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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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Community effect observed in stochastic simulations. Distributions of percentage of active cells in the community for a range of community size as indicated. 100 simulations were performed for each community size. Percentage of active cells ([Ap]> 0) at the end of simulation was calculated for each simulation, plotted as a histogram, which are combined as 3D plots. (A) The histogram for ε = 5.78 × 10 -7, a (copy number of gene A) = 1, b (copy number of gene B) = 1. (B) ε = 2.31 × 10 -6, a = 1, b = 1. (C, D) ε = 5.78 × 10 -7, a = 2, b = 2. (E, F) ε = 5.78 × 10 -7, a = 1, b = 2. (A, B, C, E) are the histograms at t = 3000 min in the simulations and (D, F) at t = 10000 min. Note that (C) and (D) are obtained at different time points from the same set of simulations, so are (E) and (F). Histograms for a = 2, b = 1 are similar to Fig. 5E and F (data not shown).
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Figure 5: Community effect observed in stochastic simulations. Distributions of percentage of active cells in the community for a range of community size as indicated. 100 simulations were performed for each community size. Percentage of active cells ([Ap]> 0) at the end of simulation was calculated for each simulation, plotted as a histogram, which are combined as 3D plots. (A) The histogram for ε = 5.78 × 10 -7, a (copy number of gene A) = 1, b (copy number of gene B) = 1. (B) ε = 2.31 × 10 -6, a = 1, b = 1. (C, D) ε = 5.78 × 10 -7, a = 2, b = 2. (E, F) ε = 5.78 × 10 -7, a = 1, b = 2. (A, B, C, E) are the histograms at t = 3000 min in the simulations and (D, F) at t = 10000 min. Note that (C) and (D) are obtained at different time points from the same set of simulations, so are (E) and (F). Histograms for a = 2, b = 1 are similar to Fig. 5E and F (data not shown).

Mentions: We performed 100 simulations for each community size n, and calculated the percentage of active cells ([Ap] > 0) at the end of each simulation: the results are shown for haploid (Figure 5A, B), homozygous diploid (C, D) and heterozygous diploid cell communities (E, F; also see the next section). When the community size is below the critical cell number nc (indicated in each panel in red), the community effect does not occur and all cells become quiescent. In contrast, when the community size n is larger than nc but close to it (n ≈ nc), the behaviour of cells becomes unpredictable: sometime all the cells are active while in other occasions they are all inactive or only partially active (Figure 5A, B, C and 5E, t = 3000 min). However, this heterogeneity is transient and the community eventually become homogeneous after a sufficiently extended time period (Figure 5D and 5F, t = 10000 min). These results indicate the probabilistic nature of a community effect when n ≈ nc , that is, the system can end up with either of two stable states with a finite probability. In contrast, if the community size is sufficiently large (n ≫ nc), all cells become active (Figure 4F and Figure 5).


Theoretical basis of the community effect in development.

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

Community effect observed in stochastic simulations. Distributions of percentage of active cells in the community for a range of community size as indicated. 100 simulations were performed for each community size. Percentage of active cells ([Ap]> 0) at the end of simulation was calculated for each simulation, plotted as a histogram, which are combined as 3D plots. (A) The histogram for ε = 5.78 × 10 -7, a (copy number of gene A) = 1, b (copy number of gene B) = 1. (B) ε = 2.31 × 10 -6, a = 1, b = 1. (C, D) ε = 5.78 × 10 -7, a = 2, b = 2. (E, F) ε = 5.78 × 10 -7, a = 1, b = 2. (A, B, C, E) are the histograms at t = 3000 min in the simulations and (D, F) at t = 10000 min. Note that (C) and (D) are obtained at different time points from the same set of simulations, so are (E) and (F). Histograms for a = 2, b = 1 are similar to Fig. 5E and F (data not shown).
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Figure 5: Community effect observed in stochastic simulations. Distributions of percentage of active cells in the community for a range of community size as indicated. 100 simulations were performed for each community size. Percentage of active cells ([Ap]> 0) at the end of simulation was calculated for each simulation, plotted as a histogram, which are combined as 3D plots. (A) The histogram for ε = 5.78 × 10 -7, a (copy number of gene A) = 1, b (copy number of gene B) = 1. (B) ε = 2.31 × 10 -6, a = 1, b = 1. (C, D) ε = 5.78 × 10 -7, a = 2, b = 2. (E, F) ε = 5.78 × 10 -7, a = 1, b = 2. (A, B, C, E) are the histograms at t = 3000 min in the simulations and (D, F) at t = 10000 min. Note that (C) and (D) are obtained at different time points from the same set of simulations, so are (E) and (F). Histograms for a = 2, b = 1 are similar to Fig. 5E and F (data not shown).
Mentions: We performed 100 simulations for each community size n, and calculated the percentage of active cells ([Ap] > 0) at the end of each simulation: the results are shown for haploid (Figure 5A, B), homozygous diploid (C, D) and heterozygous diploid cell communities (E, F; also see the next section). When the community size is below the critical cell number nc (indicated in each panel in red), the community effect does not occur and all cells become quiescent. In contrast, when the community size n is larger than nc but close to it (n ≈ nc), the behaviour of cells becomes unpredictable: sometime all the cells are active while in other occasions they are all inactive or only partially active (Figure 5A, B, C and 5E, t = 3000 min). However, this heterogeneity is transient and the community eventually become homogeneous after a sufficiently extended time period (Figure 5D and 5F, t = 10000 min). These results indicate the probabilistic nature of a community effect when n ≈ nc , that is, the system can end up with either of two stable states with a finite probability. In contrast, if the community size is sufficiently large (n ≫ nc), all cells become active (Figure 4F and Figure 5).

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