The yeast cell, as the model sees it

Proportion dd69613 · 2026-10-21
WORT INwhat the fermenter offers the cell BEER OUTwhat leaves the cell, and what the beer does with it FERMENTER BOTTOM PLASMA MEMBRANE ER: STEROLS AND LIPIDS MITOCHONDRIONnot modelled NUCLEUS VACUOLE BUD GLYCOLYSIS AND THE CARBON CORE KETO-ACID NODE: HIGHER ALCOHOLS ESTERIFICATION CARBONYLS AND ORGANIC ACIDS SULFUR GROWTH, DIVISION, DEATH HOP BIOTRANSFORMATION AND PHENOLS facilitated diffusionKm 5 g/LVmax 1.2 ng/cell/d taken as a hexose H⁺ symportrel. rate 0.85 H⁺ symportKm 18.2 g/Lmaltose Ki 9.4 g/Lrel. rate 0.55 (strain) STA1 strains onlyrel. rate 0.10 released when the addition arrivesτ 0.1 d bottle refermentation MAL12 maltase / HXK MAL12 glucoamylase HXK1/2, PGI PFK, FBA, TPIglycolysis GAPDH, PGK, ENO, PYK0.9776 × (1−X) g pyruvate per g sugar3.5 % to biomass GAPDH GPD1, GPPredox balanceale 4.0 %, lager 3.2 % of sugar+5 % per 0.010 OG above 1.050 PDC1/5/6decarboxylationk 100 /d0.4997 g CO₂ per g CO₂ evolved ADH1k 100 /d1.0458 g ethanol per g NADH reoxidised ALD6, ACS1/2via acetate6 % of the flux mass closurek 80 /d diffuses out dissolved CO₂ by Henry (head + column pressure) escape (strain leak)0.33 × pool × leak ADHtaken back and reduced (Q10 2, bed too)k 0.62 /d maintenance leak from ethanol0.85 /d × suspended fraction uptake17 mg O₂ /g dry wt /hKs 0.05 ppm, Q10 1.5 sealing + closure ingresscrown 0.5, cork 2.5 mg/L/yr ERG1, ERG11finishes the pitch's squalene1.5 /h12 O₂ per sterol HMG1, ERG9, ERG1, ERG11de novo ergosterol1.95 g acetyl-CoA per g968 mg O₂ per gQ10 4 O₂ to the oxygenases what sterol cannot use sterol per biomass0.13 % → 1 % dry wt one carrier set per sterol complement installed once the O₂ is gone96 /dKs 0.05 ppm reserve fermented to build the membrane0.85 of a store per complement GSYlaid down once growth stops1 /d, full at 25 % dry wt maintenancestore / 30 d, Q10 2 new cells bring a full set lost under nitrogen starvationt½ 9 h, floor 0.6 AGT1, MALx1 synthesisbuilt while fermenting, from the nitrogen quota6 /dinduction Ks 0.5 g/L maltose turnover + glucose inactivationt½ 2.2 d×(1 + 30 × hexose/(10 + hexose)) class A : B : C = 1 : 0.45 : 0.21Ks 80 ppmonly while fermenting folded into class A own channel, no competition0.4 × malt FAN fills the quota 10 fg/cell/h, Ks 0.3 mg/LQ10 2.4 dN/dt = μNμmax 4 /dcarbon-cappedRosso cardinal T mass per celld = 7.94 + 4.60 e^(−0.142 T) µm ∫N dt; generations death0.0059 /d × e^(1.81 σE)× Arrhenius × fragility^½ FLOflocculation when the sugar runs out; Stokes settling×(1 + (20 − T)/20) coldv = 2Δρgr²/9μ, r 2.75 µm sugar disperses flocs (NewFlo)4 /d × S/(2 + S) the bed dies too dead cells' nitrogen back to the wort as FAN0.012 /d at 10 °C, Ea/R 9960 K suspended cells at packaging secreted glucoamylasedextrin → glucose in the beer ADH, ALDHethanol + O₂ → acetic acid7.1e-13 mg/cell/d × O₂ Monod homo: 2 lactate; hetero: + CO₂ + ethanol or acetateIBU50 inhibition, lactate ceiling into the beer's acids Pediococcus spills α-acetolactate0.15 × uptake (Pedio), 0.02–0.03 (Lacto) each amino acid by its class share the rest to protein (Förster 2003 demand) BAT1/2, ARO8/90.10 to the fusel ARO10, ADH BAT1/2, ARO8/90.075 to the fusel ARO10, ADH LEU4, LEU1/2valine on to leucine0.10 BAT1/2, ARO8/90.10 to the fusel ARO10, ADH ILV1 deaminase0.10 to the fusel ARO10, ADH BAT1/2, ARO8/90.125 to the fusel ARO10, ADH BAT1/2, ARO8/90.032 × (200/FAN)^0.69 to the fusel ARO10, ADH aldehyde left unreduced0.44 % of methionol keto acids made from sugarisoamyl 0.538, 2-MB 0.140, isobutanol 0.148, propanol 0.109 mg per g sugar full yield only while FAN lasts ARO1–7 shikimatefollows biomass made yeast ADH cleans 95 % of the kilning aldehydesphenylacetaldehyde 11 % leftmethional 0.44 % of methionol to isoamyl alcohol, 2-methylbutanol, methionol (not esterified) diffuse out acetyl-CoA, the acyl donorKm 0.10 (saturated) ATF1Km 29.8 mMEa/R 8510 K ATF1 ATF1 ATF1 ATF1 ATF1first order in ethanolref. 16 750 mg/L ethanol out into the beer shelfethyl acetate τ 1640 dethyl MCFA esters τ 3460 d esters made in step with the acids' releaseprecursor-limited (Saerens 2008) all excreted 39 % retained in the cell at 20 °C 87.5 % retained lactic acid + ethanol γ-decalactone 0.8 % of the C8 + C10 esters acetyl-CoA → acids with the fluxbaseline 30 mg/LK 0.00306 × flux 30 mg/L TCA leak100 mg/L malonyl-CoA chain extension released with biomassinverse Arrheniuspitch-O₂ spill goaty, cheesy at 8 to 13 mg/L ILV2 acetolactate synthase2 pyruvate → α-acetolactate + CO₂0.63 × μ × X + 0.01 × X maintenanceFAN mod (1/fanRatio)^1.2 excreted spontaneous oxidative decarboxylation in the beer0.7 /d, Q10 2.5 BDH1 (via acetoin)taken back and reduced by live cells and the bedk 7.6 /d × suspended capacity, Q10 2 Km 1 ppm (Cherest 1997) MET3, MET14, MET16sulfate → APS → PAPS → sulfite SO₂ leak, per strain typeale 5.5, lager 11 mg/L× FAN stress (low FAN → less) MET5/MET10 sulfite reductase0.35 of the H₂S by sulfate Monod organic branch under FAN stress0.65 share× clamp(1/fanRatio, 0.5, 3) methionine → methanethiol0.30 × flux × Met × FAN stress out CO₂ stripping; maturation loss τ 7 d0.30 × flux × e^((T−20)/16.5) / (1 + P bar) DMS only stripped: the yeast makes nonee^(−0.030 × Σ breakout × ΔCO₂ g/L) evolved gas precursors dissolve, τ 0.22 ddry hop 1.0, hop stand 0.25, kettle 0.05 of the load oil into the beerdissolved share by log P: linalool 0.79, geraniol 0.47, myrcene 0.08 hop enzyme converts dextrinmin(0.25, 0.035 × g/L) of the dextrin released τ 2 d after arrival eaten by whatever cells are still suspended IRC7 β-lyaserelease ∝ fluxK 2.5 × fluxbiotrans 0.08 to 0.90 IRC7 ATF1acetylation≈1 % (Haslbeck 2017) free thiols in the beer taken up as the ferment goes−ln(1 − r) per fermentable g, r strain 0.38 to 0.70 OYE2/3 ene-reductase33 % to citronellol, rest lost CO₂ stripping by Henry constant (spunding keeps more)K_aw(T) × gas L/L/d × dissolved share adsorbs to cellsK 0.6 per M cells/mL leaves with the settling cells from the grist and the hopsferulic 2.0, coumaric 0.7, sinapic 0.1 mg per kg44 °C rest frees more PAD1 / FDC1decarboxylation (POF⁺ strains)Ea/R 3221 K PAD1 / FDC1 PAD1 / FDC1 Brett VPR0.208 of the 4VG Brett VPR0.724 of the 4VP clove, at 0.3 mg/L SUC2 invertaseperiplasmic hydrolysis ZWF1 TPS1/2 PDHrespiration, repressed by sugar (Crabtree) ATP, maintenance energy malate, citrate leak PMA1H⁺ export: wort pH 5.2 → beer 4.2 beer pH OLE1 Δ9-desaturaseO₂ to unsaturated fatty acids membrane phospholipids trub lipids taken up MET17, CYS4 MXR1DMSO → DMS by the yeast ILV22-ketobutyrate + pyruvate spontaneous IAH1ester hydrolysis back to alcohol + acetate isoamyl octanoate and kin ARO8/9, ARO10, ADHEhrlich route for Tyr, Trp malate, citrate, pyruvate excreted START, budding, bud scars amino acid, polyphosphate, Zn stores proteinase A degrades foam proteins MEP1–3ammonium permeases PUT4; PUT1 needs O₂proline is not used anaerobically Ca²⁺ bridges the FLO lectins mannoproteins, β-glucan released iso-α-acids, polyphenols lost to cell walls γ-GT, CPY, Cys-Gly dipeptidaseglutathione conjugate processing ATF1 isomerisation; nerol, geranyl acetate EXG1bound terpenes released resuspension at opening excess CO₂ makes bigger cells×e^(0.15 × g/L excess) division needs membraneKm 0.25 of the span MAL induction hexose signals MIG1Hill 2, K 1 g/L catabolite repression of MAL genes σ·E on the carriershexose k 0.62 /M from 0.33 Mα-glucoside k 0.65 /M from 0.54 M growth stops by 2.05 M σEalso Tmin +1.1 °C per % v/v death × e^(1.81 σE)Ea 262 kJ/mol, lineage-shifted σ·E on the permeasek 1.95 /M from 0.61 M Droop on zincfloor 0.1 fg, full 1.5 fg zinc on uptake (Bromberg 1997) Droop on NQmin 0.5 carbon ceilingnon-maltotriose uptake per cell thin membranes after many divisions strain flocK from published ratings Custers effect: O₂ relieves anaerobic sluggishnessuptake 1/2.67, growth 1/1.16 without O₂ Äyräpää: growth takes the keto acids for protein×(1 − 0.6 × growth activity) live O₂ represses ATF1 (Fujii 1997)0.1 + 0.9 × 0.2/(0.2 + O₂ ppm) growth-state factor: lipid synthesis takes the acetyl-CoA1 − 0.5 × (μ / carbon ceiling) dissolved CO₂ (spunding, tall tanks)e^(−0.66 × g/L excess) myrcene ceiling 60 µg/L at 2 °C gated to zero in POF⁻ strains Brettanomyces only unsaturated fatty acids repress ATF1 pantothenate, Cu²⁺ lower H₂S NCR: ammonium shuts GAP1 Crabtree repression of respiration glucose fructose sucrose maltose maltotriose dextrins sugar feeds priming sugar(bottle) sulfate SO₄²⁻ dissolved O₂pitch aeration 2 to 14 ppm (Sadler) headspace andclosure O₂ wort lipids(trub, linoleic) zinc Zn²⁺ Ca²⁺, Mg²⁺,Cu²⁺, phosphate free amino nitrogenLeu Ile Val Phe Thr Met small peptides ammonium, DAP(class A) proline (class D) ferulic, p-coumaric,sinapic acid wort Strecker aldehydes3-methylbutanal, methional… DMS (from SMM) HXT SUC2 MALx1 AGT1 dextrinuptake O₂diffusion SUL1/2 ZRT1 GAP1, BAP2permeases PTR2 MEP1–3 PMA1 H⁺-ATPasepH drop cell wall: mannoproteins,β-glucan release FLO lectinsCa²⁺ bridging iso-α-acid andpolyphenol binding glucose, fructose maltose maltotriose dextrin glucose-6-P pentose phosphatepathway (NADPH) triose-P glycerol pyruvate NADH CO₂ acetaldehyde acetyl-CoA unaccountedcarbon ethanol trehalose leucine valine isoleucine threonine phenylalanine methionine Tyr, Trp protein(biomass) α-ketoisocaproate α-ketoisovalerate α-keto-β-methylvalerate 2-ketobutyrate phenylpyruvate KMBA de novo from pyruvateILV2/5/3, LEU, ARO isoamyl alcohol isobutanol 2-methylbutanol n-propanol 2-phenylethanol methionol tyrosol,tryptophol methional ADH reduces wortStrecker aldehydes ATF1 / ATF2alcohol acetyltransferase isoamyl acetate isobutyl acetate 2-methylbutyl acetate propyl acetate phenylethyl acetate ethyl acetate IAH1 esterasehydrolysis EHT1 / EEB1ethanol acyltransferase ethyl butyrate ethyl hexanoate ethyl octanoate ethyl decanoate ethyl lactate isoamyl / phenylethylMCFA esters γ-lactones squalene ergosterol membrane: sterol share,transporters formed OLE1 desaturase:unsaturated fatty acids O₂ respired orotherwise used phospholipids PDH, TCA cycle,respiration (ATP) ATP, maintenanceenergy malate, citrate,fumarate leak α-acetolactate 2,3-butanediol α-acetohydroxybutyrate 2,3-pentanedione acetic acid lactic acid succinic acid FAS1/2 fatty-acidsynthase hexanoic, octanoic,decanoic acid malate, citrate,pyruvate excreted sulfite SO₃²⁻ sulfide H₂S homocysteine →Met, Cys, glutathione Cys / Met breakdown(FAN stress) methanethiol MXR1: DMSO → DMSreduction pantothenate, biotin,copper on H₂S nitrogen quota(Droop, Qmin 0.5) zinc quota glycogen(25 % dry wt) generations,cell-days transporters made,waiting for O₂ to go divisionμ ≤ 4 /d suspended livecells cell size(T, CO₂) dead cells maintenancedrain MIG1 cataboliterepression START, cell cycle,bud scars amino acid andpolyphosphate store proteinase A(foam) autolysis:nitrogen back out 3MH precursorsCys-3MH, G-3MH 4MMP precursor GSH → Cys-Gly → Cysconjugate (γ-GT, CPY) 3MH 4MMP 3MHA 4MMPacetylation geraniol citronellol linalool α-terpineol, nerol,geranyl acetate hop glycosidesEXG1 β-glucosidase hop oil on the cell:myrcene, limonene, pinene ferulic acid p-coumaric acid sinapic acid 4-vinylguaiacol 4-vinylphenol 4-vinylsyringol 4-ethylguaiacol 4-ethylphenol PAD1 / FDC1decarboxylase Brett vinylphenolreductase hop amyloglucosidase(hop creep) headspace, CO₂purge ethanol CO₂ dissolved glycerol higher alcohols esters shelf hydrolysisτ 295 d isoamyl acetate SO₂ H₂S methanethiol α-acetolactate diacetyl acetaldehyde acetic, lactic,succinic acid MCFA acids beer pH(4.0 to 4.5) hop oil in beer:myrcene, linalool, geraniol… 3MH, 3MHA, 4MMP(ng/L) citronellol 4VG, 4VP, 4VSvinyl phenols 4EG, 4EPethyl phenols yeast haze9 EBC per M cells/mL resuspensionat opening foam proteins(proteinase A) yeast bed:settled cells Brettanomyces lactic bacteria lactate, acetate(bacterial) dry-hop addition(arrives on a day or at a gravity) hop-creep sugarmaltose 70 %, glucose 30 % lost with the crop(bound hop oil) The yeast cell, as Proportion sees it Saccharomyces cerevisiae in a fermenter: every pathway the simulator runs as a rate law, what it keeps as a closed form, and what it does not model yet. Solid edges cite the rate laws in src/process/reactions. Proportion dd69613 · 2026-10-21 KEYrate law in the live integratora closed form or fitted factor, not a rate lawreal yeast biology, not modelledinhibits / repressesactivates / drivesgatestransport across the membranesugars and dextrinnitrogen, amino acidsgasesmineralshop compoundsintermediatesethanolhigher alcoholsestersorganic acidscarbonylssulfur compoundsphenolsthiolsterpeneslipids and membranecell stateGene names in italics are the real enzymes; the numbers are the model's constants. Click anything in the web viewer for its laws and source files.
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