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Stochastic model of yeast cell-cycle network. (English) Zbl 1100.92017

The gene-protein interaction in the four-phase cell division cycle is modeled by a probabilistic Boolean network for a yeast cell. The interaction is described by a graph with 11 nodes. Each node corresponds to some protein or protein complex. The nodes can be in active (1) or inactive (0) state. The interaction is represented by oriented vertexes which correspond to activation (positive interaction), repression (negative interaction) and self degradation (loop vertexes). The cell state is described by a combination of node states i.e., there are \(2^{11}\) different cell states. The transitions between the cell states are described by a Markov chain in which transitions for node states are conditionally independent given the previous cell state. Their probabilities are described by a kind of logistic function. The authors investigate the stationary distribution of the obtained Markov chain for different values of parameters via simulations. It is demonstrated that for low levels of noise the biological pathway is stable.

MSC:

92C37 Cell biology
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
92C40 Biochemistry, molecular biology
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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References:

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