Consider a chain of Michaelis-Menten enzyme reactions:
SE1⟶S1E2⟶S2E3⟶S3E4⟶P
for a constant concentration S=1 and given Vmax and KM values:
VmaxKME10.10.1E21.01.0E31.00.1E45.05.0
Implement the system and plot the solution in config-space.
Determine the steady state concentrations S1,S2 und S3 and the steady state flux J by simulating the system for long time periods.
Have a look at the function rootSolve::steady()
and use it to calculate the steady state concentrations and flux.
Evaluate the steady state concentrations and flux by varying the Vmax values. Use the manipulate
package for an interactive visualization and plot the original values along.
Calculate the control coefficients using the numDeriv
package. Hint: have a look at outer()
for calculating the outer product of two vectors.
Why is the cathedral tower at the bottom foursided while being octagonal at the top?