WHAT IS IT? ----------- 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 Kd 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 separation. 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 easily. 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. HOW TO USE IT -------------- 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 turtles. - 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 catalysis. 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 times. THINGS TO NOTICE ---------------- 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? THINGS TO TRY ------------- 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 affected? EXTENDING THE MODEL ------------------ 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 inhibitor? Include a slider that allows you to change the concentration of enzyme. What affect does this have on the plot? Vmax? Look closely! STARLOGOT FEATURES ------------------ 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.