Charged states of proteins. Reactions of doubly protonated alkyldiamines with NH3: Solvation or deprotonation. Extension of two proton cases to multiply protonated globular proteins observed in the gas phase

Article abstract of DOI:10.1021/ja012591e

The apparent gas-phase basicities (GB^app'S) of basic sites in multiply protonated molecules, such as proteins, can be approximately predicted. An approach used by Williams and co-workers was to develop an equation for a diprotonated system, NH<

Full text of DOI:10.1021/ja012591e

Published on Web 08/31/2002
Charged States of Proteins. Reactions of Doubly Protonated
Alkyldiamines with NH3: Solvation or Deprotonation.
Extension of Two Proton Cases to Multiply Protonated
Globular Proteins Observed in the Gas Phase
Michael Peschke, Arthur Blades, and Paul Kebarle*
Contribution from the Department of Chemistry, UniVersity of Alberta,
Edmonton, Alberta, Canada T6G 2G2
Received November 26, 2001
Abstract: The apparent gas-phase basicities (GBapp’s) of basic sites in multiply protonated molecules, such
as proteins, can be approximately predicted. An approach used by Williams and co-workers was to develop
an equation for a diprotonated system, NH3(CH2)7NH32+, and then extend it with a summation of pairwise
interactions to multiply protonated systems. Experimental determinations of the rates of deprotonation of
NH3(CH2)7NH3 by a variety of bases B, in the present work, showed that GBapp ) GB(NH3) ) 196 kcal/
2+
2+
mol. This result is supported also by determinations of the equilibria: NH3(CH2)pNH3 + NH3 ) NH3-
(CH2)pNH3‚NH32+, for p ) 7, 8, 10, 12. The described experimental GBapp is 14 kcal/mol higher than the
value predicted by the equation used by Williams and co-workers but in agreement with an ab initio result
by Gronert. Equations based on electrostatics are developed for the two proton and multiproton systems
which allow the evaluation of GBapp of the basic sites on proteins. These are applied for the evaluation of
GBapp of the basic sites and of NSB, the maximum number of protons that the nondenatured proteins, carbonic
anhydrase (CAII), cytochrome c (CYC), and pepsin, can hold. The NSB values are compared with the
observed charges, Zobs’s, when the nondenatured proteins are produced by electrospray and found in
agreement with the proposal by de la Mora that Zobs is determined by the number of charges provided by
the droplet that contains the protein, according to the charge residue model (CRM). The GBapp values of
proteins have many other applications. They can be compared with experimental measurements and are
also needed for the understanding of the thermal denaturing of charged proteins and the thermal dissociation
of charged protein complexes.
was found3 to decompose predominantly to the tetramer and
monomer. The multiple charges present on the pentamer and
on the tetramer and monomer products were found to have a
significant effect on the activation energies of the decomposi-
tion.3 These results clearly demonstrate that it is very desirable
to understand the origin of the charges on the proteins formed
by ESI, know the positions on which the protons reside, and
have an understanding of the ability of the protons to migrate
to other basic groups, when the protein is heated to higher
temperatures including temperatures that will lead to thermal
decomposition. Such an understanding might allow the evalu-
ation of the Coulombic energy terms due to the charges.
Subtraction of the Coulombic energy terms from the observed
activation energy might then lead to energy values which are
representative of the bond energy of the complex due to
noncovalent bonds, which hold it together in solution.
I. Introduction
The mass spectrometric study (ESIMS) of nondenatured
proteins, protein-protein, and protein-substrate complexes
produced by electrospray ionization (ESI) is at present a most
active area of research,1 which is making important contributions
to biochemistry and biopharmacology (ref 1 represents only a
small sampling of early and recent publications). Some of these
studies attempt to correlate the noncovalent binding energy of
the complex in the biological environment with the binding
energy determined in the gas phase by mass spectrometric
techniques.
Examples of such recent and very interesting work are
experiments using the blackbody infrared radiative dissociation
(BIRD) technique to dissociate multiply protonated protein
complexes in an FTICR mass spectrometer.2,3 For example, the
multiply protonated protein pentamer of the Shiga-like toxin
The origin of the charges on the proteins can be understood
only from a consideration of the mechanism of electrospray.
Recent research4-11 on the mechanism of the generation of gas-
* To whom correspondence should be addressed. E-mail: Paul.Kebarle@
ualberta.ca.
(1) (a) Ganem, B.; Li, Y.; Henion, J. D. J. Am. Chem. Soc. 1991, 113, 6294.
(b) Ganem, B.; Li, Y. T.; Henion J. J. Am. Chem. Soc. 1991, 113, 7818.
(c) Katta, V.; Chait, B. T. J. Am. Chem. Soc. 1991, 113, 8534. (d) Schwartz,
B. S.; Light-Wahl, K. J.; Smith, R. D. J. Am. Soc. Mass Spectrom. 1994,
5, 201. (e) Light-Wahl, K. J.; Schwartz, B. L.; Smith, R. D. J. Am. Chem.
Soc. 1994, 116, 5277. (f) Lafitte, D. Eur. J. Biochem. 1999, 261, 337.
(2) (a) Price, W. D.; Schnier, P. D.; Jockbush, R. H.; Strittmacher, E. F.;
Williams, E. R. J. Am. Chem. Soc. 1996, 118, 10640. (b) Gross, B. S.;
Zhao, Y.; Williams, E. R. J. Am. Soc. Mass Spectrom. 1997, 8, 519.
(3) Felitsyn, N.; Kitova, E. N.; Klassen, J. S. Anal. Chem. 2001, 73, 4647.
9
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J. AM. CHEM. SOC. 2002, 124, 11519-11530
11519

A R T I C L E S
Peschke et al.
phase ions by the ESI method indicates that the small ions (such
as inorganic ions Na+, NH4+, and so forth, or organic ions such
as protonated organic bases BH+) are produced by the ion
evaporation model (IEM),4-7,9-11 while large macro ions and
typically the nondenatured globular (native) proteins are pro-
duced by the charge residue model (CRM).4,6,8
The most significant evidence that the multiply charged native
proteins are produced by CRM was provided by de la Mora.8
He showed that the experimentally observed number of charges,
Zobs, reported in the ESIMS literature was equal to ZCRM, which
is the charge at the surface of the precursor water droplets which
contain the protein when the evaporating droplet has just reached
the size of the protein. ZCRM can be evaluated with the Rayleigh
equation8 and a value R for the radius of the protein (see Figure
1 in de la Mora8 and Figure 2 and discussion in Felitsyn et
al.12).
to the mass spectrometer or in the CID stage because of ion
acceleration by the electric field applied between sampling
capillary and skimmer electrodes. Charge loss via process 2b,
driven by the Coulombic repulsion between the other charges
and the leaving charged group, can also occur:
(proteinDNH2-H-NH3)Z+
f
(proteinDNH2)(Z-1)+ + NH4 (2b)
+
Therefore, Zobs will not depend only on ZCRM but also on the
ability of the protein to hold the charge when processed through
the “desolvation” stage. This contingency was not considered
by de la Mora. The number of basic sites, NSB, of a given protein
that can hold protons in the gas phase, depends on the apparent
gas-phase basicities, GBapp’s, of the basic sites near the surface
of the protein.
Williams and co-workers in a series of papers13 were the first
to try to determine GBapp and NSB. Most of their work dealt
with denatured proteins; however, calculations were made also
for one globular protein (cytochrome c).13d The approach used
was to develop a relationship based on electrostatics for GBapp
of a diprotonated molecule and then generalize this relationship
to more than two charged groups. More recently, an insightful
analysis based on ab initio calculations for the two proton system
De la Mora8 did not discuss the chemistry of protonation,
that is, how exactly the charge at the surface of the disappearing
droplets is converted to charge of the proteins. Recent work
from this laboratory12 has provided evidence that when the
protein is sprayed from aqueous solution containing ammonium
+
acetate as the major electrolyte, the charging is due to NH4
ions. Ammonium containing buffer salts are the most frequently
used buffers for nondenatured proteins. (When buffers are not
used, the small electrolyte ions needed for electrospray must
be provided by the ionization of the basic and acidic side chains.
In that case, H3O+ ions are expected on the droplet surface.
These will be in excess to the negative counterions in the droplet,
and the charging will be due to the excess hydronium ions.)
As the last water evaporates, most of the ionized basic side
chains can be expected to become neutralized by reacting with
nearby counterions. Such a process will be fostered by prior
ion pairing, because of the increasing electrolyte concentration
NH3 + H3N(CH2)7NH32+ ) (NH3(CH2)7NH3‚NH3)2+
)
+
NH3(CH2)7NH2+ + NH4 (3)
was published by Gronert.14 This analysis predicts values for
GBapp that differ significantly from those obtained by Williams
et al.13 for the same system.
Because of the importance of the two proton system as a test
case, experimental measurements involving the alkyl diamines
2+
+
NH3(CH2)pNH3
produced by ES and their solvation or
in the evaporating droplets. In the last stage, the NH4 ions at
deprotonation by NH3 and other bases were performed (see
sections a and b in Results and Discussion). The experimental
results support Gronert’s analysis for the two charge case.
Therefore, improved equations based on electrostatics are
developed for the doubly and then multiply protonated proteins
(see sections c and d in Results and Discussion).
the surface of the droplet end up on the protein and can react
with the basic side chains at the surface of the protein. The
lowest energy products will be the proton-bridged adducts:
proteinDNH2 + NH4+ ) proteinDNH2-H-NH3
(1)
+
These equations are then used for the evaluation of GBapp
and NSB of three globular proteins: carbonic anhydrase,
cytochrome c, and pepsin. The NSB values obtained are
compared with the experimentally observed charges, Zobs, and
ZCRM, the predicted charges by CRM. This comparison provides
The side chain in eq 1 models lysine but could be also any
other basic side chain. Equation 1 indicates only the first
+
attachment of an NH4+. However, there are many more NH4
ions available such that ultimately ZCRM ammonium ions can
become attached to different basic side chains at the surface of
the protein. A complete proton transfer leading to protonation
of the side chain
an answer to the following question: Which determines Zobs
?
Is it ZCRM or NSB? (See section e in Results and Discussion.)
The significance of the calculations predicting GBapp goes
much beyond the answers concerning the mechanism leading
to the observed charges on the proteins. The GBapp values can
also be determined experimentally15 (see section IIIf, in Results
and Discussion).
proteinDNH2-H-NH3+ f proteinDNH3+ + NH3 (2a)
occurs later in the “desolvation” stage in the sampling system,
either in the heated (100-200 °C) sampling capillary leading
The reactions 2a,b represent also the simplest prototype for
the dissociation of protein-substrate complexes. Therefore, the
(4) Kebarle, P.; Ho, Y. In Electrospray Ionization Mass Spectrometry; Cole,
R. B., Ed.; John Wiley & Sons: New York, 1997; p 55.
(5) Kebarle, P.; Peschke, M. Anal. Chim. Acta 2000, 406, 11.
(6) Cole, R. B. J. Mass Spectrom. 2000, 35, 763.
(7) Gamero-Castano, M.; de la Mora, J. F. Anal. Chim. Acta 2000, 406, 67.
(8) de la Mora, J. F. Anal. Chim. Acta. 2000, 406, 93.
(9) Labowsky, M.; Fenn, J. B.; de la Mora, J. F. Anal. Chim. Acta. 2000, 406,
105.
(10) Gamero-Castano, M.; de la Mora, J. F. J. Mass Spectrom. 2000, 35, 780.
(11) Kebarle, P. J. Mass Spectrom. 2000, 35, 804.
(12) Felitsyn, N.; Peschke, M.; Kebarle, P. Int. J. Mass Spectrom. 2002, 219(1),
39.
(13) (a) Gross, D. S.; Rodriguez-Cruz, S. E.; Bock, S.; Williams, E. R. J. Phys.
Chem. 1995, 99, 4034. (b) Gross, D. S.; Williams, E. R. J. Am. Chem.
Soc. 1995, 117, 883. (c) Schnier, P. D.; Gross, D. S.; Williams, E. R. J.
Am. Chem. Soc. 1995, 117, 6747. (d) Schnier, P. D.; Gross, D. S.; Williams,
E. R. J. Am. Soc. Mass Spectrom. 1995, 6, 1086. (e) Williams, E. R. J.
Mass Spectrom. 1996, 31, 831.
(14) (a) Gronert, S. J. Am. Chem. Soc. 1998, 118, 3525. (b) Gronert, S. J. Mass
Spectrom. 1999, 34, 787. (c) Gronert, S. Int. J. Mass Spectrom. 1999, 185/
186/187, 351.
9
11520 J. AM. CHEM. SOC. VOL. 124, NO. 38, 2002

Charged States of Proteins
A R T I C L E S
2+
Table 1. Thermochemical Dataa for NH3(CH2)pNH3‚NH3
)
2+
NH3(CH2)pNH3 + NH3
p
∆H °
1,0
∆G °
1,0
∆S °
1,p
10
12
20.3
19.5
13.1
12.7
24.3
22.6
a Energy values in kcal/mol. Entropy in cal/(degree‚mol). Standard state
1 atm. ∆G1,0° value at T ) 298 K.
equations developed for the evaluation of the activation energies
of these two reactions can be of significance to the development
of equations for the protein-substrate complexes. The thermal
denaturing of a multiply protonated native protein16 is at least
partially driven by the Coulombic repulsions between the
charges and represents another related area to which the GBapp
values are of significance.
II. Experimental Section
The experimental measurements relating to reaction 3 involving NH3-
(CH2)pNH32+ and NH3 were performed with a reaction chamber sampled
by a quadrupole mass spectrometer which has been described.17 The
same apparatus was used previously for determination of the hydration
equilibria.17
2+
Figure 1. Results shown are for deprotonation reaction BH2 + A )
BH+ + AH+, where BH2 ) NH3(CH2)7NH32+. Logarithmic plot of ion
2+
intensity of BH2+, observed when a constant concentration of base A is
present. Results are from several experiments with different [A] including
[A] ) 0. b ) NH3, 2 ) CH3NH2.
NH3(CH2)pNH32+ + H2O ) (NH3(CH2)pNH3‚H2O)2+ (4)
2+
The reagent ion, NH3(CH2)pNH3 (p ) 5-12), was produced by
electrospray, and the equilibria in eq 4 were determined by introducing
these ions into the reaction chamber which contained also 10 Torr of
N2 as bath gas and known low partial pressures (1-100 mTorr) of
H2O. The intensities of the ionic products of the equilibria were
determined with a quadrupole mass spectrometer.
Very similar techniques were used in the present work for the
determination of solvation equilibria involving the diprotonated di-
amines and NH3. The data obtained are presented in the Results and
Discussion section (Table 1, Figures 2 and 3). However, for these
systems, the reaction can involve not only solvation but also deproto-
nation by NH3, particularly so for p e 7, see eq 3. Therefore, it was
desirable also to determine the rates of deprotonation.
In the apparatus used,17 the reactant ion, when inside the reaction
chamber, is exposed to a weak drift field by applying a small voltage
Vd between the ion entrance orifice IN and the ion exit orifice OR (see
Figure 1 in Blades et al.17). This drift field and the pressure of the bath
gas N2 control the drift velocity and, thus, also the reaction time, t.
The value of the drift voltage Vd is low so that the drifting ions have
thermal internal energies. The drift times of the ions in the reaction
chamber are in the 100-1000 µs range depending on the value of the
drift field.
Figure 2. Plot of ion intensity ratio for ions BH22+‚NH3 and BH2+, where
BH2 ) NH3(CH2)12NH32+, versus pressure of ammonia. Linearity of plot
which goes through the origin meets equilibrium conditions, eq 12.
2+
[BH2
]A is the ion concentration after time t, that is, at the exit of the
reaction chamber, when a constant concentration [A] is present in the
reactor. [BH22+]0 is the concentration after time t, when [A] ) 0. The
ion concentration ratio in eq 6 is replaced with the corresponding ion
intensity ratio I(BH22+)A/I(BH22+)0, observed with the mass spectrom-
eter.
Relative rate constants for a given protonated ion, such as a given
doubly protonated diamine, BH22+, and different neutral bases, A, can
be determined by working at constant drift voltage Vd, which leads to
Determinations with a range of constant concentrations [A], at
constant drift field, that is, constant t, lead to plots such as those shown
in Figure 1, for BH22+ ) NH3(CH2)7NH32+ and the two bases A, equal
to NH3 and CH3NH2. The plots are linear as expected from eq 6, and
the slopes give the values for kt for each base A. The value of t is
constant, because the same reagent ion is involved. Therefore, the slopes
provide the relative values for the proton-transfer rate constants. Values
of kt obtained for several bases are tabulated in the Results and
Discussion section, see Table 2.
2+
a constant drift and reaction time t when the same reagent BH2 ion
is involved. For the proton-transfer reaction eq 5, eq 6 is used.
BH22+ + A ) BH+ + AH+
(5)
(6)
ln([BH22+]A/[BH22+]0) ) kt[A]
(15) (a) Cassady, C. J.; Carr, S. J. Mass Spectrom. 1996, 31, 247. (b) Cassady,
C. J.; Wronka, J.; Kruppa, G. H.; Laukien, F. H. Rapid Commun. Mass
Spectrom. 1994, 8, 394. (c) Ogorzalek Loo, R. R.; Winger, B. E.; Smith,
R. D. J. Am. Soc. Mass Spectrom. 1994, 5, 1064. (d) Ogorzalek Loo, R.
R.; Smith, R. D. J. Mass Spectrom. 1995, 30, 339. (e) McLuckey, S. A.;
Glish, G. L.; van Berkel, G. J. Anal. Chem. 1991, 63, 1971.
(16) Mao, Y.; Ratner, M. A.; Jarrold, M. F. J. Phys. Chem. B 1999, 103, 10017.
(17) Blades, A. T.; Klassen, J. S.; Kebarle, P. J. Am. Chem. Soc. 1996, 118,
12437.
2+
Equation 6 is obeyed even though there is also loss of the BH2
ion, by diffusion to the wall followed by discharge of the ion. Such a
loss is indicated by the observation that I(BH22+)0 decreases when t is
increased by lowering Vd. It can be readily derived that eq 6 will hold,
if the ion loss by other parallel reactions is first order in the ion
concentration. First order ion loss can be expected in the present
9
J. AM. CHEM. SOC. VOL. 124, NO. 38, 2002 11521

A R T I C L E S
Peschke et al.
The value, kt ) 3.6 × 10-13 cm3/molecule, was obtained with Vd ) 5
V, T ) 418 K. Because the gas-phase basicity GB(TEA) is very much
higher than GB(n-C4H9NH2), this reaction is expected to proceed at
collision rates. Using the polarizability R ) 13 A3 and dipole moment
µ ) 1 D for TEA, one obtains the following collision rates:18 kc )
1.28 × 10-9 cm3 molecule-1 s-1 (Langevin) and 1.30 × 10-9 cm3
molecule-1 s-1 (ADO) for reaction 11, at 420 K. Combined with kt )
3.6 × 10-13 cm3 molecule-1, this leads to a time t ) 277 µs (Vd ) 5
V).
All the rate data with BH22+ were also obtained at Vd ) 5 V. The t
) 277 µs value obtained for C4H9NH3+ can be used for rough estimates
2+
of the rate constants, k, of the BH2 ions, from the corresponding kt
data, on the basis of mobility determinations19 of singly and doubly
charged ions. See footnotes in Table 2.
III. Results and Discussion
(a) Diprotonated Diamines: Solvation and Deprotonation
by NH3. Thermochemical Results. The equilibrium constants
K for the solvation of diprotonated diamines by NH3
Figure 3. Plot of free energy values, ∆G1,0°, for the following reactions:
(NH3(CH2)pNH3‚NH3)2+ ) NH3(CH2)pNH32+ + NH3 (b) and ((NH3CH2)p-
2+
NH3‚H2O)2+ ) NH3(CH2)pNH3 + H2O ([) for various values of p.
Results for NH3 are from the present work, results for H2O, from previous
work.17 Temperature ) 283 K. Sudden drop off for value for p ) 7 (NH3)
indicates anomalous result, leading only to an apparent equilibrium. The
true equilibrium could not be determined because of rapid deprotonation
of the doubly protonated ions by NH3.
NH3(CH2)pNH32+ + NH3 ) NH3(CH2)pNH3‚NH3
(0,1)
(8a)
2+
were determined for p ) 7, 8, 10, 12.
Table 2. Reaction Rate Constantsa
Shown in Figure 2 is a plot of the equilibrium condition (eq
8b):
NH3(CH2)7NH32+ + A ) NH3(CH2)7NH2+ + AH+
3 c
A
GB (A)b R (A )
ktd
ke
kcf
NH3
pyrrole
aniline
CH3NH2
n-C3H7NH2
196
201.8
2.2
4 × 10-13 2.8 × 10-9
1.8 × 10-9
2.1 × 10-9
2.4 × 10-9
1.9 × 10-9
2.0 × 10-9
2.0 × 10-9
2.2 × 10-9
2+
[BH2‚NH3
]
9.3 9.2 × 10-13 6.6 × 10-9
K0,1
)
(8b)
(8c)
203.5 (14.0) 9.1 × 10-13 6.6 × 10-9
[BH22+][NH3]
206.8
211.5
(4.2) 8.0 × 10-13 5.8 × 10-9
(8.1) 8.2 × 10-13 6.0 × 10-9
(8.1) 8.1 × 10-13 6.0 × 10-9
∆G0,1° ) RT ln K0,1
iso-C3H7NH2 212.7
(C2H5)3N
227.5 (13.0) 8.2 × 10-13 6.0 × 10-9
where BH2 stands for the diprotonated diamine. The plot which
is for p ) 12 shows that the ratio [BH2‚NH32+]/[BH2
(2) n-C4H9NH3+ + (C2H5)3N ) n-C4H4NH2 + (C2H5)2NH+
2+
3.6 × 10-13 1.3 × 10-9 g
]
increases linearly with the pressure (concentration) of NH3 and
goes through the origin as required by eq 8b. Similar plots were
obtained also for p ) 8, 10, 12. For p ) 7, the plot was less
satisfactory. An approximately linear relationship was observed
but only at very low NH3 pressures (p < 0.5 Torr). The p ) 7
case is special as will be discussed.
Free energy values ∆G1,0° for p ) 7, 8, 10, 12 were obtained
with eq 8c. (Note: ∆G0,1° ) -∆G1,0°.) A sufficiently wide
range of temperatures required to obtain reliable values also
for ∆H1,0° and ∆S1,0° could be achieved only for p ) 10 and
12. The thermodynamic data obtained are summarized in Table
1.
Free energy values ∆G1,0° at an intermediate temperature,
382 K, are shown in Figure 3. Also given in this figure are the
free energy values for the hydration reaction eq 4 obtained in
previous work.17 The binding free energies ∆G1,0° for NH3 are
seen to be about 3 kcal/mol higher than those for H2O. This is
an expected change because the hydrogen bonding is known to
increase with increasing basicity of the proton accepting base,20
and NH3 is a much stronger base than H2O.
The free energy values are seen also to increase as the length
of the (CH2)p chain is decreased. This trend is clearly observed
for the hydrates and was attributed17 to the increasing effect of
the second charge. This charge exerts a polarizing effect on the
a Bath gas N2 at 10 Torr. Temperature ≈ 402 K. All measurements
obtained with drift voltage 5 V. b Gas-phase basicities in kcal/mol. From
Lias and Hunter.21 c Polarizabilities of bases A in (Å)3. From: Miller, K.
J. J. Am. Chem. Soc. 1990, 112, 8543. Values given in parentheses were
estimated with additivity rules. d Experimentally determined product of rate
constant k and ion drift time ) reaction time, t, from plots such as in Figure
1 and eq 10. Units are cm3‚molecule-1. Time t is the same for all reactions.
e Reaction rate constants, cm3‚molecules-1‚s-1. These are rough estimated
values based on a reaction time t ) 140 µs. This time was estimated on the
basis of the time for reaction 2. This reaction is expected to proceed at
collision rates kc ) kADO ) 1.3 × 10-9 cm3‚molecule-1‚s-1. Using kt ) 3
× 10-16 cm3‚molecule-1, one obtains t ) 280 µs. The mobility of the
NH3(CH2)7NH32+ ion is expected to be roughly twice that of the butylam-
monium ion.19 f Rough estimates of collision limit rate constants, evaluated
with the Langevin expression kL ) 2πe(R/µ)1/2 (for singly charged ions)
where e ) charge of electron, R is the polarizability of A, and µ is the
reduced mass of the colliding pair of reactant molecules. kc ) 2kL was
assumed, treating NH3(CH2)7NH32+ as two singly charged reaction centers.
Results illustrate that the collision rates do not change significantly for the
different neutral reactants. g k ) kc.
apparatus, because the ion concentration is extremely low, so that space
charge effects are negligible. Experimental proof that the ion loss is
first order is given by the fact that eq 6 is obeyed. Additional evidence
was obtained by determining kt for two different bases A, such as
triethylamine (TEA) and NH3, by plots such as those shown in Figure
1. The experiments were then repeated for three different times t
(by using Vd values of 10, 5, and 3 V). It was found that the ratio
k
TEA/kNH , obtained from the kt values, remained the same.
3
Reaction rates involving singly charged ions were also studied. Of
interest was the following reaction:
(18) Su, T.; Bowers, M. J. Int. J. Mass Spectrom. Ion Phys. 1975, 7, 211.
(19) Wu, C.; Siems, W. F.; Klasmaier, J.; Hill, H. H. Anal. Chem. 2000, 72,
391.
(20) Davidson, W. R.; Sunner, J.; Kebarle, P. J. Am. Chem. Soc. 1979, 101,
n-C4H9NH3+ + TEA ) n-C4H9NH2 + TEAH+
(7)
1675.
9
11522 J. AM. CHEM. SOC. VOL. 124, NO. 38, 2002

Charged States of Proteins
A R T I C L E S
Figure 4. Potential energy surface obtained by ab initio calculations by
Gronert14a for the following reaction: NH3(CH2)7NH3
+ NH3 )
2+
Figure 5. Potential energy diagrams and reactions associated with derived
eqs 17-20. The highest maximum for the deprotonation reaction energy
(lower right, curve) corresponds to only EPOL being considered in eq 17.
The next lowest curve corresponds to only EDIP being included, and lowest,
to both EPOL and EDIP being included. Energy scale on left side for upper
plot; right side, lower plot.
NH3(CH2)7NH2 + NH4+, where I in the figure is the doubly charged
diamine, while II is the singly charged diamine in its extended linear
configuration. EDS and EDP are the transition state energies for desolvation
and deprotonation.
+
+
(CH2)pNH3 group, making the N-H hydrogens more protic
and thus more strongly hydrogen bonding. A similar effect is
observed also with NH3 as ligand. However, the free energy
value for p ) 7 does not fit the trend, being much lower than
expected.
The potential energy diagram for the reaction of the p ) 7
diprotonated diamine with NH3, obtained by Gronert14 from ab
initio calculations, is shown in Figure 4. The exit channel to
the right, which leads to deprotonation by NH3, has an activation
energy, EDP°, which is lower than the activation energy, EDS°,
for the channel to the left, which leads to desolvation:
are sufficiently long-lived to be collisionally stabilized by the
third gas molecule. Some of the collisionally stabilized com-
plexes, BH2‚NH32+, on thermal activation are expected to
decompose via the irreversible DP channel. The rapid irrevers-
ible loss by deprotonation leads to a low concentration of
2+
observed BH2NH3 and a low apparent ∆G1,0°.
(b) Diprotonated Diamines. Desolvation or Deprotonation.
Results Based on Reaction Kinetics. As detailed in the
Experimental Section, values for the product, kt, of the rate
constant k and the time t that the reactant ion spends in the ion
source, can be determined with the present apparatus. The time
t is constant when the same reactant ion is involved.
(EDS° - EDP°) ≈ 4.6 (kcal/mol) (Gronert)
(9a)
Values for kt, obtained from plots such as that shown in
Figure 1, for the NH3(CH2)pNH32+ ion (BH22+, p ) 7) reacting
with different bases A at a constant Vd ) 5 V, are given in
Table 2 together with the gas-phase basicities, GB(A)’s, of the
bases A. For all kt values given in Table 2, the only ionic product
observed was that due to the deprotonation reaction; that is, no
significant concentrations of stabilized adducts were present.
All bases A which have a GB higher than that of NH3, GB-
(NH3) ) 196 kcal/mol, lead to a kt which is approximately
equal, kt ) (8.6 ( 0.5) × 10-13 cm3 molecule-1. Such behavior
is expected only when the GB(A) values are well above the
GBapp of BH+, where the rate constants k become equal to the
collision rate constants kc. The kt for NH3 is about half as big
as that for the other bases. This indicates that the GBapp is equal
to GB(NH3):
Thus, on the basis of these results, which correspond to the
internal energy at 0 K, deprotonation is expected to dominate.
For a more accurate prediction of the relative rates, one needs
the free energies of activation, ∆G‡DP and ∆GD‡ S. Ab initio
calculations of ∆G‡DP can be expected to be very difficult. A
qualitative estimate suggests that ∆S‡DS > ∆SD‡ P. The transition
state DS occurs at very large distances, (R1 - R2) ≈ -15 Å, of
the reactants (Figure 4). Both reactants will have three free
external rotations each. The DP transition state occurs at a much
shorter distance, R1 - R2 ≈ 5 Å, where bonding between the
reactants leads to a lowering of the energy. The bonding is
+
largely due to attractive interactions between the ion (NH4
)
and the dipole of the alkylamine group (see Figure 5 and its
discussion in section c). This bonding leads to loose rocking
vibrations whose entropy is lower than that of the free external
rotations that they replace. The entropy difference ∆SD‡ S
-
GBapp (NH3(CH2)7NH2+) ≈ GB(NH3) ) 196 kcal/mol (10)
∆S‡DP could be as large as 10 cal/deg mol, or even larger. This
would lead to T∆S differences of some 3-5 kcal/mol:
This is in good agreement with the result based on Gronert’s
calculations and entropy estimates which lead to GBapp ≈ 196
kcal/mol (see eq 9b).
∆S‡DS - ∆S‡DP ≈ 10 cal/deg‚mol
Attempts to determine the rates for proton transfer from
BH22+, p ) 7, to bases A whose GB(A) < GB(NH3), were not
successful. The available bases A in this range are ketones, such
as acetone, methyl-ethyl ketone, and methyl-propyl ketone.
These bases led to dominant formation of the (0,1) adducts,
BH22+‚A. Evidently, the much larger number of degrees
of freedom in the collision complexes (BH2A)2+, relative to
(BH2NH3)2+, led to longer lifetimes and thus more efficient
T(∆S‡DS - ∆S‡DP) ≈ 4 kcal/mol T ) 420 K
(9b)
The observed anomalous, low value for ∆G1,0° of BH22+, p
) 7, in Figure 3 must be a consequence of the rapid
2+
disappearance of BH2‚NH3 by deprotonation, which is an
irreversible reaction. The fact that some BH2NH32+ product was
observed means that some collision complexes (BH2‚NH32+)*
9
J. AM. CHEM. SOC. VOL. 124, NO. 38, 2002 11523

A R T I C L E S
Peschke et al.
collisional stabilization of the excited (BH2A)2+. Furthermore,
the lower basicity of these bases A is also expected to lead to
a longer lifetime of the collision complexes and thus also favor
the stabilization of the complexes.
Williams and co-workers,13 using an FTICR instrument, have
also made determinations for the diprotonated diamines. The
most extensive rate measurements were made for the p ) 7
isomer.13a On the basis of such measurements, they chose the
value
only to illustrate the model. The lower potential energy curve
is for the reaction of interest:
NH3(CH2)7NH32+ + NH3 ) (NH3(CH2)7NH3‚NH3)2+
)
+
NH3(CH2)7NH2+ + NH4 (14)
Calling the distance between the two N atoms on each side
of the proton RNN, we note that for large absolute values of (R1
- R2), in Figure 4, RNN is close to equal to the absolute value
of (R1 - R2). The energy at the two end points of eq 14 relative
to the zero level, see Figure 5, can be readily obtained. The
end point on the right side of the diagram
GBapp(BH+, p ) 7) ≈ 182 kcal/mol13a
(11)
This is 14 kcal/mol lower than the value obtained from the
kinetics determinations, eq 10, and the value expected from
Gronert’s results16 (see Figure 4), which, with the reasonable
assumptions about the entropies of activation (see eq 9b),
indicates that GBapp should be close to GB(NH3) ) 196 kcal/
mol.21 The value of 182 kcal/mol was obtained13a by choosing
bases A which led to rate constants k ≈ 0.02kc, a choice that is
too far removed from the condition k ) 0.5kc.
R1 ) ∞ RNN ) ∞
corresponds to the energy change for the reaction
(NH3(CH2)7NH2)+ + NH3 + H+ )
(NH3(CH2)7NH2)+ + NH4 (15)
+
2+
(c) Generalization of Results for NH3(CH2)7NH3 to
E15 ) PA(NH2(CH2)7NH2) - PA(NH3) -
Other Linear Diprotonated Ions and Polyprotonated Pro-
teins. It is desirable to develop general and relatively simple
methods with which the apparent gas-phase basicities of
diamines with p other than p ) 7, and other linear diprotonated
systems, can be calculated and then to extend these to polypro-
tonated proteins.
Williams and co-workers, in a pioneering series of papers13
involving both experimental and theoretical work, proposed the
relationships
PA(NH2(CH2)7NH2)
E15 ) -PA(NH3)
For the left side of the diagram
R2 ) ∞ RNN ) ∞
the energy corresponds to the energy change for the reaction
NH2(CH2)7NH3+ + NH3 + H+ ) NH3(CH2)7NH32+ + NH3
q2
4πꢀ0ꢀrr
app
GBsp ≈ GBint
-
(12a)
(12b)
E16 ) -PA(NH2(CH2)7NH3)+
(16a)
q2
i)1 4πꢀ0ꢀrri,j
i)n
GBsp,japp ≈ GBint,j -
E16 ) -PA(NH2(CH2)7NH2) + EREP + ECD (16b)
∑
The equality between eqs 16a and 16b was proposed by
Gronert.14c The coulomb repulsion energy term EREP
Here, sp stands for the site of protonation, q is the elementary
charge, ꢀ0 is the permittivity in a vacuum, and ꢀr is the relative
permittivity of the medium in which the charges interact. The
distance between the charges is r. Equation 12a is for two
charges while 12b applies to multiple charges with distances
ri,j between the sites of protonation. GBint stands for the
(intrinsic) basicities of the sites of protonation, in the absence
of all charges.
The evaluation of the apparent proton affinity PAapp, which
corresponds to the proton affinity of the base that leads to the
condition EDP ) EDS, does not require a complete knowledge
of the potential energy surface; only the energies of activation,
EDS and EDP, are needed (see Figure 4). These energies are in
regions where the bonding and repulsive forces can be evaluated
by electrostatic equations. The approach used is illustrated in
Figure 5. The upper curve gives the energy changes for the
proton transfer in the singly protonated system.
q2
4πꢀ0r
EREP
)
makes the major contribution. For r ) 10 Å, which corresponds
to the distance between the two N atoms in (NH3(CH2)7NH3)2+
,
EREP ) 33 kcal/mol. ECD is a smaller correction and is due to
a charge delocalization caused by the presence of the two
charges. ECD ≈ 7 kcal/mol was obtained14c by a comparison
with the ab initio results.14a Gronert did not consider in detail
the actual charge distribution leading to the term ECD. The
charge distribution becomes even more relevant in the presence
of more than two charges. Therefore, an analysis of the causes
for this term is given in section d.
E16 provides a value for the desolvation energy EDS relative
to the zero level used in Figure 5. At values R1 - R2 > 5 Å,
the reaction complex consists essentially of +NH3(CH2)7NH2
and NH4+, and the energy due to the attractive interactions
between these reactants can be approximated by the electrostatic
bond energy between a charge located on the N atom of the
H+ + NH2(CH2)7NH3+ + NH3 )
H+ + (NH2(CH2)7NH3‚NH3)+ )
H+ + NH2(CH2)7NH2 + NH4 (13)
+
+
NH4 nitrogen and a dipole µ and polarizability R located on
This potential energy curve needs not to be known and is used
(21) Hunter, E. P.; Lias, S. G. J. Phys. Chem. Ref. Data 1998, 27, 3.
9
11524 J. AM. CHEM. SOC. VOL. 124, NO. 38, 2002

Charged States of Proteins
A R T I C L E S
the neutral amino group of the +NH3(CH2)7NH2 reactant. The
distance between the two N atoms is RNN. Inclusion of this bond
energy leads to
Scheme 1
Scheme 2
R1 - R2 > 5 Å (R1 - R2) ≈ RNN
E17 ) -PA(NH3) + EREP(r + RNN) + EPOL(RNN) +
EDIP(RNN) (17)
had qualitatively deduced (see Figures 2 and 3)13c a shape of
the potential surface somewhat similar to that obtained in
Gronert’s work14a and Figure 5. However, they made the
assumption that the much simpler eq 12a is sufficiently accurate
for the purpose at hand.
The equation for polyprotonated proteins is obtained with eq
20, in a manner analogous to the approach used to obtain eq
12b from eq 12a. This leads to
where EREP(r + RNN) represents the Coulombic repulsion energy
+
between the charges on +H3N(CH2)7NH3 and NH4
q2
E
REP(r + RNN) )
(18)
4πꢀ0(RNN + r)
+
and EPOL + EDIP are the energies due to the charge on NH4
and the polarizability and dipole on the NH2 group of the
protonated diamine.
GBaj pp ) GBint,j + EDIP,j(RNN,jmax) + EPOL,j(RNN,jmax) +
The curve shown on the lower right side of Figure 5 was
obtained with eq 17. The dipole moment used, µ ) 1.3 D, to
model the dipole on the C-NH2 group on the diamine
corresponds to the literature value for the dipole of CH3NH2.
This dipole was assumed to be located on the N atom, because
most of the dipole is due to the NH2 group, as evident from the
value of µ ) 1.4 for NH3. The polarizability used for the
C-NH2 group, R ) 4 × 10-24 cm3, corresponds to the literature
value for CH3NH2. The polarizability was located in the middle
of the C-N bond, because the CH3 group makes a substantial
contribution to the total polarizability.
q2
z-1
z
T(∆Sj‡DS, - ∆Sj‡DP,) -
E
i j -
+
∫
∫
CD ,
i)1
i)1 4πꢀ0ri,j
q2
z
(21)
∫
i)1 4πꢀ0(ri,j + RNN,jmax)
(d) Use of ab Initio Calculations Involving a Positive Point
Charge for the Analysis and Evaluation of the Charge
Delocalization Terms ECDi,j and ∑ECDi,j as well as RNNmax.
For the p ) 7 alkyldiamine, the correction term ECD ) 7 kcal/
mol was needed. The correction depends also on the distances
between the charges (see Gronert14c where that correction is
included via an ꢀr ) 0.82 in the electronic repulsion term). This
correction cannot be applied directly when more than two
charges are present. A more detailed examination of the two
charge case proves useful.
EDS - EDP ) E17 - E16 ) PA(NH3) -
PA(NH2(CH2)7NH2) + EREP + ECD - EREP(r + RNNmax) -
EPOL(RNNmax) - EDIP(RNNmax) (19)
PAapp is obtained from eq 19 by setting EDS ) EDP. The PA of
the neutral base, that can either deprotonate or desolvate, is equal
to PAapp. Setting PA(NH3) ) PAapp(NH3(CH2)7NH2+) and
approximately converting the equation into a free energy
relationship by replacing the PA with the GB values and
including a T(∆S‡DS - ∆SD‡ P) term, one obtains the final,
general equation for a diprotonated molecule:
The ECD term should be mostly due to a destabilization whose
origin is illustrated by Scheme 1.
The two dipoles, induced by the two proton charges, cause a
destabilization, mainly because of repulsion between the charge
on the one nitrogen and the opposing dipole near the other
nitrogen. Such ion-dipole interactions act at relatively long
distances.
q2
4πꢀ0r
q2
The validity of this model was explored on the basis of ab
initio calculated energies (see Appendix I) for the system shown
in Scheme 2, involving a protonated n-butylamine and a x point
charge. The butyl group was chosen to represent the molecular
environment near one of the charges (that due to the protona-
tion).
GBapp ) GBint
-
+
+
4πꢀ0(RNNmax + r)
EDIP(RNNmax) + EPOL(RNNmax) + -ECD
+
T(∆S‡DS - ∆S‡DP) (20)
Using GBint ) GB(NH2(CH2)7NH2) ) 214 kcal/mol,22
T(∆S‡DS - ∆SD‡ P) ) 4 kcal/mol (at ∼420 K) (see eq 9b), and
ECD ) 7 kcal/mol, the result, GBapp(NH3(CH2)7NH2+) ≈ 196,
is obtained with eq 20 (for values of RNNmax, see Figure 5), in
complete agreement with the value of the experimental deter-
minations (see Table 2 and eq 8).
Both the distance r between the charges and the angle R
relative to the N-C bond were varied. The results are given in
Table 3. The ab initio evaluated energy, ∆E(ab initio) )
E(x‚‚‚C4H9NH3+) - E(C4H9NH3+), was found to be greater
than the charge repulsion coulomb energy, EREP ) q2/(4πꢀ0r),
at constant r ) 10 Å for all angles R where the (presumed)
+
induced dipole by the NH3 group was opposing the point
Only the first two terms in eq 20 are the same as those of eq
12a, which is from Williams and co-workers. These authors
charge. The maximum of ∆E(ab initio) - ECR was found for R
) 21.5°, indicating that the polarizability of the N-C-C region
is the major contributor to the induced dipole. The directly
opposing position at R ≈ 201.5° leads to a negative value (see
Table 3), whose absolute value is somewhat smaller than that
for R ) 21.5°, because the induced dipole is now somewhat
(22) GBintr ≈ GB(H2N(CH2)7NH2), obtained from experimental GB determina-
tions, is not available, because cyclization of the (singly) protonated diamine
by intramolecular strong hydrogen bonding leads to higher values for GB
and PA, see Yamdagni and Kebarle.23 The value of GBint ) 214 kcal/mol
is based on GB values for CnH2n+1NH2, compounds for n ) 4-8 available
in Hunter and Lias.21
9
J. AM. CHEM. SOC. VOL. 124, NO. 38, 2002 11525

A R T I C L E S
Peschke et al.
Table 3. Results from Positive Point Charge Calculations for
Evaluation of ECD
b
distance and anglea
(∆E(ab initio) − EREP
)
∆E(dipole model)c
10 Å; 10°
2.70
2.90
2.70
-0.59
-1.60
-0.50
1.80
2.84
2.95
2.85
-0.31
-1.59
-0.31
1.69
10 Å; 21.5°d
10 Å; 33° (p ) 7)e
10 Å; 111.5°
10 Å; 201.5°
10 Å; 291.5°
12.7 Å; 33° (p ) 9)e
15.2 Å; 33° (p ) 11)e
1.20
1.12
a Butylamine with a point charge at the indicated distance from the
nitrogen atom and angle with respect to the N-C bond. See Scheme 2 and
text following Scheme 2. b Relative energies in kcal/mol at the B3LYP/6-
311++G(d,p) level without zero point correction minus Coulombic
repulsion using the point charge-nitrogen distance. c Ion dipole model fitted
to computed values using an induced dipole with strength µ ) 3.11 D at a
distance of 1.54 Å from the inducing charge on the nitrogen. The point
charge, however, would experience it primarily as a permanent dipole
because of its longer distance. For these values, a dipole axis was used that
is 21.5° to the N-C bond. d The angle of the dipole axis was evaluated
with several additional bracketing calculations (not shown). e The placement
of the point charge corresponds to the position of the second nitrogen in
Figure 6. Potential energy surfaces from ab initio calculations for the model
system NH3(CH2)pNH2+, p ) 7, 8, 10, 12, interacting with NH4+. NH3-
+
(CH2)pNH2 was modeled using methylamine and a point charge at the
distance where the protonated nitrogen would be. Only a single point is
given for EDS, at RNN ) -8. The maxima of the curves shown correspond
to EDP
.
2+
NH3(CH2)pNH3 (p ) 7, 9, 11).
farther away from the charge. The value is negative because
now an attraction between the dipole and the charge is present.
The ∆E(ab initio) - EREP values at r ) 10 Å could be
reproduced by an induced dipole with magnitude µ ) 3.11 D
located at a distance of 1.54 Å from the nitrogen with the
inducing charge (see electrostatic values ∆E (dipole model) in
Table 3). For this distance, the induced dipole corresponds to a
polarizability of 1.5 Å3. This is a physically realistic value,
because the polarizability of a C atom is of a similar magnitude,
if one considers that the polarizability values in the literature
are valid only for much larger distances between the inducing
charge and the polarizable medium.
The angle R ) 33° when the x charge would be aligned
with the two nitrogens in a NH2(CH2)NH3+ molecule. The value
of ∆E(dipole model) ) 2.7 kcal/mol for this angle. Because
there are two charges and two dipoles (see Scheme 1), the total
correction term, ECD, in eq 20 is predicted to be 5.4 kcal/mol,
which is close to the more accurate ECD ) 7 kcal/mol value
based on Gronert’s results.14 Thus, the model based on Schemes
1 and 2 recovers most of the expected correction.
Gronert14c has pointed out that the choice ꢀr ) 0.82 is
equivalent to ꢀr ) 1 and a distance between the two N atoms r
) 8.2 Å rather than the actual distance of 10 Å. Scheme 1
provides a rationale for the shorter distance because the two
dipoles lead to a shift of the net positive charge corresponding
to a smaller distance.
The cause for the apparent paradox of having to use ꢀr < 1
rather than ꢀr g 1 derives from eq 16b, which includes the
intrinsic proton affinity based on experimental data. The
experimental value includes the energy release due to the
stabilization of the charge by the charge delocalization near the
N atom. Using ꢀr > 1, as in some calculations13,24 involving
the experimental proton affinities, leads to an overcounting of
this stabilization.
determination of such an induced dipole on each molecular
group close to each charge, including also neighboring side
chains or backbone carbonyls which are hydrogen-bonded to
the protonated side chain. The approach used in the present
work, which includes some approximations, is described in
Appendix II.
Equations 18-21 contain the term RNNmax. The evaluation
of this term requires finding the maximum of the activation
energy for the deprotonation, EDP. Considering the large number
of such terms (see eq 21), it is desirable to simplify the process.
Shown in Figure 6 are results from positive point charge
calculations where the approach was the same as that used to
obtain the data for Table 3. However, butylamine was replaced
with methylamine to simplify the calculations. These data
demonstrate that a choice of RNN ≈ 6.5 Å provides a good
approximation of EDP for all four alkyl diamines, which extend
from a distance r ) 10 Å (p ) 7) to r ) 16.5 Å (p ) 12). The
approximation RNNmax ) 6.5 Å was made in the calculations
for the proteins (see Appendix II).
(e) Results for GBaj pp for Different Charged States of
Three Proteins: Carbonic Anhydrase, Cytochrome c, and
Pepsin. Significance of Results to Observed Charged States
in ESI. Determinations for three selected proteins, carbonic
anhydrase, CAII (MW ) 29200), cytochrome c (MW ) 12400),
and pepsin (MW ) 34600) were made. The gas-phase basicities
GBintr of the basic side chains selected, Arg, His, Lys, Trp, Pro,
are given in Table 4. Justification for the values used is given
in Appendix II. The values for GBaj pp of each protein were
obtained with eq 21 (see also Appendix II).
The results obtained are summarized in Tables 5 and 6 for
CAII and CYC (for data on pepsin, see Felitsyn12). The tables
give GBapp for the side chain which is easiest to deprotonate
when Z protons (charges) are present. When GBaj pp - GB-
(NH3) > 0, the protein will be able to hold the assigned Z
In the alkyldiamine, the induced dipoles are forced to align
against the distant charges. In multiply protonated proteins, that
is not necessarily the case. A full treatment would involve the
+
charges when NH4 is the protonating reagent (as would be
the case when ammonium acetate was used as buffer) or (which
is equivalent) when the protonated site is solvated by a base
such as NH3. The charge Z, where GBapp - GB(NH3) is just
(23) Yamdagni, R.; Kebarle, P. J. Am. Chem. Soc. 1973, 95, 3504.
(24) Miteva, M.; Demirev, P. A.; Karshikoff, D. J. Phys. Chem. B 1997, 101,
9645.
j
above zero, corresponds to NSB
.
9
11526 J. AM. CHEM. SOC. VOL. 124, NO. 38, 2002

Charged States of Proteins
A R T I C L E S
Table 4. Gas-Phase Basicitiesa
Table 6. Cytochrome c (MW-12400)a,b
app
j
GBapp − GBNH
residue
b
c
c
GB
GB
charges z
GB
exp
int,protein
j
3
arginine
241
227
(217)
227
(212)
219
(216)
212
251
237
1
2
3
4
5
6
7
251.0
247.2
228.6
225.1
220.6
215.6
211.5
208.5
203.3
198.2
194.6
191.6
184.8
178.4
175.5
169.6
163.7
55.0
51.2
32.6
29.1
24.6
19.6
15.5
12.5
7.3
2.2
-1.4
-4.4
-11.2
-17.6
-20.5
-26.4
-32.3
ARG38
ARG91
LYS7
histidine
(imidazole)
lysine
(n-butylamine)
tryptophan
(indole)
237
234
227
LYS55
LYS13
LYS72
HIS26
LYS53
LYS27
LYS99
LYS22
LYS87
LYS79
LYS60
LYS8
proline
ammonia
Zobsd 8
ZCRMe 9
NSBf 10
11
12
13
14
15
196
a All values are in kcal/mol. b All values are from NIST database.21
Compounds which model the amino acid side chains (in parentheses) are
shown below the corresponding amino acid. The GB values for suitable
models were found only for histidine, lysine, and tryptophan. c Estimated
average intrinsic GB of amino acid in protein. The deviation for specific
amino acids in the protein is estimated to be on the order of (5 kcal/mol.
Unusual protein arrangements may lead to larger deviations, see Appendix
II.
16
17
LYS39
LYS100
a All energies are given in kcal/mol. b Total of 29 basic sites considered.
Table 5. Carbonic Anhydrase (MW 29200)a,b
c Residue that is easiest to be deprotonated in the presence of a base such
d
app
charges z
GB
GBapp − GBNH
residue
c,d
as NH3. Zobs ) observed charge with highest intensity; however, Zobs
)
j
j
3
9 was also present, see Figure 9 in ref 12. A value of Zobs ) 8 was also
obtained when pure water, without buffer electrolytes, was used (present
work). e Charge provided by CRM from precursor droplet of same radius
as protein, R ) 21 Å (based on X-ray data). f Largest number of charges
that available basic sites can hold.
2
3
4
5
6
7
8
9
247
243
240
228
224
220
218
215
212
208
205
202
200
195
193
187
185
181
179
51
47
44
32
28
24
22
19
16
12
9
6
4
-1
-3
-9
-11
-15
-17
ARG182
ARG58
ARG89
HIS36
HIS3
LYS252
LYS45
LYS168
LYS154
LYS113
LYS133
LYS39
LYS9
LYS127
LYS225
LYS159
LYS18
LYS112
LYS261
its surface and is not expected to be able to accommodate all
the protons provided by the CRM process. The results (Table
4)12 confirmed this expectation. It was estimated12 that ZCRM
≈
10
Zobse 11
ZCRMf 12
13
15, and NSB ) 9 was evaluated12 with the equations derived in
the present work. For this protein, NSB would be limiting.
Apparently, pepsin is very difficult to produce by electrospray,25
and the result used,12 Zobs ≈ 10 from Standing and co-workers,25
was obtained at pH ≈ 3.5. Information on the solvent used and
the possible presence of other small electrolyte ions such as
NSBg 14
15
16
17
18
19
NH4 is not available.25 This and the low ion intensities
+
20
observed reduce the value of these results. We hope to be able
to report in the future determinations of Zobs under controlled
solution and other experimental conditions.
a All energies are given in kcal/mol. b Total of 36 basic sites considered.
c Residue that is easiest to be deprotonated in the presence of a base such
as NH3. d The zinc center is considered to be Zn(OH)+. Zobs, observed
e
Proteins produced by ESI in the negative ion mode lead more
often to the condition Zobs < ZCRM. Recent work from this
charge with highest intensity. f Charge provided by CRM from precursor
droplet of same radius as protein, R ) 25 Å (based on X-ray data). g Largest
number of charges that available basic sites can hold.
laboratory provides evidence that the condition, NSB < ZCRM
,
occurs more frequently in the negative ion mode.26
As discussed in the Introduction, de la Mora8 found that for
the majority of globular proteins
(f) Comparison with Experimental Determinations In-
volving Proton Transfer from Protonated Proteins. Unfor-
tunately, most of the determinations of proton-transfer rates to
bases of known GB involve denatured proteins.13c,15a,b,e A study
by Smith and co-workers15c includes nondenatured CYC. The
major purpose of this study was to compare the extent of
deprotonation of a nondenatured and a denatured protein by a
strong base. The denatured protein is expected to lose fewer
protons because of the higher expected GBapp for the basic sites.
In the looser, denatured structure, the protonated basic sites are
farther apart because of the charge repulsion and their increased
mobility. This is an interesting application of the GBapp concept;
however, here we consider only the result15c for the nondena-
tured CYC. When the nondenatured CYC, Zobs ≈ 8, was
Zobs ≈ ZCRM (de la Mora8)
(22)
which leads to the requirement
N
SB g ZCRM
(23)
It is important to examine whether the condition, eq 23, holds,
because the assumption that it is NSB that determines Zobs, that
is, Zobs ≈ NSB, has also been made often. See, for example, ref
13.
The results obtained for carbonic anhydrase, Table 5, predict
NSB ) 15, while Zobs ≈ 11 and ZCRM ≈ 12. Thus, in this case,
de la Mora’s proposal holds. For cytochrome c, Table 6, NSB
≈ 10, Zobs ) 8, and ZCRM ) 9; thus, the de la Mora condition
holds also for this system.
exposed to triethylamine (TEA), the charge reduced to Zobs
4, corresponding to NSB ≈ 4 (TEA). A similar value is predicted
≈
Pepsin is an interesting case. It exhibits a large deviation to
low Zobs in the plot used by de la Mora.8 It has only four strongly
basic side chains, Lys 319, Arg 315, Arg 307, and His 53, at
(25) Chernushevich, I. V.; Ens, W.; Standing, K. G. In Electrospray Ionization
Mass Spectrometry; Cole, R. D., Ed.; Wiley: New York, 1997.
(26) Blades, A. T.; Peschke, M.; Verkerk, U.; Kebarle, P. J. Phys. Chem. A, in
press.
9
J. AM. CHEM. SOC. VOL. 124, NO. 38, 2002 11527

A R T I C L E S
Peschke et al.
by the present equations (see Table 6) when the literature GB-
(TEA) ) 227.5 kcal/mol21 is used. The side chains that are
probably protonated are Arg38, Arg91, Lys7, and Lys55.
Actually, there is a paucity of reasonably accurate proton-
transfer rate measurements involving nondenatured proteins.
This is regrettable considering the importance of such data to
the development of a gas-phase ion chemistry of proteins. For
example, Williams and co-workers13d observed a maximum
charge state of Z ) 11 for nondenatured CYC sprayed from
pure water and predicted GBapp g GB(H2O) ) 158 kcal/mol.
This result could be checked using bases with GB higher than
water. Similar checks of the very much higher values predicted
6. One can expect that the evaluation of GBapp values could
soon be made via MD simulations using force fields, such as
GROMOS-87,27 to model the proton transfer from the proto-
nated site to an attached base, such as ammonia. The electrostatic
equations for proton transfer, developed in this work, might
prove useful for the inclusion of a force field for proton transfer
in MD simulations.
Appendix I. Ab Initio Calculations for Alkyl Diamines
Model, Equation 20. All calculations were performed using
Gaussian9429 with the B3LYP density functionals as the method
of choice. This method is fast with relatively small computa-
tional hardware demands and, on the basis of previous experi-
ence with similar ion-molecule systems,30 provides a relative
energy accuracy of better than 5 kcal/mol. Because Gaussian94
does not, to our knowledge, allow geometry optimizations of
molecular systems that include point charges, a point charge
was fabricated using a “hydrogen atom” with a modified basis
set description that made it energetically prohibitive to put an
electron into the resulting orbitals. For all other atomic centers,
the 6-311++G(d,p) basis set was used.
by the present results, such as GBapp ) 208 kcal/mol for NSB
)
8 (Table 6), would also be very useful.
Conclusions
1. Results predicting the activation energies EDS and EDP for
NH3(CH2)7NH32+ can be obtained from simple and fast calcula-
tions based on electrostatics (Figure 5 and eqs 17-20). These
lead to good agreement with the result from the ab initio
calculation.14 Furthermore, these equations can be used for any
other two proton systems.
2. The ab initio calculations involving a positive point charge
(see Scheme 2 and Table 3) represent a very convenient method
for obtaining energy changes due to the position of the charge
and then finding the electrostatic counterparts. This approach
makes the use of an arbitrarily chosen relative permittivity ꢀr
unnecessary.
Appendix II. Extension of the Electrostatic Model to
Multiply Charged Proteins. The basis for the evaluation of
N
SB is eq 21. However, a number of approximations were made
in order to obtain an easily workable model for the evaluation
of GBaj pp
.
(a) Values of GBint,j. The values of GBint,j for each basic
site are difficult to estimate. Experimental GB values for the
basic amino acids are available in the literature and are listed
in Table 4. However, these values have to be used with caution.
Amino acids with long side chains such as lysine are able to
stabilize a proton further by forming a hydrogen bond between
the protonated side chain and the carbonyl group, and the
experimental GB would include that stabilization. For example,
the experimental GB for lysine is 227.3 kcal/mol. However,
the side chain for lysine is butylamine with an experimental
GB of 211.9 kcal/mol. The larger bulk of lysine would increase
the GB of the NH2 side chain analogous to octylamine, and a
value of 214 kcal/mol might be appropriate. That leaves 13.3
kcal/mol in the measured GB for lysine for the expected
hydrogen-bond stabilization. In a protein environment, additional
stabilization from other nearby groups can be expected. Such
stabilization can be anywhere from 5 to 15 kcal/mol over that
from the first hydrogen-bond stabilization.
3. The electrostatic equations can be extended to multiply
protonated globular proteins. This allows determinations of
GBapp of the basic side chains and NSB, the maximum number
of protons that a globular protein can hold when the protonating
+
agent is NH4
.
4. Comparison of NSB for carbonic anhydrase (CAII) and
cytochrome c (CYC), with the observed number of charges
(protons) Zobs and with ZCRM, the number of charges that are
expected to be provided by the water droplet that generates the
charged protein, leads to ZCRM ≈ Zobs < NSB. This means that
there are enough basic sites NSB, and therefore, ZCRM is the
charge limiting factor. For pepsin, which has an unusually small
number of basic sites, the finding is Zobs ≈ NSB < ZCRM. In this
case, the protein cannot accommodate the available charge,
ZCRM, such that NSB is the limiting factor. However, the Zobs
value was obtained from the literature, and the experimental
conditions are not well-known.
The GBint values for arginine, histidine, lysine, tryptophan,
and proline that have been used in the model are detailed in
Table 4. For histidine and lysine, whose measured GBs of the
amino acid are known to include one hydrogen-bond stabiliza-
5. The values for NSB and ZCRM given in Tables 5 and 6 are
not as reliable as one would wish. Difficulties in the evaluation
of GBapp are the following: (a) Values of intrinsic gas-phase
basicities, GBint, of the side chains of the proteins are somewhat
arbitrary. These are not available and have to be modeled on
the experimentally determined GB of the corresponding amino
acids and assumed additional stabilization by neighboring groups
(see Table 4). (b) The electrostatic calculations, while completely
satisfactory for two proton systems, become complex for the
polyprotonated proteins. For example, the reaction coordinate
at a given basic site j depends on a vector superposition of
repulsion forces from all protonated sites (see Appendix II).
These problems become much more tractable for lower charge
states. Experimentally determined GBapp values of such low
charge states of proteins would be of great value for the further
development of the modeling calculations.
(27) van Gunsteren, W. F.; Berendsen, H. J. C. Groningen Molecular Simulation
(GROMOS) Library Manual; Biomos: Gronigen, The Netherlands. For
applications of GROMOS to proteins in the gas phase, see also Miteva et
al.24 and Reitman et al.28
(28) Reitman, C. G.; Velasquez, I.; Tapia, O. J. Phys. Chem. B 1998, 102, 9344.
(29) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B.
G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.;
Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V.
G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.;
Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.;
Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.;
Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-
Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94, revision D.3; Gaussian,
Inc.: Pittsburgh, PA, 1995.
(30) (a) Smith, B. J.; Radom, L. Chem. Phys. Lett. 1994, 231, 231; 345. (b)
Soliva, R.; Orozco, M.; Luque, F. J. J. Comput. Chem. 1997, 18, 980. (c)
Bogdanov, B.; Peschke, M.; Tonner, D. S.; Szulejko, J. E.; McMahon, T.
B. Int. J. Mass Spectrom. 1999, 187, 707.
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Charged States of Proteins
A R T I C L E S
tion, only 10 kcal/mol has been added to account for additional
stabilizations. For arginine, to our knowledge, no GB has been
measured for the side chain. However, because the side chain
in arginine is also fairly long and flexible, it is highly likely
that the amino acid GB measurement includes one hydrogen-
bond stabilization. Therefore, again only 10 kcal/mol has been
added.
(c) Evaluation of the Terms ECDi,j and ΣECDi,j. In the alkyl
diamine, the induced dipoles are forced to align against the
distant charges. In proteins, that is not necessarily the case. A
correct treatment would involve the determination of such an
induced dipole on each molecular group close to each charge,
including also neighboring side chains or backbone carbonyls
which are hydrogen-bonded to the protonated side chain.
However, several general observations can be made that
facilitate estimating such complex energetic contributions. Each
interaction with neighboring side chains increases the GBint,j
of the protonated side chain j while on the other hand also
increasing ECDj because the positive end of the induced dipole
will generally point into the protein toward the other charges.
The correction would not be large because the dipole interactions
fall off rapidly with 1/r2 and depend on charges being aligned
with the dipole axis. For example, in cytochrome c where lysine
predominates, calculating the induced dipole repulsions (µ )
3.11 D) centered on the first carbon next to nitrogen of the side
chain of lysine using an NMR structure, without taking the
dipole alignment (θ ) 0 in all cases) into account, the overall
correction, ECDj ) ΣECDi,j, for 13 charges, varies from 9 to 13
kcal/mol depending on each site j. Inclusion of the dipole
alignment by using a cos(θ) term (θ is the angle between C-N
bond axis and N-N line) reduces the correction to 1-6 kcal/
mol with 4 kcal/mol as the average.
For tryptophan and proline, the GB assignment is different.
Both amino acids have inflexible or nonexistent side chains.
The measured GB therefore would not include any hydrogen-
bond stabilization. That can be shown by comparing the GB of
indole, the side chain of tryptophan, with tryptophan itself. The
increase of 3.4 kcal/mol is likely due to the increased charge
delocalization in the amino acid. It certainly lacks the ap-
proximately 10 kcal/mol stabilization energy that a hydrogen
bond would yield. Because both amino acids would be depend-
ing on other groups to be flexible enough to stabilize the charge,
it is likely that on average both tryptophan and proline would
be less stabilized than arginine, histidine, and lysine whose
flexible side chains have a longer reach to find a more suitable
protein environment. Consequently, as a reasonable guess, 15
kcal/mol was added to the measured GB to account for the first
hydrogen bond and additional stabilization. All assigned GBint
values are shown in Table 4.
(b) Evaluation of EDIP,j (RNN max), EPOL,j (RNNmax), and
T(∆S‡DS - ∆SD‡ P). For each protein considered, the X-ray
crystal structure was taken as an approximation of its gas-phase
structure. Both ri,j and RNN,jmax are vector quantities. The Ri,j
direction is determined by the position of the charged nitrogens
of each pair of amino acids considered. The RNN,jmax direction
was taken as the direction from the center of charge to the
charged nitrogen of the protonated base j. The center of charge
was based on all protonated side chains that were considered.
For carbonic anhydrase and cytochrome c, all arginine, histidine,
and lysine side chains were considered as sites that could be
protonated, while for pepsin tryptophan and proline were also
included. A more accurate approach toward finding the RNN,j
direction would be to use a superposition of force vectors from
the individual electrostatic repulsions, but that would necessitate
a trajectory calculation with many small steps because the initial
direction of the force superposition does not generally hold once
the charge has been moved any appreciable distance. The
direction approximation using a center of charge, on the other
hand, will yield good results if the charges are spread evenly
across the surface of the protein. For the three proteins
considered, the basic sites are spread out enough to allow such
an approximation. Given the other uncertainties and approxima-
tions, the elaborate trajectory calculation is not justified at this
stage.
A similar correction would be expected for other nearby
polarizable groups such as hydrogen-bonded carbonyl groups.
Using the polarizability of acetone, the induced dipole at
hydrogen-bond distances is 2.3 D, weaker than the induced
dipole on the adjacent carbon atom. However, the polarizability
of backbone carbonyls tends to be higher than that of acetone
so that the induced dipole might be expected to add corrections
of 2-3 kcal/mol per hydrogen-bonded interaction on average
if 13 charges are present. If 3 hydrogen-bonded interactions are
assumed then for 13 charges, ECDj ) 12 kcal/mol might be a
reasonable estimate. However, for only 2 charges, the ECDj
correction would be much lower because of the longer average
distance between the two charges and the probability that the
dipoles are not aligned. Using the CYC NMR structure for 2
charges, corrections between 0.4 and 0.9 kcal/mol are obtained
for the carbon induced dipole interaction. So, an estimate of
1 kcal/mol for 2 charges might be reasonable if the polariz-
able carbonyl group interactions are included. Using a linear
relationship for ΣECDi,j leads to ECDi,j ) 1 kcal/mol beyond the
first charge. This approximation assumes similar induced di-
poles for each basic site so that on average each charged
basic site induces identical dipoles. Given the small magnitude
of the correction, treating each basic site in an identical
manner for this correction is not expected to lead to significant
errors.
Figure 6 shows that the energy near the maximum for EDP
does not vary greatly with RNN, so that using a constant RNN,jmax
of 6.5 Å would be a reasonable approximation. EDIP(RNNmax)
+ EPOL(RNN max) ≈ -4 kcal/mol for the alkyl diamine (see
Figure 5). The alkyl diamines model the situation where both
side chains i and j are lysines. It was assumed that the same
value holds also for all other pairs of side chains.
The term T(∆S‡DS - ∆SD‡ P) ≈ +4 kcal/mol (at ∼420 K)
obtained for the diamine (see eq 9b) was assumed to be the
same for all basic side chains. The terms for EDIP + EPOL and
the term due to T∆S are seen to cancel.
Including the above-mentioned cancellations in eq 21 leads
to eq 24, which forms the basis of the model. The model starts
q2
4πꢀ0ri,j
GBapp ) GBint
-
+
∑
q2
(24)
∑
4πꢀ0(ri,j + RNN,jmax) -
E
CDi,j
∑
with all basic sites that have been included as charged. The
number of bases used for each protein is given in Tables 5 and
9
J. AM. CHEM. SOC. VOL. 124, NO. 38, 2002 11529

A R T I C L E S
Peschke et al.
6. Next, a visual inspection of the nitrogen that carries the charge
is done on the X-ray or NMR structure to see if all charges are
on the surface of the protein. Charges that are imbedded in the
protein are excluded (His 64 in carbonic anhydrase and Pro 41,
Trp 39, Trp 190 for pepsin). Using the assigned GBint values
from Table 4, the value for ∑q2/4πꢀ0ri,j - GBint is calculated.
Each charge is then moved 6.5 Å away from the center of charge
to calculate the term ∑q2/4πꢀ0(ri,j + RNN,jmax). The site with
the lowest GBapp is then assumed to deprotonate. This cycle is
then repeated for the remaining charges. The results are shown
in Tables 5 and 6. If ammonia is the deprotonating agent, the
number of charges where GBapp - GB(NH3) becomes positive
A global search that considers all possible combinations of
protonated sites for each charge state would be preferable.
However, such a search is likely to improve the gas-phase
basicity of the most basic protein sites for each charge state by
only a few kilocalories per mole over the current method
because such an optimization would only change long distance
electrostatic interactions. Also, the number of permutations of
possible protonated sites at charge state 10 for cytochrome c,
where 29 bases are considered, is over 20 million. Given that
the expected improvement is less than the error bars, the
additional time needed to perform a global search is currently
not warranted.
corresponds to NSB
.
JA012591E
9
11530 J. AM. CHEM. SOC. VOL. 124, NO. 38, 2002