Rewiring in biochemical networks no longer needs a full model: 30 markers compress to 10 dimensions with target accuracy matching a full-panel neural ODE

Biochemical networks rewire across cellular contexts, so signal takes a different route, and mechanistic simulators struggle here because the interaction structure is only partly known. Co2ODE instead learns only the portion the context rewrites, as a sparse neural or symbolic ODE, without requiring a trusted full-network model first. Prior model-discovery approaches either rely on prior-knowledge mechanistic simulators or are poorly identified at full network dimension under sparse, correlated measurements; existing rewiring-inference methods assume the intervention acts on a node the model contains and that the system sits at steady state. The data are the single-cell mass-cytometry phospho panel of Lun et al. (2019): 30 markers, 6 snapshots over one hour after EGF stimulation, 38 retained contexts comprising 30 single-gene overexpressions and 8 controls; context strength is a GFP-derived induction proxy, the target is p-S6, and the anchors are p-MEK1-2 and p-AKT.

The reduction costs almost nothing in prediction: the 10-dimensional Co2ODE reaches 16.0% rnMAE on p-S6 against 17.1% for the unreduced 30-state model, while a 3-state control keeping only the target and two anchors reaches 15.6%. The 3-state control selects no markers and so recovers no context-specific structure, and the full panel is no better on either metric, so on these data the reduction neither costs nor buys accuracy. The data carry a ceiling: a random-forest probe given the anchors, context and strength predicts the target, and the other 27 markers add nothing; the symbolic implementation compresses an 85-term library to 3 to 4 terms per equation and sits about 7 points behind on the target.

Prediction runs through the selected markers: at inference, giving a trained model another context's markers while leaving its context embedding and closure untouched raises target error, and random markers raise it further. The same cost appears in the closure-free models, so the selection rather than the latent carries the prediction; selections also repeat across seeds, with the Jaccard overlap of the three chosen markers well above the mismatched-context overlap. The swap is worse than the model's own markers in 36 of 38 contexts, and random markers are worse in all 38; for 19 of the 30 perturbations a single marker is kept in at least 8 of 10 seeds, while no control has one.

Adding a prior-knowledge score to the loss rearranges the recovered structure while fit barely moves: p-S6 rnMAE spans a narrow range across the four bias settings, and so does the three-marker average. The node bias lowers the node score and also moves the edge score, which it does not optimise; both biases together lower both scores, while the edge bias alone moves neither. Every arm is scored with the identical unbiased graph cost, so the biased model's own penalty is not used circularly; the authors conclude that agreement with known biology cannot validate the recovered structure as the true rewiring.

The demonstrated scope is 38 contexts of the Lun et al. (2019) single-cell mass-cytometry data, 30 single-gene overexpressions plus 8 controls, with generalisation evaluated across trajectories within a context; the architecture is conditioned on a context embedding and does not transfer to a context it has never seen. The authors propose next a mass-cytometry experiment adding a drug panel targeting phospho-proteins in the measured panel, to cut edges inside the state.

The authors report that the recovered couplings themselves do not reproduce across seeds: dependency-support agreement is at chance both with and without the closure, and only which markers a context uses repeats. Latent leakage remains, since the adversarial head acts on the encoder's sample; penalising the evolved latent lowers its strength correlation but does not remove it. Across four strength-extrapolation protocols Co2ODE is worse than the 3-state control on the three-marker average in all four, while p-S6 is mixed and never significant.