ARTICLES
E&BS
SALT BRIDGES AND CONFORMATIONAL FLEXIBILITY: EFFECT ON
PROTEIN STABILITY
A. Karshikoff 1 and I. Jelesarov 2
Karolinska Institute, Department of Biosciences and Nutrition, Stockholm, Sweden1
University of Zurich, Department of Biochemistry, Switzerland 2
Correspondence to: Andrey Karshikoff
E-mail: aka@csb.ki.se
ABSTRACT
Salt bridges are believed to have an important role in stabilisation of native protein structure. The assessment of their contribution
to the electrostatic term of the free energy is a yet unsolved task. One can point out a number of reasons: beginning with
conceptual issues, such as the complex nature of the interplay between the different types of non-covalent interactions and going
to details, such as the interactions of the participating groups with their environments. Here we focus on the interplay between
electrostatic interactions the functional groups forming salt bridges are involved in and the conformational flexibility of the
protein molecule. We show that the connection between these two factors appears to be one of the keys for a better understanding
of the forces determining stability of proteins.
Keywords: proteins, modelling,
interactions, salt bridges
stability,
electrostatic
Introduction
The tree-dimensional structure of the native proteins is result
of a very delicate balance between different types of noncovalent interactions, uniquely determined by the sequence of
the polypeptide chain. The physical principles non-covalent
interactions obey are well known and ubiquitous in proteins.
This, however, does not simplify the task of predicting their
role in protein stability and functional properties. The complex
interplay of non-covalent interactions causes sometimes
surprising behaviour of proteins. In the context of the
considerations presented in this paper an instructive example
are the charge reversal mutations, which are expected to
improve binding of charged substrates. The failure to increase
binding of, say, a negatively charged substrate by mutating
a negative group in the binding side to a positive one have
been clearly explained on the basis of theoretical calculations
[10]. This example also illustrates that rational design aiming
at improving or changing properties must be preceded by a
careful analysis of the mutual dependence of non-covalent
interactions. This point is especially important when
electrostatic interactions are in the limelight. Two reasons
can be given. First, electrostatic interactions are long-range
interactions, a feature distinguishing them from all other types
of non-covalent interactions. Hence, charges can “send signals”
to distant parts of the protein molecule. Second, electrostatic
interactions take place in an inhomogeneous dielectric medium,
since the dielectric permittivity of the protein globule is nonisotropic and differs by much from the dielectric permittivity
of water. This fact turns out to be the most serous difficulty
when electrostatic interactions are to be predicted.
606
In the following we consider one aspect of the connection
between electrostatic interactions and protein functional
properties, namely the role of salt bridges in protein stability.
Salt Bridges
In proteins, when two oppositely charged functional groups
are close to each other, one speaks about the existence of a
salt bridge. For the purposes of our considerations the term
functional group is defined as a group of atoms, which change
its charge upon protonation (or deprotonation). Hence, these
groups are also ionisable groups. The distance at which two
such groups form a salt bridge is usually taken to be r = 4 Å, a
value deduced by Barlow and Thornton [4] on the basis of the
analysis of 38 protein structures. This criterion was found to be
most appropriate for the purpose of statistical analyses of ion
pairs in proteins. Even using a limited data base, these authors
pointed out that the highest peak of separation distribution
is at r ≈ 3 Å. This value of r is close to the average distance
between the proton donor and the proton acceptor atoms in a
hydrogen bond. It is clear that the physical properties of an ion
pair connected by a hydrogen bond differ from those of a pair
separated by, say, 4 Å. Hydrogen bonds have directionality,
a feature that is often crucial for enzymatic activity, ligand
binding, protein-protein interactions, etc. To emphasize the
difference we define salt bridge as a couple of functional
groups connected by hydrogen bond(s). As a distance criterion
we chose 3.2 Å, approximately the upper limit of the proton
donor-acceptor distance in a hydrogen bond. On the other
hand, functional groups which are in close proximity, but do
not satisfy the above distance criterion we classify as ion pairs.
The chosen distance criterion neither revises the conclusions
based on other distance criteria nor introduces a new concept.
It merely reflects the nature of the physical phenomena that are
subject of this investigation. This can be seen in Table 1, where
the hydrogen bond lengths of the most common hydrogen
BIOTECHNOL. & BIOTECHNOL. EQ. 22/2008/1
TABLE 1
Mean hydrogen bond length, r(A···H), in Å, (A indicates the proton acceptor atom). For some hydrogen bonds r(A···H) values are given
within intervals illustrating the variability of this parameter. Data taken from [11]
ACCEPTOR
DONOR
R(A···H)
ACCEPTOR
DONOR
R(A···H)
-
H N
1.93
O
+
O
H N
C O
C O
C O
C O
H N
H N H
H
1.99
C
-
O
O
H
H N R
H
+
O
H
+
+
1.96 − 2.00
C
1.87 − 1.94
C
-
O
O
H
H N R
R
1.79 − 1.97
C
1.64 − 1.70
C
-
O
O
HO
C
O
bonds found in proteins are compared. As seen, the hydrogen
bond length of salt bridges (charged functional groups) does
not differ significantly from hydrogen bonds where one or both
partners are neutral.
All hydrogen bonds listed in Table 1 belong to the class
of the moderate hydrogen bonds. The energy of formation of
moderate hydrogen bonds is between −15 and −4 kcal/mol.
Hence, when considering a salt bridge as a hydrogen bond, one
should formally expect a significant stabilising contribution.
Surprisingly, the range of statements about the contribution
of salt bridges to protein stability spans from strong and
moderate to negligible [19, 25], and even destabilizing [18].
Quantitatively, the stabilizing contribution of individual salt
bridges has been evaluated to be between –0.5 kcal/mol [17]
and –3 to –5 kcal/mol [1]. It is interesting to know which are
the factors determining the large variation in the energetic
contribution of salt bridges. The answer of this question has
not only an academic value. Such knowledge is essential for
the purposes of protein modelling and protein re-design by
rational mutagenesis.
A few main factors modulating the energetics of salt
bridges can be mentioned. The first one is the desolvation of
the charged functional groups participating in a salt bridge.
In the less polar medium of the protein molecule the energy
of charging increases. Therefore, the ionisable groups tend
BIOTECHNOL. & BIOTECHNOL. EQ. 22/2008/1
-
O
H
H N H
H
+
H
H N R
H
+
1.89
1.84
H
H N R
R
1.80
HO
C
1.40
O
to adopt their neutral forms. In extreme cases the uncharged
form of ionisable group which is completely buried in the
protein (that is, the group is completely desolvated) can be
favoured by much in comparison to the completely solvated
state [24]. Hence, the desolvation of functional groups reduces
their ability to participate in salt bridges. This explains why
salt bridges are usually located on the surface of the protein
molecule. The charge-charge interactions are the second
important factor. Indeed, the close proximity of oppositely
charged groups results in a favourable interaction energy,
which opposes the unfavourable desolvation effect. The sum of
these two factors we refer to as electrostatic interactions term.
The third factor is the flexibility of the protein molecule. This
inherent property of proteins may facilitate a dynamic process
of formation and disruption of salt bridges. In the following we
will show that electrostatic interactions are strongly influenced
by the conformational flexibility. In fact, the interplay between
electrostatics and conformational flexibility determines the
electrostatic term of the unfolding free energy of proteins.
Electrostatic Term of the Unfolding Free Energy
By definition the unfolding free energy, ΔGu, is given by
,
U
where ΔG and ΔGF denote the free energy of the unfolded
and of the folded state, respectively. These free energies are
607
related to some appropriate reference state. Since the free
energy is defined up to an additive constant, we can choose
as the reference point the state where the free energies of the
unfolded and of the folded state are equal. In this way ΔGu can
also be expressed in the following way
,
ZU and ZF are the partition functions of the system in the
unfolded and folded states of the protein, respectively. If we
know the partition functions, ZU,F, the unfolding free energy
can be calculated. In order to extract the electrostatic term of
ΔGu we will assume an unfolding process in which only the
electrostatic interactions are relevant. A physical phenomenon
closest to this hypothetical process is the pH-dependent
unfolding. If one ignores all, but electrostatic interactions, for
the partition functions one can write
.
(1)
The summation is over all possible microscopic states, {x},
of the system and W(x) is the electrostatic energy of a given
microscopic state x. An appropriate expression for W(x) is
.
(2)
The superscripts U and F are omitted because the above
formula is valid for both the unfolded and folded states. The
summations are over all N ionisable (functional) groups of the
protein. The quantity pKint,i is the intrinsic ionisation constant
[20] of group i and is defined as
,
(3)
where pKmod is a reference value of the ionisation constant of
a given type of group (e.g. asp, lis, etc) and is assumed to be
known. ΔpKsol and ΔpKpc describe respectively the change of
the equilibrium ionisation constant due to the desolvation of
the functional group and the influence of all permanent charges
(which do not change with pH) of the protein. The dipole charges
of the peptide groups can be considered as permanent charges.
The term Wij(xi,xj) represents the electrostatic interactions
between group i and group j. The variables xi and xj (called also
protonation variables) reflect the protonation states of these
groups. For simplicity we assume that the ionisable groups can
adopt only two states: protonated and deprotonated. In this case,
by convention xi = 0 indicates the protonated state, whereas
xi = 1 (1 proton is released) indicates the deprotonated state
of group i. In the case of folded structures, we will make one
more assumption, namely that the positions of the functional
groups are fixed, i.e. the spatial coordinates of the charges are
determined solely by the three-dimensional structure of the
protein. In the following sections, this assumption will be a
subject of reconsideration. Nevertheless, at the current stage
of our consideration it is a useful simplification, since it allows
the description of the microscopic states of the system only by
means of the protonation variables. Thus, a single microscopic
state is completely defined by the vector x = (x1, x2, … xi, … xN)
608
with N elements, each of which can have the value 0 or 1
depending on the protonation state of the corresponding group.
The total number of microscopic states of the system, {x},
is then 2N, which is an astronomical figure even for a protein
of medium size. The methods for calculation of the sum in
Eq. (1), as well as of the quantities in Eqs. (2 and 3) are out of
the scope of our discussion. A description of the theory and the
computational methodologies is given in [13].
Eq. (2) is also valid for the unfolded state. The assumption
of a fixed structure is, however, not applicable in this case.
Since the unfolded polypeptide chain adopts any arbitrary
conformation, the positions of the ionisable groups cannot
be defined. In order to take this into account, the vector x,
describing the microscopic states of the system, should include
the variation of the spatial coordinates of the ionisable groups:
x = (x1, x2, … xN, r1, r2, … rN), where r1, r2, etc. are variables
corresponding to the spatial coordinates of the ionisable
groups. A solution of Eq. (2) with x defined as above can be
found by means of Monte Carlo simulation [13].
The theoretical outline presented above aims at showing
the basic assumption made when the electrostatic term of the
free energy, ΔGel, is of interest. These assumptions introduce
limitations, which should be kept in mind in the interpretation
of experimental data. One of these limitations has already been
mentioned: the fixed structure of the native protein molecule.
Another important assumption is the additivity of the different
terms of the free energy, i.e. the change of the electrostatic term
of the free energy of unfolding does not influence the other
terms and vice versa.
We shall skip the mathematical rearrangements and present
the final expression for ΔGel used for calculations:
.
(4)
Comprehensive descriptions of the ideology and deduction of
Eq. (4) can be found in the literature [13, 15, 26]. The quantities
νU,F are the average number of protons bound to the protein
molecule in the unfolded and in the folded state, respectively:
,
where θιU,F are the degree of protonation of ionisable group i
in the two states. As it can be seen, in order to solve Eq. (4)
one needs to know the titration curves of the folded and of
the unfolded states of the protein. Experimentally, it is not
straightforward to measure the titration curves of the two
states at identical conditions and within a given pH interval.
However, on the basis of the theory presented above it is easy
to calculate them because
,
where W(x) is given by Eq. (2).
The lower limit of the integral in Eq. (4) is the reference
pH0 value where the two states of the protein have identical
BIOTECHNOL. & BIOTECHNOL. EQ. 22/2008/1
protonation
states:
νU(pH) – νF(pH) = 0.
Obviously,
el
ΔG (pH0) = 0. In general, different reference states can be
chosen. For instance, Yang and Honig [26] have chosen pH
equal to 0, whereas Langella et al. [16] defined it as an abstract
state, at which all titratable groups in the protein are in their
neutral forms.
The pH dependence of ΔGel of the homotrimeric coiled coil
protein (Lpp-56) shown in Fig. 1 illustrates the assumptions
made above. At the reference pH0 (–14), ΔGU =ΔGF = 0.
Hence, the values of the absolute ΔGel scaled on the abscise
have no physical meaning. The pH-dependence of ΔGel is
however expected to be correctly predicted. To verify this, at
least two experimental values of ΔGu are needed. (Note that
we use ΔGu firstly, because ΔGel cannot be measured directly,
and secondly because we have assumed that at the unfolding
process only electrostatic interactions are relevant, i.e.
ΔGu = ΔGel. For Lpp-56 such experimental data are available:
ΔGu(pH3→pH7) = ΔGu(pH3) – ΔGu(pH7) = 14 kcal/mol [8].
The calculations based on the assumptions given above result
in a value of 7 kcal/mol for ΔGel, which is essentially lower
than the experimental observation. The question is now, which
of the assumptions leads to this underestimation.
15 kcal/mol
DGel, kcal/mol
80
60
40
7 kcal/mol
20
0
-10
-5
0
5
pH
10
15
20
Fig. 1. The electrostatic free energy of the homotrimeric coiled coil Lpp-56 as
a function of pH. The calculations were done using either the MD-generated
ensemble of structures (continuous line) or with the X-ray structure (dashed line)
Conformational Flexibility and Salt Bridge Dynamics
The Lpp-56 protein represents a suitable object of investigation
of electrostatic interactions and salt bridge contribution
to structural stability. Lpp-56 is a homotrimer constituted
by three α-helices forming an in-register coiled coil. The
molecule is reach of charged groups, the great majority of
which is involved in salt bridges. Due to the specifics of the
structural organisation of the protein the salt bridges form rings
of intersubunit salt bridges, which clamp the superhelix along
its length. The crystal structure and, more importantly, the
available experimental observations suggest that electrostatic
interactions and the large number of salt bridges likely
contribute to the stability of the molecule [6, 8].
As pointed out above, one of the assumptions used in
theoretical predictions of ΔGel is that the folded protein is
BIOTECHNOL. & BIOTECHNOL. EQ. 22/2008/1
represented by a single structure. This assumption is valid in rear
cases within narrow pH intervals, and severely oversimplifies
the physical reality. Proteins are flexible molecules, so that their
native structures in solution are better described by ensembles
of a large number of conformers. If electrostatic interactions
are of interest, the conformational flexibility is often simulated
by introducing a high protein dielectric constant [2, 21, 23].
It has been shown, however, that protein dielectric constant
cannot be used as a parameter to fit the calculated pK values
to the experimental data [12]. We will show below that protein
permittivity cannot be used as parameter at ΔGel calculations,
either. An alternative approach is to collect conformations
using simulation methods such as molecular dynamics [3, 5,
9, 14, 22, 26, 27, 28].
The continuous line in Fig. 1 represents ΔGel(pH) calculated
on the basis of 7 ns molecular dynamics simulation combined
with calculations of W(x) [7]. The procedure of calculations
is simple. During the molecular dynamic simulation the
coordinates of the atoms are saved each 2.5 ps (snapshots).
For each snapshot calculations of W(x), θιF and respectively νF
are carried out. The final values of νF used in Eq. (4) are the
average over the values obtained for the individual snapshots.
The value obtained for ΔGu(pH3→pH7) is 15 kcal/mol
(Fig. 1), which is very close to the experimental observation.
The good agreement with the experimental data is objective
of any computational work, but the results obtained here are
at the same time surprising. During the molecular dynamic
simulation the side chains, including those of the ionisable
groups, may adopt conformations not permitting the formation
of salt bridges. Such information lead to a reduction of the
average electrostatic energy of interactions and hence, to an
overall reduction of the magnitude of ΔGel. The simulation
shows however a different behaviour of the groups involved
in salt bridges.
In order to explain this seemingly unexpected behaviour
and to give an answer of the question posed at the end of the
previous section, we consider two salt bridges linking the
helices B and C of Lpp-56. As shown in Fig. 2, a lysine residue
from helix C (LysC38) can form alternative salt bridges with
two aspartic acids from helix B: LysC38−AspB40 (Fig. 2A)
and LysC38−AspB33 (Fig. 2B). The lifetimes of the two salt
bridges are compared in Fig. 3. It is important to note that
during the first nanosecond none of the salt bridges is formed.
The same was observed also for other salt bridges in Lpp-56.
Hence, there are salt bridges which are not present in the
X-ray structure can be formed during the simulation. (the
structure at time zero in Fig. 3). Therefore, the mentioned
underestimate value of ΔGel calculated with the assumption of
a fixed protein structure is likely caused by the longer distances
between some functional groups observed in the X-ray structure
of Lpp-56. The molecular dynamics simulation “improves” the
salt bridge geometry which leads to a more correct prediction
of the electrostatic stabilisation of the molecule.
609
still formed. However, after approximately 2.5 ns a structural
fluctuation leads to desintegration of the salt bridge for the
following 2 ns. The lifetime of this salt bridge is 48% of the
total simulation time; hence its contribution to the stability of
the protein is lower than the predicted on the basis of the X-ray
structure.
a
b
distance, Е
10
8
6
b
4
2
A
a
0
1
2
3
4
5
time, ns
6
7
Fig. 3. Lifetime of salt bridges AspB40−LysC38 (line a) and AspB33−LysC38
(line b) in the homotrimeric coiled coil Lpp-56. The distances plotted are
between the geometric mean of the coordinates of the carboxyl oxygen atoms,
(Oδ1+Oδ2)/2, of the corresponding aspartic acid and the Nζ atom of LysC38
14
12
10
Е
8
6
b
a
a
b
4
2
0
1
2
3
4
time, ps
5
6
7
Fig. 4. Lifetime of the salt bridge LysA15−GluB20 in the GCN4 leucine
zipper. The distances plotted are between the atoms GluB20-Oε1 and LysA15Nζ (line a); and GluB20-Oε2 and LysA15-Nζ (line b)
B
Fig. 2. Salt bridges linking two α-helices in Lpp-56. Panel A: LysC38
−AspB40. Panel B: LysC38−AspB33
The opposite effect can also be observed. Fig. 4 shows the
time dependence of the proton donor-acceptor distances in the
salt bridge LysA15−GluB20 in another protein: the GCN4
leucine zipper. During the first 2.5 nanosecond, including time
zero (the X-ray structure), we observe a salt bridge with perfect
proton donor-acceptor distance. As illustrated in the Fig., in
this time window there is a rotation of the around the Cβ-Cγ
bond of the carboxyl group of GluB20. As the consequence
the proton acceptor atom is exchanged, yet the salt bridge is
610
Return to Fig. 3 again. The distances plotted in the figure
are between the nitrogen atom of the ε-amino group of LysC38
and the geometrical mean between the two carboxyl oxygen
atoms of AspB33 and AspB40. (Note that since geometric
averaging is used, the plotted distances are somewhat larger
than the criterion for salt bridge used throughout this study).
If we apply the criterion of Barlow and Thornton [4], the
conclusions made in this study remain the same. Indeed,
during the first nanosecond the distance between the functional
groups of the couple AspB40−LysC38 is larger than 4 Å. The
stability in respect to time of this configuration is due to a
water molecule mediating the interactions between the groups.
Very similar situation is observed within the time window
3.5 – 4 ns. During this time period the lysine side chain
BIOTECHNOL. & BIOTECHNOL. EQ. 22/2008/1
undergoes a conformational transition leading to a swap of the
salt bridge partner. A quasi stable state is observed in which
the interactions of the ε-amino group of the lysine with the
two carboxyl groups are mediated by water molecules. Such
configurations, known as water mediated salt bridges, are often
observed in the crystal structures of proteins. The molecular
dynamics simulation carried out in this study suggests that, at
least for Lpp-56, they are not long-living formations. After the
conformational transition the cross-link between helices B and
C is restored.
The considered examples illustrate how important is
the conformational flexibility for the adequate prediction of
electrostatic interactions in proteins, and of their contribution to
protein stability in particular. Regarding the calculation of ΔGel,
as already mentioned, the simplified approach of adjusting the
protein dielectric constant has been devised and has become
very popular in fact. The presented results demonstrate that a
priori parameterizations are not a universal solution. Increasing
the protein dielectric constant may have worked for the GCN4
leucine zipper, where electrostatic interactions calculated on
the basis of the X-ray structure are overestimated. However, in
the case of Lpp-56 the charge-charge constellation in the X-ray
structure is such that the strength of electrostatic interactions
are underestimated by computation, a problem which couldn’t
have been solved by re-parameterization on sound physical
grounds.
It is important to realise the limitation of the theory and
the computational approach presented above. The molecular
dynamics simulation is carried out within an a priori determined
net charge of the molecule, which does not change during
the simulation. Hence, the ensemble of structures collected
by the molecular dynamics simulation corresponds to an a
priori selected pH. Therefore, the calculation of electrostatic
interactions at any other pH represents an extrapolation
assuming the ensemble being representative for this pH.
Finally, it should be noted that the calculations are made
assuming ergodicity of the system. There are no formal criteria
to assess this assumption. In spite of the mentioned limitations,
the combination of molecular dynamics and electrostatic
calculations is a powerful tool revealing structural properties,
including those of the salt bridges, emerging only when the
protein molecule is “seen” in motion.
Acknowledgments
Work from I.J.’s own laboratory has been supported in part by
the Swiss National Science Foundation.
REFERENCES
1. Anderson, D.E., Becktel, W.J., Dahlquist, F.W. (1990)
Biochemistry 29, 2403-22408.
2. Antosiewicz, J., McCammon, J.A., Gilson, M.K. (1996)
Biochemistry 35, 7819-7833.
3. Baptista, A.M., Teixeira, V.H., Soares, C.M. (2002) J.
Chem. Phys. 117, 4184-4200.
BIOTECHNOL. & BIOTECHNOL. EQ. 22/2008/1
4. Barlow, D.J., Thornton, J.M. (1983) J. Mol. Biol. 168,
867-885.
5. Bashford, D., Gerwert, K. (1992) J. Mol. Biol. 224, 473486.
6. Bjelic, S., Karshikoff, A., Jelesarov, I. (2006) Biochemistry
45, 8931-8939.
7. Bjelic, S., Wieninger, S., Jelesarov, I., Karshikoff, A.
(2007) Proteins in press,
8. Dragan, A.I., Potekhin, S.A., Sivolob, A., Lu, M.,
Privalov, P.L. (2004) Biochemistry 43, 14891-14900.
9. Gorfe, A.A., Ferrara, P., Caflisch, A., Marti, D.N.,
Bosshard, H.R., Jelesarov, I. (2002) Proteins 46, 41-60.
10. Hwang, J.-K., Warshel, A. (1988) Nature 334, 270-272.
11. Jeffrey G.A. (1977) An introduction to hydrogen bonding,
Oxford University Press, New York,
12. Karshikoff, A. (1995) Protein Eng. 8, 243-248.
13. Karshikoff A. (2006) Non-covalent interactions in proteins,
Imperial College Press, London,
14. Koumanov, A., Karshikoff, A., Friis, E.P., Borchert, T.V.
(2001) J. Phys. Chem. B 105, 9339-9344.
15. Kundrotas P, Karshikoff A (2004) Electrostatic
interactions in unfolded proteins. Implication for protein
stability. in: Current Topics in Peptide & Protein Research
(Richard R, Ed.) Research Trends, Poojapura, 6 21-35.
16. Langella, E., Improta, R., Crescenzi, O., Barone, V.
(2006) Proteins 64, 167-177.
17. Lyu, P.C.C., Gans, P.J., Kallenbach, N.R. (1992) J. Mol.
Biol. 223, 343-350.
18. Phelan, P., Gorfe, A.A., Jelesarov, I., Marti, D.N.,
Warwicker, J., Bosshard, H.R. (2002) Biochemistry 41,
2998-3008.
19. Ren, B., Tibbelin, G., Pascale, D., Rossi, M., Bartolucci,
S., Ladenstein, R. (1998) Nat. Struct. Biol. 5, 602-611.
20. Tanford, C., Kirkwood, J.G. (1957) JACS 79, 53335339.
21. Teixeira, V.H., Cunha, C.A., Machuqueiro, M., Oliveira,
A.S.F., Victor, B.L., Soares, C.M., Baptista, A.A. (2005)
J. Phys. Chem. 109, 14691-14706.
22. van Vlijmen, H.W.T., Schaefer, M., Karplus, M. (1998)
Proteins 33, 145-158.
23. Vanvlijmen, H.W.T., Curry, S., Schaefer, M., Karplus,
M. (1999) J. Mol. Biol. 275, 295-308.
24. Warshel, A., Russell, S.T., Churg, A.K. (1984) Proceedings
of the National Academy of Sciences of the United States
of America 81, 4785-4789.
25. Xue, W.F., Szczepankiewicz, O., Bajer, M.C., Thulin, E.,
Linse, S. (2006) J. Mol. Biol. 358, 1244-1255.
26. Yang, A.-S., Honig, B. (1993) J. Mol. Biol. 231, 459-474.
27. Yang, A.-S., Honig, B. (1994) J. Mol. Biol. 237, 602-614.
28. Zhou, H.-X., Vijayakumar, M. (1997) J. Mol. Biol. 267,
1002-1011.
611