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Modeling heterocyst pattern formation in cyanobacteria.

Gerdtzen ZP, Salgado JC, Osses A, Asenjo JA, Rapaport I, Andrews BA - BMC Bioinformatics (2009)

Bottom Line: In all cases, simulations show good agreement with reported experimental results.A simple evolution mathematical model based on the gene network involved in heterocyst differentiation was proposed.The behavior of the biological system naturally emerges from the network and the model is able to capture the spacing pattern observed in heterocyst differentiation, as well as the effect of external perturbations such as nitrogen deprivation, gene knock-out and over-expression without specific parameter fitting.

View Article: PubMed Central - HTML - PubMed

Affiliation: Centre for Biochemical Engineering and Biotechnology, Department of Chemical Engineering and Biotechnology, University of Chile, Av, Beauchef 850, Santiago 837-0448, Chile. zgerdtze@ing.uchile.cl

ABSTRACT

Background: To allow the survival of the population in the absence of nitrogen, some cyanobacteria strains have developed the capability of differentiating into nitrogen fixing cells, forming a characteristic pattern. In this paper, the process by which cyanobacteria differentiates from vegetative cells into heterocysts in the absence of nitrogen and the elements of the gene network involved that allow the formation of such a pattern are investigated.

Methods: A simple gene network model, which represents the complexity of the differentiation process, and the role of all variables involved in this cellular process is proposed. Specific characteristics and details of the system's behavior such as transcript profiles for ntcA, hetR and patS between consecutive heterocysts were studied.

Results: The proposed model is able to capture one of the most distinctive features of this system: a characteristic distance of 10 cells between two heterocysts, with a small standard deviation according to experimental variability. The system's response to knock-out and over-expression of patS and hetR was simulated in order to validate the proposed model against experimental observations. In all cases, simulations show good agreement with reported experimental results.

Conclusion: A simple evolution mathematical model based on the gene network involved in heterocyst differentiation was proposed. The behavior of the biological system naturally emerges from the network and the model is able to capture the spacing pattern observed in heterocyst differentiation, as well as the effect of external perturbations such as nitrogen deprivation, gene knock-out and over-expression without specific parameter fitting.

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Histograms for the distance between heterocysts in the absence of nitrogen. A:  wild type.  does not follow a normal distribution. B:  when patS expression is knocked-out. C:  when hetR is over-expressed. All simulations were performed using 5000 random uniformly distributed binary initial conditions, restricted to biologically feasible conditions and considering D =  = 0.767, for systems with 50–100 cells. For easier comparison frequencies were normalized to the number of cells.
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Figure 4: Histograms for the distance between heterocysts in the absence of nitrogen. A: wild type. does not follow a normal distribution. B: when patS expression is knocked-out. C: when hetR is over-expressed. All simulations were performed using 5000 random uniformly distributed binary initial conditions, restricted to biologically feasible conditions and considering D = = 0.767, for systems with 50–100 cells. For easier comparison frequencies were normalized to the number of cells.

Mentions: Histograms of LH for D = are given in Figure 4-A. This figure shows that the distance between heterocysts, LH, for systems with different numbers of cells follows a very similar distribution. In general, the shape of this distribution is narrow, not symmetrical and does not follow a normal distribution (Kolmogorov-Smirnov test). The non-symmetrical shape of the histograms in Figure 4-A indicates that the frequency of observing an LH <10 is higher than the frequency of LH >10. In fact, for the case of the 100 cells system these frequencies are 47.8% and 39.2%, respectively. Even so, Figure 4-A shows that the distribution of LH is highly concentrated in the neighborhood of 10, a fact that has been observed experimentally. Our simulated results for the distribution of LH in wild type are consistent with the heterocyst spacing distribution observed experimentally by Yoon and Golden at 48 h with a number of vegetative cells between heterocysts ranging from 5 to 18 cells, peaking around 10 cells [6]. The model however does not capture the distribution observed at later culture times, where other factors such as cell death and decay may have an effect in the pattern distribution observed experimentally.


Modeling heterocyst pattern formation in cyanobacteria.

Gerdtzen ZP, Salgado JC, Osses A, Asenjo JA, Rapaport I, Andrews BA - BMC Bioinformatics (2009)

Histograms for the distance between heterocysts in the absence of nitrogen. A:  wild type.  does not follow a normal distribution. B:  when patS expression is knocked-out. C:  when hetR is over-expressed. All simulations were performed using 5000 random uniformly distributed binary initial conditions, restricted to biologically feasible conditions and considering D =  = 0.767, for systems with 50–100 cells. For easier comparison frequencies were normalized to the number of cells.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2697639&req=5

Figure 4: Histograms for the distance between heterocysts in the absence of nitrogen. A: wild type. does not follow a normal distribution. B: when patS expression is knocked-out. C: when hetR is over-expressed. All simulations were performed using 5000 random uniformly distributed binary initial conditions, restricted to biologically feasible conditions and considering D = = 0.767, for systems with 50–100 cells. For easier comparison frequencies were normalized to the number of cells.
Mentions: Histograms of LH for D = are given in Figure 4-A. This figure shows that the distance between heterocysts, LH, for systems with different numbers of cells follows a very similar distribution. In general, the shape of this distribution is narrow, not symmetrical and does not follow a normal distribution (Kolmogorov-Smirnov test). The non-symmetrical shape of the histograms in Figure 4-A indicates that the frequency of observing an LH <10 is higher than the frequency of LH >10. In fact, for the case of the 100 cells system these frequencies are 47.8% and 39.2%, respectively. Even so, Figure 4-A shows that the distribution of LH is highly concentrated in the neighborhood of 10, a fact that has been observed experimentally. Our simulated results for the distribution of LH in wild type are consistent with the heterocyst spacing distribution observed experimentally by Yoon and Golden at 48 h with a number of vegetative cells between heterocysts ranging from 5 to 18 cells, peaking around 10 cells [6]. The model however does not capture the distribution observed at later culture times, where other factors such as cell death and decay may have an effect in the pattern distribution observed experimentally.

Bottom Line: In all cases, simulations show good agreement with reported experimental results.A simple evolution mathematical model based on the gene network involved in heterocyst differentiation was proposed.The behavior of the biological system naturally emerges from the network and the model is able to capture the spacing pattern observed in heterocyst differentiation, as well as the effect of external perturbations such as nitrogen deprivation, gene knock-out and over-expression without specific parameter fitting.

View Article: PubMed Central - HTML - PubMed

Affiliation: Centre for Biochemical Engineering and Biotechnology, Department of Chemical Engineering and Biotechnology, University of Chile, Av, Beauchef 850, Santiago 837-0448, Chile. zgerdtze@ing.uchile.cl

ABSTRACT

Background: To allow the survival of the population in the absence of nitrogen, some cyanobacteria strains have developed the capability of differentiating into nitrogen fixing cells, forming a characteristic pattern. In this paper, the process by which cyanobacteria differentiates from vegetative cells into heterocysts in the absence of nitrogen and the elements of the gene network involved that allow the formation of such a pattern are investigated.

Methods: A simple gene network model, which represents the complexity of the differentiation process, and the role of all variables involved in this cellular process is proposed. Specific characteristics and details of the system's behavior such as transcript profiles for ntcA, hetR and patS between consecutive heterocysts were studied.

Results: The proposed model is able to capture one of the most distinctive features of this system: a characteristic distance of 10 cells between two heterocysts, with a small standard deviation according to experimental variability. The system's response to knock-out and over-expression of patS and hetR was simulated in order to validate the proposed model against experimental observations. In all cases, simulations show good agreement with reported experimental results.

Conclusion: A simple evolution mathematical model based on the gene network involved in heterocyst differentiation was proposed. The behavior of the biological system naturally emerges from the network and the model is able to capture the spacing pattern observed in heterocyst differentiation, as well as the effect of external perturbations such as nitrogen deprivation, gene knock-out and over-expression without specific parameter fitting.

Show MeSH
Related in: MedlinePlus