This tool computes the complete salt, trace-metal, vitamin, and complex-supplement recipe required to grow a target dry biomass of Saccharomyces cerevisiae under aerobic batch + fed-batch conditions. Unlike fermentation calculators that target a product titer, this one is biomass-concentration driven: you specify how much dry cell weight (DCW) you want and at what final concentration, and the calculator derives the stoichiometric demand for every element and vitamin, selects pH-control-friendly salts, and produces a Procedure-ready weigh-out sheet.

Version 2.1 supports three medium classes on a single unified page:

• Defined medium — pure salts + glucose + vitamins. Maximum reproducibility.
• Semi-defined medium — defined base with 1–10 g/L yeast extract and/or peptone.
• Complex medium — ≥ 10 g/L combined complex materials (YE + peptone + CSL + molasses). Industrial-scale territory; vitamin stocks often omitted.

A live Medium Type badge (Summary Row 7) classifies the current recipe automatically. Four process additive categories (antifoam · chelator · pH buffer · osmoprotectant) cover the per-litre-of-broth additions that don't scale with biomass.

Key distinction: This is a conceptual tool for rapid what-if analysis. It assumes aerobic respiratory metabolism with Y_X/S in the 0.40–0.55 g/g range. Real-world yields are strain-specific and depend on OTR, pH control, and feed strategy — treat the outputs as a starting point, not a production recipe.

1. Open Target Production → Biomass Production Targets. Enter the Batch Phase DCW target (default 400 g — the biomass you want at the end of the batch phase, before feeding starts), Fed-Batch Phase DCW target (default 600 g — the additional biomass produced during fed-batch), Final Biomass Concentration (default 50 g DCW/L — sets the fermentor volume), and Inoculum Biomass (default 5 g DCW — drives the generations and duration estimates in the Summary).
2. Open Target Production → Stoichiometric Yield. Slide Y_X/S (0.35–0.55 g DCW per g sugar, default 0.48). Aerobic respiratory metabolism on glucose with good OTR typically delivers 0.45–0.52. Values above 0.52 imply tight process control; below 0.40 suggest partial Crabtree overflow to ethanol.
3. Process Options — keep both toggles ON (defaults). Utilisation Efficiency Correction inflates elemental demands by 10–40% element-dependent to compensate for real-world losses. Complex Supplement Credit subtracts nutrients delivered by YE/peptone/CSL/molasses from the salt recipe. Toggle either OFF to see the underlying unadjusted values.
4. (Optional) Open Complex Formulation if you want to replace some of the defined-medium salt recipe with YE, peptone, CSL, or molasses. Expand any of the five material sub-cards, set a dose (g/L as-received), pick a source variant from the dropdown, and — if you have a supplier Certificate of Analysis — type in your measured composition values to override the literature defaults. The Deficiency Analysis panel at the bottom shows real-time coverage of each nutrient. See the Complex Formulation Workflow card below for details.
5. (Optional) Set Process Additives via Biomass → General Composition → Process Additives. Four categories: Antifoam (default PPG 2000 at 0.1 mL/L), Chelator (default citric acid at 0.5 g/L), pH Buffer (default 0 — add MES or similar if you lack active pH control), and Osmoprotectant (default 0 — add glycine betaine or glycerol for VHG or high-biomass runs). Pick a source from the dropdown; 28 variants across the four categories are available.
6. Edit biomass composition only if you want to deviate from the literature baseline. Open Biomass → General Composition and expand Macroelements / Trace Metals / Vitamins. All values are editable within published Min–Max ranges. Click "Load Standard" on the Biomass card header to restore defaults.
7. Expand Results & Tabs → Total Required (or Batch Phase / Fed-Batch Feed) and read the salt weigh-out sheet. Each tab has four sub-cards (Macro / Trace / Vitamin / Process Additives). Change the dropdown in any row to pick a different salt for that element — the mass, co-element credits (✓ covered indicators), and complex-material credits update live. Check the Summary Row 7 badge to confirm your Medium Type classification.

Left column

• Target Production — three sub-cards: Biomass Production Targets, Stoichiometric Yield, and Process Options. Process Options holds two collapsible sub-menus each with an in-header toggle switch: Utilisation Efficiency Correction (ON/OFF) and Complex Supplement Credit (ON/OFF). The derived-box at the bottom shows Total Target Biomass and Total Broth Volume (inoculum + batch + feed).
• Complex Formulation (new in v1.5) — expanded by default. Five per-material sub-cards (Yeast Extract · Peptone · Corn Steep Liquor · Cane Molasses · Beet Molasses) each with a dose input, source variant dropdown, solids % (for liquids), and a 20-row editable composition table. Plus a Deficiency Analysis sub-card at the bottom showing real-time per-nutrient coverage.
• Biomass — two master tabs. General Composition holds four sub-cards: Macroelements (7 rows), Trace Metals (6 rows), Vitamins (8 rows), and Process Additives (4 categories × dropdown selector). All biomass-composition values are editable. Cost Estimate lists every compound in the sources library (salts + 19 complex-material sources + 28 additive sources) with an editable USD/kg price input; changes propagate live to the Media Cost cell in the Summary.

Right column

• Summary — seven live-computed rows. Row 1: Sugar Required · Total Biomass · Broth Volume. Row 2: Inoculum → Batch → Fed-Batch biomass progression (color-coded teal/blue/amber). Row 3: volume split & initial sugar concentration. Row 4: C:N ratio & nitrogen strategy. Row 5: O₂ demand & CO₂ evolved & heat of fermentation. Row 6: generations · duration · media cost. Row 7: Medium Type badge — Defined (< 1 g/L complex) / Semi-defined (1–10 g/L) / Complex (≥ 10 g/L), with color-coded left-border (blue / teal / amber) and a live g/L sub-label.
• Results & Tabs — six tabs. Total Required, Batch Phase, and Fed-Batch Feed each split into four sub-cards (Macro / Trace / Vitamin / Process Additives), all collapsed on load.
  • Total Required — all-up nutrient recipe for the whole batch.
  • Batch Phase — initial medium charge + Macronutrient / Trace / Vitamin A / Vitamin B / Inositol stock preparation sheets with adjustable fold and volume.
  • Fed-Batch Feed — feed composition + stock preparation sheets (chelator, pH buffer, osmoprotectant are batch-only; antifoam is volume-split).
  • Procedure — 11-step cultivation protocol with live-computed values and the batch medium concentration check table.
  • Reference — five sub-cards: Macroelements, Trace Metals, Vitamins, Process Additives (literature values), and Complex Supplements (composition per kg dry for all 19 complex-material sources), plus Process Notes.
  • Test Medium — reverse-mode: enter actual grams you weighed out and see which nutrient limits biomass first (coverage % + verdict bar).

Top-level navigation

• Brand bar — sticky teal-gradient header with the FermAxiom branding, the calculator name, and a numbered "Propagation Medium" tab. Designed to host additional top-level calculators in future releases.
• Inner sub-tabs — four sections inside the Propagation Medium calculator: ANALYSIS (the interactive tool), INSTRUCTIONS (this guide), SCIENCE (the biology and stoichiometry behind the calculations), REFERENCES (bibliography of textbooks, papers, and online resources).

• Total Sugar Required = biomass ÷ YX/S (e.g. 1000 g ÷ 0.48 g/g ≈ 2083 g glucose)
• Broth Volume = biomass ÷ finalDCW (e.g. 1000 g ÷ 50 g/L = 20 L)
• Initial Batch Volume = broth × (biomassBatch / biomass) (proportional split). The remaining volume is delivered via feed.
• Initial Sugar Conc. = batch glucose ÷ batch volume, capped at 30 g/L to avoid osmotic stress & Crabtree overflow. If your C-demand exceeds this cap, excess glucose shifts into the fed-batch phase.
• C:N Ratio (mass) = total sugar ÷ total N. For aerobic yeast biomass (8.3% N) the natural ratio lands around 15–20. Values > 20 risk N-limitation; < 10 wastes ammonia.
• Batch / Fed-Batch N Split — 20% / 80% — the default assumes most N arrives via pH control (NH₄OH) during fed-batch, consistent with the Procedure tab's protocol. Batch phase only needs ~20% of total N as starter charge.
• O₂ Demand = biomass × 1.0 g/g using Y_O/X = 1.0 g O₂ / g DCW — the literature value for aerobic S. cerevisiae. For a 1 kg DCW batch, that's 1 kg O₂ ≈ 700 L pure O₂ at STP, delivered continuously over the run via sparging.
• CO₂ Evolved = carbon-balance derivation: (sugar × 0.40 − biomass × 0.47) × 44/12. Sugar is 40% carbon, biomass 47% carbon; the difference becomes CO₂.
• Heat of Fermentation = biomass × 15 kJ/g, the standard enthalpy release for aerobic yeast growth. Tells you whether the cooling jacket can keep up.
• Generations = log₂(biomass / inoculum). For 5 g → 1000 g that's 7.6 doublings — typical for seed-train propagation.
• Expected Duration — sum of two phases: batch at μ = 0.30 h⁻¹ from inoculum to biomassBatch, then fed-batch at μ = 0.17 h⁻¹ (sub-Crabtree) to final biomass. Defaults to ~20 h total.
• Media Cost Estimate — per-compound bulk industrial pricing (USD/kg, 2024–25 averages). Includes salts + complex materials (YE, peptone, CSL, molasses) + process additives. Edit individual compound prices in the Biomass → Cost Estimate tab to match your actual supplier quotes; blank value reverts to default.
• Medium Type (Row 7) — live classification based on total dry-basis g/L of all complex materials combined: Defined (< 1 g/L), Semi-defined (1–10 g/L), or Complex (≥ 10 g/L). The left border of the row changes colour to match. Sub-label shows the actual g/L figure plus a typical-use hint.

1. Elemental demand = biomass × composition% × UE_factor. The UE factor inflates stoichiometric minimums: macro nutrients 1.10–1.30 (P, K, Mg), N gets 1.30, S 1.40, Ca 1.25, trace metals 1.20, most vitamins 1.20, biotin 1.40 (most-lost vitamin).
2. Complex material credits — if any YE, peptone, CSL, or molasses is dosed AND Complex Supplement Credit is ON, deliveries are subtracted from elemReq before the salt algorithm runs. For each material: dry_total = dose × solids_fraction × volume, then delivered(nutrient) = dry_total × composition_fraction × credit_rate. Credit rates: 100% for minerals (N, P, K, Mg, S, Ca, Na), 100% for trace metals (Fe, Zn, Mn, Cu), 50% for B-vitamins and inositol (safe margin for ±25–40% lot variance), 100% for carbon (sugar from molasses/CSL reduces the glucose demand directly). Credits are clamped at zero — a supplement can zero-out a salt but never produce a negative demand.
3. Salt mass = elementDemand ÷ elementFraction. E.g. Mg demand of 4 g via MgSO₄·7H₂O (9.86% Mg) requires 4 / 0.0986 ≈ 40.6 g salt.
4. Co-element credits — many salts deliver two nutrients (e.g. K₂SO₄ gives both K and S). The calculator runs a second pass: for every element already over-supplied as a co-element, the primary salt mass is reduced or zeroed-out, with a "✓ covered" indicator shown in the recipe.
5. Liquid pH-control reagents (NH₄OH, KOH, NaOH, H₂SO₄, H₃PO₄) count their delivered element at their solution concentration, with editable concentration widgets on each row (default 32% NH₃ for ammonia, 50% for KOH/NaOH, 85% for H₃PO₄, 96% for H₂SO₄).
6. Batch / Fed-Batch split is proportional to the biomass split, with the one exception that sugar for the batch phase is capped at 30 g/L to avoid osmotic stress; overflow shifts into feed. Process additives split differently: antifoam is volume-proportional, chelator/buffer/osmoprotectant are 100% to batch.
7. Stock solution concentrations (shown in Batch Phase and Fed-Batch Feed sub-tabs): 10× macronutrient, 100× trace element, 40× Vitamin Stock A (water-soluble B-vitamins), 20× Vitamin Stock B (sparingly soluble), 20× Inositol Stock. All dilution factors are printable recipe lines in the Procedure tab.
8. Molasses auto-pH adjustment — when cane molasses dose reaches 5 g/L, the K source auto-switches from KOH (base) to KCl (neutral). User manual override is memoised and respected. See Complex Formulation Workflow card for details.

The Complex Formulation card (between Target Production and Biomass in the left column) lets you replace some or all of the defined-medium salt recipe with complex ingredients. Five materials are supported; each has its own sub-card with dose input, source variant, solids %, and a fully editable composition table.

The five complex materials

• Yeast Extract (dry) — 4 variants (Difco / Kerry / Angel / bulk autolysate). Rich in B-vitamins, K, P. ~10% N on dry basis. Price range $8–$35/kg.
• Peptone (dry) — 7 variants (Bacteriological / Tryptone / Soy / Casamino Acids / Meat / Gelatin / Cottonseed). Rich in FAN, variable S. ~9–16% N.
• Corn Steep Liquor (CSL) (liquid, 50% solids default) — 3 variants. Cheap (~$3/kg). ~7% N dry basis. High K, partial B-vitamins. Contains lactic acid + phytate.
• Cane Molasses (liquid, 80% solids default) — 3 variants. Primary use is as a carbon source (~50% sucrose+invert on dry basis). Rich in K/Ca. Starts at pH 5.0–5.5 (already acidic).
• Beet Molasses (liquid, 80% solids default) — 2 variants. Carbon source (~50% sucrose). Rich in biotin + betaine (natural osmoprotectant). Na ~1.5%. Starts at pH 7.5–8.5 (alkaline, needs acid titration).

How the credit math works

1. Dose each material in g/L of final broth (as-received for liquids). The dose value sits next to the material's name in its sub-card header for quick editing.
2. Set the solids fraction for liquid materials — default 0.50 for CSL, 0.80 for molasses. Dry dose = as-received dose × solids fraction.
3. Pick a source variant from the dropdown — this preloads the literature-average composition. Each variant has a short note describing its typical profile.
4. Override composition values for any nutrient if you have a Certificate of Analysis for your specific lot. Type in the nutrient row's input box; leave blank to revert to the source default shown as placeholder. Values are displayed in friendly units (% w/w for macros, mg/kg for trace & vitamins) and stored internally as dimensionless fractions.
5. Credits are applied automatically when Credit nutrients from complex supplements is ON (Process Options). Every nutrient delivered by the supplements is subtracted from the defined-medium recipe at these rates:
   • 100% credit for minerals (N, P, K, Mg, S, Na, Ca) and trace metals (Fe, Zn, Mn, Cu)
   • 50% credit for B-vitamins & inositol (safer margin for ±25–40% lot variance)
   • 100% credit for sugar from molasses / CSL — the Total Sugar Required in the Summary drops accordingly
6. Remaining demand is rendered in the Results tabs as the usual salt recipe — with any salt dropping to zero when the supplements fully cover that nutrient.

Deficiency Analysis panel

The panel at the bottom of the Complex Formulation card gives you a real-time view of how well your complex recipe covers the biomass demand. Each tracked nutrient gets a row showing:

• Required — biomass demand after UE correction (pre-credit)
• Delivered — total grams supplied by all complex materials combined
• Coverage — delivered ÷ required, color-coded: ≥ 100% green, 50–99% amber, < 50% red, gray for nutrients still from the defined-salt path
• Salt top-up — remaining mass you need to add as a defined salt (0 when covered)

A verdict badge in the header summarises overall state at a glance (e.g. "6 nutrients covered", "7 low · 2 partial"). The segmented verdict bar beneath shows count-by-color.

Automatic warnings & pH adjustments

• Na / Ca / K oversupply alerts (amber strips) fire when molasses delivers > 2× the biomass demand for any of those ions. Excess Ca from cane molasses and excess Na from beet molasses are the most common issues at doses above ~25 g/L.
• Auto-switched K source (teal info strip) — when cane molasses ≥ 5 g/L, the calculator automatically switches the K salt from KOH (a base) to KCl (neutral) because the broth is already acidic. You can override by manually picking a different K salt in the Results → Total Required tab; the calculator remembers your choice and stops auto-adjusting.
• Beet molasses alkalinity reminder (teal info strip) — when beet molasses ≥ 5 g/L, a note reminds you to ensure H₃PO₄ or H₂SO₄ is active as pH-control acid (beet broth starts at pH 7.5–8.5).

Medium Type classification

The Summary's Row 7 Medium Type badge is driven by the total dry-basis g/L of all complex materials combined:

• Defined (< 1 g/L) — blue border. Pure salts + glucose + vitamins. Maximum reproducibility.
• Semi-defined (1–10 g/L) — teal border. Defined base with complex supplement. Typical for research & inoculum propagation.
• Complex (≥ 10 g/L) — amber border. Supplement-rich; vitamin stocks often omitted. Industrial baker's/brewer's yeast propagation territory.

Lot variance caveat: Every composition value shown is a literature average. Real CoA values vary ±25% for YE, ±30% for peptone, ±40% for CSL, ±20% for molasses (lot-to-lot, brand-to-brand, and season-to-season for agricultural inputs). For tight process control, always assay your specific lot and paste values into the editable composition table. The 50% vitamin credit rate is intentional padding for this variance — if you have verified CoA values, you can raise it by editing source vitamin values higher, which has the effect of crediting the actual delivered amount at 100% while the calculator continues applying the 50% reduction.

Process additives are dosed per-litre of broth (not per-gram of DCW like salts), because they are consumed by the fermentation process rather than retained in the biomass. Four categories are supported with 28 source variants total. Configure in Biomass → General Composition → Process Additives; view contributions in each Results sub-card.

Antifoam — 5 variants

• PPG 2000 (default, 0.1 mL/L) — polypropylene glycol, food-grade, autoclavable. The industrial standard.
• PPG 1200 — lower MW; more active but higher DO-probe coating risk.
• Silicone (SAG 471) — 1/3 the PPG dose (typically 0.03 mL/L) but can foul probes.
• Antifoam 204 — Sigma PDMS + organic blend.
• Struktol J 647 — industrial fatty-ester; heat-stable, re-dose on demand.

Phase split: proportional to each phase's volume (batch gets batchVol/totalVol of total dose; feed gets the rest).

Chelator — 6 variants

• Citric acid (default, 0.5 g/L) — pKa 3.1/4.8/6.4, log K(Fe³⁺) ≈ 11. Keeps trace metals soluble at pH 4–6.
• EDTA-Na₂·2H₂O — strongest universal chelator; log K(Fe³⁺) = 25. Used in trace metal stocks at 1:1 mol with metals.
• Sodium gluconate — mild chelator; biodegradable; food-safe.
• NTA (nitrilotriacetic acid) — log K(Fe³⁺) = 16; alternative to EDTA where EDTA-residue is a regulatory issue.
• Sodium tartrate — weak; used historically for Fe-chelation in trace stocks.
• DTPA — slightly stronger than EDTA but more expensive; rare in yeast media.

Phase split: 100% to batch phase (delivered with initial medium charge).

pH Buffer — 9 variants (default OFF)

• MES (free acid) — pKa 6.1, best for yeast pH 4.5–5.5 region.
• Na-MES — pre-neutralised sodium form; adds ~11% Na.
• MOPS — pKa 7.2, too high for yeast; only useful for pH 6.5–7.5 target.
• HEPES — pKa 7.5, biologically inert, typical for cell culture.
• Na-citrate / K-citrate — pKa 3.1/4.8/6.4, also chelates.
• K-phosphate — pKa 7.2, doubles as P source (adjust salt recipe to avoid over-P).
• Na-succinate — pKa 4.2/5.6, biocompatible at low cost.
• Na-acetate — pKa 4.8, cheapest; partial C source; suppresses growth > 10 g/L.

When to use: typically only for shake-flask or uncontrolled vessels where no active NH₄OH/H₃PO₄ pH control is available. Default dose 0 g/L — leave off for bioreactor runs. Phase split: 100% to batch phase.

Osmoprotectant — 8 variants (default OFF)

• Glycine betaine — most effective yeast osmoprotectant; accumulated intracellularly without metabolism. Typical 2–5 g/L for VHG or high-biomass runs.
• Proline — native compatible solute; partially metabolised (releases ~12% N). 2–10 g/L typical.
• Trehalose — non-reducing disaccharide; native stress protectant. 5–20 g/L for osmotic or thermal stress.
• Glycerol — cheap at high dose; partially metabolised, 10–30 g/L.
• Sorbitol / Mannitol — non-metabolised sugar alcohols; 10–30 g/L.
• Ectoine — bacterial-origin, extreme effectiveness at 0.5–2 g/L but expensive.
• KCl (ionic osmotica) — ionic osmoprotection via K⁺ uptake; disrupts homeostasis > 0.5 M (37 g/L).

When to use: VHG fermentations (initial sugar > 250 g/L), high-biomass runs (final DCW > 80 g/L), or temperature-stressed conditions. Default dose 0 g/L. Phase split: 100% to batch phase — protects from initial osmotic shock.

Interaction with complex materials: Beet molasses naturally contains biotin (~0.4 mg/kg) and betaine (~0.5–1% by dry mass), which can partially replace osmoprotectant and vitamin supplementation at high doses. Watch the Deficiency Analysis panel for nutrients flagged as ✓ covered by complex materials.

Defined-medium recipe

• ✓ covered rows in Total Required mean an element is auto-supplied as a co-element from another salt you already have — don't add that compound separately or you'll over-deliver.
• Grey rows (not calculated) in some result tabs indicate the element's source is a liquid reagent whose concentration you need to specify manually. Edit the concentration widget next to the salt name.
• Procedure tab concentration check flags any stock solution that exceeds the reagent's solubility limit. If red, raise the stock volume or switch to a more soluble salt.
• Test Medium tab runs the calculation in reverse — enter weights you actually measured out, and the calculator tells you the max biomass that recipe can support (limited by whichever nutrient ran out first).

Complex materials & CoA workflow

• Paste your Certificate of Analysis values into the composition table of the matching complex material. Tab between nutrient-row input fields to move down quickly; the Deficiency Analysis panel recomputes on each edit so you can watch nutrient coverage update as you work through the assay.
• Read the Deficiency Analysis verdict badge first — if it says "Defined medium" you haven't dosed anything yet; "6 nutrients covered" is healthy semi-defined territory; "7 low · 2 partial" means you either need more complex material or should accept the partial coverage and rely on the salt top-up column.
• Amber oversupply warnings (Na / Ca / K > 2× biomass demand) are not catastrophic below 5× — the excess is mostly bystander ions. Above 5×, reduce the molasses dose, switch to a lower-mineral variant (e.g., Brazilian cane vs. Blackstrap), or consider diluting with a portion of pure sucrose.
• Teal auto-adjust note (KOH → KCl) appears when cane molasses ≥ 5 g/L. The switch is automatic but fully revertible: if you prefer KOH for your process (e.g., for combined K + pH-control), pick it manually in the Results → Total Required tab. The calculator memoises your choice and stops re-adjusting on subsequent recalculations.
• Beet molasses alkalinity reminder (teal info strip at ≥ 5 g/L dose) assumes H₃PO₄ is still selected as the P source / acid. If you've manually switched P to a non-acid form (e.g., K₂HPO₄), ensure your pH controller has an acid line active.

Process additives

• Antifoam dose is often over-specified at small scale. Default 0.1 mL/L of PPG 2000 is a 20 L fermentor baseline; at 100 L+ scale, 0.05 mL/L often suffices because bubble coalescence at the increased liquid depth self-dampens foam. Over-dosing antifoam can suppress oxygen transfer.
• pH buffer default is 0 g/L because bioreactor runs use active NH₄OH / H₃PO₄ control. Only enable (with MES or citrate) for shake-flask or uncontrolled vessels. A buffer dose of 10 g/L MES costs ~$10 per 20 L batch at $50/kg — comparable to a week of pH probe calibration time, so ask whether the trade-off is worth it.
• Osmoprotectant is only needed for VHG (sugar > 250 g/L), high-biomass (> 80 g DCW/L), or temperature-stressed runs. For standard 50 g DCW/L propagation with 30 g/L batch sugar, leave at 0. Beet molasses contains natural betaine (~0.5–1% dry) — at high beet doses you may eliminate the need for external osmoprotectant entirely.

Cost, print, and quality-of-life

• Print Sheet buttons on Procedure and Reference tabs produce clean printable/PDF-friendly weigh-out sheets stripped of UI chrome.
• Cost Estimate tab — leaving a price input blank reverts that compound to the default bulk-industrial price. Paste your supplier's USD/kg quote to get a real-world estimate tailored to your lab. Every salt, complex material source, and additive source has its own editable price.
• Load Standard buttons on the Biomass and Complex Formulation cards reset their respective inputs to the default values — useful when you've been editing composition values for strain-specific work and want to start fresh.
• Process Options toggles can be flipped independently: turn off UE correction to see pure stoichiometric minimums, or turn off Complex Supplement Credit to see the full defined-medium recipe alongside your complex dosing (useful for direct defined-vs-complex cost comparison).

Limitations: This calculator does not model strain-specific kinetics, ethanol production (Crabtree conditions), lipid/fatty-acid supplementation for anaerobic operation, medium sterilisation losses beyond the UE factor, or downstream-processing yields. Complex material composition values are literature averages — for tight process control, always assay your specific lot and override via the editable composition tables. For ethanol fermentation at production scale, use the companion Ethanol Fermentation Medium Calculator instead — this tool is biomass-optimized and assumes fully aerobic, respiratory metabolism.

Saccharomyces cerevisiae is a facultative anaerobe: it can grow with or without oxygen. The two regimes give very different biomass yields, so the calculator's defaults assume the high-yield aerobic mode.

Biomass propagation deliberately drives the aerobic respiratory regime: yields are 5× higher than anaerobic, and the only carbon byproduct is CO₂ rather than ethanol. The trade-off is heavy oxygen demand (~1 g O₂ per g DCW) and substantial heat release (~15 kJ per g DCW), addressed in sections 6 and 7 below.

Even with abundant oxygen, S. cerevisiae switches to ethanol production when glucose flux exceeds the respiratory capacity of its mitochondria. This is the Crabtree effect — a regulatory choice, not an oxygen limitation.

Two triggers:

• High residual glucose — above roughly 0.1–0.5 g/L glucose, glucose-responsive transcription factors (Mig1, Snf1) repress respiratory genes (catabolite repression).
• High specific growth rate — above µ_crit ≈ 0.25–0.30 h⁻¹, glycolytic flux outruns the TCA cycle even at low glucose, and overflow ethanol appears.

Process consequences built into this calculator:

• Initial batch glucose is capped at 30 g/L — well below the catabolite-repression threshold and far below osmotic-stress territory.
• Fed-batch is exponentially fed targeting µ ≈ 0.15–0.20 h⁻¹, comfortably below µ_crit.
• Rising residual glucose (> 0.5 g/L) or measurable ethanol during fed-batch are signals to back the feed rate off 20–30 % until the system clears.

Yeast biomass has a remarkably consistent average elemental formula:

CH_1.79O_0.57N_0.15P_0.02S_0.005

This corresponds to the percentages in the Reference tab: ~47 % C, 6.5 % H, 31 % O, 8.3 % N, 1.2 % P, 0.4 % S. The remaining ~5 % is K, Mg, Ca, Na, trace metals, and vitamins — together these define the "ash" portion of dry biomass.

The composition shifts with growth conditions:

• N content tracks protein content, which scales with growth rate. Fast-growing cells (µ > 0.2 h⁻¹) reach ~50 % protein → ~9 % N. Stationary or starving cells drop to 5 % N.
• P content tracks RNA, which is also growth-rate dependent. Rapid growth needs more ribosomes → more rRNA → more P (up to 2.4 %).
• Lipid content rises under N or P limitation: division stops but C-assimilation continues, accumulating as triacylglycerol storage.
• Mineral content is fairly constant unless a specific element is limiting in the medium.

The calculator's editable Composition card lets you override these defaults for strain-specific work or known compositional shifts.

Y_X/S is the biomass yield on substrate, in g DCW per g consumed glucose. Three numbers worth knowing:

The slider range (0.35–0.55) covers everything from "decent fed-batch with some Crabtree" to "well-tuned industrial". A yield below 0.40 in your run usually means partial Crabtree overflow — check ethanol. Above 0.52 implies very tight DO and feed control.

Y_X/S drives every downstream calculation: total sugar = biomass ÷ Y_X/S, and the carbon balance feeds the CO₂ estimate. Calibrating it for your strain and equipment is the single most important parameter.

For aerobic glucose growth, all carbon entering the cell exits as either biomass or CO₂. Writing the balance:

Carbon in (sugar):

C_in  =  0.40 × m_sugar (glucose is 40 % C by mass)

Carbon retained in biomass:

C_X  =  0.47 × m_biomass (yeast is ~47 % C by mass)

Carbon as CO₂, by difference:

m_CO₂  =  (C_in − C_X) × (44 / 12)

This is exactly the formula used in the Summary panel. For a 1 kg DCW batch at Y_X/S = 0.48, the calculator predicts ~1.33 kg CO₂ — useful for sizing exhaust handling and designing oxygen-balance based growth-rate inference.

Respiratory quotient (RQ) = mol CO₂ produced / mol O₂ consumed. For pure respiration on glucose, RQ ≈ 1.0. Real-time RQ > 1.1 indicates Crabtree overflow (extra CO₂ from ethanol decarboxylation without matching O₂ uptake) — one of the most powerful online diagnostics in fed-batch propagation.

For aerobic glucose growth, Y_O/X ≈ 1.0 g O₂ per g DCW. So for a 1 kg DCW batch:

m_O₂ ≈ 1000 g  ≈  31 mol  ≈  700 L O₂ at STP  ≈  3 500 L air at STP

This must be delivered continuously over the run. The instantaneous rate at which dissolved O₂ can be supplied is the Oxygen Transfer Rate (OTR):

OTR  =  k_La × (C* − C_L)

where k_La is the volumetric mass-transfer coefficient (h⁻¹), C* is the saturation concentration of dissolved O₂ (~7 mg/L at 30 °C), and C_L is actual dissolved O₂.

Why this matters in practice: the OTR ceiling is the single most common limit on biomass productivity in industrial fed-batch. As biomass accumulates, oxygen uptake rate (OUR = q_O × X) grows linearly with X, while OTR is fixed by k_La — set by impeller, sparger, and back-pressure. When OUR catches up to OTR, dissolved oxygen crashes and metabolism shifts to ethanol overflow regardless of feed rate. The cascade control loop (DO → agitation → airflow → O₂ enrichment) defends against this.

Aerobic yeast growth releases roughly 15 kJ per g DCW produced. This is a thermochemical rather than metabolic quantity — it follows from the difference in standard enthalpy between the substrates (glucose, NH₃, O₂) and products (biomass, CO₂, H₂O).

Two ways to use the number:

• Total heat load: a 1 kg DCW run releases ≈ 15 MJ, mostly in the rapid-growth window. Cooling jackets must remove this without falling below the temperature setpoint, even with concurrent agitation heat input.
• Peak heat rate: at peak µ, heat output ≈ µ × X × 15 kJ/g. For 50 g/L at µ = 0.2 h⁻¹ in a 1 m³ vessel, peak load ≈ 150 kJ/h per kg broth, requiring ~10 K coolant ΔT through a typical jacket.

Underspecified cooling is one of the most common scale-up failures: bench-scale runs at 30 °C drift to 33–35 °C at production scale because heat removal hasn't been sized for the higher absolute heat output, even though specific heat output (per g biomass) is identical.

The goal of fed-batch propagation is to match substrate supply to demand at a chosen specific growth rate. Since biomass grows exponentially, demand also grows exponentially — so does the feed.

From the substrate balance dX/dt = µX and the feed-yield relation F·S_feed = (1/Y_X/S)·µ·X:

F(t)  =  F₀ × e^µ·t

F₀  =  (µ × X₀) / (Y_X/S × S_feed)

where X₀ is biomass at feed start (≈ end of batch), µ is the chosen sub-critical growth rate (typically 0.15–0.20 h⁻¹), Y_X/S is your calibrated yield, and S_feed is feed glucose concentration (commonly 500 g/L for compactness).

Why exponential and not constant-rate? A constant feed underfeeds late in the run (cells outpace supply) and overfeeds early (residual glucose triggers Crabtree). Exponential maintains a pseudo-steady-state where residual glucose hovers near zero — the high-yield "carbon-limited" regime. This is the single trick that separates 0.30 g/g from 0.50 g/g yield in industrial production.

Why not just match µ_max? Because µ_max for S. cerevisiae is ~0.40 h⁻¹, well above µ_crit ≈ 0.30 h⁻¹. Pushing µ to its maximum forces overflow ethanol production and collapses Y_X/S by ~40 %. Sub-critical feeding sacrifices a bit of run-time speed for a much larger yield gain.

Nitrogen is the second-largest demand after carbon (~8.3 % of dry biomass) but it presents a unique delivery problem: NH₄⁺ is toxic above ~300 mM, so loading the full N requirement into the batch medium is impossible above modest biomass targets.

The standard solution is delivery via pH control. As the cell takes up NH₄⁺, it releases H⁺ in a 1:1 stoichiometric ratio (the NH₄⁺/NH₃ proton-pump charge balance). Broth pH drops, and the controller adds NH₄OH to restore setpoint. Each g of NH₃ delivered as base supplies 0.82 g of N to the cells. Conveniently, the rate of NH₄OH consumption is also a real-time growth-rate indicator.

Practically, only ~20 % of total N is loaded as starter charge (enough for the first few generations). The remaining ~80 % arrives via pH-control NH₄OH additions during the rest of batch and all of fed-batch. The Summary panel's "N Split 20 % / 80 %" reflects this.

C:N ratio (mass): for aerobic yeast biomass at 8.3 % N, the natural C:N ratio of the medium lands in the 12–18 range. Above 20 you risk N-limitation (ribosome shortage, slow growth, lipid accumulation). Below 10 wastes ammonia and acidifies the broth.

Trace metal salts (Fe³⁺, Zn²⁺, Mn²⁺, Cu²⁺) face two problems in concentrated stock solutions and in neutral fermentor broth:

• Hydrolysis and precipitation — Fe³⁺ in particular precipitates as Fe(OH)₃ above pH ~3.
• Free-ion competition for transporters — high free Cu²⁺ outcompetes Zn²⁺ at the Zrt1/Zrt2 zinc transporters, causing functional Zn deficiency despite total Zn being adequate.

EDTA (Na₂·2H₂O) chelates these metals with characteristic stability constants (log K_n):

Adding EDTA at 1:1 mol ratio to total chelatable metals achieves three things: (1) keeps Fe in solution at physiological pH; (2) drops free Cu²⁺ by ~9 orders of magnitude, eliminating the Cu/Zn transporter conflict; (3) provides a slow, controlled release of free metal for cellular uptake (chelated metals exchange with the cell-surface metal-acquisition machinery).

The Trace Element Stock recipe in the Procedure tab includes EDTA automatically at this 1:1 stoichiometry. Without EDTA, you'd need a low-pH stock (HCl to ~pH 2) to keep metals dissolved, and the broth would experience a precipitation flash on each addition.

The "Apply utilisation efficiency correction" toggle inflates each nutrient demand above the stoichiometric minimum to compensate for real-world losses. The factor is element-specific because the loss mechanisms differ:

Turning the toggle OFF reveals the pure stoichiometric minimum — useful for theoretical analysis or for very tightly controlled lab fermentors with chelated trace stocks and minimal volatilisation. In any real production setting, leave it ON.

If this calculator helped a research or process-development project, an appropriate citation would be:

Krasucki, P. (2026). Propagation Medium Composition Calculator (v2.1)
[HTML/JavaScript application]. FermAxiom LLC.
Retrieved from peter.krasucki@fermaxiom.com

The calculator is a conceptual modelling tool. Strain-specific calibration of Y_X/S, biomass composition, and OTR is essential before applying its outputs to production. Citing this tool does not constitute attribution of any production-scale recommendations beyond what the user has independently validated.