agents predicted very different Erk activation (phosphorylation) profiles, depending on the formation rate and stability of intercellular contacts, with the slow formation of stable contacts resulting in low but sustained activation of Erk, and transient contacts resulting in a transient Erk signal. Extension of this model to a population consisting of hundreds to thousands of interacting virtual cells revealed that the activated Erk profile measured across the entire cell population was very different and may appear to contradict individual cell findings, reflecting heterogeneity in population density across the culture. This prediction was supported by immunolabelling of an epithelial cell population grown in vitro, which confirmed heterogeneity of Erk activation.

Conclusion: These results illustrate that mean experimental data obtained from analysing entire cell populations is an oversimplification, and should not be extrapolated to deduce the signal:response paradigm of individual cells. This multi-scale, multi-paradigm approach to biological simulation provides an important conceptual tool in addressing how information may be integrated over multiple scales to predict the behaviour of a biological system.

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Model flow. Information passed between agent and signalling model. Blue arrows indicate information passed per contact, green arrows represent information passed per agent.
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Figure 3: Model flow. Information passed between agent and signalling model. Blue arrows indicate information passed per contact, green arrows represent information passed per agent.

Mentions: The Erk signalling pathway is reasonably well characterised and has been the focus of several modelling studies (e.g. [14-17]). It was not our objective to develop a new model of this pathway, but to incorporate an existing mathematical description into our agent-based representation of cells, hence introducing a subcellular level 'mechanism' that is initiated by cellular scale interactions to influence emergent changes in cell behaviour. We have thus chosen to integrate and adapt existing models of this pathway [14,15] in order to consider activation of the Erk pathway in an individual cell which occurs as a result of regions of intercellular contact with one or more neighbouring cells, through activation of EGFR by cell surface-presented cognate ligands. These intercellular regions can be fixed in size, or actively growing in accordance with the reported behaviour of E-cadherin mediated contacts in cultured epithelial cells [18]. The various components of the model, and our methodology in integrating them are described in the Methods section and illustrated in Figure 1, 2, 3. We present the simulated time-varying activated Erk (Erk-PP) profile for the following scenarios: 1) a pair of cells forming a single, transient or stable contact (the latter being typical of E-cadherin-mediated adherens junctions) and 2) the ERK-PP profile averaged over a growing population of several hundred to thousands of agents in low and physiological calcium concentrations, (the latter conditions being conducive for the formation of multiple, stable E-cadherin-mediated contacts). The multi-agent simulations inherently include inter-agent microenvironment heterogeneity, as this reflects variation in the nature of intercellular contacts experienced by individual cell agents as a result of their position within the population. We also present the results of a sensitivity analysis of parameters in the signalling pathway model.


From pathway to population--a multiscale model of juxtacrine EGFR-MAPK signalling.

Walker DC, Georgopoulos NT, Southgate J - BMC Syst Biol (2008)

Model flow. Information passed between agent and signalling model. Blue arrows indicate information passed per contact, green arrows represent information passed per agent.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2651861&req=5

Figure 3: Model flow. Information passed between agent and signalling model. Blue arrows indicate information passed per contact, green arrows represent information passed per agent.
Mentions: The Erk signalling pathway is reasonably well characterised and has been the focus of several modelling studies (e.g. [14-17]). It was not our objective to develop a new model of this pathway, but to incorporate an existing mathematical description into our agent-based representation of cells, hence introducing a subcellular level 'mechanism' that is initiated by cellular scale interactions to influence emergent changes in cell behaviour. We have thus chosen to integrate and adapt existing models of this pathway [14,15] in order to consider activation of the Erk pathway in an individual cell which occurs as a result of regions of intercellular contact with one or more neighbouring cells, through activation of EGFR by cell surface-presented cognate ligands. These intercellular regions can be fixed in size, or actively growing in accordance with the reported behaviour of E-cadherin mediated contacts in cultured epithelial cells [18]. The various components of the model, and our methodology in integrating them are described in the Methods section and illustrated in Figure 1, 2, 3. We present the simulated time-varying activated Erk (Erk-PP) profile for the following scenarios: 1) a pair of cells forming a single, transient or stable contact (the latter being typical of E-cadherin-mediated adherens junctions) and 2) the ERK-PP profile averaged over a growing population of several hundred to thousands of agents in low and physiological calcium concentrations, (the latter conditions being conducive for the formation of multiple, stable E-cadherin-mediated contacts). The multi-agent simulations inherently include inter-agent microenvironment heterogeneity, as this reflects variation in the nature of intercellular contacts experienced by individual cell agents as a result of their position within the population. We also present the results of a sensitivity analysis of parameters in the signalling pathway model.

Bottom Line: A model consisting of a single pair of interacting agents predicted very different Erk activation (phosphorylation) profiles, depending on the formation rate and stability of intercellular contacts, with the slow formation of stable contacts resulting in low but sustained activation of Erk, and transient contacts resulting in a transient Erk signal.These results illustrate that mean experimental data obtained from analysing entire cell populations is an oversimplification, and should not be extrapolated to deduce the signal:response paradigm of individual cells.This multi-scale, multi-paradigm approach to biological simulation provides an important conceptual tool in addressing how information may be integrated over multiple scales to predict the behaviour of a biological system.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Computer Science, University of Sheffield, Kroto Research Institute, North Campus, Broad Lane, Sheffield, S3 7HQ, UK. d.c.walker@sheffield.ac.uk

ABSTRACT

Background: Most mathematical models of biochemical pathways consider either signalling events that take place within a single cell in isolation, or an 'average' cell which is considered to be representative of a cell population. Likewise, experimental measurements are often averaged over populations consisting of hundreds of thousands of cells. This approach ignores the fact that even within a genetically-homogeneous population, local conditions may influence cell signalling and result in phenotypic heterogeneity. We have developed a multi-scale computational model that accounts for emergent heterogeneity arising from the influences of intercellular signalling on individual cells within a population. Our approach was to develop an ODE model of juxtacrine EGFR-ligand activation of the MAPK intracellular pathway and to couple this to an agent-based representation of individual cells in an expanding epithelial cell culture population. This multi-scale, multi-paradigm approach has enabled us to simulate Extracellular signal-regulated kinase (Erk) activation in a population of cells and to examine the consequences of interpretation at a single cell or population-based level using virtual assays.

Results: A model consisting of a single pair of interacting agents predicted very different Erk activation (phosphorylation) profiles, depending on the formation rate and stability of intercellular contacts, with the slow formation of stable contacts resulting in low but sustained activation of Erk, and transient contacts resulting in a transient Erk signal. Extension of this model to a population consisting of hundreds to thousands of interacting virtual cells revealed that the activated Erk profile measured across the entire cell population was very different and may appear to contradict individual cell findings, reflecting heterogeneity in population density across the culture. This prediction was supported by immunolabelling of an epithelial cell population grown in vitro, which confirmed heterogeneity of Erk activation.

Conclusion: These results illustrate that mean experimental data obtained from analysing entire cell populations is an oversimplification, and should not be extrapolated to deduce the signal:response paradigm of individual cells. This multi-scale, multi-paradigm approach to biological simulation provides an important conceptual tool in addressing how information may be integrated over multiple scales to predict the behaviour of a biological system.

Show MeSH
Related in: MedlinePlus