# Measuring a high Michaelis constant using fluorescence

We have the task of measuring kinetic parameters of an oxidase reaction that has a $$K_M$$ of about $$2 \,\text{mM}$$. For that, we want to use a fluorescence assay based on Amplex Red. The latter is a fluorogenic substance of an upper detection limit of $$5 \, \mu \text{M}$$. At higher concentrations, the inner filter effect causes non-linear behaviour.

Usually, we would use substrate and fluorophore concentrations of a similar range of the $$K_M$$ value. Obviously, we cannot do that here, as the fluorophore concentration would be way above the upper detection limit. This led us to the idea of reducing the substrate, fluorophore, and enzyme concentration by the same factor to do measurements in a micromolar range. Later we could simply scale up the results.

We doubt that this method is possible as the Michaelis-Menthen kinetics never look at the ratio between substrates and enzyme, but only regard absolute substrate concentrations.

So our question is if the proposed method is in fact not applicable and if so, what your suggestions would be?

• What is the purpose of this kinetics? Knowing that would be helpful to suggest something else. – Mathew Mahindaratne Feb 22 at 17:04

Based on your description, it sounds like you are measuring the production of hydrogen peroxide by an oxidase enzyme. In that case, it is not necessary for the Amplex Red to be at the same concentration as the substrate. You only need enough reagent to determine the initial rate of reaction at each substrate concentration, ie when only a small portion of the substrate has been consumed. If 5 $$\mu M$$ is not sufficient for that purpose, you can determine the resorufin (produced by reaction of Amplex Red with H2O2) by absorbance rather than fluorescence for lower sensitivity and higher maximum. According to the Thermo Fisher assay kit info, resorufin has an extinction coefficient of $$58,000$$ $$M^{-1}cm^{-1}$$, so with a standard 1 cm pathlength cuvette, your linear range would probably go up to around $$50$$ $$\mu M$$, depending on your spectrophotometer. With a short path cuvette (these are available with 0.2 and 0.1 cm pathlengths), you could go quite a bit higher, certainly more than sufficient for your needs.

As for why you cannot just scale the concentrations down, consider the limiting case where the Michaelis constant is equal to the $$K_d$$ of the substrate. We have that $$K_d=\frac{[E][S]}{[ES]}$$, so $$[S] \approx K_d$$ when $$[E]=[ES]$$ (assuming $$[S]_{tot}>>[ES]$$). Thus, the absolute concentration of E is not a factor, as long as it is small enough that the amount of S bound does not substantially change the concentration of free S. You should get the same result for $$K_M$$ regardless of what concentration of enzyme you use.

A nonfluorescent derivative of dihydroresorufin, 10-acetyl-3,7-dihydroxyphenoxazine has been marketed under the name Amplex® Red (AR). AR is regarded as the best fluorogenic substrate for peroxidase because it is highly specific and stable. It has been used to detect Reactive Oxygen Species (ROS) such as $$\ce{H2O2}$$ in various experimental enzymatic systems (e.g., $$\ce{H2O2}$$ is produced by many enzymatic reactions). During these assays, nonfluorescent AR is oxidized to highly red fluorescent resorufin by ROS (excitation/emission maxima: $$\lambda_{ex} = \pu{563 nm}$$ and $$\lambda_{em} = \pu{587 nm}$$) in a peroxidase-catalyzed reaction with $$\ce{H2O2}$$ (Ref.1). The abstract of that original reference states that:

The enzymatic determination of hydrogen peroxide can be accomplished with high sensitivity and specificity using N-acetyl-3,7-dihydroxyphenoxazine (Amplex Red), a highly sensitive and chemically stable fluorogenic probe for the enzymatic determination of $$\ce{H2O2}$$. Enzyme-catalyzed oxidation of Amplex Red, which is a colorless and nonfluorescent derivative of dihydroresorufin, produces highly fluorescent resorufin, which has an excitation maximum at $$\pu{563 nm}$$ and emission maximum at $$\pu{587 nm}$$. The reaction stoichiometry of Amplex Red and $$\ce{H2O2}$$ was determined to be 1:1. This probe allows detection of $$\pu{5 pmol}$$ $$\ce{H2O2}$$ in a 96-well fluorescence microplate assay. When applied to the measurement of NADPH oxidase activation, the Amplex Red assay can detect $$\ce{H2O2}$$ release from as few as 2000 phorbol myristate acetate-stimulated neutrophils with a sensitivity 5- to 20-fold greater than that attained in the scopoletin assay under the same experimental conditions. Furthermore, the oxidase-catalyzed assay using Amplex Red results in anincreasein fluorescence on oxidation rather than adecreasein fluorescence as in the scopoletin assay. In comparison with other fluorometric and spectrophotometric assays for the detection of monoamine oxidase and glucose oxidase, this probe is also found to be more sensitive. Given its high sensitivity and specificity, Amplex Red should have a broad application for the measurement of $$\ce{H2O2}$$ in a variety of oxidase-mediated reactions and very low levels of $$\ce{H2O2}$$ in food, environmental waters, and consumer products.

As you have described it, your enzyme is better suited for designed UV–vis-based assay. Yet, adapting a UV–vis-based coupled enzyme assay to a fluorescence-based assay is not unprecedented since it has been done before. For example, Gutheil and coworkers have developed high-sensitivity fluorescent assays for D-Alanine, which use a microtiter plate format based on D-aminoacid oxidase/horseradish peroxidase (DAO/HRP)-coupled reactions (Ref.2). They have also taken the standard UV–vis-based coupled enzyme assay for D-Alanine using o-phenylenediamine (OPD) and adapted it to microtiter plates for comparison purposes. The fluorescent assays allow the sensitivity of the assay to be increased from $$\pu{2 nmol}$$ (chromogenic (UV–vis) assay) to $$\pu{2 pmol}$$, a 1000-fold increase in sensitivity. One of the two fluorogenic HRP substrates tested in this assay was AR (which is commercially available that has given a lower limit of sensitivity of $$\pu{2 pmol}$$ D-Ala, and was linear up to $$\pu{400 pmol}$$. During the assay, AR is converted to fluorescent resorufin upon oxidation in HRP-coupled reactions. Resorufin was then detected with excitation at $$\pu{546 nm}$$ and emission at $$\pu{595 nm}$$.

You may follow their design for your enzyme as well.

References:

1. M. Zhou, Z. Diwu, N. Panchuk-Voloshina, R. P. Haugland, “A Stable Nonfluorescent Derivative of Resorufin for the Fluorometric Determination of Trace Hydrogen Peroxide: Applications in Detecting the Activity of Phagocyte NADPH Oxidase and Other Oxidases,” Analytical Biochemistry 1997, 253(2), 162-168 (https://doi.org/10.1006/abio.1997.2391).
2. W. G.Gutheil, M. E. Stefanova, R. A. Nicholas, “Fluorescent Coupled Enzyme Assays for D-Alanine: Application to Penicillin-Binding Protein and Vancomycin Activity Assays,” Analytical Biochemistry 2000, 287(2), 196-202 (https://doi.org/10.1006/abio.2000.4835).