Limits...
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.

Show MeSH

Related in: MedlinePlus

Agent model results – intercellular contacts. a) Mean number of E-cadherin mediated contacts per cell predicted by the agent model for a starting cell density of 200 agents/mm and b) mean total perimeter length of each agent associated with E-Cadherin mediated contacts. Vertical lines represent standard deviation calculated from 3 simulations.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC2651861&req=5

Figure 7: Agent model results – intercellular contacts. a) Mean number of E-cadherin mediated contacts per cell predicted by the agent model for a starting cell density of 200 agents/mm and b) mean total perimeter length of each agent associated with E-Cadherin mediated contacts. Vertical lines represent standard deviation calculated from 3 simulations.

Mentions: The difference in the nature of the contacts formed in the two virtual environments is illustrated in figures 7, 8. Figure 7a shows the relative frequency of E-cadherin mediated contacts in the case of a seeding density of 200 cells/mm2 (2 × 104 cells/cm2). Figure 7b shows the mean length of the perimeter of each cell associated with this type of contact. This demonstrates that even after the simulated cell cultures reach confluence, E-cadherin-mediated contacts are significantly more common and more stable in physiological calcium conditions. Finally, figure 8a–b illustrates a virtual immunofluorescence experiment showing E-cadherin localisation (red lines) in an agent population (blue circles) after simulations have been run in low or high calcium conditions for 50 iterations (25 hours). This can be compared to figure 8c–d, which shows representative immunofluoresence microscopy images of NHU cells (nuclei labelled blue) cultured in low (c) and physiological (d) calcium conditions and labelled with an antibody that recognises E-cadherin protein (green). Virtual time lapse movies of the simulations in low (0.1 mM) and physiological (2 mM) calcium concentrations are available to view in the additional files 3 and 4 respectively.


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

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

Agent model results – intercellular contacts. a) Mean number of E-cadherin mediated contacts per cell predicted by the agent model for a starting cell density of 200 agents/mm and b) mean total perimeter length of each agent associated with E-Cadherin mediated contacts. Vertical lines represent standard deviation calculated from 3 simulations.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 7: Agent model results – intercellular contacts. a) Mean number of E-cadherin mediated contacts per cell predicted by the agent model for a starting cell density of 200 agents/mm and b) mean total perimeter length of each agent associated with E-Cadherin mediated contacts. Vertical lines represent standard deviation calculated from 3 simulations.
Mentions: The difference in the nature of the contacts formed in the two virtual environments is illustrated in figures 7, 8. Figure 7a shows the relative frequency of E-cadherin mediated contacts in the case of a seeding density of 200 cells/mm2 (2 × 104 cells/cm2). Figure 7b shows the mean length of the perimeter of each cell associated with this type of contact. This demonstrates that even after the simulated cell cultures reach confluence, E-cadherin-mediated contacts are significantly more common and more stable in physiological calcium conditions. Finally, figure 8a–b illustrates a virtual immunofluorescence experiment showing E-cadherin localisation (red lines) in an agent population (blue circles) after simulations have been run in low or high calcium conditions for 50 iterations (25 hours). This can be compared to figure 8c–d, which shows representative immunofluoresence microscopy images of NHU cells (nuclei labelled blue) cultured in low (c) and physiological (d) calcium conditions and labelled with an antibody that recognises E-cadherin protein (green). Virtual time lapse movies of the simulations in low (0.1 mM) and physiological (2 mM) calcium concentrations are available to view in the additional files 3 and 4 respectively.

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