Compare a Michaelis-Menten approximation to a reaction with explicit forward and backward rate constants.
For a simple reaction: S0 <-> S1, the flux, J0, can be given by:
J0(t) = kf*S0(t) - kb*S1(t).
S0(t) and S1(t) are reactant and product concentrations and kf and kb are forward and backward reaction constants.
Sometimes a Michaelis-Menten approximation is used in place of the full flux equation, thereby simplifying the calculations:
J0_mm(t) = Vmax*S0/(Km + S0).
Vmax is the maximum rate of the reaction and Km is the concentration, S0, at reaction rate of 1/2*Vmax.
Often the overall reaction rate is much easier to measure than the explicit forward and backward rates. To get an idea of what conditions are necessary to get J0 approximately equal to J0_mm adjust the parameters to get S1_mm(t) close to S1(t).
Load the model below and then hit the 'Start' button to run the simulation. Adjust the parameter sliders below the plot to see how they affect the S1 and S1_mm. Try to get time courses to match.