Observed Biomass Yield (Y_sx) Calculator (with Maintenance)

Calculation Explanation

The observed biomass yield (\(Y_{sx}\)) is the actual amount of biomass produced per unit of substrate consumed. It differs from the theoretical maximum or "true" yield (\(Y^{true}_{xs}\)) because cells must also consume substrate for maintenance activities (e.g., maintaining ion gradients, repairing damage) unrelated to growth. This maintenance requirement is quantified by the maintenance coefficient (\(m_s\)).

The relationship, derived by Pirt, is given by:
Y_sx = μ / ( Y^true_xs * μ + m_s )
(Note: Some texts rearrange this as 1/Y_sx = 1/Y^true_xs + m_s/μ)

Where:
- Y_sx: Observed biomass yield (e.g., g dry cell weight / g substrate).
- μ: Specific growth rate (e.g., h⁻¹).
- Y^true_xs: True biomass yield (e.g., g dry cell weight / g substrate).
- m_s: Maintenance coefficient (e.g., g substrate / g dry cell weight ⋅ h).

This equation shows that \(Y_{sx}\) approaches \(Y^{true}_{xs}\) at high growth rates (when μ is large compared to \(m_s\)) and decreases at low growth rates as maintenance becomes a more significant fraction of substrate consumption. Ensure that the units for \(Y^{true}_{xs}\), \(μ\), and \(m_s\) are consistent to obtain the correct units for \(Y_{sx}\).

Reference Data (Y^true_xs and m_s)