Learning the Cellular Dynamics as a Port-Hamiltonian System

Abstract

We present a physics-inspired classical digital twin of the cell: a graph neural network constrained to a compartmental, multi-clock port-Hamiltonian form, with parameters learned from multi-omic measurements. The port-Hamiltonian structure is a modelling choice -- it buys conservation, passivity and a clean separation of storage, routing and dissipation -- not a claim about what a cell is. The state pairs each species abundance deviation with a phase coordinate, assigned only where a per-clock rhythmicity gate certifies periodicity. Stored energy decomposes over five functional compartments, so stability is verified compartment by compartment. Two distinct clocks are included -- the 24-hour transcription-translation loop and the 20-hour transcription-independent redox oscillator -- coupled through a zero-net-power link, with the central-dogma correspondence hard-wired and moiety pools exact invariants. On a real mouse-liver three-omic dataset the verdict is mixed. Across ten seeds the trained twin is thermodynamically stable (no violations at any sampled state) and forecasts held-out segments (root-mean-square error 0.325 {+/-} 0.002). Its central prediction -- cross-omic phase lag equals arctan of clock frequency over degradation rate -- matches the aggregate transcript-to-protein lag (5.74 {+/-} 0.03 versus 4.90 hours), but the per-gene correlation is indistinguishable from zero (r = 0.06 {+/-} 0.27, sign unstable across seeds), so the law is supported in aggregate and unresolved per species. Recovery of withheld interaction edges is at chance (AUROC 0.50 {+/-} 0.13, nine of ten seeds scoreable): 24 timepoints do not identify network topology, which we report as a bound on what this data volume supports rather than as a property of the framework. Because the port-Hamiltonian form is imposed by construction, edits to the twin preserve it, so specialisation and disease can be expressed as structured perturbations of this reference twin rather than as separate models.