Q Copyright 1993 by the American Chemical Society
`
`Volume 32, Number 34
`
`August 31, 1993
`
`Art ides
`
`Separation of L-Pro-DL-boroPro into Its Component Diastereomers and Kinetic
`Analysis of Their Inhibition of Dipeptidyl Peptidase IV. A New Method for the
`Analysis of Slow, Tight-Binding Inhibition?
`William G. Gutheil and William W. Bachovchin'
`Department of Biochemistry, Tufts University School of Medicine, Boston, Massachusetts 021 I I
`Received November 30, 1992; Revised Manuscript Received May 12, I993
`
`ABSTRACT: The potent dipeptidyl peptidase IV (DP IV) inhibitor [ l-(2-pyrrolidinylcarbonyl)-2-pyrroli-
`dinyllboronic acid (L-Pro-DL-boroPro) [Flentke, G. R., Munoz, E., Huber, B. T., Plaut, A. G., Kettner,
`C. A., & Bachovchin, W. W. (1991) Proc. Natl. Acad. Sci. U.S.A. 88, 1556-15591 was fractionated into
`its component L-L and L-D diastereomers by C18 HPLC, and the binding of the purified diastereomers to
`DP IV was analyzed. Inhibition kinetics confirms that the L-L diastereomer is a potent inhibitor of DP IV,
`having a Ki of 16 pM. The L-D isomer binds at least 1000-fold more weakly than the L-L, if it binds at all,
`as the -200-fold weaker inhibition observed for the purified L-D isomer is shown here to be due entirely
`to the presence of a small amount (0.59%) of the L-L diastereomer contaminating the L-D preparation. The
`instability of Pro-boroPro, together with its very high affinity for DP IV and the time dependence of the
`inhibition, makes a rigorous kinetic analysis of its binding to DP IV difficult. Here we have developed a
`method which takes advantage of the slow rate at which the inhibitor dissociates from the enzyme. The
`method involves preincubating the enzyme and the inhibitor without substrate and then assaying the free
`enzyme by the addition of substrate and following its hydrolysis for a period of time which is short relative
`to the dissociation rate of the inhibitor. Data from experiments in which the preincubation time was
`sufficient for enzyme and inhibitor to reach equilibrium were analyzed by fitting to an appropriate form
`of the quadratic equation and yielded a Ki value of 16 pM. Data from experiments in which the incubation
`to an integrated rate equation. The appropriate integrated rate equation for an A + B * C system going
`time was insufficient to establish equilibrium, i.e., within the slow-binding regime, were analyzed by fitting
`to equilibrium does not appear to have been previously derived. The analysis of the slow-binding curves
`yielded a Ki value of 16 pM, in agreement with that of 16 pM determined in the equilibrium titrations, and
`a bimolecular rate constant of association, k,,, of 5.0 X lo6 M-l s-*. The experimentally determined k,,
`and Ki indicate that the dissociation rate constant, koff, is 78 X 10" s-' (tip = 150 min). The slow-binding
`curves are shown here to fit a simple E + I ?=t E1 model, indicating that it is not necessary to invoke a two-step
`mechanism to explain the inhibition kinetics.
`
`Dipeptidyl peptidase IV (DP IV) is a type I1 membrane-
`anchored serine exoprotease found on the proximal tubules of
`the kidney (Gossrau, 1985; Wolf et al., 19781, in the intestinal
`epithelium (Svensson et a/., 1978; Corporale et a/., 19851, on
`
`the surface of certain subsets of T lymphocytes, particularly
`CD4+ helper cells (Ansorge & Ekkehard, 1987; Scholz et al.,
`1985; Mentlein et al., 1984), and in a number of other tissues.
`This protease has been implicatedinavariety of physiological
`functions, including the salvage of amino acids (Miyamoto et
`al., 1987) fibronectin-mediated cell movement and adhesion
`f Supported by NIH Grant A13 1866.
`* Author to whom correspondence should be addressed.
`(Hanski et al., 1985), and regulation of the immune system
`0006-2960/93/0432-8723$04.00/0 0 1993 American Chemical Society
`
`AstraZeneca Exhibit 2083
`Mylan v. AstraZeneca
`IPR2015-01340
`
`Page 1 of 9
`
`

`
`8724 Biochemistry, Vol. 32, No. 34, 1993
`
`Gutheil and Bachovchin
`
`0 Ho\
`II
`
`B /OH
`I
`
`trans Pro-boroPro
`FIGURE 1: Structure of trans-Pro-boroPro showing chiral centers.
`The coupling of L-Pro with racemic LD-boropro is expected to yield
`a mixture of two diastereomers: L-Pro-L-boroPro and L-Pro+
`boroPro.
`
`(Schon et al., 1985; Flentke et al., 1991). Specific inhibitors
`of DP IV are therefore of some interest, both as tools to help
`elucidate the biological role or roles of DP IV and as potential
`therapeutic agents.
`We have previously reported the synthesis and a preliminary
`kinetic characterization of two potent inhibitors of DP IV,
`Ala-boroPro and Pro-boroPro (boroPro refers to an analog of
`proline in which the carboxylate group is replaced by a boronyl
`group) (Bachovchin et al., 1990; Flentkeet al., 1991). These
`inhibitors have an immunosuppressant activity, suppressing
`antigen-induced T-cell proliferation in T-cell culture systems
`(Flentkeetal., 1991) andantibodyproductioninmice(Kubota
`et al., 1992). These findings lend support to the hypothesis
`that DP IV plays a role in T-cell proliferation and suggest
`that DP IV inhibitors may be of therapeutic value.
`Ala-boroPro and Pro-boroPro belong to a class of serine
`protease inhibitors known as peptide boronic acids (Kettner
`& Shenvi, 1984). Inhibitors of this class can have remarkably
`high affinities for their target enzymes. For example, MeO-
`Suc-Ala-Ala-Pro-boroPhe inhibits chymotrypsin with a Ki of
`160 pM (Kettner & Shenvi, 1984), and Ac-D-Phe-Pro-boroArg
`inhibits thrombin with a Ki of 41 pM (Kettner et al., 1990).
`The potency of these inhibitors is widely attributed to the
`ability of the boronyl group to form a tetrahedral adduct with
`the active site serine, which closely mimics the transition state
`of the enzyme-catalyzed reaction (Koehler & Lienhard, 197 1;
`Lindquist & Terry, 1974; Rawn & Lienhard, 1974; Philipp
`& Maripuri, 1981; Bachovchin et al., 1988). The peptide
`moiety, however, must also contribute importantly to the
`affinity, as simple alkyl- and arylboronic acids are many orders
`of magnitude less effective as inhibitors. X-ray crystallography
`and NMR spectroscopy have confirmed the presence of a
`boron-serine tetrahedral adduct in several serine protease-
`peptide boronic acid inhibitor complexes. However, NMR
`spectroscopy has also demonstrated that in certain cases
`tetrahedral boron-histidine adducts are formed (Bachovchin
`et al., 1988; Tsilikounas et al., 1992).
`The more potent peptide boronic acid inhibitors usually
`inhibit their target enzymes in a time-dependent manner
`(Kettner & Shenvi, 1984; Shenvi, 1986; Kettner et al., 1988,
`1990), a phenomenon known as slow-binding inhibition
`[reviewed in Morrison and Walsh (1 988)]. Both Ala-boroPro
`and Pro-boroPro are slow-binding inhibitors of DP IV.
`Morrison and Walsh (1988) have postulated that most, if not
`all, slow-binding inhibitors bind to their target enzymes in
`two steps, Le., the inhibitor first forms a relatively weak
`complex with the enzyme, which then undergoes slow
`conversion to a tighter complex. The molecular mechanism
`underlying the slow binding of peptide boronic acids to serine
`proteases is not yet clear, but is of considerable theoretical
`interest as it should have important implications, both for
`
`understanding the catalytic mechanism of serine proteases
`and for the rational design of inhibitors.
`A major impediment to the study of slow-binding inhibition
`is that the kinetic analysis is not trivial. The high affinity
`these inhibitors typically have for their target enzymes means
`that kinetic experiments must often be carried out under
`conditions where I =Z E and, thus, where the approximation
`that Ifree = Itota,, which greatly simplifies the kinetic analysis
`of weaker binding inhibitors, is no longer valid. The time
`dependence of the inhibition further complicates matters
`because it may prevent a steady-state rate from being reached
`until substrate depletion becomes significant. Such a system
`is described by a set of differential equations for which an
`integrated rate equation is not available, although expressions
`have been derived for the case where substrate depletion is not
`significant during the time course of inhibitor binding (Cha,
`1975, 1976).
`The kinetic analysis of Ala-boroPro and Pro-boroPro binding
`to DP IV is even more complicated because these inhibitors
`are unstable, having half-lives of about 5 and 30 min,
`respectively, at neutral pH. In the preliminary kinetic analysis
`we reported Ki values of 2 and 3 nM, respectively, for Ala-
`boroPro and Pro-boroPro, realizing that these values sub-
`stantially overestimated the true Ki values owing to the
`simplified way in which Ki determinations were carried out
`and to the instability and slow binding of these inhibitors
`(Flentkeet al., 1991). Theoriginal analyses werealsocarried
`out with inhibitors which were diastereomeric mixtures, Le.,
`L-Ala-DL-boroPro and L-Pro-DL-boropro. The expectation is
`that only one of the isomers, presumably the L-L isomer, is the
`active inhibitor.
`Because the potency of these inhibitors is unusually high
`for such small molecules, and because DP IV appears to have
`important biological functions, a more detailed analysis of
`how these small dipeptide boronic acids interact with DP IV
`should be of considerable interest. Here we report (i) the
`purification of L-Pro-L-boroPro and L-Pro-D-boroPro from
`the L-DL diastereomeric mixture and (ii) a moredetailed kinetic
`analysis of each isomer's inhibition of DP IV. To circumvent
`the difficulties outlined above, we have developed a method
`which exploits the fact that dissociation of the inhibitor from
`the enzyme is a relatively slow process. The method involves
`incubating the enzyme with inhibitor in the absence of
`substrate. The amount of free enzyme at any time can then
`be determined by adding substrate and monitoring the time
`course of the enzyme-catalyzed reaction for a short period
`during which the inhibitor does not have time to measurably
`dissociate from the enzyme. These simplified experimental
`conditions allow the derivation of expressions which can be
`used to analyze inhibitor binding under both equilibrium and
`nonequilibrium conditions. Equilibrium conditions here refer
`to experiments in which the preincubation time was sufficient
`for enzyme and inhibitor to reach equilibrium prior to the
`addition of substrate and enzyme assay. Nonequilibrium
`conditions refer to experiments in which the preincubation
`time was insufficient for equilibrium to be reached, and thus
`the system is within the slow-binding time domain. The
`integrated rate equation needed to analyze the nonequilibrium
`data does not appear to have been previously derived and is
`therefore derived here for the first time. This approach and
`the derived equations should prove useful in the analysis of
`other slow-binding enzyme-inhibitor systems.
`MATERIALS AND METHODS
`Preparation of L-L and L-D Pro-boroPro Diastereomers by
`C18 HPLC. Pro-boroPro was synthesized as described
`
`Page 2 of 9
`
`

`
`Pro-boroPro Inhibition of DP IV
`
`Biochemistry, Vol. 32, No. 34, 1993 8725
`
`previously (Bachovchin et al., 1990). Analytical and semi-
`preparative C18 HPLC were performed on a 250 X 4.6 mm
`5-pm Nucleosil C18 HPLC column (Alltech Associates Inc.,
`Deerfield, IL) using a Hewlett-Packard 1050 quaternary pump
`HPLC equipped with a multiple wavelength detector (Hewlett-
`Packard, Rockville, MD). Several milligrams of the purified
`components could be prepared by repeatedly injecting 0.5 mg
`of the mixture on this column and then pooling and lyophilizing
`the appropriate fractions. The resulting material was redis-
`solved in 0.0 1 N HC1. Analytical C 18 HPLC chromatograms
`of the purified products are shown in Figure 2. The absolute
`configurations were assigned on the basis of a detailed NMR
`study (J. L. Sudmeier, W. G. Gutheil, and W. W. Bachovchin,
`unpublished results). An attempt to scale up this purification
`procedure on 200 X 10 mm and 400 X 10 mm Absorbosphere
`C18 HPLC columns (Alltech Associates) did not provide as
`pure a final product.
`Quantitation of Pro-boroPro by Amino Acid Analysis.
`Amino acid analysis was performed by the PITC method
`(Bidlingmeyer et al., 1984). Quantitation was based on
`proline. The boronylproline did not appear in this analysis.
`Purification of Pig Kidney DP ZV. Pig kidney DP IV was
`prepared as described previously (Wolf et al., 1978). The
`concentration of DP IV active sites was assessed by stoichi-
`ometric titration with L-Pro-L-boroPro, as described further
`below.
`Standard DPZVEnzyme Assays. Standard activity assays
`were performed in 50 mM sodium phosphate (pH 7.5) at 25
`OC with the chromogenic substrate Ala-Pro-p-nitroanilide
`(APPNA) (Bachem Inc., Torrance, CA), monitoring the A410
`on a Hewlett-Packard UV-vis spectrometer. The value Ae =
`8800 M-l cm-l upon hydrolysis of substrate was used to
`calculate rates and concentrations (Erlanger et al., 1961).
`The hydrolysis time course was monitored for 2 min. The
`initial substrate concentration was 73.7 pM, 5 times the K ,
`(vide infra).
`Equilibrium Titrations of DP ZV with L-L and L-D Pro-
`boroPro. Theseexperiments were performed by first preparing
`a DP IV stock in the assay buffer. The amount of DP IV used
`in each assay was the minimal amount necessary to obtain a
`sufficient absorbance change in 2 min with the substrate for
`accurate quantitation. A series of Pro-boroPro dilutions and
`a blank were prepared in 0.01 N HC1. To 0.980 mL of the
`stock-diluted DP IV was added 10 pL of diluted Pro-boroPro,
`the mixture was incubated for 30 min at 25 OC, and the free
`enzyme was assayed by the addition of APPNA in 10 pL of
`DMF.
`Kinetics of DP ZV and L-Pro-L-boroPro Association. For
`the association kinetics a fluorometric assay with Ala-Pro-
`7-amino-4-(trifluoromethyl)coumarin (APAFC) (Enzyme
`Systems Products, Livermore, CA) was used. Fluorescence
`was monitored on a Perkin-Elmer LS-5 fluorescence spec-
`trometer (Oak Brook, IL) with an excitation wavelength of
`400 nm and a detection wavelength of 505 nm. The response
`was calibrated with 1 pM 7-amino-4-(trifluoromethyl)-
`coumarin. The experiments were performed by incubating
`DP IV with inhibitor in the absence of substrate. After an
`appropriate time interval, APAFC was added to assay for
`free DP IV. The slow apparent rate of DP IV-inhibitor
`association under these dilute conditions gave a time course
`for the association reaction (Figure 5). Specifically, exper-
`iments were performed by diluting stock DP IV into 10 mL
`of the assay buffer to give a concentration one-fiftieth that
`used in the equilibrium binding experiments. A blank assay
`on the diluted DP IV was performed by mixing 0.990 mL of
`
`the diluted enzyme with 10 pL of 1 mM APAFC in DMF in
`a cuvette (10 pM final concentration) and monitoring the
`fluorescence change for 2 min at 25 OC. This value was
`considered to be t = 0 for the binding time course. An aliquot
`of L-Pro-L-boroPro was then added to the remaining 9.010
`mL of diluted DP IV, and 0.990-mL aliquots were removed
`and assayed at intervals with APAFC as above.
`Stability of L-L and L-D Pro-boroPro. In 0.01 N HCl these
`compounds appeared stable for at least 1 month at room
`temperature. Both the L-L and L-D Pro-boroPro preparations
`lose their DP IV inhibitory activity in the assay buffer at pH
`7.5. To partially characterize this behavior, the time course
`of inactivation was monitored at three different concentra-
`tions: two at relatively low inhibitor concentrations, using
`DP IV inhibition as an indicator of residual inhibitor
`concentration, and one at relatively high inhibitor concen-
`tration, using C18 HPLC to determine residual inhibitor
`concentration. For inactivation in the range of inhibitor used
`in the assays above, the inhibitor was diluted into assay buffer
`at a concentration sufficient to give roughly 90% inhibition
`initially (approximately 1 nM for the L-L and 100 nM for the
`L-D). At various time intervals DP IV was added, and after
`a 15-min incubation, APPNA was added to assay for the free
`enzyme analogous to the procedure used in the equilibrium
`titrations. In a second experiment the inhibitor concentration
`in the pH 7.5 buffer was 100 times the assay concentration.
`At time intervals between 1 and 150 min, 10 pL of the Pro-
`boroPro solution was added to 0.980 pL of assay buffer
`containing DP IV, and this mixture was allowed to incubate
`for 15 min. Substrate was then added to assay for free enzyme.
`The inhibition observed in these experiments was converted
`to the amount of active inhibitor using the inverse to the
`equilibrium relationships as derived in the Theory section.
`The inactivation of these compounds was also observed directly
`at higher concentrations (250 pM) by analytical C18 HPLC.
`Half-lives (tl/z) for degradation were determined empirically
`from plotted degradation time courses as the time at which
`one-half of the inhibitor remained.
`Progress Curves for Enzyme + Substrate + Inhibitor
`Assays. These experiments were performed in two ways. One
`was for the enzyme to be added to an assay mixture containing
`a known amount of both the substrate and the inhibitor. The
`other was to incubate the enzyme with inhibitor for 15 min
`to establish equilibrium and then add substrate. The control
`for this experiment was to monitor a complete time course for
`the hydrolysis of substrate by enzyme.
`Numerical Znetegration of Rate Equations. Numerical
`integrations of rate equations were performed with the GEAR
`software package (Stabler & Chesick, 1978; McKinney &
`Weigert, 1986).
`Data Analysis. Data were analyzed by fitting to the
`appropriate equation by derivative-free nonlinear regression
`using the IBM PC based version of the BMDP program AR
`(BMDP Statistical Software, Los Angeles, CA). The equa-
`tions used are derived in the Theory section.
`
`THEORY
`Derivation of Equations Describing Simple A + B i=t C
`Equilibrium. In the enzymatically monitored equilibrium
`titrations, we are titrating DP IV with Pro-boroPro. The
`concentration of the stock Pro-boroPro is accurately known
`from amino acid analysis. The observed binding of the L-L
`Pro-boroPro was very tight, and this in principle allows the
`concentration of DP IV to be accurately determined by
`titration. A simple A + B e C equilibrium can be solved
`
`Page 3 of 9
`
`

`
`8726 Biochemistry, Vol. 32, No. 34, 1993
`exactly using the quadratic equation. Using ET to represent
`the total DP IV concentration and IT to represent the total
`inhibitor concentration, the following equations can be derived:
`(ET + IT + Ki) - V ((ET + IT + Ki)’ - ~ E T I T )
`(EO =
`2
`(1)
`E = ET- (El)
`(2)
`IT - (El)
`I
`(3)
`The observable is the rate of APPNA hydrolysis, which is
`proportional to E:
`
`rate = E(SA)
`(4)
`where SA is the specific activity in units of AOD41O/min/pM
`DP IV active sites at 73.7 pM APPNA. The experimentally
`variable parameter is IT. The adjustable parameters to be fit
`are Ki, ET (in terms of active sites), and SA. In the case of
`L-Pro-D-boroPro, the less potent inhibitor, the observed binding
`appeared to bedue to contamination with the L-L diastereomer.
`This situation was analyzed by including another adjustable
`parameter, %L-L, in these equations. The actual amount of
`L-L present therefore was
` IT(^-^) = IT(^-^)%^-^/ 100
`( 5 )
`
`where IT(L-L) is the true total L-L concentration, IT(L-D) is
`the total inhibitor concentration (based upon amino acid
`analysis), and %L-L is an adjustable parameter describing the
`% contamination of L-L in the L-D preparation.
`Inversion of the Equilibrium Equation To Measure the
`Rate of Inactivation of L-Pro-L-boroPro. In the preceding
`section, an equation was derived describing the observed rate
`of DP IV catalyzed substrate turnover as a function of the
`independent variable IT(L-L)
`and the parameters Ki, ET, and
`SA, which are to be fit to experimental data. Once these
`parameters have been fit, it is possible to find the inverse
`relationship to this equation and, with the fitted parameters,
`to calculate IT(L-L)
`from an experimentally measured rate as
`required for analysis of the DP IV monitored inactivation of
`Pro-boroPro described above. The following equation is easily
`derived:
`IT(L-L) = ET - Ki - rate/SA + ETKi(SA)/rate
`(6)
`where the parameters are as defined above.
`Derivation of an Integrated Rate Equation for the A + B
`s C System. Surprisingly, the appropriate form of the
`integrated rate equation for this system was not found in a
`number of standard sources. The system
`
`(7)
`
`is described by the following set of differential equations
`dE/dt = -konEI + k,ff(El)
`dZ/dt = -konEI + koff(El)
`d(EZ)/dt ko,EI - k,fi(El)
`Substitution for E, I, and koff of
`
`(8b)
`(8c)
`
`E = ET-(EI)
`I = I T - (El)
`
`(9)
`(10)
`
`Gutheil and Bachovchin
`
`kofi = konKi
`(11)
`into the expression for d(El)/dt and then expansion and
`rearrangement gives
`d(El)/dt = kon(El)2 - (konET + konzT + konKi)(El) +
`konETIT (12)
`
`This can be rearranged for integration as
`
`The left side of this differential equation is trivial to integrate.
`The right side is given in standard math tables [CRC
`Handbook of Chemistry and Physics, Vol. 67, p A-26, eq
`110, second equation). (Note that we use q for -4 and that
`q in our nomenclature can be shown to always be greater than
`or equal to 0, a prerequisite for using this equation.)
`
`where x = (EI), X = a + bx + cx2, a = konETIT, b
`-(konET
`+ k,nIT + konKi), c = kon, and q = b2 - 4ac. The appropriate
`integrated expression is therefore (with an initial condition at
`t = 0 of x = 0 (Le., (El) = 0))
`t = l l n [ (2cx + b - f i ) ( b + fi)
`(2cx + b + f i ) ( b - fi)
`G
`Rearrangement to solve for x in terms of t gives
`
`To check this result, note that at t = 0, x = 0 as expected. Also
`note that
`
`x - - b - . \ / q
`(18)
`2c
`which is equivalent to the equilibrium expression derived above
`(eq l), also as expected.
`Analysis of Enzyme + Substrate Progress Curves. The
`data were collected at 5-s intervals over the time course of
`these experiments, up to 1.5 h. Several approaches have been
`described for the analysis of data of this type. Direct fitting
`to the integrated Michaelis-Menten equation (Kellershohn
`& Larent, 1985; Cox & Boeker, 1987) is complicated by the
`fact that this equation is a mixture of linear and transcendental
`functions in the dependent variable, and therefore t (time)
`must be fit as a function of P (product concentration). A
`more direct approach is to determine the rate (dP/dt) from
`the data and to fit this directly to the Michaelis-Menten
`equation (Canela & Franco, 1986). We use this approach
`here, but have not found it necessary to use a complicated
`weighting scheme nor to fit the time course data to a polynomial
`equation to extract derivatives. Instead, the data in terms of
`(OD,t) data pairs were converted into (P,t) data pairs and
`then into (S,dP/dt) data pairs in a Lotus 123 spreadsheet
`(Lotus Development Corporation, Cambridge, MA). ThedP/
`dt values were calculated by the method of central divided
`
`Page 4 of 9
`
`

`
`Pro-boroPro Inhibition of DP IV
`
`differences using the formula
`
`(dP/dt)i = (Pi+] -Pj-l)/(ti+l-
`(19)
`tj-1)
`Parameters ( K m and kat) were then determined by fitting to
`the Michaelis-Menten equation
`(dP/dt)i = k,,SiET/(Si + K,)
`(20)
`The predicted time course was calculated from the fit
`parameters by summation using the following equations (At
`= 5s):
`
`Po = 0
`SO = S T
`
`(21)
`(22)
`
`i
`
`n= 1
`
`ki
`
`kcat
`
`(23)
`
`(25)
`
`pi = C(E$i-lkat/(Km + s i - l ) ) ~ t
`si = so - Pi
`(24)
`which can also be performed easily in a Lotus 123 spreadsheet.
`Alteratively, the predicted time course can be obtained by
`numerical integration. The system
`E + Si=? (ES) -,E + P
`k-i
`is described by the following set of differential equations:
`dE/dt = -ESk, + (ES)(k-, + kat)
`(264
`dSldt = -ESk, + (ES)k-,
`(26b)
`d(ES)/dt = ESk, - (ES)(k-, + k,,,)
`( 2 6 ~ )
`dPldt = (ES)kat
`(26d)
`Given the initial values for the concentrations of the com-
`ponents in this system and values for the rate constants, the
`GEAR program will provide a simulated time course for
`comparison with the experimentally determined time course.
`Numerical Simulation of the Model Shown in Figure 7A.
`The model shown in Figure 7A is described by the following
`set of differential equations:
`dE/dt = -ESk, + (ES)(k-, + k,,,) - k,EI + koff(EI)
`(274
`dSldt = -ESk, + (ES)k-,
`(27b)
`d(ES)/dt = ESk1- (ES)(k-, + kat)
`( 2 7 ~ )
`dP/dt = (ES)k,,,
`( 2 7 4
`dI/dt = -k,EI + k,,(EI)
`(27e)
`d(El)/dt = k,,EI - k,ff(EI)
`(270
`Note that eqs 27 = eqs 8 + eqs 26, i.e., model(Figure 7A) =
`note that for the one species common to both models, E, the
`differential eq 27a is obtained as
`dE/dtmodel(Figure 7A) = dE/dtmcdel(E+Ia.Ef) +
`(28)
`dE/dtm,e~(,+,a~,-~+~)
`Given values for all of the initial concentration and the rate
`constants describing Figure 7A, it is possible to simulate
`experimental results for this system using the GEAR program.
`
`model(E + I s EI) + model(E + S e ES - E + P). Also
`
`RESULTS
`Puripcation of Pro-boroPro Diastereomers. The separation
`of Pro-boroProdiastereomers by C18 HPLC is shown in Figure
`
`Biochemistry, Vol. 32, No. 34, 1993 8721
`
`9 1 0 1 1 1 2 1 3 1 4 1 5
`
`0
`
`1
`
`2
`
` 3
`
`4
`
`5
`
`7
`8
`6
`TIME (min)
`FIGURE 2: C18 HPLC chromatograms showing resolution of Pro-
`boroPro diastereomers. The upper chromatogram is of the starting
`mixture, the middle chromatogram is of the purified L-D diastereomer,
`and the lower chromatogram is of the purified L-L diastereomer.
`HPLC conditions: solvent A 0.1% trifluoroacetic acid (TFA) in H20;
`solvent B 70% acetonitrile/30% H20/0.086% TFA; gradient 0-2
`min 0% B, 2-32 min 0-100% B. Only the first 15 min of each
`chromatogram are shown. The base-line disturbance at 8.15 min is
`the gradient entering the detector.
`
`8 0 0 -
`
`7 0 0 -
`
`600-
`
`500-
`400-
`
`@
`z -
`300-
`T
`-
`A 200
`-
`
`100
`
`L
`
`e
`
`e
`
`m e e
`
`Be
`
`..
`
`0
`
`-100
`
`,
`
`0
`
`I
`20
`
`I
`40
`
`I
`Bo
`
`I
`Bo
`
`I
`100
`
`I
`120
`
`I
`140
`
`I
`160
`
`TIME (mi)
`FIGURE 3: DP IV monitored inactivation kinetics of L-L (M) and L-D
`( 0 ) Pro-boroPro at the very low concentrations (- 1 nM of L-L) and
`pH (7.5) used in the equilibrium and kinetic experiments. The L-L
`concentration was calculated from the raw data using the inverse of
`the equilibrium equation derived in the Theory section (eq 6).
`
`2. Attempts to scale up this separation were unsuccessful
`owing to the decreased resolution with larger column diam-
`eters, which could not be overcome by extending the length
`of the column. For separation on analytical columns, about
`0.5 mg of the mixture was loaded for each run. A purity of
`>98% for the purified products was indicated by analytical
`HPLC (Figure 2).
`Stability ofpro-boroPro Diastereomers. The concentration
`dependence of the inactivation of Pro-boroPro was examined
`at very low (- 1 nM) and low (- 100 nM) concentrations of
`Pro-boroPro, at pH 7.5, using DP 1V inhibition to monitor the
`residual active inhibitor concentration, and at a relatively high
`(-250 pM) concentration of the inhibitors using C 18 HPLC.
`The time courses of the degradation kinetics had the same
`shapes as the curves shown in Figure 3 in all cases, but with
`somewhat different half-lives. The inactivation reaction
`appears to follow a mixture of zero- and first-order kinetics,
`with zero-order dominating. The measured half-lives at pH
`
`7.5 for the L-L isomer were 55 min at - 1 nM, 35 min at - 100
`
`nM, and 40 min at -250 pM. The half-life at pH 7.5 for the
`L-D isomer was somewhat longer: 80 min at -250 pM as
`
`Page 5 of 9
`
`

`
`3 ".," .""""'..
`B ':I
`- 3.6 x 10'40D/mln/nM DP IV
`
`............,... ..............
`' dm ' ;.J
`' & ' 0;
`FLI
`
`'
`(nM)
`
`.......................................
`
`........ n...
`
`' 1;
`
`' 1:4
`
`' I n ' 1;
`
`FIXED PARAMETERS
`SA
`FllTED PARAMETER S
`Kl= 30 nM: SE = 8
`E T = 680 pM; SE 160
`
`[W (W -
`KI- l 6 p M -
`
`.
`
`*
`
`
`
`500
`
`
`
`m
`
`zao
`
`.
`
`'
`
`loo
`
`SA
`
`*
`
`*
`
`~
`
`-
`
`3.6 x lO"OD/mIn/nM DP IV
`
`0
`"
`
`d
`
`1.J
`
`a.
`
`E
`
`0.4
`
`4.2
`4.4
`
`0.8
`o s
`0 4
`
`8728 Biochemistry, Vol. 32, No. 34, 1993
`
`Gutheil and Bachovchin
`
`FITTED PARAMETERS
`€ 7 - 670pM;SE 20
`K i m 16 pM; SE
`4
`SA = 3.6 x 10 ''0D/mln/nM DP N
`
`FIXED PARAMETERS
`E T = 11.4pM
`I~=2WpM(O)or530pM(O)
`SA = 5.6 nM/min/pM DP IV
`FrITED PARAMETERS
`
`L = 5.0 x lo6 M -' 5ec.l
`SE = 0.2
`K , =16pM;SE=7
`
`I
`
`0 -
`
`-101
`
`I
`0
`
`I
`300
`
`I
`600
`
`I
`900
`
`I
`1200
`
`I.
`15M)
`
`I
`1800
`
`TIME (Sec)
`FIGURE 5: Kinetics of L-Pro-L-boroPro binding to DP IV at two
`inhibitor concentrations. Inhibitor concentrations for the two
`experimentsareshownin theinset. Datewere fit toeq 17. Calculated
`kov = ko,Ki = 78 X 10-6 S-'.
`
`experiments yield a Ki for L-Pro-L-boroPro of 16 pM (Figure
`4A). This value is much less than the estimated DP IV
`concentration of 570 pM (SE = 20) (in terms of binding sites)
`and establishes that the titration was well into the tight binding
`regime. The L-Pro-D-boroPro binding data fit poorly to the
`simple equilibrium model (Figure 4B) but very well to a model
`in which the observed inhibition is assigned to small amounts
`of contaminating L-Pro-L-boroPro (Figure 4C). This analysis
`indicated that our preparation of L-Pro-D-boroPro contained
`0.59% of the L-L diastereomer and that the inhibition observed
`with this preparation is due to the contaminating L-L
`diastereomer. This level of contamination was confirmed by
`analytical HPLC.
`Association and Dissociation Rate Constants for L-Pro-
`L-boroPro Binding to DP ZV. To determinevalues for k, and
`k,ff, a more sensitive fluorescent assay was employed to allow
`the time course of inhibitor binding to DP IV to be monitored
`under conditions of low DP IV concentration (1 1.4 pM active
`sites). A fit of these data to the integrated rate equation
`derived above (Figure 5 ) yielded a bimolecular association
`rate constant, kon, of 5.0 X lo6 M-l s-l (SE = 0.2), a Ki of
`16 pM (SE = 7) (a value identical with that determined by
`equilibrium titration), and a unimolecular off rate, koff,
`calculatedfromthek,,and Ki,of78 X 106s-l. Thecalculated
`off rate indicates that the t l p for dissociation is 150 min,
`which is slow relative to the 2 min required for the enzymatic
`assays employed in these experiments, thereby confirming
`the original assumption on which this experimental approach
`was based. This t l p for dissociation is much longer than the
`t1p for the inactivation of free inhibitor and therefore indicates
`that inhibitor in the enzyme-inhibitor complex is more stable
`than the free inhibitor.
`Kinetics of APPNA Hydrolysis by DP IV. Progress curves
`for the hydrolysis of APPNA starting at the standard assay
`concentration of 73.1 pM APPNA are shown in Figure 6A.
`The fit to the Michaelis-Menten equation using the method
`described above is very good (Figure 6B), and only a slight
`difference between the experimental and fit curves is dis-
`cernible. Product inhibition therefore appears negligible in
`this case. This analysis yielded a k,,, of 90.8 s-l (SE = 0.9)
`and a Km of 14.3 pM (SE = 0.5).
`Progress Curves for Enzyme + Substrate + Inhibitor
`Assays and Numerical Simulation. To simulate the hydrolysis
`of substrate and also the binding and dissociation of inhibitor
`in the presence of substrate requires the extraction of the
`
`10
`E T = MO pM; SE
`% L-L = 0.59; SE = 0.03
`
`io0
`
`100
`
`500
`
`W l (nM)
`FIGURE 4: Equilibrium titration data and fits obtained for L-L and
`L-D Pro-boroPro inhibition of DP IV. Each point for the L-L titration
`is the average of threedeterminations. Each point for the L-D titration
`is the average of fivedeterminations. (A) Fit of the L-L titration data
`to a simple equilibrium model (eq 4). (B) Fit of the L-D titration data
`to a simple equilibrium model (eq 4). (C) Fit of the L-D titration
`data to a simple equilibrium model (eq 4) where observed inhibition
`by L-D is due to contamination by a fractional amount, %L-L, of L-L
`is used
`(eq 5 ) . In this figure, 0 is used to represent data points,
`to represent the residual value between the calculated value based
`upon the fitted parameter and the experimentally observed values,
`and the lines represent the calculated value of the observable based
`upon the fitted parameter values.
`
`measured by HPLC. The inactive material can be reactivated
`by acidification, a process which is relatively slow (85% in 18
`h at pH 2.0). The inactive material is the cyclic structure in
`which the N-terminal nitrogen atom forms a covalent bond
`with the boron ato