| Abstract: |
| Stochastic biochemical oscillators, such as genetic toggle switches, exhibit complex dynamics due to intrinsic molecular noise and low molecular counts. While the Chemical Master Equation (CME) provides a rigorous probabilistic description, it is often computationally intractable; Partial Integro-Differential Equation (PIDE) models offer a tractable alternative with solid theoretical foundations.
We introduce the Predictive-Switching Controller (PSC), a model-based strategy that evaluates system trajectories under a finite set of input configurations and selects the one optimizing a cost functional. This framework can stabilize low-probability states, preserve transient bimodality, and reshape complex distributions. To accelerate high-dimensional computations, a neural network predicts optimal input actions, maintaining the reliability of the model-based approach.
A key theoretical contribution is the proof of L1-contractivity of the PIDE dynamics, ensuring that probability distributions under fixed control profiles remain bounded and are robust to variations in initial conditions.
We validate PSC on stochastic toggle-switch networks, demonstrating its ability to maintain unstable states and modulate bimodal distributions effectively. These results highlight PSC as a flexible, robust, and computationally efficient method for controlling stochastic biochemical oscillators, with potential applications in synthetic biology and the design of robust genetic circuits. |
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