Team:Heidelberg/Model/iGEM Goes Green

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iGEM Goes green.

Optimisations of PACE to reduce medium consumption

Introduction

Medium consumption model

PACE usually consumes an extraordinary amount of medium per experiment. This is due to the need for a continuous supply of host E. coli with a constant cell density. This can be achieved either by using a turbidostat or a chemostat. Here we provide a tool to both the community and ourselves to calculate medium consumption based on different tunable parameters of PACE. We also want to gain an understanding of how we can reduce the amount of medium needed for an experiment. Medium consumption is critical when it comes to the energy needed for an experiment because of autoclaving needs a lot of energy. In a turbidostat the cell density is held constant by adjusting the medium influx to the cell density. That means the growht of the E. coli is not affected, instead for every new E. coli one E. coli is put to wate. In a Chemostat, the cell density is controlled by adjusting the influx of an essential nutrient to the cell density, which limits the growth of the culture. This may cause the E. coli to be less efficient in producing the proteins needed for PACE and replicating the phage genome. Additionally, there is a constant flux from the chemostat to the lagoons, that compensates the growth of the E. coli. Currently, we are using a turbidostat, because probably PACE works better when the E. coli is allowed to grow at their maximum speed under the given conditions. So their ability to produce phage as fast as possible is not impaired. Here we can make statements on how much energy we save with a specific setup relative to another one, but we do not estimate the absolute amount of energy that is used.

Configure the plot:

"Resolution" controls how many data points are calculated in each dimension, therefore the complexity of both memory and computation increased with the square of resolution. Increase for a smoother heatmap and decrease for a faster result. "Flow trough Turbidostat" \(\Phi_{T}\), the amount of medium that is pumped through the turbidostat during one hour. Depends on turbidostat volume \(V_{T}\), lagoon volume \(V_{L}\) and quantity \(N_{L}\), flow through lagoon \(\Phi_{L}\). A larger total lagoon volume with a higher flow requires higher flow through the turbidostat. For turbidostat the flow rate \(\Phi_{T}\) can be calculated using the volume of the turbidostat \(V_{T}\) and the generation time of the E. coli \(t_{E}\) and has not to be set. "Maximum Duration" \(t_{max}\) controls the upper border of the y-axis. "Generation Time E. coli" \(t_{E}\) sets the time in which the E. coli population doubles itself when in exponential phase. Only affects values for turbidostats, because chemostats control the generation time themselves. "Volume of Turbidostat" \(V_{T}\) actually the volume of the culture in the turbidostat. Only affects Turbidostats. Calculation of the flow trough a turbidostat: $$ \frac{\partial V_{M} }{\partial t} = \Phi_{T} = \frac{log(2)}{t_{E} } \cdot V_{T} $$

Read the plot:

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 heat map 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.

Caution

Submitting one of the forms recalculates all values and the heatmap based on the values in all the forms.
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.

Your experiment

You can annotate a point in the heatmap by providing its coordinates \(t_{max}\) and \(\Phi_{T}\) or \(V_{T}\) 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. Enter your specifications:
Annotate the plot

Minmal Turbidostat Volume

As larger turbidostats or chemostats with a larger flow need more medium for the same duration than smaller ones, working with the minimal required volume or flow is a way to save medium and thus energy. The minimal flow that is required can be calculated using $$ V_{T} = b \cdot V_{L} \cdot N_{L} \cdot \Phi_{L} $$ In case of fluctuations in the generation time of the E. coli it is crucial to have a buffer so that the turbidostat is not diluted when the culture grows slower. We currently use a buffer of 50 %, so \(b\) is set to \(1.5\). For a turbidostat, the volume can be calculated from the flow using $$ V_{T} = \Phi_{T} \cdot \frac{t_{E} }{log(2)} $$ The calculation is based on whether turbidostat or chemostat is picked above.
Minimal Turbidostat Volume

Minimal Lagoon Volume

Obviously smaller lagoons require smaller turbidostats or chemostats with a lower flow and are therefore saving medium. However, if there is a lower limit to lagoon size, if the phage population is too small, the sequence space that can be covered is insufficient to find variants that are better than previous ones. There are a lot of possible ways to estimate the size of the lagoons, here we show one based on the sequence length and mutation rate. The size of the phage population \(N_{P}\) per lagoon is $$ N_{P} = c_{P} \cdot V_{L} $$ The total sequence length \(L_{T}\) is $$ L{T} = N_{P} \cdot L_{S} $$ when \(L{S}\) is the length of one sequence. The number of mutations that occur during one generation \(N_{M}\) is $$ N_{M} = L_{T} \cdot r_{M} $$ Here \(r_{M}\) is the mutation rate. The number of possible n-fold mutants of a sequence with length sl can be calculated by #nm = 3^n * mr^n * sl!/((sl-n)!) $$ N_{n} = 3^{n} \cdot r_{M} \cdot \frac{L_{S}!}{(L_{S} - n)!} $$ as there are three possibilities for each basepair to be exchanged to and with each additional mutation there is one possible position less. The number of n-fold mutants that can occur in a lagoon can be calculated using $$ M_{n} = N_{P} \cdot (r_{M} \cdot L_{S})^n $$ therefore the required lagoon volume is $$ V_{L} = \frac{N_{n} \cdot t}{M_{n} } $$ With a theoretical coverage factor of the n-fold mutants of \(t\).
Minimal Lagoon Volume

References