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Reproducible Analysis Plan for Ruoff et al., Background Compensation

Goal: Reproduce and extend the central result that coherent feedback (controllers I1/I2 acting through controlled variable A) yields robust background compensation in oscillatory and non-oscillatory homeostats, while incoherent feedback does not.

Step 1 — Implement models as mass-action ODEs. Code four systems in Python (scipy.integrate.solve_ivp, method='LSODA', matching the paper's LSODE): (a) motif-2 (m2) two-layer negative-feedback oscillator with zero-order removals (Eqs 3–7); (b) motif-8 outflow-control oscillator (Eqs 11–15); (c) non-oscillatory m2 variant with first-order A removal (Eq 18); (d) incoherent-feedback m2 variant (Eqs 27–31).

Step 2 — Perturbation sweeps. For m2: apply k2 steps 1.0→2.0 … 1.0→10.0 at t=100 across multiple constant k10 backgrounds; record maximum frequency per run. For m8: k1 step 1→100 at backgrounds k3 = 0 and 1024. For non-oscillatory: measure ΔA (maximum excursion) per k2 step per background. For incoherent: k2 step 1→10 at t=500 across backgrounds — expect frequency homeostasis but declining max frequency with background (E4). Parallel ΔA/frequency-vs-step lines across backgrounds = background compensation.

Step 3 — Retinal parallel-line check. Evaluate V = I/(I+σ) with Vmax=1 and σ spanning 1×10⁻⁴ to 10 on linear, semi-log, and log-log axes; confirm parallel curves arise without any compensation mechanism, contradicting the earlier interpretation of parallel light-adaptation plots as evidence for background compensation.

Step 4 — Validation & falsification. The authors note no known biological example of the property; extend background ranges well beyond those tested — if max frequency shifts at higher backgrounds, compensation is not robust. Also test alternative integral-control implementations (e.g., antithetic feedback), which the paper did not cover.

Known blindspots: results are purely in silico, limited to two motifs with zero-order integral control, and retinal analysis restricted to Hill α=1 (rods/cones only).