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Theoretical basis of the community effect in development.

Saka Y, Lhoussaine C, Kuttler C, Ullner E, Thiel M - BMC Syst Biol (2011)

Bottom Line: We have derived the analytical formula for the threshold size of a cell population that is necessary for a community effect, which is in good agreement with stochastic simulation results.The mechanism of the community effect revealed by our theoretical analysis is analogous to that of quorum sensing in bacteria.The community effect may underlie the size control in animal development and also the genesis of autosomal dominant diseases including tumorigenesis.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institute of Medical Sciences, University of Aberdeen, Foresterhill, Aberdeen AB25 2ZD, UK. y.saka@abdn.ac.uk

ABSTRACT

Background: Genetically identical cells often show significant variation in gene expression profile and behaviour even in the same physiological condition. Notably, embryonic cells destined to the same tissue maintain a uniform transcriptional regulatory state and form a homogeneous cell group. One mechanism to keep the homogeneity within embryonic tissues is the so-called community effect in animal development. The community effect is an interaction among a group of many nearby precursor cells, and is necessary for them to maintain tissue-specific gene expression and differentiate in a coordinated manner. Although it has been shown that the cell-cell communication by a diffusible factor plays a crucial role, it is not immediately obvious why a community effect needs many cells.

Results: In this work, we propose a model of the community effect in development, which consists in a linear gene cascade and cell-cell communication. We examined the properties of the model theoretically using a combination of stochastic and deterministic modelling methods. We have derived the analytical formula for the threshold size of a cell population that is necessary for a community effect, which is in good agreement with stochastic simulation results.

Conclusions: Our theoretical analysis indicates that a simple model with a linear gene cascade and cell-cell communication is sufficient to reproduce the community effect in development. The model explains why a community needs many cells. It suggests that the community's long-term behaviour is independent of the initial induction level, although the initiation of a community effect requires a sufficient amount of inducing signal. The mechanism of the community effect revealed by our theoretical analysis is analogous to that of quorum sensing in bacteria. The community effect may underlie the size control in animal development and also the genesis of autosomal dominant diseases including tumorigenesis.

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A minimal model of a community effect. (A) A schematic depiction of the model. Each molecule or state is indicated in red, and arrows indicate reactions/transitions between those states with reaction rate parameters as indicated. See text for details. (B) Steady state of [x] plotted as a function of community size n. Parameter values used for the plot are: k1, k2, k3 = 0.02; δ1, δ 2, δ 3 = 0.01; Vc = 1; Vs = 800.
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Figure 2: A minimal model of a community effect. (A) A schematic depiction of the model. Each molecule or state is indicated in red, and arrows indicate reactions/transitions between those states with reaction rate parameters as indicated. See text for details. (B) Steady state of [x] plotted as a function of community size n. Parameter values used for the plot are: k1, k2, k3 = 0.02; δ1, δ 2, δ 3 = 0.01; Vc = 1; Vs = 800.

Mentions: Our first model of a community effect is based on a simplified abstract scheme as illustrated in Figure 2A. This model does not include transcription (mRNA) steps, and is described by Michaelis-Menten rate equations without Hill coefficient (cooperativity). The system has n cells and three components (proteins), xi, yi (i = 1, 2, ..., n) and z. yi is exported from the cell, and is added to the extracellular pool z. z in turn activates the synthesis of xi. z diffuses into and out of the cell freely. This model explicitly takes account of the system volume Vs (extracellular volume plus total cell volume) and the volume of a cell Vc, both of which remain constant in this model. Note that Vs >n Vc. In the deterministic regime, each cell has identical dynamics. The system is described by a set of ordinary differential equations (ODEs) as follows:(1)


Theoretical basis of the community effect in development.

Saka Y, Lhoussaine C, Kuttler C, Ullner E, Thiel M - BMC Syst Biol (2011)

A minimal model of a community effect. (A) A schematic depiction of the model. Each molecule or state is indicated in red, and arrows indicate reactions/transitions between those states with reaction rate parameters as indicated. See text for details. (B) Steady state of [x] plotted as a function of community size n. Parameter values used for the plot are: k1, k2, k3 = 0.02; δ1, δ 2, δ 3 = 0.01; Vc = 1; Vs = 800.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3105943&req=5

Figure 2: A minimal model of a community effect. (A) A schematic depiction of the model. Each molecule or state is indicated in red, and arrows indicate reactions/transitions between those states with reaction rate parameters as indicated. See text for details. (B) Steady state of [x] plotted as a function of community size n. Parameter values used for the plot are: k1, k2, k3 = 0.02; δ1, δ 2, δ 3 = 0.01; Vc = 1; Vs = 800.
Mentions: Our first model of a community effect is based on a simplified abstract scheme as illustrated in Figure 2A. This model does not include transcription (mRNA) steps, and is described by Michaelis-Menten rate equations without Hill coefficient (cooperativity). The system has n cells and three components (proteins), xi, yi (i = 1, 2, ..., n) and z. yi is exported from the cell, and is added to the extracellular pool z. z in turn activates the synthesis of xi. z diffuses into and out of the cell freely. This model explicitly takes account of the system volume Vs (extracellular volume plus total cell volume) and the volume of a cell Vc, both of which remain constant in this model. Note that Vs >n Vc. In the deterministic regime, each cell has identical dynamics. The system is described by a set of ordinary differential equations (ODEs) as follows:(1)

Bottom Line: We have derived the analytical formula for the threshold size of a cell population that is necessary for a community effect, which is in good agreement with stochastic simulation results.The mechanism of the community effect revealed by our theoretical analysis is analogous to that of quorum sensing in bacteria.The community effect may underlie the size control in animal development and also the genesis of autosomal dominant diseases including tumorigenesis.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institute of Medical Sciences, University of Aberdeen, Foresterhill, Aberdeen AB25 2ZD, UK. y.saka@abdn.ac.uk

ABSTRACT

Background: Genetically identical cells often show significant variation in gene expression profile and behaviour even in the same physiological condition. Notably, embryonic cells destined to the same tissue maintain a uniform transcriptional regulatory state and form a homogeneous cell group. One mechanism to keep the homogeneity within embryonic tissues is the so-called community effect in animal development. The community effect is an interaction among a group of many nearby precursor cells, and is necessary for them to maintain tissue-specific gene expression and differentiate in a coordinated manner. Although it has been shown that the cell-cell communication by a diffusible factor plays a crucial role, it is not immediately obvious why a community effect needs many cells.

Results: In this work, we propose a model of the community effect in development, which consists in a linear gene cascade and cell-cell communication. We examined the properties of the model theoretically using a combination of stochastic and deterministic modelling methods. We have derived the analytical formula for the threshold size of a cell population that is necessary for a community effect, which is in good agreement with stochastic simulation results.

Conclusions: Our theoretical analysis indicates that a simple model with a linear gene cascade and cell-cell communication is sufficient to reproduce the community effect in development. The model explains why a community needs many cells. It suggests that the community's long-term behaviour is independent of the initial induction level, although the initiation of a community effect requires a sufficient amount of inducing signal. The mechanism of the community effect revealed by our theoretical analysis is analogous to that of quorum sensing in bacteria. The community effect may underlie the size control in animal development and also the genesis of autosomal dominant diseases including tumorigenesis.

Show MeSH
Related in: MedlinePlus