Measurement of kon without a rapid-mixing device


  • James Kahn,

    1. Department of Chemistry and Biochemistry, University of San Diego, San Diego, California 92110
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  • Robert N. Dutnall,

    1. Department of Chemistry and Biochemistry, University of San Diego, San Diego, California 92110
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  • Kimberly Matulef,

    1. Department of Chemistry and Biochemistry, University of San Diego, San Diego, California 92110
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  • Leigh A. Plesniak

    Corresponding author
    1. Department of Chemistry and Biochemistry, University of San Diego, San Diego, California 92110
    2. Department of Biology, University of San Diego, San Diego, California 92110
    • Department of Chemistry and Biochemistry, University of San Diego, San Diego, California 92110
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    • Tel.: 859-692-0460; Fax: 619-260-6804

  • This work is supported by NIH AREA grant GM068431-02A1.


We have recently designed a biochemistry laboratory experiment for the purpose of providing students an advanced experience with enzyme kinetics and the kinetics of binding. Bestatin, a well-known and commercially available general protease inhibitor, is a slow-binding inhibitor of aminopeptidase isolated from Aeromonas proteolytica. The binding is on a timescale slow enough for measurement without the use of a rapid-mixing device. Aminopeptidase inhibition is detected via a standard colorimetric assay with an inexpensive commercially available substrate. The binding of bestatin follows first order binding kinetics with a rate constant kon of 59 ± 5 M−1 s−1. This aminopeptidase is well characterized with several crystal structures and a published Ki, which students can then use to calculate the value for koff.

Many introductory biochemistry laboratory courses incorporate an enzyme kinetics suite of experiments for the determination of the Michaelis-Menten constants, Km and kcat, for a given enzyme. Often, the next experiment may be a repetition of these experiments in the presence of an inhibitor and subsequent Lineweaver-Burk type analysis for the identification of Ki and the classification of the type of observed inhibition: competitive, uncompetitive, or mixed. Beyond these very important fundamental experiments, it is often difficult to design an inexpensive well-behaved advanced laboratory biochemistry kinetics experiment. Access to rapid-mixing or stopped-flow devices is also usually not practical for the purposes of a laboratory course; therefore, the measurement of the binding rate constant, kon, for an inhibitor or substrate is generally not feasible. Bestatin is a previously described slow- binding competitive inhibitor of aminopeptidase from Aeromonas proteolytica (AAP) [1]. Here, we describe a biochemistry or biophysical laboratory experiment for the measurement of kon, the second order rate constant for binding of bestatin to AAP (Fig. 1). All reagents are commercially available and relatively inexpensive. Aminopeptidase from Aeromonas proteolytica is a stable enzyme with which students can achieve reproducible results. In our version of the laboratory, we use nonlinear curve fitting analysis of the pseudo first order binding data and the equilibrium constant determination; however, useful experiments can be carried out with linear fitting of the data.

This aminopeptidase system is suitable for the expansion into a variety of experiments and exercises for an advanced laboratory. There are several crystal structures of aminopeptidase from Aeromonas proteolytica, including structures in the absence of ligands (1RTQ and 1AMP) [2, 3], in complex with bestatin (1XRY and 1TXR) [4], and in complex with transition state analogs (1FT7) [5], which can be useful for a detailed description of the catalytic mechanism. Equilibrium measurements of the bestatin binding affinity have been reported, and the enzyme recovers activity upon dilution of the bestatin complex [1]. Additionally, there is reported competitive inhibition by L-leucinephosphonic acid, which displays classic double-reciprocal plots [5].



All reagents and buffers were purchased from Sigma–Aldrich. Aeromonasproteolytica aminopeptidase was purchased from Sigma–Aldrich (catalog A8200-100UN) in lyophilized powder form, as were the substrate L-leucine-p-nitroanilide hydrochloride (pLeuNA) (catalog L2158) and bestatin hydrochloride (catalog B8385). Stock solutions of bestatin (1 mM in 20 mM Tris, pH 7.6) and pLeuNA (3.3 mM in 20 mM Tris pH 7.6) were prepared directly from commercial bottles. The substrate solution is prepared daily because pLeuNA can precipitate after freeze–thaw cycles. Aminopeptidases can have a steep pH activity profile. Therefore, it is important that all solutions for the assay have identical pH, though pH values ranging from at least 7.5 to 8.0 have been used. We chose a slightly lower pH for assays because the substrate background hydrolysis seemed to increase significantly over the range from pH 7.5 to 8.0.

Measurement of kon

For the measurement of the second order rate constant of bestatin binding to AAP, a common stock of AAP of 0.2 U/μL in 20 mM Tris buffer pH 7.6 was suspended from the lyophilized powder to be used for each inactivation experiment. AAP inactivation was initiated by diluting the stock enzyme 1:200 into 10, 20, or 30 μM bestatin at room temperature in 20 mM Tris, pH 7.6. Based upon the specific activity (98.4 U/mg protein) of the AAP and its molecular weight, (31,406 kDa), this concentration corresponds to 320 nM enzyme in the inactivation mixture. A control mixture was prepared in the absence of bestatin. The residual activity of bestatin-incubated AAP was monitored over the course of 2 hours by spectrophotometric assay of 10 μL of inactivation mixture in 2 mM pLeuNA in 20 mM Tris pH 7.6 at 25°C in an assay volume of 1 mL. Formation of product was detected at 405 nm for 2 minutes. We have also found that the inactivation can be carried out at 32 nM AAP with similar results. Activity of uninhibited AAP was monitored at the beginning and end of each inactivation experiment and showed no loss of activity over this time period. Students worked in pairs to quickly get time points at 30 seconds, 90 seconds, 3 minutes, 5 minutes, and so on in the initial time period of the inactivation. The laboratory manual for students and instructors, including preparation instructions, for this experiment has been included in the Supporting Information.


The session before this experiment, students carry out a Michaelis-Menten style substrate saturation experiment to determine Km and kcat of Aeromonas proteolyticus aminopeptidase for pLeuNA. Students use the laboratory period to get familiar with the spectrophotometric assay and to determine a suitable concentration of substrate to use for the measurement of the binding rate constant. The careful description of the relevant binding events is crucial to student understanding the big picture. Students struggle with the two time elements: (i) time = 0 for the inactivation of the AAP and (ii) time = 0 for the measurement of residual enzyme activity in the kinetic assay.

equation image(1)

This laboratory experiment aims to measure the kinetic rate constant for the binding of bestatin to aminopeptidase (kon). The rate of binding can be described at any given time, if the concentrations of the involved species are known, by the second order rate expression for binding,

equation image(2)

where [E] is the concentration of free aminopeptidase in units of molarity, and [B] is the concentration of free bestatin in molarity, and kon is the second order rate constant for the association of E and B with units of M−1 s−1; when the [B] ≫ [E], [B] is considered to be a constant. To solve for the integrated form of this equation, isolate variables,

equation image(3)

and integrate from [Eo] , the initial free concentration of aminopeptidase, to E, the instantaneous concentration at time, t.

equation image(4)

The integrated form is,

equation image(5)

which can be rearranged to a standard pseudo first order rate expression,

equation image(6)

where kobs = kon × [B] is the observed pseudo first order rate constant. For the purposes of comparison, it is useful to normalize the free concentration of enzyme, relative to its initial value, equation image. In this experiment, the relative enzymatic activity of an incubated mixture of aminopeptidase and bestatin can yield the fractional portion of enzyme that is not in complex with bestatin, equation image. This quantity is obtained by measuring the activity of inhibited aminopeptidase toward hydrolysis of pLeuNA and dividing by the activity of the enzyme that has not been incubated with bestatin, equation image.

It is worth emphasizing to students that the activity assays are a vehicle for quantifying the free aminopeptidase and the aminopeptidase in complex with bestatin. Inhibition by bestatin is reversible; however, the value for kcat for substrate and the koff for bestatin are on such different timescales that the aminopeptidase in complex with bestatin is considered essentially constant during the time period of the enzyme assay.


Determination of Km and kcat

The substrate saturation plots for pLeuNA with AAP (Fig. 2) result in a Km value of 17 μM for pLeuNA and a kcat of 60 seconds−1. These numbers compare to reported values of 10 μM and 64 seconds−1 (3840 minutes−1) at pH 8.0 [5]. The optimum pH for activity is 8.0. These values for Km and kcat can also be obtained from a linear fit of the data in double reciprocal (Lineweaver-Burk) format if students don't have access to software for nonlinear regression. Students have a chance to become familiar with the assay, gauge how much enzyme will be needed for the measurement of kon, and have little difficulty obtaining quality data on this portion of the experiment. The choice of 2 mM pLeuNA for the experiments in Day 2 should help minimize the effects from small errors in substrate concentration because this is a flat part of the substrate saturation curve.

Figure 1.

Scheme for binding of bestatin to aminopeptidase. Aminopeptidase (E) is inhibited by bestatin in a competitive fashion. The relative fraction of active aminopeptidase can be quantified with a colorimetric assay that uses pLeuNA as substrate (S). Formation of product is observed by the release of p-nitroanalide (P), which absorbs at 405 nm.

Figure 2.

Substrate saturation plot of aminopeptidase. Enzyme activity as a function of substration concentration. TheKm and kcat determined from these data were 17 μM and 60 seconds−1, respectively. Assays were carried out at 25°C in 20 mM Tris buffer, pH 7.6.

Measurement of kon

Incubation of the AAP with bestatin in the 10–30 μM concentration range results in nearly complete inhibition of the enzyme in the time frame of 2 hours (Fig. 3a). Lower concentrations of bestatin, 1 μM and 5 μM, also inhibit AAP but in the time frame for this experiment less than 60% inhibition was observed. These data were fit to Eq. (6), resulting in an average kon value of 55 ± 6 M−1 s−1. This model assumes that there is no appreciable back reaction. Figure 3 panel b shows an overlay of the experimental data with the calculated model using kon values of 50 M−1 s−1 for 10 μM and 20 μM bestatin and 60 M−1 s−1 for 30 μM bestatin, demonstrating that the back reaction is not significant. If there is no access to software for fitting nonlinear equations, the data can be plotted in the logarithmic form against time. The resulting line will have the slope of kon*[Bestatin]. For our data, plots were linear until the enzyme was 85% inhibited. Data acquired beyond this value were not included in the linear fit. These plots are shown in Fig. 4, resulting in very similar values for kon. Finally, a best value of kon was obtained with all three inactivation series and both methods of fitting, linear, and exponential, by plotting kobs against the concentration of bestatin (Fig. 5). The slope of this line will give an apparent kon, which calculates to 59 M−1 s−1. The value reported in the literature is considerably higher, 450 M−1 s−1 [1] for experiments carried out at pH 8.0. In our laboratory classes, values within a section tend to agree but between sections kon has ranged from 59 to 190 M−1 s−1. The difference between the class values and literature values for kon may, in part, be explained by the 0.4 difference in pH (7.6) for the experiments. The purity of the enzyme stock solutions were comparable, though not identical. The specific activity of the AAP used in the Wilkes and Prescott paper was 135 U/mg. AAP purchased from Sigma has a specific activity of 98.4 U/mg. The bestatin used in this experiment was greater than 98% pure.

Figure 3.

Loss of aminopeptidase activity over time. Aminopeptidase was incubated with bestatin at three different concentrations, 10 μM (•), 30 μM (▴), and 60 μM (♦). (a) Initial rates of the rate of hydrolysis of pLeuNA were measured and plotted relative to their initial activity, according to Eq. (6). The incubation was carried out at room temperature, which was monitored but not controlled. (b) An overlay of the data with the calculated model for a pseudo first order binding process [Eq. (6)] with kon values of 50 M−1 s−1 for 10 μM bestatin and 30 μM bestatin, and with a modeled kon of 60 M−1 s−1 for the 60 μM bestatin data. The quality of the fit indicates that the reversal of binding is not significant during the time frame of these experiments.

Figure 4.

Semilog plot of the binding of bestatin to aminopeptidase. The same data from Fig. 3 were replotted according to Eq. (5).

Figure 5.

Best fit for kon. The best fit value for kon is obtained through a plot of kobs as a function of the bestatin concentration. The slope of the line yields kon, the second order rate constant for binding. The plot contains values of kobs obtained from both exponential (○) and linear (•) fits of the data.

Students, working in pairs, will generally have time to collect data for one or two concentrations of bestatin in a single laboratory period. Higher concentrations of bestatin require less time for data collection, which can be a consideration in experimental design but will also require to students to act quickly to get important early time points. The quality of student data is quite good once the workable concentrations of bestatin and enzyme have been identified. The incubation of bestatin with enzyme was carried out on the bench top at room temperature. Temperature was controlled on the spectrophotometer. Both room and spectrophotometer temperatures were monitored continuously, and we noticed that if the spectrophotometer or the room heated up with use over the time period of the experiment, the quality of the data was impacted enough to affect the shape of the exponential. The largest issue in the experiment with regard to student performance is making sure that they understand that time zero for inactivation is when bestatin and AAP are mixed, not when they perform the activity assay. Because Ki = koff/kon, students can then calculate koff if they have an estimate of the equilibrium dissociation constant. The reported equilibrium binding constant for bestatin to the AAP is 18 nM [1]. With our value of kon, koff calculates to be 1.1 × 10−6 seconds−1.


The slow, tight binding of bestatin to aminopeptidase from Aeromonas proteolytica is an uncommon biochemical phenomenon that has enabled us to design a simple, inexpensive laboratory exercise for the measurement of kon. The enzyme has good thermal stability and is tolerant of freeze–thaw cycles, making it suitable for classroom experiments. The system is amenable to further addition of experiments to an advanced biochemical or biophysical laboratory class, including the measurement of koff, steady-state experiments with different inhibitors, and computer molecular modeling exploration of the crystallographic structures of the aminopeptidase.


The authors wish to thank Stephen Mills for many helpful conversations in the design of this laboratory, Helene Citeau for assistance and maintenance of the instrumentation used in these experiments, and Sharon Ferguson for assistance in preparation of solutions for the experiment.