PIZZATASTICO DOUGH ENGINE (PDE)

Coupled Dough Biochemistry in Real Time

The Pizzatastico Dough Engine (PDE) links published cereal-chemistry and yeast-kinetics models into a closed system of differential equations across your entire fermentation schedule.

MODEL ARCHITECTURE

Dynamic Computation Across Temperature Phases

During dough fermentation, yeast metabolism, enzymatic gluten relaxation, starch cleavage by amylases, and organic acid formation occur simultaneously—yet each responds differently to transitions between room and cold proofing.

The Pizzatastico Dough Engine (PDE) couples these biochemical processes in a time-resolved differential equation system, accounting for the thermal cooling and warming inertia of the dough mass as well as custom flour blends (Tipo 00, Tipo 0, Tipo 1).

Systemtopologi: sluten hybrid tillstånds- och invers reglerkrets
Systemtopologi: sluten hybrid tillstånds- och invers reglerkrets Patent-style closed-loop Reduced-Order PDE control schematic (spatially reduced, Biot-Fourier coupled hybrid continuous-discrete state-space system) of the Pizzatastico Dough Engine (PDE): exogenous input vector u(t) drives Biot-Fourier thermal conduction, Raoult-Donnan water activity, and asynchronous enzyme/yeast couplers into a non-linear multi-state ODE core with inner biochemical state feedback x(t), a discrete hybrid Staglio phase and geometry transition operator x(t_s+) = Gamma_staglio(x(t_s-)), and an outer inverse boundary-value controller regulating Y0 so expansion V(t_bake) matches target V_target at baking time. Mjöl & Blend W · Tipo · Blend Hydrering & Joner H% · NaCl · φ_lip Faser & Geometri T_amb(t) · Γ_geom(t) Styrvärde Jäst Y₀ CY / IDY / ADY Biot-Fourier Termik Biot-Fourier → T_core(t) Vattenaktivitet & Donnan a_w · Ψ_Donnan Asynkrona Hastigheter α_Yeast(T) ≠ β_Amyl(T) ∫ Hybrid multivariabel ODE-kärna dx/dt = F(x(t), u(t), T_core) Multivariabelt tillståndsrum x(t) x(t) ∈ ℝⁿ | Φ_bio(x) ⊗ Ψ_rheo(x) ⚡ Staglio-Impuls (t = t_s) Diskret fas- & geometriövergång x(t_s⁺) = Γ_staglio( x(t_s⁻) ) Inre biokemisk tillståndsåterkoppling x(t) Baktillstånd y(t_bake) • V(t_bake) [+71.5% Vol] • S_glut, P/L [Rheology] • S_sug, pH [Maillard] • 5D Radar & Pole Bars − V_target + Σ e = V_target − V(t_bake) → 0 Invers randvärdesregulator t_bake , e(t_bake) = 0 ↦ Y₀* Yttre invers krets: reglerar Y₀ till målvolym vid t_bake
Fig. 0: Blockschema över PDE. En inre återkoppling x(t) integrerar den kopplade biokemin inkl. det diskreta Staglio-språnget, medan den yttre inversa slingan reglerar startjästen Y₀ till exakt målvolym vid t_bake.
I. Insignalvektor u(t)

Mjöl- och blendreologi (proteinstyrka, utmalningsgrad, blandning), fri hydrering och jonstyrka, flerfasigt temperaturschema, deggeometri samt den reglerade jästdosen Y₀.

II. Tillståndsvektor x(t) & Staglio

Icke-linjärt kopplat multivariabelt tillståndsrum för värmeledning, enzymkinetik, jäsningsstökiometri och viskoelastisk reologi med diskret fas- och geometriövergång vid rundrivning (Staglio).

III. Utsignalvektor y(t_bake)

Konvergerad jäsvolym vid måltiden, proteolytisk tänjbarhet, bevarat Maillard-socker och aromaprekursorer projicerade på degprofilens 5 axlar.

SCIENTIFIC FOUNDATION

Published Literature in the PDE Core

Every term in the engine is grounded in established cereal chemistry and microbiology:

📚 Wieser (2007) pH- & temperature-dependent proteolysis

1. Endogenous Aspartic Proteases & Gluten Maturation

Endogenous flour aspartic proteases relax the gluten network as a function of pH and temperature. The PDE models structural maturation across bulk and final proof independently of gas production.

🌡️ Sharpe-DeMichele / Schoolfield Thermodynamic S. cerevisiae kinetics

2. Cardinal Temperature & Membrane-Lipid Transition

Biophysical temperature model for Saccharomyces cerevisiae covering the full range from cold membrane-lipid phase transition in the fridge to the cardinal optimum.

💧 Raoult / Norrish / Donnan Free water · NaCl Donnan binding · Osmotic pressure

3. Water Activity & Osmosis

Accounts for biopolymer-bound water in flour, electrostatic Donnan ion binding of NaCl to the gluten network, and osmotic effects on yeast kinetics.

⚖️ Embden-Meyerhof-Parnas + Neuberg Amylase replenishment & fermentation balance

4. Closed Substrate & Hexose Stoichiometry

Closed mass balance from enzymatic cleavage of damaged starch by α/β-amylases through the Embden-Meyerhof-Parnas glycolytic pathway and Neuberg fermentation byproducts.

MODEL TRAJECTORIES

PDE i praktiken – Två exempel

PDE för samma referensmjöl (Tipo 00 · 12,5 % protein · 63 % hydrering · 2,8 % NaCl · 4 × 250 g · 430 °C).

Jäsning / Expansion Glutennätverk Restsocker Amylas pH-värde (höger) Kärntemp. T(t)
Optimalt Bak- & Glutenfönster (62–78 %) Maillard- & Arom-pH-Zon (44–62 % · pH 5.50–5.66) 7 °C Kryo-Frikoppling
Fig. 1a: Exempel 1 – Direktdeg 23 °C (12 h)
Fig. 1a: Exempel 1 – Direktdeg 23 °C (12 h) Coupled 6-state observable Reduced-Order PDE trajectory for 12 h room-temperature direct wheat dough (23 °C, Tipo 00 flour, 12.5% protein, 63% hydration, 2.8% NaCl, 4 x 250 g = 1000 g, 0.129% fresh yeast): 9.64 h bulk fermentation reaching +111.5% physical volume expansion, Staglio balling degassing at t = 9.64 h to +25.9%, and 2.36 h final proof converging at t = 12.0 h inside the emerald Optimal Baking & Gluten Window (+71.5% expansion, 64.3% proteolytic gluten structure) and golden Maillard & Aroma-pH Corridor (51.9% residual sugar = 0.86 g/100g, pH 5.54, 13.2% amylase starch cleavage). Staglio 120 100 80 60 40 20 0 Relativt tillstånd [%] 6.0 5.8 5.6 5.4 5.2 pH-värde [-] 0 2 4 6 8 10 12 Jästid t [h]
Fig. 1b: Exempel 2 – Flerfas kalljäsning 23 °C → 7 °C → 23 °C (24 h)
Fig. 1b: Exempel 2 – Flerfas kalljäsning 23 °C → 7 °C → 23 °C (24 h) Coupled 6-state observable Reduced-Order PDE trajectory for 24 h multi-phase cold maturation (1.39 h warm puntata at 23 °C, 19.00 h cold maturation at 7 °C, 0.75 h Biot-Fourier block acclimation to 13.8 °C, Staglio dividing at t = 21.14 h, and 2.86 h residual-chill-calibrated ball proof at 23 °C, 0.143% fresh yeast): Biot-Fourier cooling inertia and two-stage re-warming across bulk and ball geometry; convergence at t = 24.0 h inside the emerald Optimal Baking & Gluten Window (+71.5% expansion, 73.3% gluten structure) and golden Maillard & Aroma-pH Corridor (59.8% residual sugar = 0.99 g/100g, pH 5.56, 13.1% amylase starch cleavage). 7 °C Staglio 120 100 80 60 40 20 0 Relativt tillstånd [%] 6.0 5.8 5.6 5.4 5.2 pH-värde [-] 0 4 8 12 16 20 24 Jästid t [h]
Fig. 1: Kopplade 6-tillståndskurvor inkl. Staglio. Vid gräddning möts volym och gluten i det gröna bakfönstret (62–78 %), medan restsocker och pH landar i den gyllene Maillard- och aromzonen (44–62 % / pH 5,50–5,66).
Amylasöverskott (< 20 °C) Jästdominans (> 20 °C) Faktor β/α (höger) Bevarad maltosreserv (∫ ΔJ dt)
Fig. 2a: Termisk differens Δr(T) = Amylas − Jäst
Fig. 2a: Termisk differens Δr(T) = Amylas − Jäst Thermal rate differential Delta r(T) = beta_amylase(T) - alpha_yeast(T) across dough temperatures 2 °C to 32 °C (normalized to 100% at 20 °C = 0 percentage points): exact bifurcation at T = 20.0 °C; teal positive enzyme surplus zone below 20 °C driven by Sharpe-DeMichele yeast membrane-lipid phase transition (+10.3 pp / 1.31x decoupling at 7 °C; +23.2 pp / 2.81x at 4 °C); rust negative yeast-dominance zone above 20 °C (-4.5 pp at 23 °C down to -36.5 pp at 32 °C). 7°C: +10.3 pp (1.31×) 20 °C (Δr = 0) 23°C: −4.5 pp +40 +20 0 −20 −40 Hastighetsdifferens Δr [pp] 8× 6× 4× 2× 0× Kvot Amylas / Jäst [×] 2 7 12 17 22 27 32 Degtemperatur T [°C]
Fig. 2b: Netto-hexosflöde ΔJ_hex(τ) = Tillförsel − Förbrukning
Fig. 2b: Netto-hexosflöde ΔJ_hex(τ) = Tillförsel − Förbrukning Time-resolved net hexose mass flux dS_sug/dt = J_amylase(tau) - J_yeast(tau) in [mg / (100g * h)] over normalized process progress tau (0..100%) comparing 12 h direct dough at 23 °C (rust dashed curve descending from -35 to -97.5 mg/100g*h with Staglio CO2-relief step at tau = 80.3%) against 24 h cold-matured dough (navy solid curve rising into a flat -17.4 mg/100g*h cryo-preservation plateau across tau = 5.8%..85.0%). The emerald-shaded integral area between both trajectories depicts the preserved natural maltose reserve (+15.2% more residual reducing sugar at baking time). 7 °C Plateau: −17.4 mg/(100g·h) ∫ ΔJ_hex dt (+15.2% Sugar) 23 °C (12 h) 0 −20 −40 −60 −80 −100 Nettosockerflöde [mg/100g·h] 0 20 40 60 80 100 Normaliserat förlopp τ [%]
Fig. 2: Varför kyla förädlar degen: under 20 °C överträffar mjölets amylas den bromsade jästen (2a, turkos), vilket vid 7 °C skapar en kryoplatå som bevarar naturlig maltos för Maillard-bryning och esterarom (2b, grön).
Fig. 3: 5-Axlars harmoni & Bipolärt reologispektrum vid gräddning
Spindelnät
Fig. 3: 5-Axlars harmoni & Bipolärt reologispektrum vid gräddning 5-axis rheological and sensory radar comparison at baking time between the 12 h direct dough at 23 °C (99% overall harmony: aroma 97.8%, gluten maturation 99.2%, Maillard browning 100.0%, ball relaxation 97.5%, hydration binding 99.2%) and the 24 h multi-phase cold-matured dough 23 °C -> 7 °C -> 23 °C (97% overall harmony: aroma 94.4%, gluten maturation 95.2%, Maillard browning 100.0%, ball relaxation 99.3%, hydration binding 99.2%) on identical 12.5% protein Tipo 00 flour. Both schedules place all 5/5 axes deep inside the outer emerald Sweet-Spot ring. Arom & Jäst Mjölmognad & Gluten Färg & Socker Bollar & Jäsning Inkråm & Hydrering
Pol-staplar
Jästsmak Arom & Jäst Mogen smak
Mjuk / Brister Mjölmognad & Gluten Seg / Spänstig
Blek deg Färg & Socker Bränns snabbt
Flyter ut Bollar & Jäsning Drar ihop sig
Kompakt / Fast Inkråm & Hydrering Mycket fuktig
Kall 23→7→23 °C (24 h) — 97 % (5/5 Sweet Spot) Direkt 23 °C (12 h) — 99 % (5/5 Sweet Spot) Sweet Spot
Fig. 3: Både 12 h direktdeg vid 23 °C (99 %) och 24 h kalljäsning (97 %) placerar alla 5 axlar i Sweet Spot (vänster), medan polstaplarna (höger) visar kalljäsningens djupare estermognad (92 % mot 82 %) och strukturerade spänst (60 % mot 48 %).
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