Site- and species-specific hydrolysis rates of heroin

Article abstract of DOI:10.1016/j.ejps.2016.04.028

The hydroxide-catalyzed non-enzymatic, simultaneous and consecutive hydrolyses of diacetylmorphine (DAM, heroin) are quantified in terms of 10 site- and species-specific rate constants in connection with also 10 site- and species-specific acid-base equilibrium constants, comprising all the 12 coexisting species in solution. This characterization involves the major and minor decomposition pathways via 6-acetylmorphine and 3-acetylmorphine, respectively, and morphine, the final product. Hydrolysis has been found to be 18-120 times faster at site 3 than at site 6, depending on the status of the amino group and the rest of the molecule. Nitrogen protonation accelerates the hydrolysis 5-6 times at site 3 and slightly less at site 6. Hydrolysis rate constants are interpreted in terms of intramolecular inductive effects and the concomitant local electron densities. Hydrolysis fraction, a new physico-chemical parameter is introduced and determined to quantify the contribution of the individual microspecies to the overall hydrolysis. Hydrolysis fractions are depicted as a function of pH.

Full text of DOI:10.1016/j.ejps.2016.04.028

European Journal of Pharmaceutical Sciences 89 (2016) 105–114
Contents lists available at ScienceDirect
European Journal of Pharmaceutical Sciences
journal homepage: www.elsevier.com/locate/ejps
Site- and species-specific hydrolysis rates of heroin
Levente Szöcs a, Gábor Orgován a, Gergő Tóth a, Márta Kraszni a, Lajos Gergó b, Sándor Hosztafi a, Béla Noszál a,
⁎
a
Semmelweis University, Department of Pharmaceutical Chemistry, Research Group for Drugs of Abuse and Doping Agents, Hungarian Academy of Sciences, Hőgyes E. u. 9, H-1092
Budapest, Hungary
b
Eötvös Loránd University, Faculty of Informatics, Department of Numerical Analysis, Hungary
a r t i c l e i n f o
a b s t r a c t
Article history:
The hydroxide-catalyzed non-enzymatic, simultaneous and consecutive hydrolyses of diacetylmorphine (DAM,
heroin) are quantified in terms of 10 site- and species-specific rate constants in connection with also 10 site-
and species-specific acid-base equilibrium constants, comprising all the 12 coexisting species in solution. This
characterization involves the major and minor decomposition pathways via 6-acetylmorphine and 3-
acetylmorphine, respectively, and morphine, the final product. Hydrolysis has been found to be 18–120 times
faster at site 3 than at site 6, depending on the status of the amino group and the rest of the molecule. Nitrogen
protonation accelerates the hydrolysis 5–6 times at site 3 and slightly less at site 6.
Received 11 March 2016
Received in revised form 15 April 2016
Accepted 24 April 2016
Available online 27 April 2016
Keywords:
Heroin
Hydrolysis rate constants are interpreted in terms of intramolecular inductive effects and the concomitant local
electron densities. Hydrolysis fraction, a new physico-chemical parameter is introduced and determined to quan-
tify the contribution of the individual microspecies to the overall hydrolysis. Hydrolysis fractions are depicted as a
function of pH.
Ester hydrolysis
Protonation
Rate constant
Microconstant
© 2016 Elsevier B.V. All rights reserved.
1. Introduction
Nevertheless, the inevitable decomposition of diacetylmorphine pre-
cludes the distinct identification of its specific activity.
Heroin (diacetylmorphine hydrochloride, diamorphine, DAM) is a
semi-synthetic morphine derivative with powerful analgesic and nar-
cotic activities.(Sawynok, 1986) Heroin is, however, best known today
as the most infamous drug of abuse. The pharmaceutically prepared
heroin is prescribed in the therapy of severe acute and chronic pains,
and in the treatment of heroin addicts who do not respond to metha-
done or buprenorphine interventions (BVan den Brink et al., 2003;
Klous et al., 2005; van den Brink and van Ree, 2003).
Diacetylmorphine is known to deacetylate in solution mainly to 6-
acetylmorphine (6AM) which further deacetylates to morphine (M)
(Rentsch et al., 2001; Rook et al., 2006). In vivo, these reactions are
mainly catalyzed by serum butyrylcholinesterase (DAM to 6AM) and
erythrocyte acetylcholinesterase (DAM to 6AM to M) (Salmon et al.,
1999). Several studies dealt with the enzyme-catalyzed hydrolysis of
heroin (Hatfield et al., 2010; Jones et al., 2013; Owen and Nakatsu,
1983; Qiao et al., 2013, 2014; Smith and Cole, 1976).
The stability of heroin has long been recognized to be significantly
affected by pH, temperature and light (Blinkovsky et al., 1986; Hay
and Morris, 1972; Noszal et al., 2006; Robson Wright, 1968; Roy and
Guillory, 1995; Visky et al., 2000). A uniform feature of all previous stud-
ies is that the major hydrolysis pathway (DAM → 6AM → M) is taken
into account as the only decomposition route, while 3-acetylmorphine
(3AM), the other degradation product and the related pathway are
ignored, the concurrence of simultaneous and consecutive processes is
not handled. Another feature of the hydrolysis of heroin is that each of
the reactants and products occurs in more than one states of proton-
ation and charges, superimposing equilibria on the highly complex de-
composition rates. The interfering acid-base and kinetic processes
have not been taken into account in any reports either.
Determination of nearly so complicated species-specific rate param-
eters of such molecules has become possible recently (Noszal et al.,
2006), which can well be the reason why no thorough, quantitative
description on heroin hydrolysis appeared so far.
Here we report the complete characterization of the protonation
and hydrolysis processes of heroin and its degradation products.
Hydrolysis experiments were carried out independently on heroin,
3-acetylmorphine, 6-acetylmorphine and auxiliary compounds 6-
acetyl-N-methylmorphine and 6-acetylcodeine as a function of pH
and time. Acid-base equilibria under identical circumstances were
studied on all the reactants and products at the macroscopic and mi-
croscopic levels. Calculation of the species-specific rate constants of
3AM, 6AM and DAM needed improved, case-tailored relationships.
The pharmacological activity of heroin has been attributed to its me-
tabolites, 6-acetylmorphine and morphine. Some of the morphine me-
tabolites are also active on opioid receptors (Selley et al., 2001; White
and Irvine, 1999), and even the existence of a specific diacetylmorphine
receptor was reported, indicating that diacetylmorphine itself could
produce the biological effect (Brown et al., 1997; Rossi et al., 1997).
⁎
Corresponding author.
E-mail address: noszal.bela@pharma.semmelweis-univ.hu (B. Noszál).
http://dx.doi.org/10.1016/j.ejps.2016.04.028
0928-0987/© 2016 Elsevier B.V. All rights reserved.

106
L. Szöcs et al. / European Journal of Pharmaceutical Sciences 89 (2016) 105–114
detection gradient (IDPFG) probehead. The substances were dis-
solved in 95% H2O and 5% D2O. Double pulse field gradient spin
echo (dpfgse) pulse sequence was used to suppress the resonance
of H2O. Typically 32 transients were coadded. As an internal stan-
dard pyrazine was used instead of the commonly accepted
dimethyl-silapentane-sulfonate (DSS), since it interfered with our
substances. The interference of DSS was observed as line broaden-
ing which would have precluded accurate integration. The chemi-
cal shift of pyrazine was determined relative to DSS (8.619 ppm).
All spectra were processed using VNMRJ 3.2. In the kinetic studies
integration of selected peaks were also relative to the integral of
the pyrazine peak. Automatic baseline correction was performed
before integration. Before the kinetic experiments d1 was mea-
sured, and it was set to 5 s.
Fig. 1. Scheme of DAM hydrolysis in a pH-stat mode.
These are deduced and discussed in detail and the related chemical
and biological conclusions are drawn. Hydrolysis fraction, a new,
species-specific physico-chemical parameter is introduced, deter-
mined and depicted as a function of pH.
2.2. Protonation equilibria
2. Material and methods
Protonation constants were determined by NMR-pH titrations. pH
was measured with Metrohm 780 pH meter equipped with a Metrohm
6.0234.110 pH combination electrode. Concentrations of 5 mM were
used in all titration experiments. All pH data are pH meter readings
based upon NBS primary standards: 0.05 M potassium tetroxalate
(pH = 1.690), 0.05 M potassium hydrogen phthalate (pH = 4.022),
0.025 M KH2PO4 + 0.025 M Na2HPO4 (pH = 6.841) and 0.01 M borax
buffer (pH = 9.088). The substances were dissolved in 0.01 M HCl and
in 0.01 M NaOH solutions containing 5% (v/v) deuterium oxide. The
solutions were mixed, pH was measured, and the 1H NMR spectra
were recorded. Evaluation of the titration data was performed with
Origin 8 for Windows.
All experiments were performed at 310 0.1 K (body temperature)
and the ionic strength was held constant at 0.15 M using NaCl as auxiliary
electrolyte. 3,6-diacetylmorphine, 6-acetylmorphine, 3-acetylmorphine,
morphine hydrochloride, codeine hydrochloride, 6-acetylcodeine and 6-
acetyl-N-methylmorphine were products of ICN Hungary. All other sub-
stances and solvents used were of analytical grade.
2.1. NMR measurements
1H NMR spectra were recorded at 599.9 MHz with Varian
VNMRS spectrometer equipped with a dual 5-mm inverse-
Fig. 2. Scheme of the site-and species-specific hydrolysis kinetics of heroin. Rate constants are in red, protonation constants are in green. See text for the sub- and superscripts of the rate
and equilibrium constants.

L. Szöcs et al. / European Journal of Pharmaceutical Sciences 89 (2016) 105–114
107
2.3. Kinetic studies
tions. The progress of hydrolysis was followed gradually by NMR spec-
troscopy until at least 75% decomposition. NMR spectra were recorded
at pH b 8.5 in every 20–30 min, and in every 5–7 min at pH ≥ 8.5. Pyr-
azine was used as an internal standard for the integration. Integrals of
the aromatic protons, N-methyl protons and methoxy protons are the
best linear measures of concentration, since the applied water suppres-
sion disturbs the shape of the proton peaks in the vicinity of the solvent
signal. Evaluation of the kinetic data was performed with Origin 8 for
Windows.
The progress of decomposition was monitored and quantified by
NMR experiments. Processes were followed in situ: the decomposition
took place in the NMR tube. Hydrolysis experiments were carried out
in buffered solutions containing 0.05 M NaH2PO4 and 0.025 M
Na2B4O7 at different pH values (see Table 2). 2–5 mg substance of the
morphine-ester in question was separately dissolved in 2.00 mL buffer
solutions containing 5% D2O. Its pH was set using NaOH or H3PO4 solu-
3. Results
In kinetic terms, the hydrolysis of heroin is a highly complex process. Since deacetylations at sites 3 and 6 both take place, and each of the
first-step decomposition products further hydrolyze, simultaneous and consecutive hydrolyses coexist. On top of that, heroin, 6-
acetylmorphine, 3-acetylmorphine and morphine occur in solution in 2, 4, 2 and 4 protonation forms, respectively, comprising 12 also
coexisting species in every hydrolyzing heroin solution.
Fig. 1 shows the decomposition scheme of DAM under buffered circumstances (pH-stat mode), which is the actual case in various com-
partments in the body, and in our kinetic experiments. The rate constants k'DAM(6), k'DAM(3), k'6AM, k'3AM obtained under such circumstances
are conditional (apparent) ones, valid only at the pH of the experiment.
These hydrolysis rates, however, are doubly pH-dependent. Primarily, these hydroxide-catalyzed second order processes are accelerated upon
increasing pH. Secondarily, electron density at the ester group and the concomitant hydrolysis rates are usually modulated by the protonation
state of the adjacent basic site(s) in the decomposing molecule and the leaving group. In hydrolyses of DAM, the leaving groups are actually 6AM
and 3AM, while in the hydrolyses of 6AM and 3AM, morphine itself is a leaving group, in various states of protonation.
Thus, the species-specific rate of hydrolysis and the species-specific acid-base equilibria of heroin and its degradation products are interrelated.
Their summary scheme is in Fig. 2. The complete characterization of the system takes 10 rate constants and also 10 equilibrium constants. These rate
constants are species- and site-specific, pH-independent ones.
Oval sections in Fig. 2 contain covalently uniform molecules in different stages of protonation. These species are bound in terms of acid-base equi-
librium constants along the double arrows. Since hydrolysis rates are specified here to species in definite stages of protonation, a sound knowledge of
protonation equilibria was a sine qua non precondition of the kinetic evaluation processes.
3.1. Acid-base equilibria
Evaluation of the protonation constants from NMR-pH titration curves was based on the principle that nonexchanging NMR nuclei near the pro-
tonating site sense different electronic environments upon protonation. Since protonation processes are fast on the NMR time scale, the observed
chemical shift of a nucleus can be expressed as the weighted average of chemical shifts of the protonated and unprotonated forms (Szakacs et al.,
2004).
Contents of the oval sections (Fig. 2) indicate that diacetylmorphine and 3-acetylmorphine occur in solution in two protonation states, whereas 6-
acetylmorphine and morphine occur in four ones.
The protonation equilibrium and its constant of diacetylmorphine are as follows:
DAM0 þ Hþ↔DAMþ
ð1Þ
ð2Þ
ꢀ
ꢁ
DAMþ
h
i
ꢀ
KDAM
¼
ꢁ
DAM0 Hþ
where [DAM0] and [DAM+] are the equilibrium concentrations of the respective neutral and protonated forms of DAM, and KDAM is the
protonation constant. The relation for 3-acetylmorphine is analogous.
Morphine and 6AM are involved in microscopic protonation equilibria, examples can be seen below:
6AM− þ Hþ↔6AMþ−
ð3Þ
h
i
6AMþ=−
½6AM−ꢀ Hþ
kN
¼
ð4Þ
ð5Þ
ꢀ
ꢁ
6AM
6AM0 þ Hþ↔6AMþ
ꢀ
ꢁ
6AMþ
6AM0 Hþ
kON
¼
ð6Þ
h
i
ꢀ
ꢁ
6AM
where [6AM−], [6AM+/−], [6AM0] and [6AM+] are the equilibrium concentrations of the anionic, zwitterionic, non-charged and cationic forms of
6AM, kN6AM and kNO are protonation microconstants quantifying the tertiary amino basicity when the phenolate is anionic and protonated, respec-
tively. Microconsta6nAMts kO6AM and kON refer analogously to the phenolate basicities of 6AM. In general, superscript N or O denotes here the tertiary
6AM

108
L. Szöcs et al. / European Journal of Pharmaceutical Sciences 89 (2016) 105–114
amino or phenolate site of protonation, respectively, subscript N or O denotes that the site in question is protonated. Relationships between K1 and K2
successive macroconstants and the microconstants are as follows:
K1 ¼ kN6AM þ kO
ð7Þ
ð8Þ
6AM
K
1ð6AMÞ ꢁ K2ð6AMÞ ¼ kN6AM ꢁ kO
¼ kO6AM ꢁ kN
:
O6AM
Nð6AMÞ
Table 1 summarizes all the protonation constants of DAM, 3AM, 6AM, morphine and the auxiliary compounds. The microscopic protonation con-
stants were evaluated by deductive method, using the macroscopic protonation constant of 6-acetyl-N-methylmorphine (6ANMM) for the micro-
scopic protonation constant of the zwitterionic form of 6AM, and the macroscopic protonation constant of codeine for the non-charged form of
morphine (Mazak et al., 2015).
As data in Table 1 show the tertiary amino site typically protonates near pH 8 and basicity of the phenolate exceeds that of the tertiary amino by
0.77 and 0.07 log units in 6AM and morphine, respectively. Acetylation at sites 3 or 6 or both significantly decreases the tertiary amino basicity. Com-
parison of microconstants of the same site (e.g. kN and kON in the same molecule) shows that protonation at one site decreases the basicity of the other
site by 0.59 log units in 6AM and 0.92 log units in morphine.
3.2. Hydrolysis rates
One way red arrows and the attached constants in Fig. 2 identify a kinetic component of the decomposition. For example kDAM0(6) is the specific
hydrolysis rate constant of diacetylmorphine in its neutral form, rupturing at site 3, forming 6-acetylmorphine, k6AM+/− is the specific hydrolysis rate
constant of 6AM in its zwitterionic form. All the other constants are named analogously. Note that each of these rate constants are pH-independent,
species- and site-specific ones and they bear no superscript. In order to evaluate the hydrolysis rates of heroin, the relatively simple component pro-
cesses of the intermediates could be studied independently and were quantified first.
3.2.1. Hydrolyses of 3-acetylmorphine
Hydrolyses of 3-acetylmorphine take place in its neutral and cationic forms, resulting in the corresponding morphine microspecies as depicted in
and between ovals B and D in Fig. 2.
The hydrolysis rate of 3-acetylmorphine is the sum of two second-order kinetic processes:
h
i
ꢀ
ꢁ
d½3AMꢀT
−
¼ k3AM0 3AM0 ½OH−ꢀ þ k3AMþ 3AMþ ½OH−
ꢀ
ð9Þ
dt
where k3AM0 and k3AM+ are the pH-independent, specific rate constants, characterizing the hydrolysis of the neutral and cationic forms of 3AM, re-
spectively, [3AM]T is the total concentration of 3AM.
h
i
ꢀ
ꢁ
½3AMꢀT
¼
3AM0 þ 3AMþ
ð10Þ
Mole fractions of the neutral and cationic forms of 3AM can be expressed in terms of the protonation constant and the hydrogen ion
concentration:
h
i
3AM0
1
h
i
ꢀ
ꢀ
ꢁ
α3AM0
¼
¼
¼
¼
ð11Þ
ð12Þ
ꢁ
1 þ K3AM Hþ
3AM0 þ 3AMþ
ꢀ
ꢁ
ꢀ
K3AM Hþ
ꢀ
ꢁ
3AMþ
h
i
ꢀ
ꢁ
α3AMþ
:
ꢁ
1 þ K3AM Hþ
3AM0 þ 3AMþ
Concentrations of the neutral and cationic forms of 3AM are related to the total concentration through the α values:
h
ꢀ
i
3AM0 ¼ α3AM0½3AMꢀ
ð13Þ
ð14Þ
T
ꢁ
3AMþ ¼ α3AMþ½3AMꢀ :
T
Table 1
Protonation constants of the compounds studied.
Protonation constants at 37 °C (310 K)
3-acetyl morphine
6-acetyl morphine
3,6-diacetyl-morphine
Morphine
6-acetyl-N-methylmorphine
Codeine
logK1
logK2
logkN
logkO
logkNO
logkON
7.90 0.03
9.46 0.02
7.95 0.02
8.61 0.03
9.38 0.04
8.02 0.03
8.79 0.03
7.83 0.01
9.37 0.02
7.84 0.02
9.03 0.01
9.10 0.03
8.11 0.01
8.18 0.02
8.79 0.03
8.11 0.01
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–

L. Szöcs et al. / European Journal of Pharmaceutical Sciences 89 (2016) 105–114
109
Table 2
Observed rate constants of 3AM, 6AM, 6-acetylcodeine and 6-acetyl-N-methyl-morphine.
3-acetyl morphine
pH
6-acetyl morphine
pH
6-acetyl codeine
pH
6-acetyl-N-methyl morphine
k′ (10−6 s−1
)
k′ (10−6 s−1
)
k′ (10−6 s−1
)
pH
k′ (10−6 s−1
)
6.84
7.05
8.20
8.41
8.68
9.09
9.48
9.70
10.18
2.46 0.03
4.68 0.03
22.0 0.3
40.0 0.7
70.1 0.3
7.88
8.25
8.50
8.85
9.14
9.33
9.65
10.15
10.49
11.30
0.71 0.02
1.54 0.06
2.50 0.05
6.23 0.05
8.98 0.02
11.3 0.1
21.7 0.2
79.7 0.1
8.09
8.29
8.50
9.11
9.63
9.89
1.60 0.04
2.50 0.05
3.55 0.03
9.87 0.07
29.1 0.4
51.0 0.5
8.38
8.54
9.10
9.39
9.69
4.46 0.04
7.48 0.02
21.0 0.1
50.3 0.2
77.5 0.2
152
262
2
5
10.28
11.09
201
1
1240 15
428 15
1200 35
183
2
1230 16
Introducing the mole fractions into Eq. (9) yields:
d½3AMꢀT
−
¼ k3AM0α3AM0½3AMꢀ ½OH−ꢀ þ k3AMþα3AMþ½3AMꢀ ½OH−ꢀ:
ð15Þ
T
T
dt
Expressing the α values and rearranging, we obtain:
ꢀ
ꢁ
k3AM0½OH−ꢀ þ k3AMþK3AM Hþ ½OH−
ꢀ
dt:
d½3AMꢀT
½3AMꢀT
ꢀ
ꢁ
−
¼
ð16Þ
ð17Þ
1 þ K3AM Hþ
After integration:
k3AM0½OH−ꢀ þ k3AMþK3AMKw
ꢀ
ꢁ
− ln½3AMꢀT
¼
t þ C
1 þ K3AM Hþ
where C is the integration constant, and Kw =[H+][OH−], the ionic product of water. Taking the initial condition that at time t = 0, [3AM]T =
[3AM]T , Eq. (18), a practical relationship can be obtained:
0
½3AMꢀT
0
ln
k3AM0½OH−
ꢀ
k3AMþK3AMKw
½3AMꢀ
Tt
ꢀ
ꢁ
ꢀ
ꢁ
¼
þ
ð18Þ
1 þ K3AM Hþ
1 þ K3AM Hþ
t
where [3AM]T is the total concentration of 3AM at time t. The left-hand side of Eq. (18) is actually k'3AM, the conditional or observed rate constant of
t
3AM hydrolysis (see Fig. 1). [3AM]T , [3AM]T , t, [H+] and [OH−] are experimental data, Kw and K3AM are previously determined equilibrium constants,
0
t
thus k3AM0 and k3AM+ can be obtained from an appropriate set of kinetic experiments carried out at several pH values. Observed rates are collected in
Table 2, the pH-independent, species-specific rate constants are in Table 4.
3.2.2. Hydrolyses of 6-acetylmorphine
6-Acetylmorphine bearing one ester group and two protonating sites exists in 4 forms of protonation. It therefore undergoes 4 types of hydrolysis
(see ovals C and D and the connecting red arrows in Fig. 2).
Thus, the 6AM overall hydrolysis is the sum of 4 microspecies-specific rates:
h
i
h
i
ꢀ
ꢁ
d½6AMꢀT
¼ k6AM−½6AM−ꢀ½OH−ꢀ þ k6AM0 6AM0 ½OH−ꢀ þ k6AMþ=− 6AMþ=− ½OH−ꢀ þ k6AMþ 6AMþ ½OH−ꢀ:
ð19Þ
−
dt
Microspecies concentrations [6AM−], [6AM0], [6AM+/−] and [6AM+] can be related to their mole fractions and the total concentration of 6AM.
They can be expressed in terms of the corresponding protonation microconstant and hydrogen ion concentration, instantiated below by microspecies
6AM+/−, in Eqs. (20) and (21):
h
i
h
i
ꢀ
ꢁ
6AMþ=−
6AMþ=−
kN
Hþ
6AM
h
i
h
i
α6AMþ=−
¼
¼
¼
ð20Þ
ꢀ
ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
2
1 þ K1ð6AMÞ Hþ þ K1ð6AMÞK2ð6AMÞ Hþ
½6AM−ꢀ þ 6AMþ=− þ 6AM0 þ 6AMþ
½6AMꢀT
ꢀ
ꢁ
kN
Hþ
h
i
6AM
6AMþ=− ¼ α6AMþ=− ½6AMꢀ
¼
½6AMꢀT:
ð21Þ
ꢀ
ꢁ
ꢀ
ꢁ
T
2
1 þ K1ð6AMÞ Hþ þ K1ð6AMÞK2ð6AMÞ Hþ

110
L. Szöcs et al. / European Journal of Pharmaceutical Sciences 89 (2016) 105–114
Fig. 3. The course of heroin hydrolysis at pH = 8.44, T = 310 K, showing the methyl signals by 1H NMR as a function of time.
Introducing Eq. (21) and the analogous relationships for [6AM−], [6AM0] and [6AM+] into Eq. (19), and rearranging, yields:
ꢂ
ꢂ
ꢃ
ꢃ
ꢀ
ꢁ
ꢀ
ꢁ
2
k6AM−
þ
k6AM0 kO6AM þ k6AMþ=−kN
Hþ þ k6AMþK1ð6AMÞK2ð6AMÞ Hþ
½OH‐ꢀ
6AM
d½6AMꢀ
½6AMꢀTT
−
¼
dt:
ð22Þ
ð23Þ
ꢀ
ꢁ
ꢀ
ꢁ
2
1 þ K1ð6AMÞ Hþ þ K1ð6AMÞK2ð6AMÞ Hþ
After integration:
ꢂ
ꢃ
ꢀ
ꢁ
k6AM−½OH−ꢀ þ k6AM0 kO6AM þ k6AMþ=−kN
Kw þ k6AMþK1ð6AMÞK2ð6AMÞ Hþ Kw
6AM
− ln½6AMꢀT
¼
t þ C:
ꢀ
ꢁ
ꢀ
ꢁ
2
1 þ K1ð6AMÞ Hþ þ K1ð6AMÞK2ð6AMÞ Hþ
Taking the initial condition that at t = 0 time [6AM]T=[6AM]T , the following formula can be obtained:
0
½6AMꢀT
ꢂ
ꢃ
0
ꢀ
ꢁ
k6AM−½OH−ꢀ þ k6AM0 kO6AM þ k6AMþ=−kN
Kw þ k6AMþK1ð6AMÞK2ð6AMÞ Hþ Kw
ln
6AM
½6AMꢀT
t
¼
ð24Þ
ꢀ
ꢁ
ꢀ
ꢁ
2
1 þ K1ð6AMÞ Hþ þ K1ð6AMÞK2ð6AMÞ Hþ
t
Table 3
Values of the conditional k'DAM(6) and k'DAM(3) rate constants of DAM in solutions of various basicity.
pH
k'DAM(6) (10−6 s−1
)
k'DAM(3) (10−6 s−1
)
7.22
8.40
8.60
8.75
9.21
9.44
9.74
10.19
9.30 0.04
32.1 0.7
61.5 0.5
65.0 0.6
0.81 0.09
2.43 0.89
4.52 0.1
5.2 0.7
12.5 0.1
18.5 0.1
181
240
1
8
469 13
1118 32
35
86
2
4

L. Szöcs et al. / European Journal of Pharmaceutical Sciences 89 (2016) 105–114
111
Table 4
Species-specific hydrolysis rate constants of heroin and related compounds.
Rate constant (dm3·mol−1·s−1
)
Compound
Symbol
Value
Symbol
Value
3,6-Diacetylmorphine
kDAM0(6)
kDAM+(6)
k3AM0
k6AM−
k6AM0
2.30 0.08
12.81 0.84
1.89 0.03
0.13 0.002
0.14 0.05
0.14 0.002
0.24 0.002
kDAM0(3)
kDAM+(3)
k3AM+
k6AM+/−
k6AM+
0.13 0.002
1.17 0.16
15.4 2.6
0.22 0.06
1.04 0.21
0.89 0.16
1.14 0.15
3-Acetylmorphine
6-Acetylmorphine
6-Acetylcodeine
6-Acetyl-N-methylmorphine
k6AC0
k6ANMM+/−
k6AC+
k6ANMM+
where the left-hand side of Eq. (24) is actually k'6AM, the conditional rate constant of 6AM hydrolysis.
Species-specific rate constants k6AM− and k6AM+ can be calculated directly from Eq. (24). In order to determine the individual values of k6AM0 and
k6AM+/−, further pieces of information are needed. Such information can be obtained from derivative compounds of close similarity, but reduced
complexity.(Noszal et al., 2006) The closest derivative of the zwitterionic form of 6-acetylmorphine is 6-acetyl-N-methylmorphine which contains
a permanently cationic quaternary nitrogen. The basic form of this compound has only one protonating site, the phenolate group. Since the number
of connecting bonds is identical, electron densities and steric factors are highly similar, the hydrolysis rate constant of 6-acetyl-N-methylmorphine
could well be equated with k6AM+/−. Nevertheless, an even closer subtle approach offers if not the rates themselves, but the rate-accelerating effects
are considered identical. Eq. (25) implies that the hydrolysis-acceleration at site 6 upon protonation of the phenolic hydroxyl group in 6ANMM is
identical with that in the zwitterionic form of 6AM.
k6ANMMþ
k6ANMMþ=− k6AMþ=−
k6AMþ
¼
ð25Þ
The determination of k6ANMM+ and k6ANMM+/−, the species-specific hydrolysis rate constants of 6-acetyl-N-methylmorphine, bearing one ester
group and one protonating site, can be carried out analogously to that of 3-acetylmorphine from independent ester hydrolysis rate measurements.
In Eq. (25), k6AM+/− is the only unknown quantity. Calculating it from Eq. (25), and introducing into Eq. (24), k6AM0 the hydrolysis rate constant of the
non-charged 6AM species can be calculated. As a probe of the process, the value of k6AM0 can also be calculated from 6-acetylcodeine which is cer-
tainly a non-charged molecule above the protonation pH of the tertiary amino site.
3.2.3. Hydrolyses of diacetylmorphine
Diacetylmorphine exists in the form of two species. Each of them can hydrolyze at site 3 and 6 as shown in ovals A, B, C and the connecting red
arrows in Fig. 2.
In order to quantify the hydrolysis rate of DAM, not only the concentration of DAM, but also, that of 6AM and 3AM must be monitored as a function
of time due to the simultaneous, two-sited character of the decomposition.
Fig. 4. Mole fractions (solid lines) and hydrolysis fractions (dashed lines) of 6-acetylmorphine microspecies.

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L. Szöcs et al. / European Journal of Pharmaceutical Sciences 89 (2016) 105–114
Excessiveness of formulation, can be minimized here if the hydrolyses are considered first in pH-stat fashion (Fig. 1), where conditional rate
constants sufficiently characterize the processes. The conditional constants are, in fact, composite ones, the pH-dependent series of which can
then be decomposed into pH-independent, species- and site-specific constants. The hydrolysis rates in terms of conditional constants are as follows:
d½DAMꢀ
′
′
DAMð3Þ
¼ −k
½DAMꢀ−k
½DAMꢀ
ð26Þ
ð27Þ
ð28Þ
DAMð6Þ
dt
d½6AMꢀ
′
¼ k
½DAMꢀ−k06AM½6AMꢀ
DAMð6Þ
DAMð3Þ
dt
d½3AMꢀ
′
′
¼ k
½DAMꢀ‐k
½3AMꢀ:
3AM
dt
Where Eq. (26) shows the simultaneous, while Eqs. (27) and (28) show the consecutive processes.
Integration and rearrangements of differential Eqs. (26)–(28) provide the following concentrations for DAM, 6AM, and 3AM:
ꢂ
ꢃ
k0DAMð6Þ þk0DAMð3Þ
t
½DAMꢀ ¼ ½DAMꢀ0e‐
ð29Þ
ð30Þ
ꢂ
ꢃ
!
′
′
′
k
½DAMꢀ
k
DAMð6Þþk
t
½
6AMꢀ ¼
½3AMꢀ ¼
e−
−e−k
′
DAMð6Þ
0
DAMð3Þ
6AM t
ꢂ
ꢃ
′
′
′
DAMð3Þ
k
6AM− k
þ k
DAMð6Þ
ꢂ
ꢃ
!
k0DAMð6Þ þk0DAMð3Þ
t
k0DAMð3Þ ½DAMꢀ0
0
e−
−e−k
:
ð31Þ
3AM t
ꢂ
ꢃ
k03AM − k0DAMð6Þ þ k0DAMð3Þ
Conditional constants k′6AMand k′3AM have actually been determined in the hydrolysis studies of 6AM and 3AM (Eqs. (24) and (18)), respectively.
In the knowledge of k′6AM and k′3AM, Eqs. (29)–(31) provide a sound mathematical set for the determination of k′DAM(6) and k′DAM(3). Experimen-
tal determination of [DAM], [6AM] and [3AM] could be carried out from their integral values in time-dependent series of NMR spectra as shown in
Fig. 3.
The concentration of acetate and morphine are monotonously, non-linearly increasing, while that of DAM, in contrast, is monotonously decreas-
ing. Peaks of 6AM and 3AM undergo maxima. The amount of 3AM is certainly non-negligible relative to 6AM. Table 3. shows the k′DAM(6) and k′DAM(3)
rate constants in solutions of various basicity.
The pH-dependent k'DAM(6) and k'DAM(3) conditional rate constants are analogous to k'3AM (Eq. (18)) in terms of their relationships with the pH-
independent rate constants.
kDAM0ð6Þ½OH−
ꢀ
kDAMþð6ÞKDAMKw
ð32Þ
ð33Þ
′
ꢀ
ꢁ
ꢀ
ꢁ
k
k
¼
¼
þ
þ
DAMð6Þ
DAMð3Þ
1 þ KDAM Hþ
1 þ KDAM Hþ
kDAM0ð3Þ½OH−
ꢀ
kDAMþð3ÞKDAMKw
′
ꢀ
ꢁ
ꢀ
ꢁ
1 þ KDAM Hþ
1 þ KDAM Hþ
Thus the knowledge of KDAM, and the series of data pairs k′DAM(6), [H+] and k'DAM(3), [H+] allows the calculation of the pH-independent kDAM0(6)
,
kDAM+(6) and kDAM0(3), kDAM+(3) rate constants. Since hydrolysis at site 3 takes place much faster than at site 6, the analytical signals of 3AM and the
concomitant accuracy of its determination are below those of 6AM. In order to assess reliability of the values of kDAM0(3) and kDAM+(3), the constants of
the minor decomposition pathway were compared to the related rate constants of 6AM, 6-acetylcodeine and 6-acetyl-N-methylmorphine. Table 4
summarizes all the pH-independent rate constants determined in this study.
3.2.4. Determination of hydrolysis fractions
Hydrolysis fraction is a new, derived physico-chemical parameter that shows the contribution of the individual microspecies to the overall
hydrolysis at a particular pH, as shown for the zwitterionic microspecies of 6 AM:
h
i
k6AMþ=− 6AMþ=− ½OH−
ꢀ
h
i
h
i
αhydr
¼
:
ð34Þ
ꢀ
ꢁ
6AMþ=−
k6AM−½6AM−ꢀ½OH−ꢀ þ k6AM0 6AM0 ½OH−ꢀ þ k6AMþ=− 6AMþ=− ½OH−ꢀ þ k6AMþ 6AMþ ½OH−
ꢀ
Applying the central–left relationship of Eq. (21) and analogous ones for [6AM‐], [6AM0] and [6AM+], and rearranging, yields:
α
6AMþ=−k6AMþ=−
αhydr
¼
α
ð35Þ
6AMþ=−
6AM−k6AM− þ α6AMþ=−k6AMþ=− þ α6AM0k6AM0 þ α6AMþk6AMþ

L. Szöcs et al. / European Journal of Pharmaceutical Sciences 89 (2016) 105–114
113
where αhydr
is the hydrolysis fraction of microspecies 6AM+/−. Introducing the mole fractions into (35) and rearrangements yields:
6AM+/−
ꢀ
ꢁ
kN
Hþ k6AMþ=−
6AM
ꢂ
ꢃ
αhydr
¼
:
ð36Þ
ꢀ
ꢁ
ꢀ
ꢁ
6AMþ=−
2
k6AM−
þ
kN6AMk6AMþ=− þ kO6AMk6AM0 Hþ þ k6AMþk1ð6AMÞk2ð6AMÞ Hþ
4. Discussion
into quantified hydrolysis rates of every single protonation stage,
revealing intramolecular effects that influence electron density at the
ester group and the concomitant hydrolysis rates.
Our data also provide information on the hydrogen ion binding
propensities of the basic sites in the molecules studied and the related
pharmacokinetic and pharmacodynamic behavior, in which also hydro-
gen bondings tether the molecules to the active loci of the decomposing
enzymes and the opiate receptors.
This in-depth analysis is also a submolecular map with synthetic
drug development perspectives by side-chain amendments to increase
or decrease covalent stability and binding capacity for molecules in
the opiate family.
The macroscopic and microscopic protonation constants (Table 1)
are not only sine qua non input data of the kinetic analysis, but also,
they provide information on the electron density at the protonation site.
The two phenolate forms of 6AM (microspecies [6AM−] and
[6AM+/−]) are, in fact, the hydrolysis products of heroin-3 hydrolysis,
while the two phenolate forms of morphine (the anionic and zwitter-
ionic ones) are the hydrolysis products of 3AM hydrolysis. The lower
the electron density at the phenolic oxygen the lower the phenolate
basicity and the faster the hydrolysis.
All the site- and species-specific rate constants are collected in
Table 4, allowing several comparisons and conclusions. Rates and effects
at various sites are paired so that the rest of the compared molecules are
identical. Hydrolysis takes place 11–18 times faster at site 3 than at site
Conflict of interest
6, as pairs of constants kDAM0(6) and kDAM0(3), kDAM+(6) and kDAM+(3)
,
The authors report no conflict of interest.
k3AM0 and k6AM0, k3AM+ and k6AM+ quantify. This phenomenon is a con-
sequence of the electron-withdrawing effect of the aromatic ring which
makes the ester group in position 3 vulnerable to nucleophilic attacks.
The propensity to rupture is further increased upon the nitrogen pro-
tonation which decreases electron density and bonding strength
throughout the molecule. As a result, a 6 and 9 fold hydrolysis accelera-
tion occurs at site 3 (see kDAM+(6) vs. kDAM0(6)and k3AM+ vs. k3AM0). Al-
though ester 6 is closer to the nitrogen in terms of chemical bonds, the
aromatic ring conducts well the electron-withdrawing inductive effects,
resulting in higher hydrolysis acceleration at ester 3 upon protonation
of the nitrogen. The effect of phenolate protonation on the hydrolysis
rate at ester 6 can be assessed if values of k6AM‐ vs. k6AM0 and k6AM+
vs. k6AM+/−are compared. When the phenolate protonates only, a slight
increase in hydrolysis occurs only (k6AM− vs. k6AM0), however when
both the phenolate and the nitrogen are protonated the hydrolysis
takes place 8 times faster. (k6AM− vs. k6AM+). The exchange of a hydrox-
yl moiety for an acetoxy site slows down the hydrolysis as shown at site
3 in kDAM+(6) vs. k3AM+. In solutions of diacetylmorphine and 3-
acetylmorphine, the overall hydrolyses are composites of hydrolyses
of the neutral and cationic forms. In the case of 6-acetylmorphine, how-
ever, 4 microspecies exist which all contribute to the overall rate, ac-
cording to their occurrence probability and species-specific rate
constants. The biggest difference in the rate constants is between the
protonated form of 3AM and the anionic form of 6AM (k3AM+vs. k6AM−),
due to cumulated effects. The protonated form of 3AM hydrolyses
almost 120 times faster than the anionic form of 6AM.
Acknowledgements
This research was supported by TÁMOP 4.2.1 B-09/1/KMR and OTKA
T 73804.
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