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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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Simulation results of the community effect model. (A, B) Numerical simulations of the deterministic rate equations Eqs.7-14. (A) is the plot for [Ap] and (B) for [Bpout]. Simulation results for different community size are shown. With 100 cells, very little gene expression occurs at steady state (not shown) as 100 cells are close to nc ≈ 97. (C) Average number of Ap at steady state (10000 min) as a function of community size (solid lines). Dotted curves indicate number of Ap at steady state ([Ap]*) obtained by Eqs.35 in additional file 1. Plots are shown for ε = 2.31 × 10-6 and 5.78 × 10-7. (D, E) Time series of [Ap] and [Bpout] as overlays of 100 stochastic simulation results (temperature map) for community size of 300 cells and ε = 5.78 × 10 -7. Solid lines show a typical simulation result. (F) Probability distributions of [Ap] at steady state (t = 10000 min in stochastic simulations) for community size n = 140, 200, and 500 cells. ε = 5.78 × 10 -7. All simulations in this figure are with one gene copy each for gene A and gene B.
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Figure 4: Simulation results of the community effect model. (A, B) Numerical simulations of the deterministic rate equations Eqs.7-14. (A) is the plot for [Ap] and (B) for [Bpout]. Simulation results for different community size are shown. With 100 cells, very little gene expression occurs at steady state (not shown) as 100 cells are close to nc ≈ 97. (C) Average number of Ap at steady state (10000 min) as a function of community size (solid lines). Dotted curves indicate number of Ap at steady state ([Ap]*) obtained by Eqs.35 in additional file 1. Plots are shown for ε = 2.31 × 10-6 and 5.78 × 10-7. (D, E) Time series of [Ap] and [Bpout] as overlays of 100 stochastic simulation results (temperature map) for community size of 300 cells and ε = 5.78 × 10 -7. Solid lines show a typical simulation result. (F) Probability distributions of [Ap] at steady state (t = 10000 min in stochastic simulations) for community size n = 140, 200, and 500 cells. ε = 5.78 × 10 -7. All simulations in this figure are with one gene copy each for gene A and gene B.

Mentions: We first performed numerical simulations of the deterministic rate equations Eqs.7-14 (parameter values in Table 1). Figure 4A and 4B show the time course of [Ap] and [Bpout] (ε = 5.78 × 10-7). The analysis revealed that following induction at t = 0 with [Bpout] = 500, gene expressions increase after a time lag and become self-sustaining. But the cell's activity becomes self-sustaining only when the number of cells present is above a certain critical number nc. This is a community effect, which is analogous to the one observed in Xenopus embryos. We asked how this critical community size nc is determined. In fact, nc can be derived from the steady state solution of Eqs.7-14 as(15)


Theoretical basis of the community effect in development.

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

Simulation results of the community effect model. (A, B) Numerical simulations of the deterministic rate equations Eqs.7-14. (A) is the plot for [Ap] and (B) for [Bpout]. Simulation results for different community size are shown. With 100 cells, very little gene expression occurs at steady state (not shown) as 100 cells are close to nc ≈ 97. (C) Average number of Ap at steady state (10000 min) as a function of community size (solid lines). Dotted curves indicate number of Ap at steady state ([Ap]*) obtained by Eqs.35 in additional file 1. Plots are shown for ε = 2.31 × 10-6 and 5.78 × 10-7. (D, E) Time series of [Ap] and [Bpout] as overlays of 100 stochastic simulation results (temperature map) for community size of 300 cells and ε = 5.78 × 10 -7. Solid lines show a typical simulation result. (F) Probability distributions of [Ap] at steady state (t = 10000 min in stochastic simulations) for community size n = 140, 200, and 500 cells. ε = 5.78 × 10 -7. All simulations in this figure are with one gene copy each for gene A and gene B.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: Simulation results of the community effect model. (A, B) Numerical simulations of the deterministic rate equations Eqs.7-14. (A) is the plot for [Ap] and (B) for [Bpout]. Simulation results for different community size are shown. With 100 cells, very little gene expression occurs at steady state (not shown) as 100 cells are close to nc ≈ 97. (C) Average number of Ap at steady state (10000 min) as a function of community size (solid lines). Dotted curves indicate number of Ap at steady state ([Ap]*) obtained by Eqs.35 in additional file 1. Plots are shown for ε = 2.31 × 10-6 and 5.78 × 10-7. (D, E) Time series of [Ap] and [Bpout] as overlays of 100 stochastic simulation results (temperature map) for community size of 300 cells and ε = 5.78 × 10 -7. Solid lines show a typical simulation result. (F) Probability distributions of [Ap] at steady state (t = 10000 min in stochastic simulations) for community size n = 140, 200, and 500 cells. ε = 5.78 × 10 -7. All simulations in this figure are with one gene copy each for gene A and gene B.
Mentions: We first performed numerical simulations of the deterministic rate equations Eqs.7-14 (parameter values in Table 1). Figure 4A and 4B show the time course of [Ap] and [Bpout] (ε = 5.78 × 10-7). The analysis revealed that following induction at t = 0 with [Bpout] = 500, gene expressions increase after a time lag and become self-sustaining. But the cell's activity becomes self-sustaining only when the number of cells present is above a certain critical number nc. This is a community effect, which is analogous to the one observed in Xenopus embryos. We asked how this critical community size nc is determined. In fact, nc can be derived from the steady state solution of Eqs.7-14 as(15)

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