Reaction velocity and substrate concentration
Fig. 2 Change in reaction velocity with substrate concentration
Fig. 2 shows a graph of reaction velocity vs. substrate concentration. A curve such as this can be generated based on theoretical considerations directly from the Michaelis-Menten equation. At a fixed initial substrate concentration, the reaction has a particular initial velocity, indicated by the large arrow. However, as time goes by and the reaction progresses, substrate is used up. The substrate concentration decreases, causing the reaction velocity to decrease as well. Eventually the reaction comes to a stop when no substrate is left (represented by the point 0,0 on the graph). If we repeated the reaction using different initial substrate concentrations, each [substrate concentration, V0] point would fall somewhere on this line. From this plot we can see that no matter how high we make the initial substrate concentration, the reaction velocity will not exceed Vmax . This is because at Vmax the active sites of all enzyme molecules are saturated. Thus the curve approaches Vmax asymptotically.
The substrate concentration associated with ½ Vmax has a special status. It is called Km or the Michaelis-Menten constant and it represents the substrate concentration at which half of the enzyme molecules are bound to substrate. Because Km is inversely related to substrate binding, it can be used to characterize the affinity of the enzyme for that particular substrate. A low Km indicates that the enzyme has a great binding affinity since it takes very little substrate to bind substrate to half of the enzyme molecules.
Emperical determination of reaction velocity
Fig. 3 Moles of product as a function of time
Since we cannot measure reaction velocity directly, we cannot directly generate a graph like Fig. 2 experimentally. However, we can use indirect measurements and analysis to construct a similar graph.
Fig. 3 shows a plot of absorbance vs. time for the reaction shown in Fig. 2. Since in our tyrosinase-catalyzed reaction absorbance is directly proportional to moles of product, we can simply change the scale of the axis to make the axis represent moles of product. The moles of product increase over time, but reach a limit as the substrate is depleted and the reaction slows.
Since the reaction velocity is the rate at which product is produced from substrate, the rate of change of moles of product per unit time represents the reaction velocity. In graphical terms, in Fig. 3 the slope of a line tangent to the curve at a particular time represents the instantaneous reaction velocity at that time. At time=0 when there is only substrate and no product, the velocity is at a maximum and the curve is nearly linear. Thus a best-fit line through the points soon after time=0 will approximate the velocity at time=0 (V0).
Although the shape of the curve in Fig. 3 looks superficially like Fig. 2, the two graphs have different meanings. (Notice the difference in axis labels.) However, the two graphs are related and this relationship can be used to generate graphs similar to Fig. 2 from data derived from graphs similar to Fig.3. In Fig. 3, if you consider what happens over time to the slope of the tangent line (the reaction velocity) and the amount of substrate that remains, you can see how points on Fig. 2 could be generated from Fig. 3. In reality, it is not practical to generate a reaction velocity/substrate concentration graph from a single graph like Fig. 3 because the instantaneous slopes cannot be measured accurately. However, V0 can be measured fairly accurately for a given initial substrate concentration, so a graph similar to Fig. 2 can be constructed from V0 data collected from several trials. This is the approach we will take in this week's experiment.
