Negative Feedback vs Open-Loop Gene Circuit

Perturbation

Type

Simulation speed 1.0×

Negative-Feedback Circuit

Protein level

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Deviation

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Open-Loop Circuit

Protein level

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Deviation

–

Target level

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How it works

Both circuits are the same gene → mRNA → protein pipeline, degraded at the same fixed rate. The only difference: in the feedback circuit, the protein represses its own gene through a steep Hill function — high protein throttles production down, low protein relaxes repression and production ramps up. The open-loop circuit produces at a constant rate no matter how much protein is already present.

feedback:  dP/dt = β / (1 + (P/K)^n) − γ·P
open-loop: dP/dt = α − γ·P

Inject perturbation — fires a pulse of extra degradation or extra production into both circuits at once, so the comparison is apples-to-apples.
Feedback loop (curved arrow) — only present on the left; particle flow along it shows repression strength in real time.
Why the feedback circuit snaps back faster — near the setpoint, the Hill repression term adds extra restoring "gain" on top of plain decay, so its effective relaxation rate is several times faster than γ alone. The open-loop circuit only has γ to fall back on, so within the same observation window it stays visibly displaced.

Real-world relevance: this is why so many biological genes — from bacterial operons to human hormone axes — are autoregulated by their own product. Negative feedback is what turns a noisy, drift-prone production line into a stable homeostatic setpoint.

🧬 Negative-Feedback ⚠️ Open-Loop

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