Peptourbillon — the calculator under the hood
A tourbillon in a watch exists to fight gravity with mechanics; the Peptourbillon exists to fight formulation guesswork with physics. It is S3Pulse's recipe engine for the two-liquid Lyoprester world — the cake side that will be lyophilized and the P-EARL reconstitution liquid, kept as strictly separate domains — and every number it shows is computed by a named equation, not fitted adjectives.
The calculator's own results panel ends with a section titled "Equations applied (tribute to the scientists)". This page reproduces that list from the source code, names the scientist behind each equation, and says what the calculator uses it to compute. The hard constants are doctrine, not defaults: a P-EARL fill of 1.30 mL delivers 1.00 mL with 0.30 mL retained; the cake chamber and the P-EARL chamber never share components silently; polysorbates are banned from P-EARL outright (they bubble under VANA vacuum cycling); the isotonicity target band is 280–320 mOsm/kg.
The list — every equation, its scientist, its job
| Equation / model | Scientist(s) | What Peptourbillon computes with it |
|---|---|---|
| Gordon–Taylor equation | M. Gordon & J. S. Taylor (1952) | Glass-transition temperature of the formulation mixture — dry Tg, frozen Tg′, and moisture-plasticized Tg with the Gordon–Taylor constant (canonical range 1.0–6.25). |
| Fox equation | T. G. Fox (1956) | Inverse-weighted multi-component Tg (1/Tg = Σ wᵢ/Tgᵢ) — the simplified mixing rule used in the advanced lyophilization calculator. |
| Couchman–Karasz relation | P. R. Couchman & F. E. Karasz (1978) | Multi-component Tg from heat-capacity increments — the thermodynamically rooted alternative mixing rule. |
| Pikal correlation | M. J. Pikal | The mass-transfer coefficient K_v for sublimation — the vial/cartridge resistance the drying rate must push vapour through. |
| Clausius–Clapeyron relation | B. Clapeyron & R. Clausius | Ice vapour pressure as a function of temperature — the driving force behind every sublimation calculation. |
| Doran–Liou modification | Doran & Liou | Product-temperature correction inside the drying model, on top of the classical heat/mass-transfer frame. |
| Dicoias ETT model | B. Dicoias (Panacea) | Empirical drying-time prediction — PDT = k·h² over the stacked Lyoprester cake height, calibrated for Lyochrysalis equipped with Cryolapse, TgShift, LyoLevit and DiastolVAC under S3Pulse control. |
| Dicoias DCP Ψ model | B. Dicoias (Panacea) | Formulation-space compatibility potential — ranks candidate compositions inside the defined formulation space. |
| Avrami kinetics | M. Avrami (1939–41) | Crystallization progress — e.g. mannitol crystallizing out of the frozen matrix, which changes cake structure and phase behaviour. |
| GAB isotherm | Guggenheim–Anderson–de Boer | Moisture sorption — how much water the dried cake holds at a given activity, the language of residual-moisture reasoning. |
| D'Arcy flow equation | H. Darcy (1856) | Vapour transport through the porous cake — flow driven by the pressure differential across a permeable medium. |
| Henderson–Hasselbalch equation | L. J. Henderson & K. A. Hasselbalch | Buffer pH and capacity, protonation fractions, and net peptide charge vs pH — the backbone of the buffer solver and pI logic. |
| Debye–Hückel theory | P. Debye & E. Hückel (1923) | Ionic-strength effects — activity corrections where the ideal-solution assumption stops being honest. |
| Stokes–Einstein relation | G. G. Stokes & A. Einstein | Diffusion coefficients — how fast species actually move through the liquid phases the model describes. |
| WLF equation | Williams, Landel & Ferry (1955) | Viscosity–temperature behaviour near the glass transition — the kinetics of a matrix approaching Tg. |
| Arrhenius–Eyring kinetics | S. Arrhenius & H. Eyring | Temperature-dependent degradation — post-reconstitution stability windows and pathway-specific acceleration factors (per-pathway activation energies, not a single generic set). |
| Cake porosity ε = 1 − ρ_cake/ρ_solid | — (definition) | The void fraction of the dried cake — the geometry the vapour and the reconstitution liquid both travel through. |
| Ideal-solution osmolality accounting | — (engineering rule) | Tonicity: per-component osmolality summed and NaCl-adjusted into the 280–320 mOsm/kg isotonic band, with the gap stated in mg/mL. |
Dicoias Ψ — the computational intelligence stack
Dicoias Ψ is the substance-intelligence programme inside S3Pulse — and its defining feature is a wall: the whole spine is display-only and advisory. It never enters the engine, the recipe, the actuators, or any seed/calibration state. Layers that compute molecular insight present it; the only path into a real recipe is a governance flow with fifteen-invariant verification, a sha256 fingerprint, and an explicit operator apply click. Where the stack cannot compute something, it says so — a missing backend returns an honest decline, never an invented number.
W1–W5 — scoring and selection
τ-score (τ = 0.615) set scoring over the substance inventory, what-to-add analysis, Ψ-selection and correction proposals — the diagnostic surface of the stack, with pathway-specific Arrhenius parameters locked by contract tests.
W6 Mendeleev — structure → Λ
The periodic-table engine: 27-anchor ridge-NNLS maps molecular structure to the Λ property (9/12 leave-one-out on anchors), filling 68 of 101 derived periodic-table rows — every derived value marked provisional until bench review promotes it.
W6-electronic — the QM sidecar
True HOMO/LUMO/gap (highest occupied / lowest unoccupied molecular orbital) computed by a real GFN2-xTB backend (xtb 6.7.1, checksum-verified): 38 eligible single-molecule rows computed, 30 multi-component salts and 148 non-derived rows honestly declining. No backend installed → the panel says backend_missing, never a number. Display-only, isolated from Λ/Φ/Ψ/W7 by contract test.
W7 — Bayesian layer
A Bayesian calibration overlay whose writes leave the seed byte-identical — verified, not asserted. The bridge composes in prior_only mode by default; the live overlay is operator state outside the repository.
W8 — Health Direction
Per-axis structural directions with certainty hard-capped by the W6b known-space distance. Biological-resemblance scoring is deliberately declined in v1 — the heaviest honesty gate in the programme — and no health verdict of any kind is emitted.
Governance — the one door into a recipe
Dicoias Ψ governs a Peptourbillon recipe only through: diagnose (Ψ vs target band) → propose (mathematically-checked corrections from live resolvers) → verify (15 invariants + sha256 fingerprint) → operator-confirmed apply through the engine recompute path. Never silent, never automatic.