Parameter Estimation, Analysis, and Design of Synthetic Gene Switching Models: System Behavior- and Performance-based Approaches

Abstract This paper studies the parameter-dependent characteristics of a gene switching model that consists of dual positive feedback loops. Developing a predictive mathematical model for large regulatory networks in biological systems would be useful for their analysis and design. A parameter estimation scheme is proposed based on the observation of the steady-states for a gene switching model. 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 ∞ - and H 2 -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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