Laboratory Exercises

Measurement of kon Without a Rapid-Mixing Device* s&

Received for publication, September 18, 2009, and in revised form, October 26, 2009

James Kahn‡, Robert N. Dutnall‡, Kimberly Matulef‡, and Leigh A. Plesniak‡§†

From the ‡Department of Chemistry and Biochemistry, University of San Diego, San Diego, California 92110§Department of Biology, University of San Diego, San Diego, California 92110

We have recently designed a biochemistry laboratory experiment for the purpose of providing studentsan advanced experience with enzyme kinetics and the kinetics of binding. Bestatin, a well-known andcommercially available general protease inhibitor, is a slow-binding inhibitor of aminopeptidase isolatedfrom Aeromonas proteolytica. The binding is on a timescale slow enough for measurement without theuse of a rapid-mixing device. Aminopeptidase inhibition is detected via a standard colorimetric assaywith an inexpensive commercially available substrate. The binding of bestatin follows first order bindingkinetics with a rate constant kon of 59 6 5 M21 s21. This aminopeptidase is well characterized withseveral crystal structures and a published Ki, which students can then use to calculate the value for koff.

Keywords: Enzyme kinetics, binding, aminopeptidase, rate constant, kon.

Many introductory biochemistry laboratory coursesincorporate an enzyme kinetics suite of experiments forthe determination of the Michaelis-Menten constants, Km

and kcat, for a given enzyme. Often, the next experimentmay be a repetition of these experiments in the presenceof an inhibitor and subsequent Lineweaver-Burk type anal-ysis for the identification of Ki and the classification ofthe type of observed inhibition: competitive, uncompeti-tive, or mixed. Beyond these very important fundamentalexperiments, it is often difficult to design an inexpensivewell-behaved advanced laboratory biochemistry kineticsexperiment. Access to rapid-mixing or stopped-flow devi-ces is also usually not practical for the purposes of a labo-ratory course; therefore, the measurement of the bindingrate constant, kon, for an inhibitor or substrate is generallynot feasible. Bestatin is a previously described slow-binding competitive inhibitor of aminopeptidase fromAeromonas proteolytica (AAP) [1]. Here, we describe abiochemistry or biophysical laboratory experiment for themeasurement of kon, the second order rate constant forbinding of bestatin to AAP (Fig. 1). All reagents are com-mercially available and relatively inexpensive. Aminopepti-dase from Aeromonas proteolytica is a stable enzyme withwhich students can achieve reproducible results. In ourversion of the laboratory, we use nonlinear curve fittinganalysis of the pseudo first order binding data and the equi-librium constant determination; however, useful experi-ments can be carried out with linear fitting of the data.

This aminopeptidase system is suitable for the expan-sion into a variety of experiments and exercises for an

advanced laboratory. There are several crystal structuresof aminopeptidase from Aeromonas proteolytica, includ-ing structures in the absence of ligands (1RTQ and1AMP) [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 thecatalytic mechanism. Equilibrium measurements ofthe bestatin binding affinity have been reported, and the

FIG. 1. Scheme for binding of bestatin to aminopeptidase.Aminopeptidase (E) is inhibited by bestatin in a competitivefashion. The relative fraction of active aminopeptidase can bequantified with a colorimetric assay that uses pLeuNA as sub-strate (S). Formation of product is observed by the release ofp-nitroanalide (P), which absorbs at 405 nm.

s&Additional Supporting Information may be found in the

online version of this article.*This work is supported by NIH AREA grant GM068431-02A1.† To whom correspondence should be addressed. Tel.: 859-

692-0460; Fax: 619-260-6804. E-mail: lplesniak@gmail.com.

DOI 10.1002/bmb.20369 This paper is available on line at http://www.bambed.org238

Q 2010 by The International Union of Biochemistry and Molecular Biology BIOCHEMISTRY AND MOLECULAR BIOLOGY EDUCATION

Vol. 38, No. 4, pp. 238–241, 2010

enzyme recovers activity upon dilution of the bestatincomplex [1]. Additionally, there is reported competitiveinhibition by L-leucinephosphonic acid, which displaysclassic double-reciprocal plots [5].

EXPERIMENTAL PROCEDURES

Reagents

All reagents and buffers were purchased from Sigma–Aldrich.Aeromonas proteolytica aminopeptidase was purchased fromSigma–Aldrich (catalog A8200-100UN) in lyophilized powderform, as were the substrate L-leucine-p-nitroanilide hydrochlor-ide (pLeuNA) (catalog L2158) and bestatin hydrochloride (cat-alog 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 pre-pared directly from commercial bottles. The substrate solutionis prepared daily because pLeuNA can precipitate after freeze–thaw cycles. Aminopeptidases can have a steep pH activityprofile. Therefore, it is important that all solutions for the assayhave identical pH, though pH values ranging from at least 7.5 to8.0 have been used. We chose a slightly lower pH for assaysbecause the substrate background hydrolysis seemed toincrease significantly over the range from pH 7.5 to 8.0.

Measurement of kon

For the measurement of the second order rate constant ofbestatin binding to AAP, a common stock of AAP of 0.2 U/lLin 20 mM Tris buffer pH 7.6 was suspended from the lyophilizedpowder to be used for each inactivation experiment. AAPinactivation was initiated by diluting the stock enzyme 1:200into 10, 20, or 30 lM bestatin at room temperature in 20 mMTris, pH 7.6. Based upon the specific activity (98.4 U/mg pro-tein) of the AAP and its molecular weight, (31,406 kDa), thisconcentration corresponds to 320 nM enzyme in the inactiva-tion mixture. A control mixture was prepared in the absence ofbestatin. The residual activity of bestatin-incubated AAP wasmonitored over the course of 2 hours by spectrophotometricassay of 10 lL of inactivation mixture in 2 mM pLeuNA in 20mM Tris pH 7.6 at 258C in an assay volume of 1 mL. Formationof product was detected at 405 nm for 2 minutes. We have alsofound that the inactivation can be carried out at 32 nM AAPwith similar results. Activity of uninhibited AAP was monitoredat the beginning and end of each inactivation experiment andshowed no loss of activity over this time period. Studentsworked in pairs to quickly get time points at 30 seconds, 90seconds, 3 minutes, 5 minutes, and so on in the initial time pe-riod of the inactivation. The laboratory manual for students andinstructors, including preparation instructions, for this experi-ment has been included in the Supporting Information.

PRELABORATORY PREPARATION

The session before this experiment, students carry outa Michaelis-Menten style substrate saturation experimentto determine Km and kcat of Aeromonas proteolyticusaminopeptidase for pLeuNA. Students use the laboratoryperiod to get familiar with the spectrophotometric assayand to determine a suitable concentration of substrate touse for the measurement of the binding rate constant.The careful description of the relevant binding events iscrucial to student understanding the big picture. Stu-dents struggle with the two time elements: (i) time ¼ 0for the inactivation of the AAP and (ii) time ¼ 0 for themeasurement of residual enzyme activity in the kineticassay.

E þ B Ðkonkoff

E : B: (1)

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

�d½E�dt

¼ kon½E�½B�; (2)

where [E] is the concentration of free aminopeptidase inunits of molarity, and [B] is the concentration of free besta-tin in molarity, and kon is the second order rate constant forthe association of E and B with units of M21 s21; when the[B] � [E], [B] is considered to be a constant. To solve forthe integrated form of this equation, isolate variables,

�d½E�½E� ¼ kon½B�dt; (3)

and integrate from [Eo] , the initial free concentration ofaminopeptidase, to E, the instantaneous concentration attime, t.

Z½E�

½E0�

�d½E�½E� ¼

Z t

0

kon½B�dt: (4)

The integrated form is,

� ln½E�½E0�

� �¼ kon½B�t; (5)

which can be rearranged to a standard pseudo first orderrate expression,

½E� ¼ ½E0� � e�kon½B�t; (6)

where kobs ¼ kon � [B] is the observed pseudo first orderrate constant. For the purposes of comparison, it is use-ful to normalize the free concentration of enzyme, relativeto its initial value, ½E�

½E0� ¼ e�kon½B�t. In this experiment, therelative enzymatic activity of an incubated mixture ofaminopeptidase and bestatin can yield the fractional por-tion of enzyme that is not in complex with bestatin, ½E�

½E0�.This quantity is obtained by measuring the activity ofinhibited aminopeptidase toward hydrolysis of pLeuNAand dividing by the activity of the enzyme that has notbeen incubated with bestatin,

m0;tm0;t¼0

¼ ½E�½E0�.

It is worth emphasizing to students that the activityassays are a vehicle for quantifying the free aminopepti-dase and the aminopeptidase in complex with bestatin.Inhibition by bestatin is reversible; however, the value forkcat for substrate and the koff for bestatin are on such dif-ferent timescales that the aminopeptidase in complexwith bestatin is considered essentially constant duringthe time period of the enzyme assay.

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RESULTS

Determination of Km and kcat

The substrate saturation plots for pLeuNA with AAP(Fig. 2) result in a Km value of 17 lM for pLeuNA and akcat of 60 seconds21. These numbers compare toreported values of 10 lM and 64 seconds21 (3840minutes21) at pH 8.0 [5]. The optimum pH for activity is8.0. These values for Km and kcat can also be obtainedfrom a linear fit of the data in double reciprocal (Line-weaver-Burk) format if students don’t have access tosoftware for nonlinear regression. Students have achance to become familiar with the assay, gauge howmuch enzyme will be needed for the measurement ofkon, and have little difficulty obtaining quality data on thisportion of the experiment. The choice of 2 mM pLeuNAfor the experiments in Day 2 should help minimize theeffects from small errors in substrate concentrationbecause this is a flat part of the substrate saturationcurve.

Measurement of kon

Incubation of the AAP with bestatin in the 10–30 lMconcentration range results in nearly complete inhibitionof the enzyme in the time frame of 2 hours (Fig. 3a).Lower concentrations of bestatin, 1 lM and 5 lM, alsoinhibit AAP but in the time frame for this experiment lessthan 60% inhibition was observed. These data were fit toEq. (6), resulting in an average kon value of 55 6 6 M21

s21. This model assumes that there is no appreciableback reaction. Figure 3 panel b shows an overlay of theexperimental data with the calculated model using konvalues of 50 M21 s21 for 10 lM and 20 lM bestatin and60 M21 s21 for 30 lM bestatin, demonstrating that theback reaction is not significant. If there is no access tosoftware for fitting nonlinear equations, the data can beplotted in the logarithmic form against time. The resultingline 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 invery similar values for kon. Finally, a best value of kon wasobtained with all three inactivation series and both meth-ods of fitting, linear, and exponential, by plotting kobsagainst the concentration of bestatin (Fig. 5). The slopeof this line will give an apparent kon, which calculates to59 M21 s21. The value reported in the literature is con-siderably higher, 450 M21 s21 [1] for experiments carriedout at pH 8.0. In our laboratory classes, values within asection tend to agree but between sections kon hasranged from 59 to 190 M21 s21. The difference betweenthe class values and literature values for kon may, in part,be explained by the 0.4 difference in pH (7.6) for theexperiments. The purity of the enzyme stock solutionswere comparable, though not identical. The specific ac-tivity of the AAP used in the Wilkes and Prescott paperwas 135 U/mg. AAP purchased from Sigma has a spe-cific activity of 98.4 U/mg. The bestatin used in thisexperiment was greater than 98% pure.

Students, working in pairs, will generally have time tocollect data for one or two concentrations of bestatin ina single laboratory period. Higher concentrations of bes-

FIG. 3. Loss of aminopeptidase activity over time. Amino-peptidase was incubated with bestatin at three different concen-trations, 10 lM (l), 30 lM (~), and 60 lM (^). (a) Initial rates ofthe rate of hydrolysis of pLeuNA were measured and plotted rela-tive to their initial activity, according to Eq. (6). The incubationwas carried out at room temperature, which was monitored butnot controlled. (b) An overlay of the data with the calculatedmodel for a pseudo first order binding process [Eq. (6)] with konvalues of 50 M21 s21 for 10 lM bestatin and 30 lM bestatin, andwith a modeled kon of 60 M21 s21 for the 60 lM bestatin data.The quality of the fit indicates that the reversal of binding is notsignificant during the time frame of these experiments.

FIG. 2. Substrate saturation plot of aminopeptidase.Enzyme activity as a function of substration concentration.The Km and kcat determined from these data were 17 lM and60 seconds21, respectively. Assays were carried out at 258C in20 mM Tris buffer, pH 7.6.

240 BAMBED, Vol. 38, No. 4, pp. 238–241, 2010

tatin require less time for data collection, which can be aconsideration in experimental design but will also requireto students to act quickly to get important early timepoints. The quality of student data is quite good oncethe workable concentrations of bestatin and enzymehave been identified. The incubation of bestatin withenzyme was carried out on the bench top at room tem-perature. Temperature was controlled on the spectropho-tometer. Both room and spectrophotometer temperatureswere monitored continuously, and we noticed that if thespectrophotometer or the room heated up with use overthe time period of the experiment, the quality of the datawas impacted enough to affect the shape of the expo-nential. The largest issue in the experiment with regard tostudent performance is making sure that they understandthat time zero for inactivation is when bestatin and AAPare mixed, not when they perform the activity assay.Because Ki ¼ koff/kon, students can then calculate koff ifthey have an estimate of the equilibrium dissociationconstant. The reported equilibrium binding constant forbestatin to the AAP is 18 nM [1]. With our value of kon,koff calculates to be 1.1 3 1026 seconds21.

SUMMARY

The slow, tight binding of bestatin to aminopeptidasefrom Aeromonas proteolytica is an uncommon biochemi-cal phenomenon that has enabled us to design a simple,inexpensive laboratory exercise for the measurement ofkon. The enzyme has good thermal stability and is toler-ant of freeze–thaw cycles, making it suitable for class-

room experiments. The system is amenable to furtheraddition of experiments to an advanced biochemical orbiophysical laboratory class, including the measurementof koff, steady-state experiments with different inhibitors,and computer molecular modeling exploration of thecrystallographic structures of the aminopeptidase.

Acknowledgments—The authors wish to thank Stephen Millsfor many helpful conversations in the design of this laboratory,Helene Citeau for assistance and maintenance of the instrumen-tation used in these experiments, and Sharon Ferguson for as-sistance in preparation of solutions for the experiment.

REFERENCES

[1] S. H. Wilkes, J. M. Prescott (1985) The slow, tight binding of bestatinand amastatin to aminopeptidases, J. Biol. Chem. 260, 13154–13162.

[2] B. Chevrier, C. Schalk, H. D’Orchymont, J. M. Rondeau, D. Moras,C. Tarnus (1994) Crystal structure of Aeromonas proteolytica amino-peptidase: A prototypical member of the co-catalytic zinc enzymefamily, Structure 2, 283–291.

[3] W. Desmarais, D. L. Bienvenue, K. P. Bzymek, G. A. Petsko, D.Ringe, R. C. Holz (2006) The high-resolution structures of the neutraland the low pH crystals of aminopeptidase from Aeromonas proteo-lytica, J. Biol. Inorg. Chem. 11, 398–408.

[4] C. C. Stamper, D. L. Bienvenue, B. Bennett, D. Ringe, G. A. Petsko,R. C. Holz (2004) Spectroscopic and X-ray crystallographic charac-terization of bestatin bound to the aminopeptidase from Aeromonas(Vibrio) proteolytica, Biochemistry 43, 9620–9628.

[5] C. Stamper, B. Bennett, T. Edwards, R. C. Holz, D. Ringe, G. Petsko(2001) Inhibition of the aminopeptidase from Aeromonas proteolyticaby L-leucinephosphonic acid. Spectroscopic and crystallographiccharacterization of the transition state of peptide hydrolysis, Bio-chemistry 40, 7035–7046.

FIG. 4. Semilog plot of the binding of bestatin to amino-peptidase. The same data from Fig. 3 were replotted accordingto Eq. (5).

FIG. 5. Best fit for kon. The best fit value for kon is obtainedthrough a plot of kobs as a function of the bestatin concentra-tion. The slope of the line yields kon, the second order rate con-stant for binding. The plot contains values of kobs obtained fromboth exponential (*) and linear (l) fits of the data.

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