Determination of Km - Substrate
[The following is a brief and general summary about enzyme kinetics.]
In the first week of our program, we learned that
the rate of a reaction varies directly with the amount of enzyme added to
the assay solution. We also learned that this was not true when we varied
the amount of substrate or coenzyme in the assay solution. In these experiments
we learned that the rate of activity declined dramatically as the concentration
of substrate [or coenzyme[ increased. These are examples of "saturation
kinetics" - at higher concentrations of substrate a point is reached
wherein "the substrate binding site of every molecule of enzyme has
bound a molecule of substrate".
When you plotted initial enzyme activity versus substrate concentration, you observed a curve which became asymptotic to a horizonal line that represents "maximum activity", often referred to as Vmax. "Km" is defined as that concentration of substrate that gives "half-maximal activity". If you plot the "other end" of this curve, it becomes asymptotic to a vertical line at -1/Km [Figure 7]. However, presentation of kinetic data as in Figure 2 is not especially useful. Such data may be better presented in a different form. A frequently used alternative presentation is the "double reciprocal" or "Lineweaver-Burk" plot [Figure 8]. In double reciprocal plots the Y-intercept represents 1/ Maximal Velocity while the X- intercept represents 1/Km. The "down-side" of double reciprocal plots is that low concentrations of substrate contribute unevenly to "errors" with these plots. Much of this problem is avoided if one plots Substrate Concentration versus Substrate Concentration / Initial Velocity [Figure 9, Hanes plots]. [Biochemists have known this problem for two decades but most still use Lineweaver-Burk plots; Cornish- Bowden]. We will use Lineweaver-Burk plots to determine Km's but we will also use Hanes and / or Hofstee [Figure 10] plots to determine what the differences might be. [Refer to Cornish-Bowden for a thorough discussion of enzyme kinetics.]
Determining Km for Substrate
1. Use seven concentrations of substrate. Dilute
original concentration* by 2, 4, 8, 12, 16, 20.
2. Prepare enough assay buffer to run all concentrations in triplicate. Place in water bath.
3. Run triplicate assays for all concentrations, according to standard assay procedures. Be careful, rinse cuvettes well, and change pipet tips between each assay.
4. Repeat the whole procedure two times, i.e., the final Km will be the mean of three determinations.
*Prepare substrates in concentrated form using 1.5 mL centrifuge tubes.
Since an assay requires 10 µl of substrate solution per mL of assay solution, these concentrated solutions must be 100 X's the assay concentration.
Calculation of Km
1. Determine OD / min for each assay.
2. Determine mean OD / min for each concentration of substrate or
co-enzyme [slope @ 1A].
3. Determine V0 for each concentration. V0 = OD / Min [0.1613]
4. Lineweaver-Burke Plot: Plot 1 / V0 vs [S]
5. Hofstee Plot: Plot V0 vs V0 / [S]
Dilutions of Substrate for Km
|Tube||Dilution||µl ||ul H2O||Molarity||1 / [S]||V0||1 / V0|
Figure 7. The dependence of initial velocity on substrate concentration for a reaction obeying Michaelis-Menton kinetics. [After Cornish-Bowden].
Figure 8. Plot of 1/Initial Velocity versus 1/Substrate concentration. Plots such as this are referred to as "double-reciprocal" plots as "Lineweaver-Burk" plots.
Figure 9. Plot of Substrate Concentration/Initial Velocity. Such plots are known as Hanes [or Woolf] plots
Figure 10. Hofstee plot to determine Km for substrate.
Figure 11. Km for isocitrate - isocitrtate dehydrogenase from Silene alba.
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