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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 two coupled oscillators () in the vicinity of .(A) , ; (B) , ; (C) , ; (D) , .
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pone-0019696-g010: Probability distributions for a system of two coupled oscillators () in the vicinity of .(A) , ; (B) , ; (C) , ; (D) , .

Mentions: Although the region of stability of the anti-phase oscillators is small, for small noise intensities () the peaks of the probability distributions can be related to the deterministic positions of the present attractors which are stable. One could speculate that since both stable attractors are located very close to each other in the phase plane (Fig. 9b), the noise leads to the appearance of plateaus in the probability distribution (Fig. 10a). The peaks are now wide, which results in larger interval values where the concentration of the expressed protein can be found. In contrast to the case for , the peak at the middle of the probability distribution is not observed here. For the increased noise intensity (), we observe a clear bimodal distribution (Fig. 10b). For values exactly after the (), even small noise intensity () helps to pronounce the peaks corresponding to the deterministic cycle. Thus, the peaks, each located to low respectively high values are characteristic for the corresponding probability distribution, as shown in Fig. 10c. A stochastic bifurcation is observed then for a noise intensity of order , manifested through a transition to a bimodal distribution. The probability that a given protein concentration will be expressed in the genetic network is now restricted to two separate concentration intervals, one for low and one for high protein values.


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 two coupled oscillators () in the vicinity of .(A) , ; (B) , ; (C) , ; (D) , .
© Copyright Policy
Related In: Results  -  Collection

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

pone-0019696-g010: Probability distributions for a system of two coupled oscillators () in the vicinity of .(A) , ; (B) , ; (C) , ; (D) , .
Mentions: Although the region of stability of the anti-phase oscillators is small, for small noise intensities () the peaks of the probability distributions can be related to the deterministic positions of the present attractors which are stable. One could speculate that since both stable attractors are located very close to each other in the phase plane (Fig. 9b), the noise leads to the appearance of plateaus in the probability distribution (Fig. 10a). The peaks are now wide, which results in larger interval values where the concentration of the expressed protein can be found. In contrast to the case for , the peak at the middle of the probability distribution is not observed here. For the increased noise intensity (), we observe a clear bimodal distribution (Fig. 10b). For values exactly after the (), even small noise intensity () helps to pronounce the peaks corresponding to the deterministic cycle. Thus, the peaks, each located to low respectively high values are characteristic for the corresponding probability distribution, as shown in Fig. 10c. A stochastic bifurcation is observed then for a noise intensity of order , manifested through a transition to a bimodal distribution. The probability that a given protein concentration will be expressed in the genetic network is now restricted to two separate concentration intervals, one for low and one for high protein values.

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