7074
`
`J. Am. Chem. Soc. 1986, 108, 7074-7078
`Isotopically Sensitive Branching and Its Effect on the Observed
`Intramolecular Isotope Effects in Cytochrome P-450 Catalyzed
`Reactions: A New Method for the Estimation of Intrinsic
`Isotope Effects
`Jeffrey P. Jones, Kenneth R. Korzekwa, Allan E. Rettie, and William F. Trager*
`Contribution from the Department of Medicinal Chemistry, BG-20, University of Washington,
`Seattle, Washington 98195. Received December 6, 1985
`
`Abstract Two selectively deuterated «-octanes (octane-1 -2H3 and octane-/, 2,3-2 4//7) were synthesized and subjected to hydroxylation
`by phenobarbital-induced rat liver microsomes and purified cytochrome P-450b. The results of these experiments provide
`evidence which clarifies the interplay between a branched reaction pathway and the equilibration of an enzyme-substrate complex,
`in determining the magnitude of an observed isotope effect. An equation is derived that allows limits to be placed on the intrinsic
`isotope effect. The equation is based on the observed isotope effect and the regioselectivity of a branched reaction pathway,
`catalyzed by an enzyme that forms two products via a single enzyme-substrate complex. The intrinsic isotope effect for the
`formation of 1-octanol was determined by this equation to lie between 9.5 and 9.8.
`
`Isotope effects have played a major role in the determination
`of reaction mechanisms and in the elucidation of transition-state
`structure in organic chemistry. Their application to enzymatically
`mediated systems, however, has proven to be less successful be-
`cause of the complexity of the multistep reaction sequences that
`describe many of these processes.
`In general the ambiguities
`arising from these systems have restricted the use of isotope effects
`to estimating the rate of the bond-breaking step relative to the
`rates of all other steps in the kinetic scheme, e.g., substrate binding
`and dissociation, product release, and other steps that may mask
`the intrinsic isotope effect. However, in recent years, Northrop1
`has provided a fundamental basis for interpreting isotope effects
`in enzymatic systems by clarifying the relationship that exists
`between an observed isotope effect and the intrinsic isotope effect
`that is associated with the bond-breaking step.
`To circumvent the problems associated with these complicated
`schemes and the attenuation or “masking” of the intrinsic isotope
`effect, which make transition-state structure determination dif-
`ficult, many workers in the field have employed a technique which
`In such an experiment,
`uses intramolecular isotope effects.2'5
`a molecule that has two positions that are equivalent in all respects
`except for isotopic substitution is used as the substrate. The
`observed isotope effect then reflects the intramolecular competition
`In most cases an
`between the two otherwise equivalent sites.
`intramolecular isotope effect more nearly approximates the in-
`trinsic isotope effect since it depends primarily upon the prod-
`uct-determining step rather than other potential rate-limiting
`steps,5 e.g., the magnitude of an observed intramolecular isotope
`effect will be independent of product release but the magnitude
`of an intermolecular isotope effect will not. The magnitude of
`an isotope effect measured by an experiment of intramolecular
`design, that proceeds via an irreversible linear reaction pathway,6
`is inherently less sensitive to masking effects. However, it is
`dependent upon (!) the rate of rotation between the two isotop-
`ically distinct sites within the substrate molecule and/or (2) the
`rate of dissociation of the enzyme-substrate complex to give free
`If these rates are slow or are of the same
`substrate and enzyme.
`order of magnitude as the bond-breaking step, [ESH] will not equal
`(see Scheme I), and the intrinsic isotope effect will be
`[ESd]
`
`(1) Northrop, D. B. Biochemistry 1975, 14, 2644.
`(2) Miwa, G. T.; Garland, W. A.; Hodshon, B. J.; Lu, A. Y. H.; Northrop,
`D. B. J. Biol. Chem. 1980, 255, 6049.
`(3) Gelb,  . H.; Heimbrook, D. C.; Malkonen, P.; Sligar, S. G. Bio-
`chemistry 1982, 21, 370.
`(4) Hjelmeland, L. M.; Aronow, L.; Trudell, J. R. Biochem. Biophys. Res.
`Commun. 1977, 76, 541.
`(5) Lindsay Smith, J. R.; Nee, N. E.; Noar, J. B.; Bruice, T. C. J. Chem.
`Soc., Perkin Trans. 2 1984, 255.
`(6) Such a sequence is represented in Scheme I, when k¡ and k¡
`
`= 0.
`
`0002-7863/86/1508-7074S01.50/0
`
`Scheme I. Kinetic Model for Isotopically Sensitive Branched
`Reaction Pathways"
`
`CE]
`
`+ [P23
`
`*s
`CESh]
`
`CE] + CP,3
`
`CES03
`
`CE3 + CP,3
`
`CE3 + C P23
`"The model assumes
`that there is no isotope effect associated with
`binding (i.e., a single rate constant k2 describes the fractionation of
`[ES] to [ESh] and [ESD] and a single rate constant fc_2 describes the
`formation of [ES] from [ESH] and [ESD]) and that product formation
`is irreversible.
`masked. Recently Harada et al.7 have shown that within a
`branched reaction sequence,
`i.e., one in which more
`than one
`product can arise from an enzyme-substrate complex (Scheme
`I, k¡ and k¡   0), another factor termed “metabolic switching”
`can affect the magnitude of the isotope effect that will be observed.
`Metabolic switching or
`isotopically sensitive branching8 can be
`defined as a change in the relative ratios of products, due to isotopic
`substitution, arising from the same intermediate in the case of
`a chemical system or from the same enzyme-substrate complex9
`
`(7) Harada, N.; Miwa, G. T.; Walsh, J. S.; Lu, A. Y. H. J. Biol. Chem.
`1984, 259, 3005.
`(8) Isotopically sensitive branching may be a better term than metabolic
`switching since this effect is not restricted to enzymatic systems. For example,
`Melander and Saunders (Reaction Rates of Isotopic Molecules·, Melander,
`L., Ed.; Wiley: New York, 1980; pp 293-297) have described the kinetics
`that pertain to an analogous chemical system. Metabolic switching has also
`been used in a more general way to denote switching from one enzymatic
`pathway to another due to isotopic substitution; see; Horning, M. G.; Haegele,
`K. D.; Sommer, K. R.; Nowlin, J.; Stafford, M.; Thenot, J. P. Proceedings
`of the Second International Conference on Stable Isotopes, National Infor-
`mation Service, US Department of Commerce, Springfield, VA, 1976; p 41.
`Switching of this type is fundamentally different to that described above since
`it involves another enzyme or
`isozyme. This would not effect the observed
`isotope effect at saturating conditions since the two products would arise from
`different enzyme-substrate complexes.
`(9) A branched reaction pathway implies separate enzyme-substrate com-
`plexes, leading to the formation of two distinct products. However, if one
`that a rapid equilibrium exists between these two complexes, they
`assumes
`become kinetically indistinguishable and thus can by treated as a single
`enzyme complex. The proximity of a C-l hydrogen to a C-2 hydrogen in
`octane justifies this assumption.
`© 1986 American Chemical Society
`
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`Apotex Ex. 1015
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`

`

`Isotopically Sensitive Branching
`in the case of an enzymatic system.
`The regioselectivity of the hydroxylation reactions catalyzed
`by cytochrome P-450 is very broad and has been shown to be a
`function of both the inherent chemical reactivity of the substrate
`and the apoprotein structure of the enzyme.10
`In many cases,
`the cytochrome P-450 contained in microsomal preparations has
`been shown to hydroxylate  -alkyl chains to several regioisomeric
`alcohols. Whether the various isomers are the product of a single
`or different isozyme remains in question.* 11™16 Data from purified
`enzymes would appear to suggest that a single isozyme can carry
`out a number of regioisomeric oxidations on the same substrate.17
`Conversely, work with antibodies and mechanism-based inhibitors
`indicate that different isozymes have different regioselectivity,15·16
`suggesting that a single isozyme catalyzes the formation of a single
`product. Thus, some doubt remains as to the homogeneity of some
`purified enzyme preparations.18
`The oxidation of octane to 1-octanol by cytochrome P-450
`microsomal preparations has been shown previously to exhibit a
`“significant” isotope effect.19 Moreover, the oxidation of octane
`by cytochrome P-450 is also carried out at
`the C-2 and C-3
`In this papier a kinetic model for the effect
`positions (vide infra).
`of branched pathways on isotope effects will be developed and
`evaluated by using the oxidation of octane to various regioisomeric
`alcohols by cytochrome P-450. The kinetic model will be used
`to predict an intrinsic isotope effect for the hydroxylation of octane
`at the C-l position, and data will be presented that conclusively
`implicate a single isozyme in the production of at least two re-
`gioisomers.
`Experimental Section
`Materials. Heptafluorobutyric anhydride and acetonitrile were ob-
`tained from Pierce Chemical Co., diethyl ether was obtained from J. T.
`Baker, and pentane was purchased from Burdick & Jackson. All other
`organic chemicals were obtained from Aldrich Chemical Co., while all
`biochemicals were obtained from Sigma Chemical Co. All materials
`were used as received unless stated otherwise.
`Instrumentation. Gas chromatography was performed by using an HP
`5840A gas chromatograph modified for use with a J & W DB-5 or DB-1
`capillary column. Difference spectra were recorded on an HP 8451A UV
`spectrophotometer. GC/MS analysis of the product alcohols was per-
`formed on a VG 7070H mass spectrometer in the selected ion recording
`mode, interfaced to a HP-5710A GC fitted with a J & W DB-5 fused
`silica capillary column. The derivatized metabolites were cold trapped
`at 40 °C, and then the temperature was ramped at 20 °C/min to 90 °C
`followed by isothermal elution. Mass spectral parameters were as follows:
`dwell, 5 ms; ionizing voltage, ca. 70 eV; source temperature, 200-205 °C.
`The deuterium incorporation in each substrate was determined by
`bleeding each compound into the source of the mass spectrometer at a
`steady rate through the reference inlet and monitoring the ion current
`of the various isotopically substituted species using selected ion recording
`of the molecular ion. The mass spectrometric parameters for the sub-
`strate were the same as those for the analysis of the product alcohols
`except the dwell time was increased to 50 ms. The measured intensity
`of each ion monitored was corrected for the natural isotopic abundance
`of 2H, 13C, 170,
`lsO, 29Si, and 30Si.
`Synthesis and Incorporation of Substrates. Octane- /-2H3. Methyl-
`octanoate (0.016 mol) in diethyl ether was added dropwise to lithium
`
`(10) White, R. E.; McCarthy,  . B.; Egeberg, K. D.; Sligar, S. G. Arch.
`Biochem. Biophys. 1984, 228, 493.
`(11) Frommer, U.; Ullrich, V.; Standinger, H.; Orrenius, S. Biochem.
`Biophys. Acta 1971, 280, 487.
`(12) Albro, P. W.; Chae, K.; Philpot, R.; Corbett, J. T.; Schroeder, J.;
`Jordan, S. Drug Metab. Disp. 1984, 12, 742.
`(13) Ichihara, K.; Kusonose, E.; Kusonose, M. Biochem. Biophys. Acta
`1969, 176, 713.
`(14) Bjorkhem, 1. Proceedings of the Second International Conference on
`Stable Isotopes, National Information Service, US Department of Commerce,
`Springfield, VA, 1976; p 32.
`(15) Nashlund, B. M. A.; Halpert, J. J. Pharmacol. Exp. Ther. 1985, 231,
`(16) Ortiz de Monteliano, P. R.; Reich, N. O. J. Biol. Chem. 1985, 259,
`4136.
`(17) Jensen, I.; Mole, J.; Schenkman, J. J. Biol. Chem. 1985, 260, 7084.
`(18) Bansal, S. K.; Love, J. H.; Gurtoo, H. L. Eur. J. Biochem. 1985,146,
`(19) Shapiro, S.; Piper, J. U.; Caspi, E. J. Am. Chem. Soc. 1982, 104,
`2301.
`
`23.
`
`16.
`
`J. Am. Chem. Soc., Vol. 108, No. 22, 1986
`
`7075
`
`aluminum deuteride (0.016 mol) suspended in ether. The reaction was
`stirred at room temperature for 6 h. Then 0.5 mL of water, 1 mL of 15%
`NaOH, and finally another 1 mL of water were added. The solution was
`filtered and then extracted with pentane. The pentane-ether layer was
`dried over sodium sulfate and evaporated to yield l-octanol-/-2#2 (2.05
`reacted with tosyl chloride
`g). The 1 -octanol- /-2#2 (0.016 mol) was
`(0.016 mol) in ca. 150 mL of dichloromethane containing 6 mL of tri-
`ethylamine. The reaction solution was washed with water followed by
`saturated sodium bicarbonate. The organic phase was dried over an-
`hydrous sodium sulfate and filtered and the solvent evaporated in vacuo.
`The residue was dissolved in ether and was reduced with lithium alu-
`minum deuteride (0,014 mol) without further purification to yield oc-
`tane-/-2#) (4 mmol after chromatography and evaporation of the sol-
`vent). The octane-/-2#) was purified via column chromatography using
`silica gel (60 Á, 230-240 mesh) with pentane as the eluant. The resulting
`octane-/-2#) was greater than 99.8% pure by GC with a deuterium
`enrichment of 96.94% ± 0.01% octane-/-2#), 2.24% octane-/-2#2, and
`0.82% octane-/-2#].
`Octane-/,2,3-2H-,. 2-Octanone (0.063 mol) was added to metha-
`nol-2# (ca. 20 mL) in which sodium metal (0.002 mol) had been dis-
`solved. The mixture was refluxed for 14 h, and the octanone was isolated
`via pentane-D2G extraction and then analyzed for deuterium enrichment.
`This procedure was repeated until greater than 94% of the octanone was
`composed of octanone-¡,3-2H¡ (yield 0.034 mol). The ion corresponding
`to C2H)C=0+ was used to determine incorporation of deuterium at the
`C-l position, and the ion corresponding to CH3(CH2)4C2H2C=0+ was
`used to determine incorporation of deuterium at the C-3 position. The
`apparent deuterium enrichment at the C-l position was 96%, while at the
`C-3 position it was found to be 95%. The ketone (0.034 mol) was then
`reduced to 2-octanol-1,2,3-2H6 (0.029 mol) with lithium aluminum deu-
`teride (0.017 mol). The incorporation at the C-l position was determined
`to be about 96.5% based on fragment ions from the Me3Si derivative of
`the alcohol. 2-Octanol-/,2,3-2#6 was reacted with tosyl chloride and then
`reduced with lithium aluminum deuteride to yield octane-/,2,J-2#7 (0.8
`mmol after purification) which was purified as octane-/2-#). The final
`compound was greater than 99.8% pure and had deuterium enrichment
`of 88.7% octane-/,2,J-2#7, 8.8% octane-/,2,3-2H6, and 2.5% octane-
`7,2,3-2#s.
`Octane-/,8-2H2. 1,8-Octanediol was reacted with tosyl chloride and
`the resulting ditosylate reduced with lithium aluminum deuteride in THF
`to yield octane-/,8-2#2. Reaction conditions and purification procedure
`were similar to those for octane-/-2#). The final compound was greater
`than 99.8% pure and had a deuterium enrichment of 98.3% octane-/,8-
`2#2 and 1.7% octane-/-2#].
`Microsomal Preparation and Incubation Conditions. Microsomal re-
`action mixtures were prepared as described previously by Porter et al.20
`The incubations were run from 20 to 25 min and contained between 7
`and 8 nmol of P-450, as determined by the method of Omura and Sato,21
`12.3 Mmol of NADPH, and 2.47 Mmol of octane diluted to a volume of
`2 mL with Trizma buffer (0.2 M, pH 8.2 at 25 °C). Each incubation
`was terminated by addition of 5 mL of pentane and stored at -70 °C until
`workup.
`Purified P-450b Preparation and Incubation Conditions. The purifi-
`cation of the major phenobarbital inducible form of P-450 was accom-
`plished by using the procedure of Waxman and Walsh.22 NADPH-
`dependent cytochrome P-450 reductase was purified as described by
`Shepard et al.23 The incubations were carried out in closed scintillation
`vials for 10 min. Each incubation contained 1 nmol of P-450, 1 nmol of
`P-450 reductase, 0.6 miho! of NADPH, and 0.5 nmol of phosphotidyl-
`choline diluted to a final volume of 2 mL with 100 mM Trizma buffer,
`pH 8.2. Each reaction was initiated by addition of 2.4 Mmol of the
`appropriate octane in 5 mL of methanol. Upon termination each incu-
`bation was extracted with (2X) 5 mL of pentane.
`Derivitization of Octanols for GC/MS. The pentane extracts were
`dried over sodium sulfate and evaporated until ca. 30 mL remained. To
`the remaining volume, 25 mL of acetonitrile was added. Prior to analysis,
`pyridine (1 mL) and BSTFA (4 mL) were added to each sample.
`Gas Chromatographic Analysis of n -Octane Hydroxylation Products.
`When protio octane was subjected to hydroxylation by either P-450b- or
`three metabolites were obtained
`phenobarbital-induced microsomes,
`which corresponded to authentic 1-octanol, 2-octanol, and 3-octanol by
`their gas chromatographic and mass spectral characteristics. The ratios
`of 1-octanol to 2-octanol to 3-octanol based on nine determinations were
`
`(20) Porter, W. R.; Branchfiower, R. V.; Trager, W. F. Biochem. Phar-
`macol. 1977, 26, 549.
`(21) Omura, T.; Sato, K. J. Biol. Chem. 1964, 239, 2370.
`(22) Waxman, D. J.; Walsh, C. J. Biol. Chem. 1982, 257, 10446.
`I. R. Anal.
`(23) Shephard, E. A.; Pike, S. F.; Rabin, B. R.; Phillips,
`Biochem. 1983, 129, 430.
`
`Apotex Ex. 1015
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`

`7076
`
`J. Am. Chem. Soc., Vol. 108. No. 22, 1986
`
`Jones et al.
`
`Table I. Fraction of Deuterium Present in Substrate, Sn/(Sn + Sn -
`dn/(dn + dn -
`1)
`
`1), and the Fraction of Deuterium Remaining in the 1-Octanol Product,
`
`1)
`
`except the form of the correction factor F changes since the octane-2/f6
`arising from incomplete deuteration is actually composed of three distinct
`species in which the hydrogen is contained at either the C-l, C-2, or C-3
`The ratio d2/d2 + d¡ was again taken from octane-
`position (eq 4).
`(Sd6/Sd6 + Sd2)x(d2/d2 + dx) + (SdJSd, + 5ti7)2i3
`(4)
`F6 =
`1,8-2H2 since it contains the statistically correct number of hydrogens vs.
`deuteriums at the two carbons (C-l and C-8) being hydroxylated. The
`fraction of protium present at the C-2 and C-3 carbons in the substrate
`(S6/S6 + S7)2,3 was obtained by subtracting the value 0.05 for (S6/S6
`+ S7), from the fraction 0.09 representing the total amount of St, i.e.,
`[S6/(S6 + 57)]u_3 present in the octane-/,2,3-2   substrate, Table I.
`Since the absolute ion intensities of d2, d6, d3, and d2 vary from ex-
`periment to experiment depending upon mass spectral conditions, they
`are best represented as fractions, e.g., the value of d6/d2 + </6 should be
`invariant from experiment to experiment. The values for the fraction of
`deuterium present in substrate and retained in the product are given in
`Table I. The isotope effects can be calculated directly from the values
`in Table I if the form of eq 3 is changed to eq 5. Eq 5 lends itself to the
`propagation of errors such that the reliability of the measurements can
`readily be assessed.
`
`(kn/kO)oXxi =
`
`dn/(dn + dn -
`+
`
`1)
`
`(5)
`
`dn/(dn + dn -
`1 /(Sn + Sn -
`Sn/(Sn + Sn - 1)°
`substrate
`Sn -
`P-450b
`microsomes
`1)
`0.8849 ± 0.0077 (8)e
`0.9774 ± 0.0001 (3)»
`0.0226 · 0.0001 (3)
`0.9025 ± 0.0009 (5)
`octan e-l-2H3
`0.0903 ± 0.0055 (3)
`0.9097 ± 0.0055 (3)
`0.7517 ± 0.0026 (5)
`0.7408 ± 0.0058 (5)
`octane-/, 2,3-2H2
`0.9830 ± 0.0002 (3)
`0.9196 ± 0.0018 (5)
`0.0170 ± 0.0002 (3)
`0.9224 ± 0.0080 (5)
`octane-/, 8-2H2
`“n equals the number of deuterium atoms. 6The mean ± the standard deviation for () separate determinations. cThe mean ± the standard
`deviation for () separate incubations.
`1:5:0.6 for the microsomal preparations and 1:23:7 for the purified
`preparations. These ratios were measured via gas chromatography of the
`corresponding heptafluorobutyrate ester derivatives.
`Calculation of Isotope Effects.
`In theory the isotope effect, kH/kD,
`should be directly related to the ratio of the ion intensities measured for
`metabolites arising from the hydroxylation at the protio site vs. that at
`the deuterio site. For example, for the substrate octane-/-2//3, kH/kD
`should be equal to the ratio of I-octanol-8-2//3 to 1-octanol-/-2//2 which
`can be obtained by measuring the ratio of the ion intensities of a suitable
`ion for the two products. The M-CH3 peak of the trimethylsilyl deriv-
`ative would be a suitable ion for this measurement provided the substrate
`was 100% octane-/-2//3.
`Under these circumstances the isotope effect can be calculated from
`eq 1 where d3 is the ion intensity of the product l-octanol-8-2//3 arising
`from hydroxylation of a terminal carbon hydrogen bond and d2 is the ion
`(kn/kD)obti = d3/d2
`(1)
`intensity of the product, l-octanol-/-2//2, arising from hydroxylation of
`a terminal carbon-deuterium bond.
`In practice, absolute incorporation is essentially impossible to achieve
`and the incompletely labeled substrate must be taken into account. The
`ion intensity at d2 will be contaminated with ion intensity from 1-octa-
`nol-/-2/^ and l-octanol-8-2//2 arising from incompletely deuterated
`substrate, and this value must be subtracted from the measurement. The
`fraction of ion intensity due to this contaminant, F2, is given by eq 2
`F2 = Sd2/(Sd3 + Sd2)[d2/(d2 + </,)]
`(2)
`where Sd2/(Sd3 + Sd2) is the fraction of octane-l-2H2 present in total
`substrate and d2/(d2 + d¡) is the fraction of 1 -octanol- 1-2H2 plus 1-oc-
`formed by hydroxylation of the
`the total 1-octanol
`tanol-8-2H2 over
`It is important to realize that this fraction,
`octane-/-2//2 contaminant.
`d2/(d2 + d¡ ), is simply the fraction of deuterium in the 1-octanol derived
`from the octane-l-2H2 contaminant in the octane-l-2H3 substrate and
`reflects the isotope effect (kH/kD) associated with hydroxylation of this
`substrate times a statistical factor. This statistical factor accounts for
`the fact that in this substrate there are twice as many carbon-hydrogen
`bonds available for hydroxylation as there are equivalent carbon-deu-
`terium bonds.
`The amount of contamination that must be subtracted from the in-
`tensity d2 is equal to d2F2 and eq 1 becomes eq 3.
`(kn/kD)obíi = d3/(d2-d2F2)
`(3)
`The value of F2 was obtained by determining the fraction of octane-
`1-2H2 contaminating the octane-/-2//3 substrate and multiplying it by
`d2/(d2 + dx) which was obtained directly from the ion intensities of
`1-octanol-/,8-2//2 and 1-octanol-/-2// when octane- 1,8-2H2 was used as
`substrate. Octane-/,8-2H2 is an appropriate substrate for calculation of
`the correction factor since its hydroxylation would be accompanied by
`the same isotope effect and since it contains the same number of deu-
`terium atoms as the octane-/,l-2H2 contaminant.24
`An analogous equation to eq 3 can also be used to determine the
`isotope effect associated with terminal hydroxylation of octane-/,2,3-2H2
`
`=
`
`(
`
`}
`
`Theory
`A kinetic model
`that describes the formation of multiple
`products from a single substrate and enzyme by branched reaction
`In this scheme the products P[
`pathways is shown in Scheme I.
`and P2 are assumed to arise from kinetically indistinguishable
`enzyme-substrate complexes, the combination of which can be
`expressed by [ESH]· An equation expressing the effect of
`branching on the isotope effect was derived from Scheme I, as-
`suming steady-state kinetics, as follows. Equation 6 expresses the
`effect of the concentrations of ESH and ESD on the observed
`isotope effect. Equations 7 and 8 express the steady-state con-
`(*  ß)  
`(fcHAD)[ESH]/[ESD]
`(6)
`centrations of the two enzyme-substrate complexes. The con-
`centrations of ESh and ESD obtained by rearrangement of eq 7
`and 8 can be substituted into eq 6 and rearranged to yield eq 9.
`[ESH](&_2 + k} + kH)
`d[ESH]/df = 0 =
`*2[ES] -
`(7)
`[ESD](k_2 + k3' + kD)
`d[ESD]/dr = 0 =
`(8)
`fc2[ES] -
`*»Ad + W(*-2 +
`(Á,_2 + *j)/(*_2 + *j0 + ku/{k_2 + k3')
`Analysis of the limits of this model for the two substrates, oc-
`into how
`tane-/-2/^ and octane-7,2,3-2  , provides insight
`branching can effect
`[ESH] and [ESD] and thus the observed
`isotope effect.
`If P, is taken to be the
`Consider the substrate octane-7-27/3.
`product 1-octanol and P2 is taken to be the product 2-octanol (see
`Scheme I), the effect of branching to product P2 and in turn its
`affect on the observed isotope effect for formation of product P¡
`can be evaluated. For this substrate the rate of C-2 hydroxylation
`on the protio half of the molecule will be identical with the rate
`of C-2 hydroxylation on the deuterio half of the molecule. That
`is k3 = k3, assuming negligible ß secondary isotope effects. Thus,
`eq 9 can be rewritten as eq 10.
`*hAd + W(fc-2 + h)
`1 + *«/(*-2 + *s')
`
`( h/ Dictad
`
`-
`
`(24) The correspondence between octane-/,8-2H2 and octane-/, 1-2H2 as-
`sumes rapid rotation of a given methyl group in the active site and negligible
`secondary isotope effects. Contamination of d¡ by contributions from incom-
`pletely deuterated substrate, i.e., octane- 1-2H2, was corrected for by measuring
`the fraction of octane-/-2// present in the substrate (octane-/,8-2H2), multi-
`plying it by d3, and subtracting the product from d¡. Since this contaminant
`contains a single deuterium atom, the effect of isotope discrimination on the
`value of d¡ was ignored.
`is true for k3 » or « kH. However, if k3/k3 <
`(25) This statement
`kH/kD, it is theoretically conceivable that the two isotope effects for the two
`regioisomers could differ by less than 2-fold if k3 < kH. From the GC analysis
`of the protio substrate (see Experimental Section), it is known that kH/k3 =
`1 /23; thus, if k3/k3 < kH/kD, then k3 must be greater than ZcH. Therefore,
`least 2-fold smaller then tH/kD if the
`given this system, k3/k3 must be at
`boundaries are to be satisfied.
`
`(fcH/^D)obsd _
`
`(10)
`
`Apotex Ex. 1015
`
`

`

`Isotopically Sensitive Branching
`
`Table II. Observed Intramolecular Isotope Effects for the
`Hydroxylation of Selectively Deuterated Octanes
`isotope effect
`P-450b
`substrate
`microsomes
`9.45 ± 0.15
`7.85 ± 0.76“
`octane-1 -2H3
`3.30 ± 0.10
`3.12 ± 0.17
`octane-7,2,3-2H2
`“The mean ± standard deviation as calculated by propagation of
`error.
`Evaluation of the limits of eq 10 leads to the conclusion that
`if L·2 » kH, (kH/fcD)obad approaches the intrinsic isotope effect.
`However, if k_2 « kH, the value of (A:H/A:D)obsd will depend upon
`the magnitude of k3. That is, as k3 increases, (kH/kD)obed will
`approach the intrinsic isotope effect. Thus, the overall effect of
`In effect the branching
`k3 is to unmask the intrinsic isotope effect.
`pathway k3 siphons-off “excess” [ESD] and tends to keep the ratio
`of the concentrations of the two enzyme-substrate complexes closer
`to unity.
`Consider the substrate octane-7,2,3-2  . For this substrate,
`in contrast to octane-7-2/73, the rate of C-2 hydroxylation on the
`protio half of the molecule will clearly be different than the rate
`of C-2 hydroxylation on the deuterio half of the molecule provided
`an isotope effect is associated with 2-octanol formation, i.e., k3
`¿é k3 in Scheme I. Hence, eq 9 is needed to evaluate the limits.
`If the ratio of the rate constants for C-l hydroxylation relative
`to C-2 hydroxylation on the protio half of the molecule kK/k3 is
`assumed to be approximately equal to the ratio of rate constants
`for the analogous reactions on the deuterio half of the molecule,
`kD/k3, i.e., the isotope effect at the C-l position is equal to the
`isotope effect at the C-2 position, then the following conclusions
`(a) if k.2 » kH and k3, [ESH] approaches [ESD]
`can be reached:
`and (fcH/A:D)obad approaches the intrinsic isotope effect; (b) if k.2
`and k3, (fcH/fcD)obsd approaches 1. For the first limit,
`«
`(fcn/fcu)^ is totally independent of both k3 and k3 because both
`branching rate constants are too small relative to fc_2 to have an
`if k_2 s or > fcH, the
`effect. However, in the second limit, or
`isotope effect for C-2 hydroxylation, k3jk3, will mask the intrinsic
`isotope effect for C-l hydroxylation. The masking of the isotope
`effect associated with C-2 hydroxylation is a result of an effective
`increase in concentration of [ESD] relative to [ESH],
`Results and Discussion
`The observed isotope effect for the C-l hydroxylation of oc-
`tane-7-2^ is 7.9 for the microsomal system and 9.5 for the P-450b
`preparation (see Table II). By contrast the corresponding values
`for octane-7,2,3-2   are 3.1 and 3.3, respectively. The difference
`in (kH/kD)abii for octane-7-27/3 in microsomes vs. P-450b un-
`doubtedly is due to the fact that microsomes are a complex mixture
`of a number of different isozymes in which more than a single
`isozyme may be active in catalyzing the formation of 1 -octanol
`and/or 2-octanol. Thus, the observed value would represent an
`average value of the various activities.
`Of more interest to the present discussion is the large differnce
`in the observed isotope effects for the C-1 hydroxylation of oc-
`tane-7-2^ vs. octane-7,2,3-2  . Based on the analysis of the limits
`of the kinetic model these results would be inconsistent with k.2
`» kH and k3, since under these conditions both substrates would
`give the same (&   )  .
`and this value would approach the
`If k.2« kH and k3 and k3/k3 = kH/kD, then the
`intrinsic value.
`isotope effect for octane- 7 -2H3 should be close to the intrinsic value
`and the isotope effect for octane-7,2,3-    should approach 1.
`While the large value of 9.5 for octane-27T3 (from P-450b) is
`consistent with these boundaries for the rate constants, the value
`of 3.3 for the octane-7,2,3-27/7 is not. However, these boundaries
`if the assumption that kH/kD is equal to
`might still be correct
`If the latter were true the isotope effect at
`k3/k3 is incorrect.
`the C-2 position would have to be 2-fold less than the isotope effect
`at the C-l position.23 Although such a large difference in the
`isotope effects for the hydroxylation at a primary vs. a secondary
`carbon might seem unrealistic in a simple chemical system, such
`a difference is not necessarily unreasonable for an enzymatic
`system. Finally if k.2 s kH and k3, the kinetic model readily
`
`J. Am. Chem. Soc., Vol. 108, No. 22, 1986
`
`7077
`
`accounts for the difference in observed isotope effects for the two
`substrates.
`As predicted by eq 10, the effect of a branched pathway on
`octane- 7 -2H3 would be to unmask the intrinsic isotope effect. This
`prediction is supported by the large observed isotope effect of 9.5
`(Table II). The isotope effect associated with this substrate can
`also be used to predict the limits for the intrinsic isotope effect.
`An expression for the intrinsic isotope effect can be obtained by
`rearrangement of eq 10 to eq 11. Evaluation of the limits of eq
`^h/^d =
`(W^obsd + [(W*D)obsdW(fc-2 + *3')] - kH/(L·2 + k3')
`(11)
`If k-2 approaches infinity
`11 leads to the following conclusions.
`the observed isotope effect equals the intrinsic isotope effect, i.e.,
`(kH/kD)oisá = kn/kD. Thus, the lower limit of the intrinsic isotope
`effect is 9.5. The upper limit is approached as &_2 approaches
`0. To determine this limit, the value of kH/k3 must be known.
`An estimation of kH/k3 can be obtained as follows. For the
`substrate, octane-7-27T3, k3 will be approximately equal to k3
`provided that any ß secondary isotope effects are small. Thus,
`kH/k3 s kH/k3 which in turn should equal the product ratio,
`1 -octanol/ 2-octanol, obtained from the nondeuterated substrate,
`1. e., octane. The product ratio was measured by gas chroma-
`If
`tography and was found to be 1 -octanol/2-octanol = 1/23.
`this value is substituted in eq 11, the upper limit of the intrinsic
`isotope effect is found to be 9.8.
`In the Experimental Section, it was reported that the incubation
`of octane with purified P-450b led to the formation of 3-octanol
`in addition to 1- and 2-octanol. Gas chromatography indicated
`that the ratio of 3-octanol to 1-octanol was 7:1.
`If deuteration
`of C-l
`leads to an increase in the formation of 3-octanol, this
`If this is the case, kH/k3
`process would also tend to deplete [ESD],
`would equal 1 /30. However, substitution of this ratio into eq 11
`does not significantly change the calculated value for the upper
`limit of the intrinsic isotope effect. Work pertaining to whether
`branching to multiple positions is directly additive is presently
`in progress.
`The increase in the observed isotope effect for the P-450b
`preparation relative to the microsomal preparation, Table II, can
`be attributed to one or more of the following processes:
`(1) an
`increase in the rate of interchange between ESH and ESD, (2) an
`inherently larger intrinsic isotope effect associated with the purified
`enzyme preparation and no branching effects, or (3) a purified
`enzyme capable of branching; i.e., more than one product is formed
`If either of the first two processes were
`by a single enzyme.
`responsible for the difference, the isotope effects for both substrates
`should be increased by the same relative amount. The fact that
`this is not observed indicates that a single enzyme catalyzes the
`formation of the two products.
`On first analysis the isotope effect associated with the P-450b
`hydroxylation of octane- 7-2H3 would generally be taken to rep-
`resent the “true" intramolecular isotope effect associated with the
`aliphatic hydroxylation of octane. Moreover, the large value that
`was obtained for this substate (9.5) would seem to imply that the
`rate of interchange between [ESH] and [ESD] in Scheme I is fast,
`and t