v2ecoli → PDMP Whole-Cell Model Reformulation in_progress

Incrementally transforms v2ecoli from a hybrid algorithmic whole-cell model into a piecewise-deterministic Markov process. Six phases each swap one WCM component -- characterization, a metabolism ODE, jump processes, an inference layer, a compiled runtime, and causal discovery -- while leaving the rest intact.

Question. Can v2ecoli's hybrid algorithmic whole-cell model be incrementally transformed into a piecewise-deterministic Markov process (PDMP) suitable for likelihood-based inference and causal discovery, without discarding the biological knowledge encoded in the current WCM, and while maintaining viable E. coli growth at every phase boundary?

Hypothesis. A six-phase incremental replacement — (0) Markov-blanket characterization, (1) v2ecoli's multi-objective FBA → kinetic ODE metabolism, (2) discrete-time → continuous-time jump processes, (3) observation-likelihood and Bayesian-interface infrastructure, (4) compiled column-centric runtime, (5) Bayesian gene-function annotation — yields a PDMP-class WCM that (a) reproduces Phase-0 interface statistics within tolerance at every later phase, (b) admits well-formed process likelihoods at Phase 3, (c) achieves ≥10³ parallel single-cell trajectories with near-zero marshalling overhead at Phase 4, and (d) recovers known E. coli gene functions with credible intervals on a benchmark set at Phase 5.

E. coli grows by integrating metabolism, gene expression, replication, and division — processes on very different timescales that admit different mathematical idealizations. The current v2ecoli WCM fuses these into a fixed-step loop: a single multi-objective FBA linear program solves metabolism each timestep (`wholecell.utils.modular_fba` with GLPK-linear: biomass production + homeostatic concentration targets + optional kinetic-constraint targets driving enzyme-catalysed flux toward Vmax×[E]; output fluxes converted to molecule count changes via `stochasticRound`), discrete-time Poisson draws fire transcription and translation events scaled by timestep, a teleonomic doubling-time target triggers division, and an allocator gates each layer's access to shared bulk pools (metabolism runs LAST in the timestep, deriver-style, on the post-partition state). This reproduces growth across roughly a dozen conditions, but its trajectory is that of an algorithm, not of any well-defined dynamical system.

A PDMP separates this into deterministic evolution between events (ODE flow on continuous state) and discrete jumps at event times (state-dependent probability kernels on countable state). Mass-action kinetics for central carbon metabolism, like Millard et al. 2017's curated ODE model, naturally inhabit the deterministic flow; gene-expression events, division, and resource competition inhabit the jump layer. The PDMP formalism makes both layers inspectable, compilable, and likelihood-bearing.

Main claim. The PDMP class — ODE segments interrupted by discrete jump events — is the appropriate mathematical model class for a next-generation E. coli WCM: it has process likelihoods by construction, enforces an explicit causal/teleonomic parameter partition, and aligns with the causal-modelling literature for dynamical systems.

Key figures

• · — Phase 2 closeout report — cell_mass is the wrong observable for jump-process variance.
• · — Phase 3 report — count-vector grid-separation diagnostic (3.06× next-nearest-cell ratio) on a self-generated 3×3 toy grid; not a posterior. Gate unmet.
• · — Phase 4 report — real per-tick profile is genuine; the "~1500×" speedup is an illustrative projection (toy factor 3× × N), not a measured result. Column-centric runtime not built or timed.
• · — Count-based ABC distance grid-separation diagnostic; the "~100× sharper" figure is a hardcoded literal, not computed.
• · — SMC sequential ε refinement on the toy grid; the "observed" data are generated at the truth node, so apparent concentration there is tautological, not a recovered posterior.
• · — 2D parameter sweep reveals anti-diagonal ridge under aggregate log-likelihood.
• · — Per-channel vs aggregate ABC — diagnoses the self-calibration issue.
• · — Phase-3 ensemble figure with intra-ensemble noise floor.
• · — Phase 4 hotspots: 13,817 isinstance + 4,213 __array_finalize__ + 52 process_update/tick.
• · — Per-tick decomposition: 76% framework overhead, no single Process dominates.
• · — Column-centric prototype: constant per-trajectory wall regardless of N.
• · — Real WCM per-tick baseline + an illustrative projection: the "~1500×" at N=10³ is a toy factor 3× × N by construction (no measured column-centric runtime), NOT a measured speedup.
• · — TI-shaped recalibration: 1.5× per-tick (vs toys' 3×) under realistic per-tick work.
• · — 3-step composite: speedup does not compound — pbg overhead is per-process.
• · — Phase-2 trajectory-shape divergence: max |Δcell_mass| = 150 fg between configs (transient, single trajectory pair), measured on the cell_mass quantity.
• · — Phase-2 sparse-injection ensemble — homeostat washes per-tick variance.

Caveats

• Resource estimates in the roadmap assume 2–4 FTE per phase; absent that staffing, phases will run serially over much longer wall time.
• Phases 1–2 are designated parallelizable with Phase 4; Phase 3 strictly depends on Phase 2; Phase 5 depends on all preceding phases.
• Phase 2 observable-choice — cell_mass is the wrong observable for jump-process variance. The consumption_matched homeostat washes per-tick variance out by construction. Three controller-tuning attempts (tau-EMA, open-loop, sparse) all failed; Phase 3 correctly pivoted to count-level listeners.
• Phase 3 self-calibration — emitted log-likelihood is `log P(simulated | simulated_param)`, not the ABC-correct `log P(observed | proposed)`. Log-likelihood-based ABC works but is the strictly weaker tool vs the count-based metric Phase 3 sprints 12-13 established.
• Phase 4 projection is not a measured speedup — the "3000×" and "~1500×" figures are an illustrative projection: the script hardcodes a toy factor 3× and sets column-centric wall = per_tick/3.0 with no N-dependence, so total speedup = 3× × N by construction. The column-centric runtime was never built or timed; treat these numbers as a toy order-of-magnitude motivation, not a result.
• Pbg wiring quirk (task #14) — scalar listener fields with no downstream consumer get silently pruned from the merged state. Bit sprints 1 and 12; worked around via pin-via-consumer input declarations. Real fix lives at the pbg merger layer.
• Phase 5 information-theoretic ceiling — sprints 2-3 together reclassify the Phase-5 bottleneck. Sprint 2 confirmed at N=4 the unbiased posterior is essentially uniform (log BF +0.01, truth 24.4% vs baseline 20%). Sprint 3 projected to N=1024 and found N CANNOT rescue the signal — the kernel-mean gap between truth and runner-up θ=1.15 is only Δlog=+0.011 nats; as N→∞, the log BF CI tightens around that near-zero gap, not toward a decisive threshold. Levers in order of impact: (1) wider hypothesis spacing, (2) richer observable (Phase-3 sprint 13 combined count vector), (3) tighter ε; (4) N — last and least useful at the current setup.