This model demonstrates the kinetics of single-substrate enzyme-catalysis. The interactions between enzymes and substrates are often difficult to understand and the model allows users to visualize the complex reaction.

The standard equation for this reaction is shown below.

		  Kc	      Kr
	E + S <=======> E-S ------> E + P

Where E represents Enzyme, S Substrate, E-S, Enzyme-Substrate complex, P
product. The rate constants are Kc for complex formation, Kd for complex
dissociation, Kr for catalysis. The first step in catalysis is the
formation of the E-S complex, this can consist of either covalent or
non-covalent bonding. The rates of complex formation and dissociation are
very fast because they are determined by collision and separation of the
molecules. The next step is for the enzyme to catalyze the conversion of
substrate to product. This rate is much slower because the energy required
for catalysis is much higher than that required for collision or

The model demonstrates several important properties of enzyme kinetics.
Enzyme catalysis is often assumed to be controlled by the rate of complex
formation and dissociation, because it occurs much faster than the rate of
catalysis. Thus, the reaction becomes dependent on the ratio of Kc / Kd.
The efficiency of catalysis can be studied by observing catalytic behavior
at different substrate concentrations.

By measuring the rate of complex formation at different substrate
concentrations, a Michaelis-Menten Curve can be plotted. Analysis of the
plot provides biochemists with the maximum rate (Vmax) at which the
reaction can proceed. As can be seen from the model, this plot is linear
at low levels of substrate, and non-linear at higher levels of substrate.
By examining the model, the reasons for this relationship can be seen

Enzyme catalysis can also be controlled using inhibitors. Inhibitors are
molecules that are structurally similar to substrate molecules that can
complex with the enzyme and interfere with the E-S complex formation.
Subsequently, the shape of the Michaelis-Menten Curve will be altered. The
model demonstrates the effects of inhibitors on catalysis.


Choose the values of Kr, Kc, and Kd with appropriate sliders:
     - Kr controls the rate of the forward reaction by which one green
substrate turtle is converted to a blue product turtle by the red enzyme
     - Kc controls the rate at which green substrates and red enzymes
stick together so that catalysis can occur, Kd controls the rate at which
they come apart.

Having chosen appropriate values of the constants, press SETUP to clear
the screen and create an initial number of red turtles. Play with several
different values to observe variable effects on complex formation and

Press RUN to start the simulation. Green turtles will be generated and the
reaction will proceed. The rate of complex formation, product formation
and substrate loss are plotted in the REACTION RATE window.

When PLOT-MM? is turned ON, the Michaelis-Menten Curve will be plotted.
The simulation will repeat continuously, adding  more green turtles
according to the number set with the ADDITION slider. The simulation will
stop once a noticeable curve is generated. The rate of change of substrate
each run is output to the command center each time and the =maximum rate
(Vmax) will be output to a monitor window.

If WITH-INHIBITOR? is turned ON before the Michaelis-Menten Curve is
plotted, the simulation will add a number of yellow inhibitor molecules,
set with the ADDITION slider, each run. The effect of this can be observed
on the plot.

Use ADD-INHIBITOR and ADD-SUBSTRATE to observe the effects of adding more
molecules to the system manually as it runs.

If you want to compare different assay conditions, turn KEEP-PLOT? on
before you press RUN. The pen color will change for the Michaelis-Menten
Curve and plot next to the previous curve. You can repeat this several


Watch the rate at which the enzyme and substrate stick together. How does
this affect the conversion of substrate into product? What would happen if
Kd is very high and Kc is very low? If Kr were the same order of magnitude
as Kd and Kc?
Watch the Michaelis-Menten Curve. Does it match up with the discussion of
enzyme kinetics discussed above? Why is the plot initially linear and
then flatten out?

Why is the rate (v) negative in the command center? Which variables can
alter the magnitude of v?

How does the magnitude of Kd and Kr affect the smoothness of the
Michaelis-Menten Curve?


Run the simulation with ADDITION set to various amounts. How does this
affect the curve?

If Kr is MUCH greater than Kd, what affect does this have on the reaction?
How important does complex formation become in this situation?

If Kc is MUCH less than Kd, what does this mean in the real-world? How are
the enzyme and substrate related under these conditions?

What effect does adding inhibitor to the model have on the plot? Is Vmax


What would happen if yellow inhibitor molecules could react to form a
product? How would this affect the plot?

Inhibitors can be irreversible or reversible. That is, they can bind to an
enzyme and never let go, or they can stick and fall off. Currently, the
model simulates reversible inhibitors. Modify the code so that the yellow
molecules irreversibly bind to the enzyme. How does this affect catalysis?

Often, the product of catalysis is an inhibitor of the enzyme. This is
called a feedback mechanism. In this model, product cannot complex with
enzyme. Modify the procedures so that the product is a reversible
inhibitor. How does this affect catalysis with and without yellow

Include a slider that allows you to change the concentration of enzyme.
What affect does this have on the plot? Vmax? Look closely!


Note the large number of variables that are used in this model. Turtles can keep track of the complex interactions between molecules by using variables such as ID and COMPLEXED?. For example, the ID variable allows turtles to identify other turtles with which they can react. COMPLEXED? prevents bound turtles from react with free turtles with a label that says they are unavailable to react.