Analysis of a synthetic gene switching motif: Systems and control approaches

• Analyzes gene switching model that consists of dual positive feedback loops.
• Analyzes deterministic and stochastic stability and convergence to steady-state.
• Quantifies hysteresis dynamics and sensitivities with respect to system parameters.
• Enables the synthesis of a gene regulatory network to produce desired responses.

Developing predictive mathematical models for regulatory networks in biological systems would be useful for their analysis and design. This paper studies the parameter-dependent characteristics of a gene switching model that consists of dual positive feedback loops. Deterministic and stochastic stability are studied for this model, as well as other important system behaviors such as convergence rate to a stable equilibrium point, hysteresis induced by two time scales of the system model, and noise sensitivity with respect to the system parameters. Sensitivity of system performance indices with respect to the system parameters are analyzed in terms of H∞H∞- and H2H2-norms of the linearized system model with their closed-form solutions. The presented qualitative and quantitative studies of the system characteristics enable the synthesis of a robust gene regulatory network that achieves desired static and dynamic responses.

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