# Team:Heidelberg/Model/Medium

Modeling
Medium consumption
All three tools on this page assume a steady state in the turbidostat. The mutation rates in the calculation of the minimal lagoon volume are assumed to be constant over time and the same for every position in the sequence. This basic model does not apply well when highly conserved regions are subject to mutation. However, if the length of conserved regions is substracted from the total sequence length this should lead to more accurate results.

## About the medium consumption heatmap

When working with a turbidostat the upper x axis is relevant, when working with a chemostat the lower is. Put the mouse pointer on the heatmap to show the exact values for that point. You can zoom in by drawing the rectangle that should be shown with pressed left mouse button. You can always save the current plot by clicking on the camera icon.

## Note

Submitting one of the forms recalculates all values and the heatmap based on the values in all the forms. When a high resolution is chosen this may take a moment.

Table 1: Additional Variables and Parameters used in the numeric solution of the model List of all additional paramters and variables used in the numeric solution of this model. The assumed relations are described on the theory page of this model.

Symbol Unit Explanation
$V_{T}$ [ml] Volume of Turbidostat
$V_{M}$ [ml] Volume of Medium consumed
$t_{E}$ [min] E. coli generation time
$\Phi_{T}$ [ml/h] Flow rate through turbidostat
$t_{max}$ [min] Duration of the experiment
Configure the plot
Medium consumption by turbidostats of different volumes over different durations
Depending on turbidostat volume and E. coli generation time the needed flow rate for a turbidostat changes. The flow rate can be fixed for chemostats, when E. coli growth is controlled. For comparison coditions used by Badran et al.RN31, Dickinson et al.RN158.

## A specific experiment

You can annotate a point in the heatmap by providing it's coordinates $t_{max}$ and $\Phi_{T}$ or $V_{T}$ and and it's name. If you have a turbidostat, the value for the flow rate $\Phi_{T}$ is ignored, if you have a chemostat, the volume $V_{T}$ is ignored. For the calculation of the flow through the turbidostat, the value for generation time from the form above is used.
Calculate your experiments medium consumption

## Minmal Turbidostat Volume

The calculation is based on wether turbidostatat or chemostat is picked above.

Table 2: Additional Variables and Parameters used for this calculation List of all additional paramters and variables used in the numeric solution of this model. The assumed relations are described on the theory page of this model.

Symbol Unit Explanation
$V_{L}$ [ml] Volume of Lagoons
$N_{L}$ Number of Lagoons
$\Phi_{L}$ [ml/min] E. coli generation time
$b$ $1.5$ Buffer
Minimal Turbidostat Volume

## Minimal Lagoon Volume

Table 3: Additional Variables and Parameters used for this calculation List of all additional paramters and variables used in the numeric solution of this model. The assumed relations are described on the theory page of this model.

Symbol Unit Explanation
$N_{P}$ [pfu] Amount of phages per lagoon
$c_{P}$ [pfu/ml] Phage concentration
$L_{S}$ [bp] Sequence length in basepairs
$L_{T}$ [bp] Total sequence length in basepairs in lagoon
$N_{M}$ Number of mutations
$r_{M}$ [1/generation] Number of mutated basepairs per basepair per generation
$n$ [bp] Number of mutated basepairs
$M_{n}$ Number of real sequences with $n$ mutations
$N_{n}$ Number of possible sequences with $n$ mutations
$t$ Theortical coverage of double
Minimal Lagoon Volume