Impact of Stochasticity on Gene Regulation Networks
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We studied the impact of stochasticity on gene regulation networks, using the cell-to-cell communication mechanism in <em> Escherichia coli </em> as an example. First we explored signal mediated positive autoregulation networks and their stochastic bistability, in the presence of which an initially homogeneous cell population would evolve into two distinct subpopulations. We proposed the simplification of the full network into one that can be theoretically studied. Simulation results indicate the simplifications retain the bistability and the distribution shapes so that the simplified network can be used to predict the bistable behavior of the full network. Moreover, it was shown that the bistability can be influenced by the signal molecule number, and that stochastic simulation is necessary for bistable systems. The self-promotion network for SdiA protein, with the autoinducer-2 (AI-2) signal molecule, was used as an example. The results further motivate the need for modeling of the AI-2 uptake mechanism. We next explored cell age distribution in the case where the number of a key protein for cell division has a stochastic bifurcation. With this bifurcation, the alive probability function (the probability that the cell has not divided) can be written in a double-exponential form. This analytical form allow the use of Laplace transform to calculate an analytical cell age distribution from the population balance model. The computation results indicate that if the key division protein number has a bifurcation, there is likely to be a significant fraction of first-generation cells in the cell population. Finally, we developed deterministic and stochastic models for the regulation network of the AI-2 uptake in <em> Escherichia coli </em>. This network is regulated by a set of <em> lsr </em> genes, and we proposed that the LsrD protein needs to reach a threshold for uptake to take place. Based on the deterministic model, kinetic parameter values were estimated by fitting to experimental data from the literature. During the step-by-step fitting procedure, data for mutant cells and effective data for wild type cells were used to avoid the complexity of the full wild-type network. With the estimated parameters, the deterministic simulation results matched experimental data well, except for a steep change and spike. A stochastic model was also developed and simulation results showed a mild change and no spike for the population means. The difference between stochastic means and deterministic paths is due to the LsrD protein number threshold and indicates that stochastic simulation may be necessary for a monostable system if it has a threshold mechanism.