Modelling bacterial threonine metabolism

1. Download the model file. Consult the lecture slides (slide 27) from day 2 for a diagram of the threonine pathway. For accurate determination of these control coefficients, it is necessary to change the default value of one of the parameters, the perturbation used for the numerical differentiation of the variable response. The ScaledSensits function that returns the control coefficients should be called as in the following example:

   • CJak = m.ScaledSensits("F1", ["ak"], Pert=0.03)

2. Try to answer the following using the model:
   1. What are the flux control coefficients of the 5 steps? For the purposes of this question, we have multiplied the rate equations for the 5 steps by the factors F1 ... F5. These are initially set to 1 (the reference state), but they can be used as the enzyme activity parameter for calculating the flux control coefficients.
   2. What degree of inhibition (or suppression of expression) of each of the enzymes is needed to reduce the flux to 50% of its initial value? To answer this, you need to adjust the parameters that act on the enzyme values. The factors F1 ... F5 are initially set to 1 (the reference state), so setting F1 to 0.5 halves the rate of reaction 1, and so on.
   3. Which single enzymes can be over-expressed (and by how much) to achieve a 50% increase in threonine flux relative to the initial state of the model and what relative level of over-expression is needed? For comparison, you can simultaneously over-express all enzymes to the same extent by increasing the relative protein content (parameter prot, initial value 1.0).
   4. In fact, aspartate kinase 1 (with Vmax as parameter vm11) and homoserine dehydrogenase (Vmax is parameter vm3f) are a bifunctional enzyme transcribed from a single gene, so they would actually be over-expressed together. Can you model the effect of over-expressing this gene?