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Analysing dynamical behavior of cellular networks via stochastic bifurcations.

Zakharova A, Kurths J, Vadivasova T, Koseska A - PLoS ONE (2011)

Bottom Line: The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation.However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood.Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types.

View Article: PubMed Central - PubMed

Affiliation: Center for Dynamics of Complex Systems, University of Potsdam, Potsdam, Germany. zakharova-as@mail.ru

ABSTRACT
The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types.

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Probability distributions for a system of  oscillators in the presence of noise.(A) , ; (B) , ; (C) , ; (D) , .
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pone-0019696-g011: Probability distributions for a system of oscillators in the presence of noise.(A) , ; (B) , ; (C) , ; (D) , .

Mentions: The results presented for the case of coupled cells can be easily generalized to larger networks, since they reflect the dynamical properties of networks of any size. We therefore investigate next the stochastic bifurcation structure of a genetic network consisting of separate cells, and analyze the stochastic behavior both, when the parameter is in the vicinity of and , but also for close to . Fig. 11 shows that on both sides of the parameter interval, changes in the dynamical structure of the system can be captured through stochastic bifurcations, when varying the noise intensity .


Analysing dynamical behavior of cellular networks via stochastic bifurcations.

Zakharova A, Kurths J, Vadivasova T, Koseska A - PLoS ONE (2011)

Probability distributions for a system of  oscillators in the presence of noise.(A) , ; (B) , ; (C) , ; (D) , .
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3102061&req=5

pone-0019696-g011: Probability distributions for a system of oscillators in the presence of noise.(A) , ; (B) , ; (C) , ; (D) , .
Mentions: The results presented for the case of coupled cells can be easily generalized to larger networks, since they reflect the dynamical properties of networks of any size. We therefore investigate next the stochastic bifurcation structure of a genetic network consisting of separate cells, and analyze the stochastic behavior both, when the parameter is in the vicinity of and , but also for close to . Fig. 11 shows that on both sides of the parameter interval, changes in the dynamical structure of the system can be captured through stochastic bifurcations, when varying the noise intensity .

Bottom Line: The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation.However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood.Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types.

View Article: PubMed Central - PubMed

Affiliation: Center for Dynamics of Complex Systems, University of Potsdam, Potsdam, Germany. zakharova-as@mail.ru

ABSTRACT
The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types.

Show MeSH