Practical Steady-State Enzyme Kinetics

Jon R. Lorsch 1    Department of Biophysics and Biophysical Chemistry, Johns Hopkins University School of Medicine, Baltimore, MD, USA
1 Corresponding author: email address: jlorsch@jhmi.edu

1 Theory

Enzymes catalyze reactions, accelerating the rate in the forward and reverse directions (substrate to product, product to substrate) to the same extent. In steady-state kinetics, initial rates of reactions are measured in a regime in which each enzyme molecule binds substrate and catalyzes its conversion to product multiple times. Hence, steady-state kinetics is also frequently referred to as multiple-turnover kinetics. The experiments must be set up such that the concentration of the enzyme in the system is always much less than the concentration of the substrate. This situation ensures that the concentration of free substrate ([S]), unbound to enzyme, is approximately equal to the total substrate concentration in the system ([S]t; i.e., how much substrate you added) and thus, they do not have to be accounted for separately. It is also important to measure the rates of the reactions in the initial rate regime – that is, when only a few percent of the substrate has been converted to product. This ensures that the concentration of substrate does not change appreciably over time – ‘steady-state’ conditions – and that product accumulation does not interfere with the analysis (i.e., approximately no product has built up). Initial rates are measured as the slope of the linear portion of the product versus time (or substrate vs. time) curve. The fact that this region is linear indicates that substrate concentration has not decreased enough and product concentration has not built up enough to appreciably alter the rate of the reaction (i.e., [S] is essentially constant at its initial value in this region). To perform a steady-state kinetics experiment, the initial rates of the reaction at a fixed enzyme concentration are measured as a function of substrate concentrations (with concentration of substrate [S] always fivefold or more greater than [E]T).

Under these conditions, the rate of the reaction is given by the Michaelis–Menten equation:

The quantity kcat[E]t is called the Vmax, the maximal rate of the reaction at a given concentration of enzyme. Vmax is the rate the enzyme-catalyzed reaction approaches at very high substrate concentrations (i.e., saturation). kcat is the apparent first-order rate constant for the enzyme-catalyzed reaction at saturating concentrations of substrate. It reflects the slowest step (or steps) along the reaction pathway after formation of the enzyme–substrate complex. Km, the Michaelis constant, is the concentration of the substrate required to give a rate that is ½Vmax. Km has units of M, and is a reflection of how well the enzyme binds the substrate in question. However, it is important to note that Km is a kinetic constant and does not necessarily equal the Kd for the enzyme–substrate complex. Thus, statements such as “the Km for substrate X is lower than for substrate Y, therefore the enzyme binds X more tightly than Y” should not be made unless additional information is available indicating that the Km values in question reflect the relevant Kd values. The safest way to think about Km values is that they indicate how much substrate must be added to get half the maximal rate of the reaction.

It is also possible to get information about the mode of action of an enzyme inhibitor using steady-state kinetics. To do this, the (apparent) Vmax and Km of the reaction are measured at different concentrations of the inhibitor. If the presence of the inhibitor increases Km but does not affect kcat, the inhibitor is said to be competitive; that is, the inhibitor slows the reaction, but this effect can be overcome – out-competed – by adding more substrate. Competitive inhibition indicates that the substrate and the inhibitor cannot bind to the enzyme at the same time – they compete for binding. If the inhibitor reduces the apparent kcat of the reaction but does not change the apparent Km, it is said to be a noncompetitive inhibitor. This mode of inhibition happens when the inhibitor can bind to both the free enzyme and the enzyme–substrate complex, but when it is bound, the enzyme has diminished activity. Uncompetitive inhibitors bind only to the enzyme–substrate complex, not to the free enzyme, and they decrease both kcat and Km (the decrease in Km stems from the fact that their presence pulls the system away from free enzyme toward the enzyme–substrate complex). If the inhibitor increases Km and decreases Vmax, the inhibition is said to be ‘mixed.’ Other, more complicated forms of inhibition are possible, but they are outside the scope of this chapter.

A wide variety of assays can be used to perform steady-state enzyme kinetics experiments. These include radioactivity-, absorbance-, and fluorescence-based assays. No particular assay is described here, and instead, a generic protocol is presented.

Finally, it should be noted that steady-state kinetics does not give information about the fundamental rate constants for the steps in an enzyme-catalyzed reaction and thus, its utility for dissecting the mechanism of the process is limited. However, it is useful for an initial characterization of an enzyme or inhibitor, or when comparing the effects of mutations or modifications on enzyme function. More information about steady-state and pre-steady-state kinetic approaches can be found in several excellent books (Johnson, 2003; Fresht, 1998).

2 Equipment

Equipment required for the enzyme assay will vary. Examples include a spectrophotometer, fluorometer, HPLC, or phosphorimager.

For the data analysis, a computer with a graphing program that can do curve fitting is required. KaleidaGraph or Sigma Plot both work well, although other programs, including Microsoft Excel, can be used.

3 Materials

Materials required for the enzyme assay will vary.

4 Protocol

4.1 Preparation

Prepare a homogenous enzyme sample.

4.2 Duration

See Fig. 1.1 for the flowchart of the complete protocol.

5 Step 1 Measure Initial Rates of the Enzyme-Catalyzed Reaction as a Function of Substrate Concentration

5.1 Overview

The initial rates of the reaction are measured at different substrate concentrations from 10-fold below Km to 10-fold above it (if possible).

5.2 Duration

1 day

1.1 Prepare reaction mixes by adding a concentrated stock of reaction buffer (e.g., 10×) such that the final buffer concentration will be 1× after addition of substrate, enzyme, and other reaction components (as required).

1.2 Add serial dilutions of substrate to tubes of reaction mix. The range covered should be from ~ 10-fold below Km to ~ 10-fold above it, if possible.

1.3 Start each reaction by adding enzyme. If a large volume of enzyme is to be added (> 10% of the total reaction volume), it is best to have it preincubated at the reaction temperature. Include a control in which no enzyme is added (but an equivalent amount of the buffer in which the enzyme is stored is added) to measure the background rate of the reaction. Remember that [Enzyme]total must be much less (in practice greater than fivefold less is sufficient) than the lowest concentration of the substrate...