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Feedback Regulation

Mechanisms where the output of a signaling pathway regulates its own activity, maintaining homeostasis and fine-tuning cellular responses.
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The statement of the theorem

Consider a system of two molecular species, AA and BB, governed by the following coupled ODE system: d[A]dt=k1[S]−k2[A][B]\frac{d[A]}{dt} = k_1 [S] - k_2 [A][B] d[B]dt=k3[A][B]−k4[B]\frac{d[B]}{dt} = k_3 [A][B] - k_4 [B] For negative feedback, the rate constant k3k_3 must be dependent on the concentration of the product BB, such that k3=k3,max[B]KB+[B]k_3 = k_{3,max} \frac{[B]}{K_B + [B]}, leading to a self-limiting production rate for BB that stabilizes the system around a steady state [B]ss[B]_{ss}.