Deuterium kinetic isotope effects on the dissociation of a protein-fatty acid complex in the gas phase

Article abstract of DOI:10.1021/ja300092w

Deuterium kinetic isotope effects (KIEs) are reported for the first time for the dissociation of a protein-ligand complex in the gas phase. Temperature-dependent rate constants were measured for the loss of neutral ligand from the deprotonated ions of the 1:1 complex of bovine β-lactoglobulin (Lg) and palmitic acid (PA), (Lg + PA)^n- → Lg^n- + PA, at the 6- and 7- charge states. At 25 °C, partial or complete deuteration of the acyl chain of PA results in a measurable inverse KIE for both charge states. The magnitude of the KIEs is temperature dependent, and Arrhenius analysis of the rate constants reveals that deuteration of PA results in a decrease in activation energy. In contrast, there is no measurable deuterium KIE for the dissociation of the (Lg + PA) complex in aqueous solution at pH 8. Deuterium KIEs were calculated using conventional transition-state theory with an assumption of a late dissociative transition state (TS), in which the ligand is free of the binding pocket. The vibrational frequencies of deuterated and non-deuterated PA in the gas phase and in various solvents (n-hexane, 1-chlorohexane, acetone, and water) were established computationally. The KIEs calculated from the corresponding differences in zero-point energies account qualitatively for the observation of an inverse KIE but do not account for the magnitude of the KIEs nor their temperature dependence. It is proposed that the dissociation of the (Lg + PA) complex in aqueous solution also proceeds through a late TS in which the acyl chain is extensively hydrated such that there is no significant differential change in the vibrational frequencies along the reaction coordinate and, consequently, no significant KIE.

Full text of DOI:10.1021/ja300092w

Article
pubs.acs.org/JACS
Deuterium Kinetic Isotope Effects on the Dissociation of a Protein−
Fatty Acid Complex in the Gas Phase
Lan Liu,†,‡ Klaus Michelsen,§ Elena N. Kitova,†,‡ Paul D. Schnier,§ Alex Brown,† and John S. Klassen*,†,‡
‡
†Department of Chemistry and Alberta Glycomics Centre, University of Alberta, Edmonton, Alberta, Canada T6G 2G2
§Molecular Structure, Amgen, Thousand Oaks, California 91320, United States
S
* Supporting Information
ABSTRACT: Deuterium kinetic isotope effects (KIEs) are
reported for the first time for the dissociation of a protein−
ligand complex in the gas phase. Temperature-dependent rate
constants were measured for the loss of neutral ligand from the
deprotonated ions of the 1:1 complex of bovine β-lactoglobulin
(Lg) and palmitic acid (PA), (Lg + PA)n− → Lgn− + PA, at the
6− and 7− charge states. At 25 °C, partial or complete
deuteration of the acyl chain of PA results in a measurable
inverse KIE for both charge states. The magnitude of the KIEs is
temperature dependent, and Arrhenius analysis of the rate constants reveals that deuteration of PA results in a decrease in
activation energy. In contrast, there is no measurable deuterium KIE for the dissociation of the (Lg + PA) complex in aqueous
solution at pH 8. Deuterium KIEs were calculated using conventional transition-state theory with an assumption of a late
dissociative transition state (TS), in which the ligand is free of the binding pocket. The vibrational frequencies of deuterated and
non-deuterated PA in the gas phase and in various solvents (n-hexane, 1-chlorohexane, acetone, and water) were established
computationally. The KIEs calculated from the corresponding differences in zero-point energies account qualitatively for the
observation of an inverse KIE but do not account for the magnitude of the KIEs nor their temperature dependence. It is
proposed that the dissociation of the (Lg + PA) complex in aqueous solution also proceeds through a late TS in which the acyl
chain is extensively hydrated such that there is no significant differential change in the vibrational frequencies along the reaction
coordinate and, consequently, no significant KIE.
phase). The advantage of a “gas-phase” approach is that it
affords an opportunity to probe the kinetics and mechanisms of
dissociation reactions free from the complicating effects of
solvent.11,12 Furthermore, comparison of the gas-phase data
with kinetic data measured in solution can, in principle, provide
quantitative insights into the role of solvent in the dissociation
reactions.11−13
Recently, the dissociation reactions of bovine β-lactoglobulin
(Lg) complexed with a series of long-chain fatty acids (FAs)
were investigated in the gas phase.14 Lg, an 18 kDa whey
protein, possesses a large and flexible cavity that can
accommodate a variety of hydrophobic ligands, including FAs
such as palmitic acid (PA).15,16 According to the crystal
structure of the (Lg + PA) complex (PDB 1B0O), the acyl
chain of PA is fully buried within the hydrophobic cavity, while
the carboxyl group is located near the top of the cavity and is
exposed to solvent. It was shown using electrospray ionization
mass spectrometry (ESI-MS) that the interaction between Lg
and PA, and other long chain FAs, can be transferred, intact,
from aqueous solution to the gas phase.14 Notably, gaseous
deprotonated (Lg + FA)n− ions, where n = 6 and 7, adopt one
of two non-interconverting structures, which are referred to as
INTRODUCTION
■
The association and dissociation of noncovalent protein−ligand
interactions are critical events in many biological processes,
such as transport, signaling, chemical transformation, and
molecular and cellular recognition.1−4 Knowledge of the forces
that control the rates of these processes and the underlying
reaction mechanisms is of fundamental importance and
facilitates the design of novel therapeutics. The rates of
protein−ligand association reactions are often dominated by
the diffusion properties of the ligand,5 although other factors
such as electrostatic effects and binding site accessibility may
also play a role.5−7 In contrast, the details of the dissociation
reactions are poorly understood.8 The rate of ligand escape
from the binding pocket of a protein may be strongly affected
by many factors, such as the number and nature of the
intermolecular interactions that must be broken in order for the
ligand to be released from the pocket, protein structural
changes that accompany ligand release, and reorganization of
solvent molecules during the dissociation process.5,9
Given the inherently intricate nature of the dissociation
process, developing a detailed, quantitative understanding of
how a ligand escapes from the binding pocket represents a
significant challenge.10 One promising approach to this
problem is based on the dissociation kinetics of protein−ligand
complexes measured in their desolvated state (i.e., in the gas
Received: January 4, 2012
Published: March 12, 2012
© 2012 American Chemical Society
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the fast and slow dissociating components, (Lg + PA)fn− and
(Lg + PA)sn−, respectively. The kinetic data measured for the
loss of neutral FA from (Lg + FA)n− ions, together with the
results of molecular dynamics (MD) simulations, suggest that
the acyl chain of the FAs is retained within the hydrophobic
cavity of Lg in the gas phase, at least for the fast components.13
In the (Lg + PA)fn− ions, PA is believed to be stabilized
predominantly by protein−lipid interactions, while for the (Lg
+ PA)sn− ions, H-bonds between the ligand carboxyl group and
Lg are also thought to contribute to the stability of the
complex.14 Interestingly, comparison of the dissociation rate
constants measured for gaseous deprotonated (Lg + FA)n− ions
with those determined in aqueous solution (at pH 8) revealed
that the hydrated (Lg + FA) complexes are kinetically less
stable at room temperature. The lower kinetic stability of the
hydrated (Lg + FA) complexes results from a lower dissociation
activation energy (Ea).13 Importantly, the differences in Ea
values measured in the gas phase and in water are consistent
with the enthalpy changes expected for the hydration of the
acyl chain of the FAs. These results led to the hypothesis that
dissociation of the (Lg + FA) complexes, both in aqueous
solution and in the gas phase, proceeds through a late transition
state (TS), in which the ligand has almost fully escaped the
binding pocket.13
Here, deuterium kinetic isotope effects (KIEs) were
exploited to further investigate the dissociation mechanism of
the (Lg + PA) complex in aqueous solution and in the gas
phase. A deuterium KIE corresponds to the ratio of the rate
constants for the non-deuterated and deuterated reactants, i.e.,
kH/kD. Deuterium KIEs typically arise from changes in the
vibrational frequencies of the bonds involving the isotopes in
the reactant form (R) and the TS. These changes, which differ
for the non-deuterated and deuterated forms of the reactant,
affect the change in zero-point energy (ΔZPE) and,
correspondingly, the Ea of the reaction.17 The magnitude of
the KIE resulting from the differential change in ΔZPE can be
estimated using transition-state theory:
These kinetic data were then compared to those reported
recently for non-deuterated PA (D0) with the goal of probing
the structure of the dissociative TS.13 The effects of deuteration
and solvation on the vibrational frequencies of PA were
investigated computationally to assist in the interpretation of
the observed KIEs. Rate constants were also measured for the
dissociation of the (Lg + PA) complex, composed of PA (D31),
in aqueous solution at pH 8 and temperatures ranging from 5
to 32 °C using surface plasmon resonance (SPR) spectroscopy.
These data were then compared to results reported for the (Lg
+ PA) complex composed of PA (D0) to evaluate the influence
of solvent on the KIEs.13
EXPERIMENTAL SECTION
■
Sample Preparation. Bovine β-lactoglobulin (Lg, monomer
average MW 18 281 Da), palmitic acid (PA, 256 Da), and PA-d31
(D31, 287 Da) were purchased from Sigma-Aldrich Canada (Oakville,
Canada). Palmitic acid-methyl-d3 (D3, 259 Da), PA-7,7,8,8-D4 (D4,
260 Da), and PA-9,9...16,16,16-D17 (D17, 273 Da) were purchased
from ACP Chemicals (St. Leonard, Canada). The Lg was dissolved
and exchanged directly into Milli-Q water using an Amicon
microconcentrator with a molecular weight cutoff of 10 kDa. The
concentration of the Lg solution was determined by lyophilizing a
known volume of the filtrate and measuring the mass of the protein.
The protein stock solution was stored at −20 °C. The ligand stock
solutions were prepared by dissolving PA into aqueous ammonium
acetate. The ESI solutions were prepared from stock solutions of
protein and ligand; imidazole (10 mM) was also added in order to
stabilize the (Lg + PA) complexes during ESI-MS analysis. Aqueous
ammonium hydroxide was added to adjust the pH of the solution to
8.5.
Mass Spectrometry. Experimental measurements were performed
using an Apex II 9.4 T Fourier-transform ion cyclotron resonance
(FTICR) mass spectrometer (Bruker, Billerica, MA) equipped with a
modified external nanoflowES (nanoESI) ion source. NanoESI was
performed using borosilicate tubes (1.0 mm o.d., 0.68 mm i.d.), pulled
to ∼5 μm o.d. at one end using a P-2000 micropipet puller (Sutter
Instruments, Novato, CA). The electric field required to spray the
solution in negative-ion mode was established by applying a voltage of
∼ −800 V to a platinum wire inserted inside the glass tip. The solution
flow rate was typically ∼20 nL min−1. The gaseous ions produced by
nanoESI were introduced into the mass spectrometer through a
stainless steel capillary (i.d. 0.43 mm) maintained at an external
temperature of 66 °C. The gas flow rate into the instrument was
measured to be 0.6 L min−1. The ions sampled by the capillary (−50
V) were transmitted through a skimmer (0 V) and accumulated
electrodynamically in an rf hexapole. Ions were then ejected from the
hexapole and accelerated (+2700 V) into the superconducting magnet,
decelerated, and introduced into the ion cell. The trapping plates of
the cell were maintained at a constant potential of −1.4 V throughout
the experiment. Two flexible heating blankets placed around the
portion of the vacuum tube that surrounds the ion cell were used to
control the temperature of the ion cell for the BIRD experiments. The
typical base pressure for the instrument was ∼5 × 10−10 mbar. Data
acquisition was controlled by an SGI R5000 computer running the
Bruker Daltonics XMASS software, version 5.0. Mass spectra were
obtained using standard experimental sequences with chirp broadband
excitation. The time domain signal, consisting of the sum of 50
transients containing 128K data points per transient, was subjected to
one zero-fill prior to Fourier transformation.
−ΔΔZPE/RT
(1)
KIE ≈ e
where ΔΔZPE is the difference in ΔZPE corresponding to
reactions involving the non-deuterated and deuterated reactants
(ΔΔZPE = ΔZPEH − ΔZPED). Deuterium KIEs for
unimolecular reactions are also sensitive to differential changes
in the rotational and vibrational partition functions of the non-
deuterated and deuterated reactants on going from R to the TS.
However, the influence of changes in the rotational and
vibrational partition functions on the rate constant is usually
small compared to those resulting from changes in ΔZPE.17
Deuterium KIEs can serve as a sensitive probe of reaction
mechanisms and have been used extensively to characterize a
variety of chemical and biochemical reactions in solution.18−22
Deuterium KIEs have also been used to probe mechanisms of
reactions occurring in the gas phase.11,12,23−27 However, to our
knowledge, no quantitative studies of deuterium KIEs for the
dissociation of biological complexes in the gas phase have been
previously reported. In the present study, rate constants for the
dissociation of deprotonated (Lg + PA)7− and (Lg + PA)6− ions
composed of partially and fully deuterated PA
CD3(CH2)14COOH (D3), CH3(CH2)7(CD2)2(CH2)5COOH
( D 4 ) , C D 3 ( C D 2 ) 7 ( C H 2 ) 7 C O O H ( D 1 7 ) , a n d
CD3(CD2)14COOH (D31)were measured using the black-
body infrared radiative dissociation (BIRD) technique28,29 and
Fourier-transform ion cyclotron resonance (FTICR) MS.
Analysis of Kinetic Data. As described above, the deprotonated
(Lg + PA)n− ions, where n = 6 or 7, exist in two kinetically distinct
structures, designated as the (Lg + PA)fn− and (Lg + PA)sn− ions. At
the temperatures investigated, both structures dissociate exclusively by
the loss of neutral PA with dissociation rate constants, kf and ks,
respectively:
k
f
n−
n−
→ Lg + PA
(Lg + PA)
(2a)
f
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Figure 1. (a) Plots of the natural logarithm of the normalized intensity (I/Io) of (Lg + PA)7− ions versus reaction time measured at 25 °C for PA =
D0 (red), D3 (blue), D4 (black), D17 (green), and D31 (orange). The solid curves correspond to the best fits of double exponential decay functions
to the experimental data. (b) Simulated kinetic plots calculated from the rate constants determined from plots in (a) and using a constant fraction of
fast and slow components, 0.37 and 0.63, respectively.
k
s
n−
n−
→ Lg + PA
Computational Methods. Geometries of PA were optimized
using Becke’s three-parameter hybrid functional (B3LYP)30−33 and the
hybrid Perdew, Burke, and Ernzerhof functional (PBE0),34−36 both
with the standard 6-311+G(d,p) basis set for all atoms.37 Geometry
optimizations were performed in the gas phase and in solvents (n-
hexane, 1-chlorohexane, acetone, and water) using the IEF-PCM
polarizable continuum model,38−40 as implemented in Gaussian09.41
The dielectric constants for the solvents n-hexane, 1-chlorohexane,
acetone, and water are 1.88, 5.95, 20.49, and 78.36, respectively. All
geometry optimizations used tight convergence thresholds as defined
by maximum force equal to 1.5 × 10−5 a.u., rms force of 1.0 × 10−5
a.u., maximum displacement of 6.0 × 10−5 a.u., and rms displacement
of 4.0 × 10−5 a.u. In all cases, the optimized geometry was that of the
fully extended PA chain, although all calculations were carried out with
C1 symmetry. From the X-ray crystal structure of the (Lg + PA)
complex (PDB 1B0O), the chain is not fully extended due to the
specific interactions within the protein cavity. However, the use of the
fully extended geometry is satisfactory for the static structure and
continuum models considered here. In the vibrational analysis,
corrections for hindered and free internal rotations42−44 were made
in order to assess the influence of neglect/inclusion of these effects on
the ZPE.
(Lg + PA)
(2b)
s
The dissociation rate constants and abundance of the individual
components were determined by fitting a double exponential function
to the time-dependent normalized intensities (I/I0) of the (Lg + PA)n−
ions:
−k t
−k t
s
f
I/I = X
e
+ X
e
s,0
0
f,0
(3)
where Xf,0 and Xs,0 correspond to the initial fractions of the fast and
slow components, respectively. At a given reaction time, the
normalized intensity of the reactant ion was calculated using eq 4:
I/I = I
/(I
+ I )
Lg
0
(Lg+PA) (Lg+PA)
(4)
where I(Lg+PA) and ILg are the measured intensities of the
corresponding (Lg + PA)n− and Lgn− ions, respectively. To improve
the accuracy of the curve fitting, Xs,0 and ks were first estimated by
fitting the kinetic data obtained at long reaction times, which reflect
only the slow component, with a single exponential function.
Incorporating the ks and Xs,0 values into eq 3 and fitting this to the
I/I0 versus reaction time data allowed kf and Xf,0 to be determined.
Surface Plasmon Resonance Spectroscopy. Surface plasmon
resonance (SPR) spectroscopy measurements were performed on a
Biacore T100 instrument (GE Healthcare). Reagents used were
obtained from Sigma-Aldrich, Isotec, or GE Healthcare. Immobiliza-
tion running buffer consisted of 10 mM Hepes pH 7.4, 150 mM NaCl,
and 0.2 mM TCEP. Lg was immobilized onto a carboxymethyl dextran
(CM5) chip using amine coupling chemistry at 25 °C. Surfaces were
first pre-conditioned with two 6 s pulses each of 100 mM HCl, 50 mM
NaOH, and 0.5% (w/v) SDS at a flow rate of 100 μL min−1. At a flow
rate of 10 μL min−1, CM5 surface was activated for 7 min with a
mixture of NHS/EDC, followed by a 90 s injection of 20 μg mL−1 Lg
in 10 mM sodium acetate pH 4.0. Remaining activated groups were
subsequently blocked with a 7 min injection of ethanolamine. Using
this approach, 600 RU of Lg was immobilized. Kinetic measurements
were conducted in buffer consisting of 25 mM Tris pH 8.0, 1 mM
TCEP, 0.2 mM CHAPS, and 8% (v/v) methanol. Stock solutions of
PA and PA(D31) were prepared in methanol, and serial dilutions of
the FAs were performed in methanol. Diluted FAs were subsequently
added to the buffer to a final methanol concentration of 8% (v/v)
methanol. The FAs were injected over the Lg surface for 30 s
association and dissociation monitored for 60 s at a flow rate of 80 μL
min−1. The sample analysis temperature was varied between 5 and 32
°C.
RESULTS AND DISCUSSION
■
Deuterium Kinteic Isotope Effects in the Gas Phase. At
reaction temperatures of 25−66 °C, BIRD of the (Lg + PA)7−
ions results exclusively in the loss of neutral PA. Shown in
Figure S1 (Supporting Information) are natural log plots of the
normalized intensities of the reactant ions versus time
measured for the (Lg + PA)7− ions composed of non-
deuterated (D0) and deuterated forms of PA (D3, D4, D17,
and D31) at several temperatures. Notably, each of the kinetic
plots exhibits non-linear behavior, which can be described by
double exponential functions, consistent with the presence of
two distinct structures. Shown together in Figure 1a are the
kinetic data for each of the (Lg + PA)7− ions measured at 25
°C. Because the relative abundance of the (Lg + PA)f7− and
(Lg + PA)s7− ions tends to vary between experiments
(presumably due to differences in the ESI droplet histories),
it is difficult to establish the influence of deuteration on the
kinetic stability directly from visual inspection of the kinetic
plots. Shown in Figure 1b are synthesized kinetic plots
constructed from the rate constants measured from the data
shown in Figure 1a for the (Lg + PA)f7− and (Lg + PA)s7− ions
(kf and ks, respectively) and using constant fractions for the
(Lg + PA)f7− and (Lg + PA)s7− ions (Xf,0 = 0.37 and Xs,0 = 0.63,
respectively). It can be seen that, at 25 °C, deuteration of PA
results in larger rate constants for both the fast and slow
components. The deuterium KIEs range from 0.82 0.10 (D3)
Data were processed using the Biacore T100 analysis software and
Igor Pro (Wavemetrics Inc.). Sensorgrams were corrected for
systematic noise and baseline drift by subtracting the response of
the reference spot, which was activated but not exposed to protein.
The average response from blank injections was used to double-
reference the binding data. The dissociation portion of the
sensorgrams were de-spiked, binomial smoothed, and fitted to an
exponential function to determine the dissociation rate constants.
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to 0.42 0.09 (D31) for the fast component and from 0.57
Table 2. Arrhenius Parameters (Ea, A) and Corresponding
ΔEaIE Values Determined for the Dissociation of the
Gaseous Deprotonated (Lg + PA)f7− and (Lg + PA)s7− Ions
for Non-deuterated PA (D0) and Deuterated PA (D3, D4,
0.10 (D3) to 0.36
0.04 (D31) for the slow component
(Table 1). Deuterium KIEs were also determined for the (Lg +
a
D17, and D31)
Table 1. Rate Constants (k) and Kinetic Isotope Effects
(KIE) Measured at 25 and 51 °C for Dissociation of the
Gaseous Deprotonated (Lg + PA)f7− and (Lg + PA)s7− Ions
Composed of Non-deuterated (D0) and Deuterated PA (D3,
b
PA
Ea (kcal mol−1
)
ΔEaIE (kcal mol−1
)
A (s−1
)
Fast
0.1
0.2
0.1
0.4
0.2
D0
16.2 0.2
15.4 0.2
15.1 0.2
13.8 0.5
12.9 0.2
−
1010.3
109.8
109.7
108.7
108.2
a
D4, D17, and D31)
D3
0.8 0.3
1.1 0.3
2.4 0.5
3.3 0.3
Slow
T (°C)
PA
k (s−1
Fast
)
KIE
D4
D17
D31
25
D0
0.026 0.0013
0.031 0.00323
0.038 0.004
0.043 0.0046
0.060 0.0130
Slow
D3
0.82 0.10
0.68 0.08
0.60 0.03
0.42 0.09
0.4
0.3
0.2
0.1
0.3
D0
23.6 0.6
21.1 0.4
19.9 0.3
19.3 0.2
16.8 0.5
−
1014.2
1012.6
1011.8
1011.3
109.6
D4
D3
2.5 0.7
3.7 0.7
4.3 0.6
6.8 0.9
D17
D31
D4
D17
D31
D0
0.00076 0.000081
0.0013 0.00018
0.0014 0.000049
0.0012 0.000073
0.0021 0.00013
Fast
a
b
D3
0.57 0.10
0.55 0.06
0.60 0.07
0.36 0.04
The reported errors are one standard deviation. ΔEaIE = Ea,D0
Ea,Dx, where x = 3, 4, 17, or 31.
−
D4
D17
D31
obtained following incubation of Lg in D2O for 30 min at 25
°C. Analysis of the mass spectrum reveals an average increase of
∼80 Da in the MW of Lg. Because water is excluded from the
cavity of Lg, even in the absence of ligand binding,45 the
residues in the cavity are expected to undergo little or no
exchange. Plotted in Figure S4 are the kinetic data measured for
the (Lg + PA)7− and (D-Lg + PA)7− ions at 66 °C. Comparison
of these kinetic data with those measured for non-deuterated
(Lg + PA)7− ions, under identical conditions, fails to reveal a
KIE. These results indicate that the incorporation of deuterium
remote from the binding cavity does not produce a KIE. These
results also serve to exclude the possibility that the KIEs
measured for the (Lg + PA)n− ions consisting of deuterated PA
reflect subtle differences in the temperature of the deuterated
and non-deuterated ions due to differences in radiative energy
transfer or any mass discrimination effects resulting from
differential trapping of the deuterated and non-deuterated (Lg
+ PA)n− ions.
Origin of Deuterium KIEs in Gas Phase. There is
abundant evidence for equilibrium deuterium isotope effects on
non-covalent interactions involving nonpolar or weakly polar
molecules. For example, Shi and Davis reported on the gas
chromatographic separation of pairs of deuterated and non-
deuterated molecules using squalane and silicone oil columns.46
For each pair of compounds they observed an inverse isotope
effect with the deuterated analogues eluting first. Their results
were interpreted in terms of a differential decrease in the C−
H/C−D vibrational modes, and correspondingly the ZPEs, of
the compounds due to van der Waals interactions with the
condensed phase. Several laboratories have employed reversed-
phase liquid chromatography to investigate deuterium isotope
effects on hydrophobic bonding.17,47,48 These studies have
consistently shown that, in the presence of a polar mobile
phase, deuterated compounds are less well retained than their
non-deuterated counterparts. Solvent-induced changes in the
vibrational frequencies of C−H/C−D bonds, in particular the
high-frequency stretching modes, have been suggested as the
origin of these isotope effects.47,48
51
D0
0.22 0.016
0.25 0.020
0.29 0.014
0.23 0.017
0.36 0.032
Slow
D3
0.88 0.10
0.75 0.07
0.96 0.10
0.61 0.07
D4
D17
D31
D0
0.016 0.0010
0.026 0.0034
0.022 0.0012
0.017 0.0016
0.018 0.0014
D3
0.63 0.09
0.74 0.06
0.96 0.11
0.89 0.09
D4
D17
D31
a
Errors correspond to one standard deviation.
PA)7− ions at 51 °C (Table 1) and the corresponding (Lg +
PA)6− ions at 25 and 51 °C (Table S1). Notably, the KIEs
measured for the dissociation of the (Lg + PA)6− ions are
consistent in magnitude with those observed for the (Lg +
PA)7− ions.
Shown in Figure S2 are Arrhenius plots for the dissociation
of the (Lg + PA)f7− and (Lg + PA)s7− ions for deuterated and
non-deuterated PA. Inspection of the Arrhenius parameters (Ea,
A) reveals that deuteration results in a decrease in Ea, although
the magnitude of the effect does not scale linearly with
deuterium incorporation (Table 2). For the fast components,
the decrease in Ea ranges from 1 to 3 kcal mol−1, while for the
slow components the effect is more significant, 2−7 kcal mol−1.
Because deuteration results in a change in Ea, as well as A, the
magnitude of the KIE is temperature dependent. As a result,
inverse KIEs (<1) observed near room temperature will
eventually become normal KIEs (>1) at higher temperatures.
For this reason it is, perhaps, more convenient to describe the
effect of deuteration on the dissociation kinetics in terms of the
change in Ea, i.e., the activation energy isotope effect, ΔEaIE
(Table 2).
To establish whether the incorporation of deuterium into Lg
also influences the rate of ligand loss from the (Lg + PA)n−
ions, kinetic measurements were performed on deuterated (Lg
+ PA)7− ions, i.e., (D-Lg + PA)7− ions, produced from D2O.
Shown in Figure S3 is a representative ESI mass spectrum
The observation of inverse of the KIEs for the dissociation of
the gaseous (Lg + PA)n− ions are qualitatively consistent with
differential changes in the vibrational frequencies of non-
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Table 3. Vibrational Zero-Point Energies of PA (D0), Partially Deuterated PA (D3), and Deuterated PA (D31) As Determined
a
at the B3LYP/6-311+G(d,p) and PBE0/6-311+G(d,p) Levels of Theory
solvent
ZPE for D0 (ΔZPE)
ZPE for D3 (ΔZPE)
ΔΔZPE for D3
ZPE for D31 (ΔZPE)
ΔΔZPE for D31
B3LYP/6-311+G(d,p)
gas phase
n-hexane
1-chlorohexane
acetone
287.461
281.451
−
223.236
−
287.217 (0.244)
286.917 (0.544)
286.774 (0.687)
286.723 (0.738)
281.214 (0.237)
280.924 (0.527)
280.785 (0.666)
280.735 (0.716)
0.007
0.017
0.021
0.027
223.042 (0.194)
222.804 (0.432)
222.692 (0.544)
222.651 (0.585)
0.050
0.112
0.143
0.153
water
PBE0/6-311+G(d,p)
gas phase
n-hexane
1-chlorohexane
acetone
289.140
283.107
−
224.749
−
288.903 (0.237)
288.583 (0.557)
288.420 (0.720)
288.361 (0.779)
282.877 (0.230)
282.567 (0.540)
282.409 (0.698)
282.351 (0.756)
0.007
0.017
0.022
0.023
224.561 (0.188)
224.307 (0.442)
224.179 (0.570)
224.133 (0.616)
0.049
0.115
0.150
0.163
water
a
. Energies are in kcal mol−1. The differences between the gas-phase and solvent-phase ZPE values, ΔZPE = ZPEgas phase − ZPEsolvent, are given, as are
the corresponding ΔΔZPE.
deuterated and deuterated complex along the reaction
coordinate (i.e., in going from R to the TS). In the bound
form, the acyl chain of PA is solvated by the hydrophobic
residues that line the binding pocket of Lg. The major
interactions are expected to involve dipole−induced dipole and
London dispersion forces. In the dissociative TS, the acyl chain
will necessarily be solvated less by Lg. As discussed elsewhere,
the C−H stretching modes of alkanes exhibit solvent-induced
frequency shifts of several cm−1; generally, the frequencies are
lower in solution than in the gas phase.48,49 As a result, a net
increase in the magnitude of the acyl chain C−H vibrational
frequencies is expected to occur along the reaction coordinate.
An increase in the vibrational frequencies will lead to an
increase in the TS vibrational ZPE, compared to that of R.
Because of the larger mass of D, compared to H, the amplitude
of vibrations, as well as polarizabilities and average volumes, of
C−D bonds are smaller than those of the corresponding C−H
bonds.17 Due to the lower bond polarizabilities and smaller
average volumes of the C−D bonds, the interactions between
Lg and deuterated PA are expected to be weaker than those
involving PA. Therefore, the influence of protein solvation on
the vibrational frequencies associated with the acyl chain will be
greater for PA (D0), compared to the deuterated analogues.
Consequently, desolvating the acyl chain along the reaction
coordinate will influence differently the ΔZPEs for the
deuterated and non-deuterated PA.
To assess whether differential changes in the vibrational
frequencies of PA, alone, during dissociation can account for
the magnitude of the inverse deuterium KIEs, the vibrational
frequencies of fully deuterated (D31), partially deuterated
(D3), and non-deuterated PA (D0) and the influence of solvent
thereon, were investigated computationally. The PCM
approach, which gives reasonable predictions of the change in
vibrational frequency upon solvation,50,51 was used to
approximate the dielectric properties of the Lg cavity (the
“solvent”), while neglecting any specific solute−“solvent”
interactions. The ZPEs of PA (D0), PA (D3), and PA (D31)
in the gas phase and in solvent were determined at the B3LYP/
6-311+G(d,p) and PBE0/6-311+G(d,p) levels of theory (Table
3). From these results, the change in ZPE (i.e., ΔZPE) in going
from the solvent, which is taken to approximate R, to the gas
phase, which approximates the late TS, was determined. From
these values, the difference in ΔZPE (i.e., ΔΔZPE) was
calculated. As seen in Table 3, the effects are very small
(ranging from ∼0.01 to 0.02 kcal mol−1 for D3 and from ∼0.1
to 0.2 kcal mol−1 for D31) and increase going from n-hexane to
water, i.e., with increasing dielectric constant. The ZPEs can be
corrected using known gas-phase scaling factors,52 but while
scaling changes the magnitude of the ΔZPE values, it does not
significantly impact the magnitude of the ΔΔZPE values (Table
S2). One can also consider the change in internal energies
(ΔEint), at 25 °C, in going from R to TS, and, more
importantly, the effects of isotopic substitution on this change
(ΔΔEint). As seen in Table S3, the ΔΔEint are similar in
magnitude to the calculated ΔΔZPE values. Incorporation of
frequency scaling (Table S4) or accounting for hindered
rotations (Table S5) results in a small increase in the ΔΔEint
values, up to 0.3 kcal mol−1.
Analysis of the vibrational frequencies calculated for PA
(D0), PA (D3), and PA (D31) in the gas phase and using the
IEF-PCM polarizable continuum model reveals small positive
ΔΔZPEs, which would result in an inverse KIE. However, the
magnitudes of the calculated ΔΔZPE values do not account
quantitatively for the observed KIEs and systematically
underestimate the ΔEaIE values. For example, at 25 °C, a
ΔΔZPE of 0.2 kcal mol−1 corresponds to a KIE of 0.71, which
is approximately 2 times “smaller” than the experimentally
determined KIEs for PA (D31), 0.42 (fast), and 0.36 (slow).
The discrepancies between the experimental and calculated
KIEs and ΔEaIEs can reasonably be attributed to the neglect of
the protein structure and the specific intermolecular
interactions (which are expected to be dominated by dipole−
induced dipole and dispersion forces) that stabilize the
complex, in the analysis. The increased conformational
flexibility of the acyl chain in the TS may also contribute to
the experimental KIEs and ΔEaIEs. In an effort to better
understand why the IEF-PCM approach underestimates the
magnitude of the measured KIEs, our laboratory is currently
applying DFT methods that take into account dispersion forces
to evaluate interactions between PA and the amino acids that
are located in the binding cavity of Lg.
The theoretical treatment of the vibrational frequencies of
PA (D0), PA (D3), and PA (D31) in the gas phase and using
the IEF-PCM polarizable continuum model, together with
transition state theory, does not account quantitatively for the
observed KIEs, nor the ΔIEaE values. However, the results of
this analysis do suggest that a reduction in the intermolecular
Lg−lipid interactions along the reaction coordinate leads to a
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differential change in the vibrational frequencies of the
deuterated and non-deuterated complexes and give rise to an
inverse KIE. It follows that the measurable KIE found for PA
(D3), in which only the methyl group is deuterated, together
with computational evidence of the collapse of the Lg cavity
upon removal of PA in the gas phase,14 is consistent with a late
dissociative TS, wherein the acyl chain is free of the cavity or
nearly so. It should be noted that this hypothesis is also
supported by the similarity in the Ea values determined for the
gaseous deprotonated (Lg + FA)7− ions composed of FAs with
different chain lengths and the enthalpies estimated for the
solvation of the acyl chain of the FAs by nonpolar or weakly
polar organic solvents.14
Absence of Deuterium KIEs in Solution. To our
knowledge, deuterium KIEs have not been previously reported
for the dissociation of protein−ligand complexes in solution.
Therefore, it was also of interest to test whether KIEs could be
detected for the dissociation of the (Lg + PA) complex in
aqueous solution. Dissociation rate constants were measured
for the (Lg + PA) complex, composed of PA (D31) at pH 8
and temperatures ranging from 5 to 32 °C, using SPR
spectroscopy, and these results were compared to kinetic data
reported previously for PA (D0). Plotted in Figure 2 are the
albumin (BSA) binding to long-chain FAs.53 From their
analysis of the entropies and activation entropies determined
for the dissociation of the (BSA + FA) complexes in water, they
concluded that the apolar chains of the FAs are similarly
hydrated in the TS and in aqueous solution.
CONCLUSIONS
■
In summary, deuterium KIEs for the dissociation of a protein−
ligand complex in the gas phase are reported for the first time.
Partial or complete deuteration of the acyl chain of PA results
in measurable inverse KIEs for the dissociation of gaseous,
deprotonated (Lg + PA)n− ions. The magnitude of the KIE is
temperature dependent, and Arrhenius analysis of the rate
constants reveals that deuteration results in a decrease in the
dissociation Ea. It is proposed that deuterium KIEs arise, at least
in part, from differential changes in the vibrational frequencies
of the deuterated and non-deuterated complex, resulting from
cleavage of the Lg−FA interactions, along the reaction
coordinate. Furthermore, observation of a measurable KIE
upon deuteration of only the methyl group of PA is consistent
with the hypothesis of a late dissociative TS, wherein the acyl
chain is close to being completely free of the binding pocket. In
contrast, there is no measurable deuterium KIE for the
dissociation of the (Lg + PA) complex in aqueous solution. It
is proposed that the dissociation of the hydrated complex also
proceeds through a late TS, in which the acyl chain is
extensively solvated by water such that there is no significant
change in vibrational frequencies along the reaction coordinate
and, consequently, no KIE.
ASSOCIATED CONTENT
■
S
* Supporting Information
Kinetic data for (Lg+PA)6− ions, computed geometries, ZPEs,
and internal energies. This information is available free of
charge via the Internet at http://pubs.acs.org.
AUTHOR INFORMATION
Corresponding Author
john.klassen@ualberta.ca
■
Figure 2. SPR kinetic plots and exponential fits for (Lg + PA) (filled
symbols) and (Lg + D31) (open symbols) at the temperatures
indicated.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
dissociation portions of SPR sensorgrams for the (Lg + PA)
complex composed of PA (D31) and PA (D0) versus time at
the temperatures indicated. Interestingly, there is no meas-
urable KIE at any of the temperatures investigated. Based on
the aforementioned arguments, these observations, on their
own, could be viewed as evidence of an early dissociative TS, in
which there is little change in the extent to which the ligand is
solvated by Lg. However, the alternative scenario, in which
dissociation proceeds through a late TS, is also plausible. If the
acyl chain is extensively hydrated in the TS, such that there is
no significant net change in vibrational frequencies along the
reaction coordinate, no KIE would be detected. Indeed, the
latter view of the dissociation mechanism is consistent with that
drawn in the recent comparison of the Ea values for the
dissociation of (Lg + FA) complexes in aqueous solution and
the corresponding gaseous deprotonated (Lg + FA)n− ions,
where n = 6 and 7, vide supra.13 This conclusion is also
supported by the findings of Bojesen and Bojesen, who
investigated the thermodynamics and kinetics of bovine serum
The authors are grateful for financial support provided by the
Natural Sciences and Engineering Research Council of Canada
and the Alberta Centre for Glycomics. A.B. thanks the
Canadian Foundation for Innovation (New Opportunities
Fund) for support for computational infrastructure. The
computational work has been (partially) enabled by use of
resources from Westgrid and Compute/Calcul Canada.
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