# Model Explorer

## Model Explorer

In the manuscript, we present a minimal model describing the relationship between cell volume, growth rate, and ribosome abundance. We consider that the rate of translation, termed the elongation rate \(r_t\) is dependent on the effective concentration of free amino acids \([AA]_{eff}\) and their affinity to the elongating ribosomes, defined by a generalized dissociation constant \(K_D\). This magnitude of \([AA]_{eff}\) relative to $K_D$ tunes the elongation rate between \(\approx 0\) (complete cessation of translation) and some maximum value \(r_t^{(max)}\). This is defined mathematically as

\(r_t = \frac{r_t^{(max)}}{1 + \frac{K_D}{[AA]_{eff}}}.\) (1)

The effective amino acid concentration \([AA]_{eff}\) is defined as the difference between the rate at which amino acids are produced \(r_{AA}\) and the rate at which they are consumed,

\([AA]_{eff} = {1 \over V N_A} (r_{AA} - r_t \times R \times f_a),\) (2)

where \(R\) is the number of ribosomes, \(f_a\) is the fraction of the ribosome pool that is actively translating, and \(V N_A\) is the product of the volume and Avogadro’s number to maintain units of concentration.

The cell growth rate \(\lambda\) is related to the elongation rate \(r_t\) by the number of peptide bonds that need to be formed for a cell to divide, \(N_{pep}\), via

\(\lambda = \frac{r_t \times R \times f_a}{N_{pep}}.\) (3)

In the interactive figure below, we provide a means to get a sense for the quantitative predictions of this model. Use the sliders at the top of the figure to adjust the corresponding parameter value and see how that changes the translation rate and the cellular growth rate.

This figure was made using the Bokeh Python plotting framework. The code used to generate this figure can be accessed via the associated GitHub Repository.