Energy Production

This section discusses the technical details of this module.

It was assumed that a single respiration cycle yielded 26 ATP molecules, which convert to \(E_{resp}=8.229 meV\) (data element ‘Energy_per_Respiration’ in the GoldSim representation).

For simplicity, it was assumed that a cycle of fermentation yielded 13 ATP molecules (half the production of a respiration cycle), which convert \(E_{ferm}=4.114 meV\) meV$$ (data element ‘Energy_per_Fermentation’ in the GoldSim representation).

The total respiration power was calculated as:

\[\begin{equation} W^{tot}_{resp} = \frac{M^{tot}_{resp}}{M^{B}_{resp}} E_{resp} \, . \label{eq:W_resp} \end{equation}\]

Here, \(M^{tot}_{resp}\) is the rate of biomass being processed by respiration (the details will be discussed in Metabolism ), \(M^{B}_{resp}\) is the mass of a single respiration cycle, and \(E_{resp}\) is the energy generated by a single respiration cycle. The equation assumes that the power generated by respiration is the number of respiration cycles per hour multiplied by the energy generated by a single respiration cycle. In the GoldSim representation, this is function element ‘Respiration_Power’

The total fermentation power was calculated in a similar way:

\[\begin{equation} W^{tot}_{ferm} = \frac{M^{tot}_{ferm}}{M^{B}_{ferm}} E_{ferm} \, . \label{eq:W_ferm} \end{equation}\]

Eq \ref{eq:W_ferm} correspond to function element ‘Fermentation_Power’ in the GoldSim representation. The respiration and fermentation power in Eq. \ref{eq:W_resp} and Eq. \ref{eq:W_ferm} are dumped into the ‘Energy’. Bacteria request (or outflow) power from ‘Energy’ :

\[\begin{equation} W_{req}=B(t) W_b V \, , \label{eq:W_tot} \end{equation}\]

where \(W^a_b=1.39 \cdot 10^{-13}\) W is the active metabolic rate of E. Coli DeLong et al, 2010. We assume that the active metabolic rate is the power required by a cell to duplicate. \(B(t)\) is the bacterial concentration at time \(t\), and \(V\) is the volume of the system. The GoldSim translation of \ref{eq:W_tot} is the function element ‘Community_requested_power’: the product of data element ‘Metabolic_Rate’, times ‘Volume’, times pool element ‘Bacteria’ in Bacterial growth container.

The power produced by the available resources in the system is given by the available energy in the ‘Energy’ pool. This is given by:

\[\begin{equation} W_{av}= W^{tot}_{resp} + W^{tot}_{ferm} \, , \label{W_av} \end{equation}\]

which corresponds to function element ‘Actual_Request’ in the GoldSim representation. This element acts as