Team:Rice/Model/CircuitOutputMinimal
Metabolism
Overview
Cellular energy is generated via two co-expressed enzymes: a transporter and a metabolic enzyme. The base model assumes that the cells grow in a chemostat with a constant concentration of nutrients. The cells import the nutrients and then convert them to cellular energy.
Details
To convert nutrients into energy, first the cell must import the nutrients from the outside source ($s_e$) to the inside ($s_i$). The transporter protein ($p_T$) accomplishes this via Michaelis-Menten kinetics, with a maximum speed of $v_T$ and a import threshold of $k_T$. Conversion to cellular energy is accomplished in a similar manner with the metabolic enzyme ($p_E$) and with constants $v_E$ and $k_E$. However, conversion is not perfect, and the efficiency of the conversion is given by the factor $\phi_E$. Energy is used during translation at a rate of $\gamma \sum c_i$, where the sum runs over all translation complexes. In addition, the cell slowly grows at a rate of $\lambda = \gamma \frac{\sum c_i}{M_p}$, where $M_p$ is the total mass (in amino acids) of the proteome. As a result, all species are diluted with a rate constant of $\lambda$.
Equations
\begin{equation*} \begin{aligned} \frac{ds_i}{dt} &= v_T p_T \frac{s_e}{k_T+s_e} - v_E p_E \frac{s_i}{k_E+s_i} - \lambda s_i \\ \frac{dE_c}{dt} &= \phi_E v_E p_E \frac{s_i}{k_E+s_i} - \gamma \sum c_i - \lambda E_c \\ \end{aligned} \end{equation*}