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Practical 6

Threonine metabolism: Control Coefficients and ''in silico'' engineering

1. Download the model file. The model is a slightly simplified version of the published model (see below) for the purposes of this exercise. Consult the lecture slides (slide 27) from day 2 for a diagram of the threonine pathway.

2. Try the following exercises using the model:

   1. Determination of the flux control coefficients of the 5 steps. Normally we would use the built-in method ScaledSensits to determine control coefficients, but this model needs different settings from the standrd method. In addition, it is useful to expose the workings of the calculation in case you want to obtain control coefficients in a modelling environment that doesn't offer the facility. Carry out the following steps:

      1. Load the model and bring i to steady state:

         • >>> m=ScrumPy.Model()
           >>> m.FindSS(20)
           >>> m.IsOK()

      2. By examining the model file and the following code, see if you can understand how this calculates the flux control coefficients of the five steps. Note that F1 is a dummy parameter that is used to modulate both isoenzymes of aspartate kinase in parallel.

         • >>> vnames = ["F1","vm2f","vm3f","vm4f","vm5"]
           >>> de = 0.003                  # Set the fractional change to be used to perturb the parameter.
           >>> ccsum=0.0                   # Initialise the total of the flux control coefficients
           >>> oriJ=m["ts"]                # Save the pathway flux at the current SS
           >>> for v in vnames:
                   m.FindSS(20)
                   originalv = m[v]        # Save the current value of the parameter
                   m[v] *= 1.0 + de        # Perturb the parameter upwards
                   m.FindSS(20)
                   up = m["ts"]            # Record the new flux
                   m[v] = originalv*(1.0-de)  # Perturb the parameter  downwards
                   m.FindSS(20)
                   down = m["ts"]
                   fcc = (up-down)/(2*de*oriJ)  # Calculate a numerical approximation to the flux control coefficient
                   ccsum += fcc                 # Update the sum of fccs
                   print v, fcc
                   m[v] = originalv        # Restore the parameter to its original value
                   m.FindSS(20)            # Make sure we exit with the starting SS
           >>> ccsum

      3. Run the code and see the results. If for any reason you get an error message indicating that a steady state was not found, it would be advisable to reload the model and obtain a baseline steady state before proceeding any further.
   2. Guided by the above results, try the following:
      • 1.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?
      • 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?
      • What happens if you over-express all the enzymes together by the same amount?
   3. Check your answers against, and find more information, in the papers. Bear in mind there are some small differences between the published model and this version used for teaching, so there may be small differences in the values obtained.
   4. Advanced:

      1. How sensitive are the results of the control coefficient calculations to the size of de?

      2. 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 any changes in their expression would be coordinated. Can you determine the control coefficients of vm11+vm3f. vm13, vm2f, vm4f and vm5, as more representative of the response to changing amounts of enzyme protein.
      3. Does this affect any of your conclusions above?
      4. Which of your over-expression strategies above had the least effect on the intermediate metabolite concentrations? Consider especially homoserine, which is said to be toxic to cells.