The exponential feed rate is calculated as F(t) = (μ_set / Y_xs) × (X₀ × V₀ / S_f) × e^(μ_set × t), where μ_set is your desired specific growth rate, Y_xs is the biomass yield on substrate, X₀ is initial biomass, V₀ is initial volume, and S_f is the feed substrate concentration. This calculator implements this exact formula and generates a time-resolved feed schedule. The key principle is that the feed rate must increase exponentially to match exponential cell growth while maintaining substrate at growth-limiting (not growth-inhibiting) concentrations. Start with μ_set at 60-80% of μ_max to avoid overflow metabolism in E. coli.

The Monod equation describes microbial growth rate as a function of substrate concentration: μ = μ_max × S / (K_s + S). In fed-batch fermentation, the feeding strategy directly controls substrate concentration S, and therefore the growth rate. When S >> K_s, growth is at μ_max; when S is near K_s, growth is substrate-limited. Fed-batch feeding exploits this relationship by maintaining S just above K_s, keeping cells growing at a controlled sub-maximal rate. This prevents acetate overflow in E. coli (which occurs above the critical μ of ~0.3 h⁻¹) and Crabtree effects in yeast, while ensuring cells are not starved.

Use exponential feeding when you want to maintain a constant specific growth rate throughout the fed-batch phase -- this is the gold standard for recombinant protein production in E. coli and gives the most predictable biomass accumulation. Linear feeding provides a simple alternative that gradually becomes growth-limiting as biomass increases, naturally decelerating growth without complex pump programming. Constant feeding is the simplest approach and works well for low-density cultures or when your pump cannot be programmed, but leads to feast-famine cycles. For CHO cultures, constant or step-wise bolus feeding is common. For Pichia methanol induction, a stepped ramp is standard to avoid methanol toxicity.

For E. coli fed-batch, a glucose feed concentration of 500-700 g/L (50-70% w/v) is standard for high-cell-density cultivation. This minimises dilution of the culture while providing sufficient carbon source. The practical upper limit is around 700 g/L due to glucose solubility and viscosity at room temperature. At these concentrations, the feed also typically contains MgSO4 (typically 5-20 g/L) and trace elements to prevent mineral limitation at high cell densities. This calculator uses organism-specific presets with these standard concentrations. For defined media processes, ensure your feed is supplemented with any amino acids or vitamins that may become limiting above 50 g/L DCW.

This calculator replaces the need for a custom Excel spreadsheet. It generates a complete time-resolved feed schedule with pump flow rates that you can export as a CSV file and import into your bioreactor control software or print as a bench reference. Unlike static spreadsheets, it supports seven different feeding strategies (exponential, linear, constant, DO-stat, pH-stat, step-wise, and Pichia methanol induction), includes organism-specific presets for E. coli, CHO, Pichia, yeast, and Bacillus, and recalculates instantly when you change parameters. The exported CSV includes timestamps, cumulative feed volume, instantaneous flow rate, and estimated biomass at each time point.

The substrate feed rate F (in L/h) is derived from a mass balance: F = (μ/Y_xs + m_s) × X × V / S_f, where μ is the desired specific growth rate (h⁻¹), Y_xs is the biomass yield on substrate (g biomass/g substrate), m_s is the maintenance coefficient (g substrate/g biomass/h), X is biomass concentration (g/L), V is culture volume (L), and S_f is the feed substrate concentration (g/L). The maintenance term m_s is often small relative to μ/Y_xs and can be neglected for fast-growing cultures. This calculator uses this mass-balance approach with literature values for Y_xs and m_s for each organism preset. Typical Y_xs for E. coli on glucose is 0.4-0.5 g/g.