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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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Convergence plot of the network for an array of 100 cells starting from random uniformly distributed binary initial conditions, 0/black or 1/white for ntcA, hetR and patS. Each new row represents the expression levels after one random iteration starting from the state of the previous row. The system converges to one attractor where only some cells differentiate to heterocysts, represented by high values in HetR (the stable vertical lines formed in the figure). The average distance between heterocysts is approximately 10 with a transport factor D = 0.767.
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Figure 2: Convergence plot of the network for an array of 100 cells starting from random uniformly distributed binary initial conditions, 0/black or 1/white for ntcA, hetR and patS. Each new row represents the expression levels after one random iteration starting from the state of the previous row. The system converges to one attractor where only some cells differentiate to heterocysts, represented by high values in HetR (the stable vertical lines formed in the figure). The average distance between heterocysts is approximately 10 with a transport factor D = 0.767.

Mentions: The convergence state for heterocyst distribution achieved by the system from a random initial condition for the state vector is illustrated in Figure 2. As time (iteration) progresses the pattern formed is clearly defined.


Modeling heterocyst pattern formation in cyanobacteria.

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

Convergence plot of the network for an array of 100 cells starting from random uniformly distributed binary initial conditions, 0/black or 1/white for ntcA, hetR and patS. Each new row represents the expression levels after one random iteration starting from the state of the previous row. The system converges to one attractor where only some cells differentiate to heterocysts, represented by high values in HetR (the stable vertical lines formed in the figure). The average distance between heterocysts is approximately 10 with a transport factor D = 0.767.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 2: Convergence plot of the network for an array of 100 cells starting from random uniformly distributed binary initial conditions, 0/black or 1/white for ntcA, hetR and patS. Each new row represents the expression levels after one random iteration starting from the state of the previous row. The system converges to one attractor where only some cells differentiate to heterocysts, represented by high values in HetR (the stable vertical lines formed in the figure). The average distance between heterocysts is approximately 10 with a transport factor D = 0.767.
Mentions: The convergence state for heterocyst distribution achieved by the system from a random initial condition for the state vector is illustrated in Figure 2. As time (iteration) progresses the pattern formed is clearly defined.

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