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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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Effect of the transport factor of PatS (D) on the average distance between heterocysts. A: Simulations were performed using 1000 random uniformly distributed binary initial conditions, restricted to biologically feasible conditions.  is independent of the number of cells for D < 0.8. With higher values of D, the inhibitory activity of PatS to adjacent cells increases. For D close to 1 the average  corresponds to the total number of cells as only one cell differentiates, which corresponds to an average distance equal to the number of cells. B: Simulations were performed using 5000 random uniformly distributed binary initial conditions, restricted to biologically feasible conditions. The minimum value of this function is for D = 0.767 which gives a  of 10.
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Figure 3: Effect of the transport factor of PatS (D) on the average distance between heterocysts. A: Simulations were performed using 1000 random uniformly distributed binary initial conditions, restricted to biologically feasible conditions. is independent of the number of cells for D < 0.8. With higher values of D, the inhibitory activity of PatS to adjacent cells increases. For D close to 1 the average corresponds to the total number of cells as only one cell differentiates, which corresponds to an average distance equal to the number of cells. B: Simulations were performed using 5000 random uniformly distributed binary initial conditions, restricted to biologically feasible conditions. The minimum value of this function is for D = 0.767 which gives a of 10.

Mentions: The analysis is started with the relationship between the transport factor and the system's behavior. Figure 3-A shows the effect of the transport factor D on the average distance between heterocysts . D was sampled in the interval [0, 1] in steps of 0.005 units and its effect studied for systems whose size ranges from 20 to 100 cells. was calculated as the average distance between heterocysts obtained after the system converged for 1000 random initial conditions (it is assumed that using a larger number of initial conditions will not modify the results and discussion significantly). It was observed that noisier results are generated in the simulation of systems with a cell number lower than 50, due to the small size of the system and border effects. The relative importance of these anomalies decreases as the number of cells in the system increases. Based on this observation, the following analysis considers systems with more than 50 cells. Figure 3-A illustrates that the effect of D on the behavior of systems with different sizes is very similar, i.e., it is independent of the number of cells. This indicates stability and shows good behavior for the model since is not expected to vary with the number of cells when the transport factor is kept constant. The effect of D on is very weak and almost linear until D = 0.700, indicating that low transport coefficient for PatS could cause heterocyst proliferation and, consequently, reduce . Starting from D = 0.700, the effect increased dramatically until D = 0.920 when heterocyst distance reaches a maximum. Higher values of D generate a scenario where the transport of PatS is greatly facilitated through the system. The saturation of the system with PatS inhibits the generation of heterocysts leading to a maximum in . It was found that these curves follow a power law before saturation. The coefficient of determination for LH following a power law with the equation law, where a, b and c are the adjustable parameters, were of R2 > 0.94 in all cases. According to Figure 3-A the behavior of the system, in terms of , could be controlled by means of the modification of D, the transport factor for PatS. Since the effects of changes in the transport of the PatS pentapeptide are difficult to test in an experimental setting, the usefulness of a mathematical model is clear. The transport factor D necessary to reach a specific is shown in Figure 3-A. In particular, an average distance between heterocysts of ten cells ( = 10) is obtained when D ≈ 0.7–0.8. More accurate values require a closer examination as shown in Figure 3-B.


Modeling heterocyst pattern formation in cyanobacteria.

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

Effect of the transport factor of PatS (D) on the average distance between heterocysts. A: Simulations were performed using 1000 random uniformly distributed binary initial conditions, restricted to biologically feasible conditions.  is independent of the number of cells for D < 0.8. With higher values of D, the inhibitory activity of PatS to adjacent cells increases. For D close to 1 the average  corresponds to the total number of cells as only one cell differentiates, which corresponds to an average distance equal to the number of cells. B: Simulations were performed using 5000 random uniformly distributed binary initial conditions, restricted to biologically feasible conditions. The minimum value of this function is for D = 0.767 which gives a  of 10.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 3: Effect of the transport factor of PatS (D) on the average distance between heterocysts. A: Simulations were performed using 1000 random uniformly distributed binary initial conditions, restricted to biologically feasible conditions. is independent of the number of cells for D < 0.8. With higher values of D, the inhibitory activity of PatS to adjacent cells increases. For D close to 1 the average corresponds to the total number of cells as only one cell differentiates, which corresponds to an average distance equal to the number of cells. B: Simulations were performed using 5000 random uniformly distributed binary initial conditions, restricted to biologically feasible conditions. The minimum value of this function is for D = 0.767 which gives a of 10.
Mentions: The analysis is started with the relationship between the transport factor and the system's behavior. Figure 3-A shows the effect of the transport factor D on the average distance between heterocysts . D was sampled in the interval [0, 1] in steps of 0.005 units and its effect studied for systems whose size ranges from 20 to 100 cells. was calculated as the average distance between heterocysts obtained after the system converged for 1000 random initial conditions (it is assumed that using a larger number of initial conditions will not modify the results and discussion significantly). It was observed that noisier results are generated in the simulation of systems with a cell number lower than 50, due to the small size of the system and border effects. The relative importance of these anomalies decreases as the number of cells in the system increases. Based on this observation, the following analysis considers systems with more than 50 cells. Figure 3-A illustrates that the effect of D on the behavior of systems with different sizes is very similar, i.e., it is independent of the number of cells. This indicates stability and shows good behavior for the model since is not expected to vary with the number of cells when the transport factor is kept constant. The effect of D on is very weak and almost linear until D = 0.700, indicating that low transport coefficient for PatS could cause heterocyst proliferation and, consequently, reduce . Starting from D = 0.700, the effect increased dramatically until D = 0.920 when heterocyst distance reaches a maximum. Higher values of D generate a scenario where the transport of PatS is greatly facilitated through the system. The saturation of the system with PatS inhibits the generation of heterocysts leading to a maximum in . It was found that these curves follow a power law before saturation. The coefficient of determination for LH following a power law with the equation law, where a, b and c are the adjustable parameters, were of R2 > 0.94 in all cases. According to Figure 3-A the behavior of the system, in terms of , could be controlled by means of the modification of D, the transport factor for PatS. Since the effects of changes in the transport of the PatS pentapeptide are difficult to test in an experimental setting, the usefulness of a mathematical model is clear. The transport factor D necessary to reach a specific is shown in Figure 3-A. In particular, an average distance between heterocysts of ten cells ( = 10) is obtained when D ≈ 0.7–0.8. More accurate values require a closer examination as shown in Figure 3-B.

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