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I have the following question in systems biology: a) Draw a graph showing the relationship of growth (Vbio) and Vefni for the system here. (Let the horizontal axis represent Vbio and the vertical axis represent Vefni)

My first thought was that it would simply be straight line from (0.5,0.5) to (1,0). But now I'm thinking that I have to take V4 into account as well.

b) Determine one or more reactions that are such that if they are taken out the production of M4 is coupled to growth (growth-coupling). Draw a graph showing the relationship Vbio and Vefni for the mutant.

Here I thought it would be V1 and V4. I'm not sure though because I haven't found a good explanation for what growth-coupling is exactly.

c) Why is it desirable to couple chemical production to growth? i.e. what advantages do those systems have over the ones where no such coupling is present?

Here I have no idea.

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Why is it desirable to couple chemical production to growth?

When designing new metabolic pathways for chemical production, one has to keep in mind that the purpose of it is to get scaled up (i.e. to reach industrial size).

From the industrial point of view, the faster/simpler a process is, the better. Growth coupled chemical production means that only one step is necessary in order to produce the desired product (before downstream processes). Otherwise, one would have to produce the biomass first (growth step) and then to proceed to the chemical production step. One step is cheaper and faster than two, not mentioning the intermediary steps that could be necessary (cells washing, centrifugation, filtration ...).

The main drawback of growth coupled chemical production is that the final yield ($mol_{final~product}/mol_{substrate}$) is hindered by biomass production. This can be a real issue if the substrate is expensive.

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