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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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Results of sensitivity analysis. Diagrammatic representation of results sensitivity analysis of signalling pathway model a) maximum amplitude of Erk-PP associated with transient contact b) duration of Erk-PP associated with transient contact c) maximum amplitude of Erk-PP associated with growing then stable contact d) duration of Erk-PP associated with growing then stable contact.
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Figure 5: Results of sensitivity analysis. Diagrammatic representation of results sensitivity analysis of signalling pathway model a) maximum amplitude of Erk-PP associated with transient contact b) duration of Erk-PP associated with transient contact c) maximum amplitude of Erk-PP associated with growing then stable contact d) duration of Erk-PP associated with growing then stable contact.

Mentions: The distribution of the ten largest values of S for both contact types is shown in figure 5. Although there is variation in the amplitude and duration of the ERK-PP signals when kinetic parameters are altered, none of the parameter variations affected the fundamental result that transient contacts result in a relatively large, transient response, compared to the smaller but sustained response associated with slowly-growing stable contacts. The durations of the signals were relatively insensitive to the model parameters. Interestingly, the parameters associated with the highest sensitivity values were typically those describing dephosphorylation reactions in the downstream section of the pathway. For instance, V16, V18 and V24, (which describe the maximal rate of Raf, Mek and Erk dephosphorylation respectively – see table 3), all had a significant influence on signal amplitude; by contrast, parameters describing the rate of receptor ligand binding, receptor dimerisation, activation and internalisation had a much less significant effect. These results suggest that the inclusion of rate constants that have been derived from interaction of soluble ligands with cell surface receptors in a model of juxtacrine signalling is not likely to be the largest cause of error and uncertainty in the model, and irrespective of the exact values of these constants, the temporal pattern of Erk activation is likely to depend on the nature of intercellular contacts.


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

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

Results of sensitivity analysis. Diagrammatic representation of results sensitivity analysis of signalling pathway model a) maximum amplitude of Erk-PP associated with transient contact b) duration of Erk-PP associated with transient contact c) maximum amplitude of Erk-PP associated with growing then stable contact d) duration of Erk-PP associated with growing then stable contact.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 5: Results of sensitivity analysis. Diagrammatic representation of results sensitivity analysis of signalling pathway model a) maximum amplitude of Erk-PP associated with transient contact b) duration of Erk-PP associated with transient contact c) maximum amplitude of Erk-PP associated with growing then stable contact d) duration of Erk-PP associated with growing then stable contact.
Mentions: The distribution of the ten largest values of S for both contact types is shown in figure 5. Although there is variation in the amplitude and duration of the ERK-PP signals when kinetic parameters are altered, none of the parameter variations affected the fundamental result that transient contacts result in a relatively large, transient response, compared to the smaller but sustained response associated with slowly-growing stable contacts. The durations of the signals were relatively insensitive to the model parameters. Interestingly, the parameters associated with the highest sensitivity values were typically those describing dephosphorylation reactions in the downstream section of the pathway. For instance, V16, V18 and V24, (which describe the maximal rate of Raf, Mek and Erk dephosphorylation respectively – see table 3), all had a significant influence on signal amplitude; by contrast, parameters describing the rate of receptor ligand binding, receptor dimerisation, activation and internalisation had a much less significant effect. These results suggest that the inclusion of rate constants that have been derived from interaction of soluble ligands with cell surface receptors in a model of juxtacrine signalling is not likely to be the largest cause of error and uncertainty in the model, and irrespective of the exact values of these constants, the temporal pattern of Erk activation is likely to depend on the nature of intercellular contacts.

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