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.
9
11528 J. AM. CHEM. SOC. VOL. 124, NO. 38, 2002