JOURNAL OF MOLECULAR RECOGNITION
J. Mol. Recognit. 2004; 17: 1–16
Published online in Wiley InterScience (www.interscience.wiley.com). DOI:10.1002/jmr.657
Review
Protein stabilization by salt bridges: concepts,
experimental approaches and clarification of
some misunderstandings
Hans Rudolf Bosshard*, Daniel N. Marti and Ilian Jelesarov
Biochemisches Institut der Universität, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
Salt bridges in proteins are bonds between oppositely charged residues that are sufficiently close to each
other to experience electrostatic attraction. They contribute to protein structure and to the specificity of
interaction of proteins with other biomolecules, but in doing so they need not necessarily increase a protein’s
free energy of unfolding. The net electrostatic free energy of a salt bridge can be partitioned into three
components: charge–charge interactions, interactions of charges with permanent dipoles, and desolvation of
charges. Energetically favorable Coulombic charge–charge interaction is opposed by often unfavorable
desolvation of interacting charges. As a consequence, salt bridges may destabilize the structure of the folded
protein. There are two ways to estimate the free energy contribution of salt bridges by experiment: the pKa
approach and the mutation approach. In the pKa approach, the contribution of charges to the free energy of
unfolding of a protein is obtained from the change of pKa of ionizable groups caused by altered electrostatic
interactions upon folding of the protein. The pKa approach provides the relative free energy gained or lost
when ionizable groups are being charged. In the mutation approach, the coupling free energy between
interacting charges is obtained from a double mutant cycle. The coupling free energy is an indirect and
approximate measure of the free energy of charge–charge interaction. Neither the pKa approach nor the
mutation approach can provide the net free energy of a salt bridge. Currently, this is obtained only by
computational methods which, however, are often prone to large uncertainties due to simplifying assumptions and insufficient structural information on which calculations are based. This state of affairs makes the
precise thermodynamic quantification of salt bridge energies very difficult. This review is focused on
concepts and on the assessment of experimental methods and does not cover the vast literature. Copyright
# 2004 John Wiley & Sons, Ltd.
Keywords: protein electrostatics; protein thermodynamics; pKa determination; double mutant cycle; NMR
spectroscopy; salt bridge
Received 9 October 2003; revised 7 November 2003; accepted 17 November 2003
INTRODUCTION
The stability of a protein results from a delicate balance
between opposing forces. The folded native protein structure is maintained at the edge of thermodynamic stability,
the free energy of unfolding being in the range of at most a
few tens of kilojoules per mol (Pace, 1975; Privalov, 1979).
Probably the major contributor to stability is the hydrophobic effect, a term coined to describe the energetically
*Correspondence to: H. R. Bosshard, Biochemisches Institut der Universität,
Winterthurerstrasse 190, CH-8057 Zürich, Switzerland.
E-mail: hrboss@bioc.unizh.ch
Contract/grant sponsors: Swiss National Science Foundation; Bundesamt für
Bildung und Wissenschaft.
Abbreviations used: pKa, negative logarithm of the acid dissociation constant
of an ionizable group; GU, free energy difference between the unfolded and
folded state of a protein; GU, free energy difference between the unfolded
and folded state of a protein in the presence and absence of a certain feature, e.g.
charge, salt bridge, mutation.
Copyright # 2004 John Wiley & Sons, Ltd.
favorable sequestration of non-polar groups in the protein
interior. The process is accompanied by the entropically
favorable release of caged water molecules around exposed
hydrophobic groups (Kauzmann, 1959; Dill, 1990). Other
important stabilizing factors are van der Waals interactions
and hydrogen bonds among polar residues (Dill, 1990; Pace,
2001). Yet what is the contribution of electrostatic interactions to protein stability, notably the contribution of salt
bridges? Electrostatic effects are highly variable, sometimes
favorable and sometimes unfavorable. One reason is that
electrostatic interactions are attractive as well as repulsive.
Another reason is that the formation of electrostatic interactions requires ordering of the protein structure, and a
third, related reason is that charges have to be desolvated in
order to interact. Ordering and desolvation are costly in
entropy and enthalpy and counteract favorable electrostatic
interaction between opposite charges.
Charges on ionizable groups whose charging is pHdependent, as well as pH-independent partial charges (dipoles as in peptide bonds and in polar yet non-ionizable
2
H. R. BOSSHARD ET AL.
groups) are taking part in electrostatic interactions. Salt
bridge and salt link are colloquial terms for a pH-dependent,
non-covalent bond between oppositely charged residues that
are sufficiently close to each other to experience electrostatic attraction. Salt bridges, which can be considered a
special form of hydrogen bonds, are composed of negative
charges from Asp, Glu, Tyr, Cys and the C-terminal carboxylate group, and of positive charges from His, Lys, Arg and
the N-terminal amino group. Since the side chain charge of
these residues depends on pH, the free energy contributions
of salt bridges to protein stability are pH dependent.
The electrostatic potential between partial or full point
charges qi and qj is inversely proportional to the distance rij
separating the charges, as described by Coulomb’s law:
qi qj
Uijelec ¼ k
ð1Þ
"rij
where " is the dielectric constant and k is a conversion factor
to the desired energy units. The Coulombic potential between opposite charges is favorable, but charge–charge
attraction is counteracted by costly desolvation and ordering
of the interacting charges. Therefore, the net contribution of
a salt bridge is balanced between favorable charge–charge
interaction and unfavorable desolvation and structural ordering. Hence, the net stability contribution of a salt bridge
can be favorable as well as unfavorable.
In this review we present the experimental methods to
estimate the free energy of salt bridges and discuss the
partitioning of the favorable and unfavorable energetic contributions to electrostatic interactions. Experimental methods
are based either on measuring the change of pKa of ionizable
groups upon protein folding or on determining protein
stability after mutation of residues forming salt bridges. We
aim at a balanced overview of concepts and methods, which
we illustrate by only a few examples from the literature and
from our own laboratory. We also wish to clarify some
misunderstandings about the net free energy contribution of
a salt bridge to protein stability and about the results that can
be obtained from experiment and computation.
GENERAL CONSIDERATIONS ABOUT
THE NATURE OF SALT BRIDGES
Salt bridges occur in different protein environments
The salt bridges of a protein can be grouped according to
location and number of interacting charges (Fig. 1). Simple
salt bridges are formed between two oppositely charged
residues. Salt bridge networks (complex salt bridges) are
composed of three or more interacting charges. Some salt
bridges are exposed on the protein surface in an aqueous
environment, others are buried in the protein interior, which
forms a low dielectric environment.
The energy of a salt bridge can be partitioned into
contributions from direct and indirect effects. The direct
energy contribution is the direct Coulombic interaction
between the charges. The strength of the Coulombic forces
depends on pH, on the geometry of the salt bridge and on the
distance between the interacting charges. Indirect effects,
which are also geometry-dependent, comprise the desolvaCopyright # 2004 John Wiley & Sons, Ltd.
Figure 1. Classification of salt bridges in a protein whose polypeptide chain is represented as a heavy line. Salt bridges are
exposed on the protein surface in a high dielectric environment
(a and b), or fully buried in the protein interior in a low dielectric
environment (c, stippled), or half-buried (d). Salt bridges can be
affected by other charges such as helix dipoles (e). Charge–
charge distances are variable and geometries differ (geometry
is defined as the angle between the vectors from the C atom to
the centre of the interacting charges). Most salt bridges are built
from only two opposite charges (a–e), but several charges may
form a network in a complex salt bridge (f).
tion energy used to change the hydration shell of the charges
and the energy of background interactions. These are the
electrostatic interactions with permanent dipoles of peptide
bonds, helices and other polar yet non-ionizable groups.
The stability of a salt bridge is defined relative to the
unfolded state of the protein
The stability of a protein is the difference between the free
energies of the folded and unfolded state:
GU ¼ GU GF
ð2Þ
where GU is the free energy necessary to unfold the native
protein, and GU and GF are the absolute free energies of the
unfolded and folded state, respectively. Here and elsewhere
the reference state is the folded (native) state of the protein.
Therefore, GU is positive when the folded state is more
stable than the unfolded state.
In analogy to the above definition of the stability of a
protein, the stability contribution of a salt bridge can be
defined as the free energy of unfolding of the protein with the
salt bridge minus the free energy of unfolding of the protein
without the salt bridge. This is written as:
GijU ¼ GU GU;no sb
ð3Þ
where GU and GU,no sb are the free energies of unfolding
in the presence and absence of the salt bridge, respectively,
and the double difference GijU is the net energetic
contribution of the salt bridge between residues i and j to
the free energy of unfolding of the protein. It is very
important to note that the magnitude of GijU depends
on the way the salt bridge has been removed. Obviously,
there are multiple ways to remove a salt bridge, as will be
J. Mol. Recognit. 2004; 17: 1–16
PROTEIN STABILIZATION BY SALT BRIDGES
Figure 2. Energy diagram for the free energy of unfolding of a
protein, GU, and for the contribution of a salt bridge to protein
ij
. In this scheme, removal of the salt bridge affects
stability, GU
only the free energy of the folded protein, the free energy of the
unfolded state is assumed to be unchanged. Note that the
ij
depends on the way the salt
magnitude and the sign of GU
bridge is removed. For example, protonation of an acidic side
chain yields a different GU;no sb than replacement by an
uncharged residue through mutation. Accordingly, the magniij
tude and direction of the heavy-lined arrows representing GU
depend on the nature of the mutation introduced (mutation
approach) or on whether the positive or negative charge is being
removed by increasing or decreasing the pH (pKa approach).
discussed shortly. For example, the value of GijU obtained if GU;no sb refers to protonation of a negatively
charged side chain of a salt bridge (GluO ! GluOH) is
not the same as GijU obtained if GU;no sb refers to the
mutation of a negatively charged to an uncharged residue,
for example Glu ! Ala. In other words, eqn (3) is a logical
and commonsensical definition of the free energy contribution of a salt bridge yet it cannot provide a single and unique
net free energy contribution for a given salt bridge without
defining how the salt bridge is being removed. The free
energy relationships defined by eqns (2) and (3) are presented schematically in Fig. 2.
According to eqn (3), GijU is positive if the salt bridge
stabilizes the folded conformation of the protein. This is an
arbitrary definition. Some authors prefer to change the sign
on the right hand side of eqn (3) so that a stabilizing salt
bridge has a negative free energy. GijU comprises the
direct and the indirect effects contributing to the salt bridge.
GijU is sometimes called Gele , or only Gele called
the ‘free energy of a salt bridge’. Note, however, that the
‘free energy of a salt bridge’ is a misnomer as it is not a
single free energy difference as defined by eqn (2) but
always a double difference as defined by eqn (3).
Two ways to measure the free energy contribution of a
salt bridge
To determine GijU , the salt bridge has to be broken or
removed. To remove a salt bridge without distorting the
conformation of the rest of the protein is no simple task. In
Copyright # 2004 John Wiley & Sons, Ltd.
3
principle, there are two possibilities, which we call the ‘pKa
approach’ and the ‘mutation approach’ (Fig. 3). In the pKa
approach, the salt bridge is broken by protonation of the
acidic group or by deprotonation of the basic group (Fig. 3,
left). In the mutation approach the charges are mutated to
non-ionizable groups (Fig. 3, right). The pKa approach is a
non-invasive way to eliminate charge–charge interactions.
However, residual electrostatic interactions between the
uncharged (neutralized) and the charged side chain may
remain at both low and high pH (Fig. 3, left). The mutation
approach is an invasive method. Not only are the charges of
the salt bridge removed but also the structure of the residues
of the salt bridge are being changed (Fig. 3, right). A
mutation may alter non-electrostatic interactions and
change the conformation of the protein. The resulting
complications can be partially circumvented by a thermodynamic double mutant cycle (Carter, 1984; Ackers and
Smith, 1985; Horovitz et al., 1990; Serrano et al., 1990). A
double mutant cycle yields the so-called coupling free
energy between the interacting charges of a salt bridge.
Unfortunately, neither the pKa approach nor the mutation
approach provide the net free energy of a salt bridge with
regard to a given mode of destruction of the salt bridge, as
defined by eqn (3). Currently, there is no simple experimental method to separate direct and indirect energy contributions and to determine the net free energy of a salt
bridge. This state of affairs has caused much of the controversy about the ‘energy content’ of salt bridges. In
principle, the computational approach can provide the net
free energy contribution of a salt bridge and separate direct
from indirect contributions. For example, the net ‘value’ of a
salt bridge can be calculated with regard to the mutation of
the salt-bridging side chains to their hydrophobic isosters
(Fig. 3, right). Computation can be performed at any pH and
without distorting the protein conformation. (Note, however, that computation may miss pH-dependent structural
changes.) The results from computation may differ widely
depending on the chosen parameters of the computation and
the accuracy of the structural protein models used (Hendsch
and Tidor, 1994; Kumar and Nussinov, 1999; Dong and
Zhou, 2002).
THE pKa APPROACH: ASSESSING
ELECTROSTATIC EFFECTS FROM
pKa CHANGES
We now discuss how to measure the energy contribution of
salt bridges by the pKa approach. The procedure yields the
relative contribution of charges to the pH-dependent stability profile of a protein. This profile reflects the effect of
changing the charge of one residue of a salt bridge while the
other residue remains charged. By the pKa approach one can
neither separate the direct from the indirect energy contributions nor is it possible to determine the net energetic
contributions of both residues of a salt bridge to protein
stability at a given pH.
In the pKa approach salt bridges are broken by protonation of acidic groups and deprotonation of basic groups with
the aim of measuring the pKa of ionizable residues in the
folded and unfolded protein. NMR spectroscopy is perhaps
J. Mol. Recognit. 2004; 17: 1–16
4
H. R. BOSSHARD ET AL.
Figure 3. The two experimental approaches to determine the contribution of a salt bridge to stability. Left: in
the pKa approach charge–charge interaction is disrupted by protonation of acidic groups or deprotonation of
basic groups. However, electrostatic interactions (H-bonding) between side chains may remain. Right: in the
mutation approach one or both charges are replaced by mutation (mutation to Ala is just an example).
Mutation does not only remove the charge but also changes the structure and chemical nature of the side
chains. This effect can be partly circumvented by a thermodynamic double-mutation cycle (see Fig. 10).
Table 1. Relationship between pKa in folded and unfolded protein, stability contribution of charged and
uncharged side chain, and sign of GUi
pKaF < pKaU
pKaF > pKaU
Stabilizing group in native protein
GiU [eqn (4c)]
Minus charged Glu, Asp, Tyr, Cys, C-term
Uncharged His, Lys, Arg, N-term
Uncharged Glu, Asp, Tyr, Cys, C-term
Plus charged His, Lys, Arg, N-term
GiU is positive
the most straightforward method to measure pKas, but also
the change with pH of enzyme activity or inhibitor binding,
or any other pH-dependent property, can be adduced to
obtain pKa values (Fersht, 1971; Anderson et al., 1990).
The electrostatic free energy contribution of an ionizable
group is related to its pKa in the folded and unfolded
protein
The well-known dependence of the stability of a protein on
pH is caused by its pH-dependent charge pattern. Let us
consider a single ionizable side chain and let pKaF and pKaU
be the pKa of the ionizable side chain in the folded and
unfolded protein, respectively. If the deprotonated group
stabilizes the native state, pKaF is lower than pKaU . If the
protonated group is stabilizing, pKaF is higher than pKaU . It
follows that any electrostatic effect from an ionizable group
must lead to a pKa shift between the folded and unfolded
state (Tanford, 1970; Yang and Honig, 1993). If
pKaU ¼ pKaF , the group has no electrostatic effect on stabiCopyright # 2004 John Wiley & Sons, Ltd.
GiU is negative
lity. The relationships between pKa, charge and stabilization
of the folded protein is summarized in Table 1.
Relationship between pKa change and free energy
of unfolding
Let GiU be the free energy of unfolding of the protein
carrying an ionizable residue i. GiU depends on the charge
of residue i in the folded and unfolded protein, qiF and qiU ,
and is calculated from:
ð
i
GU ¼
2:3RTðqiU qiF ÞpH
ð4aÞ
pH
The pH-dependent charges qiF and qiU are calculated from
the pKaU;i of group i in the unfolded state and from pKaF;i of
the same group in the folded state according to:
qi ¼
1
1
i
i pH or q ¼
i
pK
a
1 þ 10
1 þ 10pHpKa
ð4bÞ
J. Mol. Recognit. 2004; 17: 1–16
PROTEIN STABILIZATION BY SALT BRIDGES
5
Considering an entire protein with n ionizable groups, the
free energy contribution of all the n groups (whether or not
involved in salt bridges) is defined by:
ð
2:3RTðQU QF ÞpH
ð5aÞ
GU ¼
pH
Pn
P
where QU ¼ i¼1 qiU and QF ¼ ni¼1 qiF .
Integration of eqn (5a) over the entire pH range yields the
stability difference between the fully protonated and the
fully deprotonated protein molecule:
GU ¼ GU;dp GU;p ¼ 2:3RT
n X
pKaU;i pKaF;i
i¼1
ð5bÞ
Figure 4. Thermodynamic cycle of the relationship between the
proton association constants KF;i and KU;i of residue i in the
folded (F) and unfolded (U) protein and the free energies of
U;i
unfolding GU;i
p and Gdp of the protein carrying the protonated
U;i
(p) or the deprotonated (dp) residue i. GF;i
prot and Gprot are the
free energies of protonation of residue i in the folded and
unfolded protein, respectively. The contribution of group i to
stability results from different pKa values in the folded and
unfolded protein and is calculated according to eqn (4c) of the
text, which is shown at the bottom of the figure.
where qi refers to qiU and qiF , and pKai to pKaU;i and pKaF;i ,
respectively. The left equation is for negative charges
(acidic residues) and the right one for positive charges
(basic residues). Integration of the combined eqns (4a)
and (4b) over the entire pH range yields the stability
difference between the protein with the fully protonated
(subscript p) and the fully deprotonated (subscript dp) group
i:
GiU ¼ GiU;dp GiU;p ¼ 2:3RT pKaU;i pKaF;i
ð4cÞ
Equation (4c) says that the contribution of charged residue i
to protein stability is directly related to the pKa shift of
residue i between the unfolded and folded protein. This is
shown graphically by the thermodynamic cycle of Fig. 4.
From Table 1 it is seen that GiU is positive if the
deprotonated form of the side chain (charged acidic or
uncharged basic group) is stabilizing, and negative if the
protonated side chain makes the protein more stable (uncharged acidic or charged basic group).
It is very important to note that GiU and GiU defined
by eqns (4a) and (4c) are not the total contribution of group i
to the stability of a protein. As already mentioned above, it
is the relative stability contribution due to electrostatics with
regard to a reference pH value. Hence, GiU is sometimes
called Gi;ele
U . For example, the carbon atoms of the side
chain of an ionizable residue may contribute to molecular
packing in the folded protein but this effect on the free
energy of unfolding cannot be deduced from the change of
pKa and is not included in GiU and GiU (Bashford and
Karplus, 1990; Yang and Honig, 1993). That means, the
starting value for integration of eqn (4a) is arbitrary, for
example pH ¼ 0. GiU of eqn (4a) then provides the free
energy difference in the interval pH–pH 0, which is the
relative electrostatic contribution to the overall free energy
change obtained from the titration of group i.
Copyright # 2004 John Wiley & Sons, Ltd.
Equation (5b) relates the difference in the free energy of
unfolding of the entirely protonated and deprotonated protein, respectively, to the change in the pKa of all ionizable
groups upon unfolding and assuming there is no conformational difference between the fully protonated and the fully
deprotonated protein. This equation was derived by Tanford
in his seminal treatment of protein unfolding (Tanford,
1970). If all the values of pKaU;i and pKaF;i are known, the
relative pH dependent stability profile of the protein
[eqn (5a)] and, consequently, the free energy difference
between the protein carrying n fully deprotonated and
protonated ionizable residues, respectively, [eqn (5b)] can
be calculated. This is the basis of the computational methods to calculate the energetic contribution of charges.
It should be noted that in some cases experimental
titration curves (e.g. observed pH-induced chemical shifts)
may not display a simple sigmoidal shape conforming to the
Henderson–Hasselbalch relationship expressed by eqn (4b)
(Spitzner et al., 2001). Since multi-sigmoidal titration
curves are often caused by strong electrostatic coupling
between neighboring charges, careful assessment of the
protonation behavior is necessary in order to calculate
GU according to eqn (5) (Koumanov et al., 2001b).
Among all the charges of a protein, only a subset is
involved in salt bridges. For a simple salt bridge composed
of residues i and j, eqn (5b) reduces to:
GijU ¼ 2:3RT pKaU;i pKaF;i þ pKaU;j pKaF;j
ð5cÞ
The above equation describes the different contributions to
stability of the salt bridge residues when they are entirely
deprotonated and entirely protonated, respectively. The
equation does not give the net energetic contribution of
the salt bridge as expressed by eqn (3).
Examples of salt bridge energies calculated from
changes of pKa
A salt bridge in T4 lysozyme. Bacterial lysozyme T4
contains a partially buried salt bridge between His31 and
Asp70 (Anderson et al., 1990). In the folded protein, pKaF of
His31 is 9.1 and pKaF of Asp70 is 0.5. The corresponding
pKaU values of the unfolded protein are 6.5 (His) and 3.9
(Asp), respectively. These are remarkably large pKa changes
between the unfolded and the folded state, 2.6 pH units for
His and þ3.4 for Asp. Accordingly, positively charged His
J. Mol. Recognit. 2004; 17: 1–16
6
H. R. BOSSHARD ET AL.
respectively) to the stability of T4 lysozyme is 19 and
15 kJ/mol, respectively. The curve is bell-shaped because
the salt bridge is broken at low and high pH through
protonation of the Asp side chain and deprotonation of the
His side chain, respectively. The inflection points of the
stability curve indicated by circles are the midpoints between pKaF and pKaU (not pKaF of the salt bridge’s ionizable
groups in the native protein, as is sometimes assumed). The
free energy difference between the fully protonated and
deprotonated protein is about 4.6 kJ/mol. This value is
calculated by eqn (5c) and is indicated by the arrow on
the right hand side of Fig. 5(A).
Figure 5. (A) Relative pH–stability profile of the His31–Asp70 salt
bridge of T4 lysozyme obtained by the pKa approach. The free
energy contribution of charged His (short dashed line) and
charged Asp (long dashed line, partly buried under solid line)
to protein stability, and the sum of the two contributions (solid
line) are shown. The curves are calculated [eqns (4a) and (5a)]
using pKFa of 0.5 and 9.1 and pKU
a of 3.9 and 6.5 for His and Asp,
respectively (Anderson et al., 1990). The relative maximum free
energy at pH 5.2 is 19 kJ/mol (arrow at center). The energy
difference between the fully protonated and the fully deprotonated protein is 4.6 kJ/mol [arrow at right, eqn (5c)]. The inflection points marked by circles correspond to the midpoints
between pKFa and pKU
a of Asp and His, respectively. (B) Hypothetical pH–stability profile of the His31–Asp70 salt bridge calculated by assuming a net free energy contribution of 11 kJ/mol at
pH 5.2 (arrow at center), which results from a highly favorable
direct energy contribution of 23 kJ/mol and from unfavorable
indirect contributions (desolvation and background interactions)
of 8 kJ/mol for His and 4 kJ/mol for Asp [see eqn (6b)]. If His
and Asp interact only with each other but not with other charged
residues nearby, the net energies at the low and high pH limits
correspond to the indirect terms of the basic and the acidic salt
bridge partner, respectively (arrows on left and right). The
shapes of the curves in (A) and (B) are identical since the same
pKa shifts of Asp and His were used in the calculation.
and negatively charged Asp contribute very strongly to
stability when compared to their uncharged forms.
Figure 5(A) shows the calculated relative free energy contributions of the two residues in the pH range 0–12. The
relative contribution to stability from charging (deprotonation) of Asp70 is 19 kJ/mol [long dashed line in Fig. 5(A)].
Charging of His31 provides 15 kJ/mol (short dashed line).
The summed energy contributions are indicated by the solid
bell-shaped curve, which corresponds to the integral of
eqn (5a) with QU ¼ qiU þ qjU and QF ¼ qiF þ qjF . The
function peaks at pH 5.2 where both side chains are
>99% charged. At this pH, the relative contribution of the
positive and negative charge (with regard to pH 0 and pH 12,
Copyright # 2004 John Wiley & Sons, Ltd.
Salt bridges in leucine zippers. There has been much work
and also some controversy about the electrostatic contribution of salt bridges to the stability of leucine zippers and
other coiled coils. Dimeric leucine zippers are composed of
two -helices wound around each other to form a lefthanded, parallel super helix. Formation of the coiled coil
structure originates from a repeating seven-residue sequence motif in which the first and the fourth residue are
mostly non-polar and are stabilizing the coiled coil structure
through hydrophobic interaction at the interface between
the two helices. In addition, there are several acidic and basic
residues positioned such that they may form salt bridges
between the helices. Whether or not such interhelical
salt bridges are adding to the stability of the coiled coil
has been debated (Krylov et al., 1994; Zhou et al., 1994;
Lumb and Kim, 1995; Krylov et al., 1998; Marti et al.,
2000; Phelan et al., 2002). We have determined the stability
contribution from charges located on Glu and His residues
by the pKa approach, using the model leucine zipper ABSS.
In this dimeric coiled coil six interhelical salt bridges are
formed between the side chains of Glu residues in one helix
and those of Lys and Arg in the other helix (Marti et al.,
2000; Marti and Bosshard, 2003). The sequence of the
model leucine zipper ABSS and the salt bridges observed
by NMR spectroscopy are shown in Fig. 6. Table 2 shows
the values of pKaF and pKaU determined by 11H-NMR
spectroscopy of the folded leucine zipper ABSS and of
unfolded reference peptides (Marti and Bosshard, 2003).
The free energy contribution of each charged Glu side chain
participating in a salt bridge was calculated according to
eqn (4c). Of the six charged Glu side chains, two are stabilizing, three are destabilizing, and one contributes negligibly. The net relative contribution of the six Glu residues
involved in the six salt bridges is slightly unfavorable.
Together they destabilize the coiled coil by 1.1 kJ/mol
relative to the six uncharged, protonated Glu side chains.
This was confirmed by independent measurement of the
unfolding free energy of ABSS at different pH values: the
stability of ABSS increases at low pH, as predicted if the
charged Glu side chains are destabilizing (Phelan et al.,
2002). Incidentally, additional destabilization of ABSS is
caused also by charged Glu’s not involved in salt bridges
(Marti and Bosshard, 2003).
To assess the energetic contributions of all charges
involved in the six salt bridges to the relative pH dependent
stability profile of the protein one also needs to know the
pKaF and pKaU values of the basic partner residues Lys and
Arg. Experimental determination of Lys and Arg side chain
pKas was not possible for technical reasons (Marti and
J. Mol. Recognit. 2004; 17: 1–16
PROTEIN STABILIZATION BY SALT BRIDGES
7
Figure 6. Upper part: sequence of leucine zipper ABSS composed of an acidic and a basic chain connected by a disulfide
bridge (vertical line at right). Six interhelical salt bridges observed by NMR spectroscopy are indicated by double headed
arrows. Dashed numbers refer to sequence positions in the basic
chain. Lower part: ensemble of 25 NMR structures of ABSS. Only
the backbone trace and the side chains of acidic and basic
residues are shown. Salt bridges Glu8–Lys130 , Glu15–Lys200
and Glu22–Arg270 are encircled. The remaining three salt
bridges are on the ‘back’ of the molecule and are not seen in
this representation. NMR data from Marti et al. (2000).
Bosshard, 2003). Using computed pKa values for Lys200 and
Arg270 , the relative stability contributions of two of the six
salt bridges have been calculated and are shown in Fig. 7. In
the salt bridge Glu15–Lys200 , charged Glu as well as
charged Lys contribute to stability, charged Glu being
more stabilizing than charged Lys whose contribution is
small. Compared with the His31–Asp70 salt bridge of T4
lysozyme shown in Fig. 5(A), the free energy of the salt
bridge Glu15–Lys200 shows a plateau between pH 6 and 9
because the pKas of Glu and Lys are farther apart than those
of Asp and His (upper panel of Fig. 7). The situation is
peculiar for the salt bridge Glu22–Arg270 (lower panel of
Fig. 7). Here, the charged side chain of Glu22 is destabilizing the native protein while charged Arg270 is stabilizing.
Hence the summed energy contributions are not bell-shaped
Figure 7. Calculated contributions of charged side chains to two
salt bridges of the leucine zipper ABSS shown in Fig. 6. The
contribution of the negative charge of Glu is indicated by long
dashed lines, that of the positive charge of Lys and Arg by short
dashed lines, and the total contributions of both charges by solid
lines. The following pKa-values were used for the calculation:
pKFa ¼ 3.96 (Glu15), 4.86 (Glu22), 10.4 (Lys200 ), 12.7 (Arg270 );
0
0
pKU
a ¼ 4.31 (Glu15), 4.53 (Glu22), 10.3 (Lys20 ), 12.0 (Arg27 ).
The inflection points marked by circles correspond to the midpoints between pKFa and pKU
a . Data from Marti and Bosshard
(2003) and unpublished calculations.
Table 2. Values of pKFa and pKU
a of Glu side chains involved in salt bridges with side chains of Lys or Arg in leucine
zipper ABSS (Fig. 6). The free energy change GUi was calculated according to eqn (4c). Data from Marti and
Bosshard (2003)
Residue
pKaF
pKaU
GiU for Glu side
chain (kJ/mol)
Glu8
Glu13
Glu15
4.45
4.34
3.96
4.33
4.36
4.31
0.71
0.12
2.08
Destabilizing
Negligible
Stabilizing
Glu20
Glu22
4.41
4.86
4.61
4.53
1.19
1.96
Stabilizing
Destabilizing
Glu27
Sum of GiU
4.65
4.35
1.78
1.1
Destabilizing
Destabilizing
a
Effect of charged Glu
side chain on stability
Salt bridge
partner residue
Lys130
Arg80
Lys200
pKaF ¼ 10:4a
Arg150
Arg270
pKaF ¼ 12:7a
Lys220
From computation.
Copyright # 2004 John Wiley & Sons, Ltd.
J. Mol. Recognit. 2004; 17: 1–16
8
H. R. BOSSHARD ET AL.
but exhibit a step-pattern. Increasing the pH up to 6
decreases the free energy because the pair Glu –Argþ is
more stabilizing than the charge–charge pair Glu–Argþ.
The plateau between pH 6 and 11 is caused by the salt
bridge. The decrease above pH 11 is due to deprotonation of
the Arg side chain. Note that the experimental and calculated pKa values used for generating the curves in Fig. 7
result from interactions with all charged residues positioned
close to the residue under investigation. The interaction
with the ion paired residue has the highest impact on the
pKa, nonetheless, the sum of the interactions with the
remaining charged residues may affect the pKa. Hence, in
case of truly isolated salt bridges, the shape of the curves in
Fig. 7 might look slightly different.
As is evident from the NMR structure and from the
mutation of Arg270 to norvaline (see below), the salt bridge
Glu22–Arg270 is real despite that the charged Glu side chain
is destabilizing. This is an important conclusion: a destabilizing charge is no evidence against a salt bridge. Destabilization revealed by the pKa approach is relative to a
reference pH, in this case relative to pH 0 at which pH
Glu22 is fully protonated. Only the net free energy of a salt
bridge, which is the sum of the net energetic contributions of
both charges together, reveals net stabilization or destabilization. To get this information, one needs to decompose the
free energy into favorable and unfavorable contributions, as
will be discussed now.
The electrostatic free energy difference between the
folded and unfolded state can be decomposed into
three components
During folding the charged groups of a protein undergo three
types of changes as defined by Bashford and Karplus (1990)
and shown in Fig. 8. (i) The groups are brought from a freely
Figure 8. Model according to Bashford and Karplus (1990) depicting the partitioning of the electrostatic free energy difference
[GUi, eqns (4a) and (4c)] of the ionizable group i (black circle)
between the unfolded and the folded protein. Moving group i
from a high dielectric environment in the unfolded protein
(dotted circle at right) to a low dielectric environment in the
folded protein (stippled area at left) is accompanied by unfavorable desolvation of group i and leads to GUi,desolv . Electrostatic
interactions of group i with partial charges of the peptide backbone and polar, non-ionizable side chains (open circles, dashed
arrows) are different in the unfolded and folded state and lead
to the term GUi,backgrd . Direct electrostatic interactions between charged group i and other charged groups (grey circles,
solid arrows) are formed in the folded protein leading to
GUi,bridge .
Copyright # 2004 John Wiley & Sons, Ltd.
water-accessible, high dielectric environment to an environment of low dielectricity. As a consequence, the groups have
to be partly or fully desolvated. (ii) In the folded as well as
the unfolded protein, charged groups are interacting with
permanent partial charges such as dipoles of peptide bonds
or polar non-ionizable side chains. These so-called background interactions differ in the unfolded and folded state.
(iii) In the folded protein, charges are interacting with other
full charges. Such direct charge–charge interactions are
attractive (e.g. salt bridges) or repulsive. No direct charge–
charge interactions are expected to occur in the unfolded
protein if it is considered to be a fully extended polypeptide
chain. Note, however, that his assumption may not be
justified since some residual direct charge–charge interaction
can exist in the denatured state (see the section ‘Electrostatic
Interactions in the Denatured State’).
Accordingly, the electrostatic free energy difference can
be decomposed into three components:
þ Gi;backgrd
þ Gi;bridge
ð6aÞ
GiU ¼ Gi;desolv
U
U
U
Gi;desolv
and Gi;backgrd
are the indirect energy conU
U
is the direct contribution.
tributions and Gi;bridge
U
is the free energy difference caused by desolvaGi;desolv
U
is the
tion of charge i. It is an unfavorable term. Gi;backgrd
U
free energy difference due to background interactions of
charge i with permanent dipoles of the peptide backbone, of
helices, or of non-ionizable polar side chains. Gi;backgrd
U
can be favorable or unfavorable. The indirect energy con¼ Gi;desolv
þ
tributions are summed as Gi;indirect
U
U
i;backgrd
i;desolv
. Both GU
and Gi;backgrd
are conGU
U
sidered to be independent of the pH. (Note that the interacting charge i itself is, of course, pH dependent.)
is the free
The direct free energy contribution Gi;bridge
U
energy difference due to electrostatic interactions of the
charge of group i with other charges of the protein. This
direct interaction term is pH dependent. Salt bridges add
, repulsions contribute unfavorably.
favorably to Gi;bridge
U
From the decomposition according to eqn (6a) follows
that the net free energy of a salt bridge as defined by eqn (3)
may differ from the relative free energy difference calculated from the changes of pKa, since the latter is a relative
free energy contribution with respect to the starting pH of
the integration according to eqn (5a) and does not necessarily account for exactly the same bridge, desolvation and
background contributions. This point is again illustrated by
the His–Asp salt bridge of T4 lysozyme and the two salt
bridges of the leucine zipper ABSS, as discussed now.
Decomposition of the free energy contribution of the salt
bridge His31–Asp70 of T4 lysozyme. For a simple salt
bridge between residues i and j, eqn (6a) has the form:
GijU ¼ Gi;desolv
þ Gj;desolv
þ Gi;backgrd
U
U
U
1
1
þ Gj;backgrd
þ Gi;bridge
þ Gj;bridge
U
U
U
2
2
ð6bÞ
of direct charge–charge
In eqn (6b), the term Gbridge
U
interaction is equally divided between the two ion pairing
is
partners. In this way, the common term Gbridge
U
summed only once in the calculation of the net energy
contribution of the salt bridge, GijU (Yang and Honig,
J. Mol. Recognit. 2004; 17: 1–16
PROTEIN STABILIZATION BY SALT BRIDGES
1993). If the energy of the salt bridge His31–Asp70 of
lysozyme were due only and exclusively to direct Coulombic charge–charge interaction, eqn (6b) would reduce to
þ 12 Gj;bridge
. In this ideal case,
GijU ¼ 12 Gi;bridge
U
U
both charges would equally contribute to Coulombic interaction so that the decrease of pKaF of Asp70 would exactly
match the increase of pKaF of His31. Clearly, this cannot be
true. First, the pKa shifts of His31 and Asp70 are different,
2.6 and þ3.4 pH units, respectively (Anderson et al.,
1990). The reason is that the side chains of His and Asp
‘feel’ other charges apart from the charge of the reciprocal
partner residue. Second, both residues are partly buried in
the folded protein (Anderson et al., 1990). Hence, the
indirect energy terms from desolvation and formation of
new background interactions are non-zero.
Unfortunately, there is no experimental method to deterand Gbackgrd
. One has to resort to
mine Gdesolv
U
U
computational methods, which are approximate and sometimes even ambiguous. Estimates for the unfavorable free
energy of desolvation of the His31–Asp70 salt bridge range
from 48 kJ/mol (Hendsch and Tidor, 1994) to 8 kJ/mol
(Dong and Zhou, 2002). The first, strongly negative value is
based on the computed mutation of both residues to the
uncharged isosters. The second, less negative value was
obtained from the computed mutations His ! Asn and
Asp ! Asn. Also, the surface accessibility was computed
on the basis of different dielectric boundary conditions
(Hendsch and Tidor, 1994; Dong and Zhou, 2002). Thus,
despite all the experimental and computational efforts, we
still do not know with certainty whether the ‘archetypal’
His–Asp salt bridge is stabilizing or destabilizing the
structure of T4 lysozyme.
For the sole purpose of illustrating the relationship
between the net free energy GijU and the direct and
indirect energy terms [eqns (6a) and (6b)], we present a
hypothetical pH-stability profile for the His31–Asp70 salt
bridge in Fig. 5(B). The dash-dotted curve in Fig. 5(B)
represents the net free energy of the salt bridge, which peaks
at 11 kJ/mol, about 8 kJ/mol less than GijU calculated
from the pKa shifts in Fig. 5(A). This lower net free energy
is caused by unfavorable indirect contributions (desolvation
and background interactions) of 8 kJ/mol for His and
4 kJ/mol for Asp (the values are arbitrarily chosen).
Thus, when both His and Asp are charged, the unfavorable
indirect contributions add up to 12 kJ/mol (arrow at pH
5.2). According to eqn (6b), the direct contribution,
, is 23 kJ/mol, which is higher than the 19 kJ/
Gbridge
U
mol calculated from the pKa shifts in Fig. 5(A). This is an
important result: the relative GijU from the pKa approach
is smaller than the direct contribution from charge–charge
, whenever the indirect contributions
interaction, Gbridge
U
are unfavorable. Only if the indirect contributions are
negligible, GijU from the pKa approach is equivalent to
, which is the interaction free energy between the
Gbridge
U
charges. However, formation of a salt bridge with negligible
desolvation and unaltered background interactions is very
rare. A possible example is a Glu–Lys salt bridge in an IgGbinding protein (Kumar and Nussinov, 1999).
Decomposition of the free energy contributions of salt
bridges in leucine zipper ABSS. The salt bridges Glu15–
Lys200 and Glu22–Arg270 of the leucine zipper ABSS have
Copyright # 2004 John Wiley & Sons, Ltd.
9
Figure 9. Calculated free energy contributions of the charges
forming the salt bridges Glu15–Lys200 (top) and Glu22–Arg270
(bottom) of the leucine zipper ABSS (Fig. 6). Calculations included favorable and unfavorable contributions from desolvation, background and charge–charge interactions as defined
by eqn (6a). Bars 1–4 represent GUi ¼ GUi,charged GUi,uncharged of Glu (circled ) and Arg (circled þ ) in the
presence or absence of the opposite charge (faint circled þ or
, or empty circle if charge is absent). Bar 5 shows the net free
energy contribution of the salt bridge. Data from Marti and
Bosshard (2003) and unpublished calculations.
been analyzed in terms of direct and indirect energy contributions using the program DelPhi (Nicholls and Honig,
1991). Figure 9 shows the results as bar plots in which the
contribution of each single residue (bars 1–4) is presented
together with the net free energy contribution of the salt
bridge (bar 5). According to this calculation, both salt
bridges are destabilizing the coiled coil conformation by
about 5 kJ/mol. This means that the favorable direct charge–
charge interactions are outbalanced by unfavorable desolvation [the background terms are small or even negligible
(Marti and Bosshard, 2003)]. In the case of the Glu15–
Lys200 salt bridge, only the negative charge on Glu15 adds
favorably when placed opposite to charged Lys20 (bar 1 in
the top panel of Fig. 9). When the charge on Lys200 is
removed, the ‘lonely’ negative charge on Glu15 becomes
slightly destabilizing (bar 2 of top panel). The positive
charge of Lys200 is destabilizing whether or not juxtaposed
to a negative charge on Glu15 (bars 3 and 4 of top panel). In
the case of the salt bridge Glu22–Arg270 , only the positive
charge of Arg270 is stabilizing when next to the negative
charge of Glu22 (bar 3 of bottom panel). Charged Glu22 is
destabilizing irrespective of the presence of a counter
charge (bars 1 and 2 of bottom panel). Even though opposing stability, the two salt bridges are nevertheless
present in the folded structure of ABSS as shown by
NMR spectroscopy and by the results from mutation
(see below).
J. Mol. Recognit. 2004; 17: 1–16
10
H. R. BOSSHARD ET AL.
It is sometimes said that salt bridges are more stabilizing
in the protein interior than at the surface because the
dielectric of the interior is low. This assumption is based
on attributing the strength of a salt bridge to the Coulombic
potential, which is indeed stronger when the dielectric
constant is low [eqn (1)]. However, burying a salt bridge
in the interior increases the desolvation penalty. In terms of
(because of a low
eqn (6b), a more favorable Gbridge
U
dielectric constant) is counterbalanced by a more unfavor(because of stronger desolvation in the low
able Gdesolv
U
dielectric environment). Therefore, a buried salt bridge is
not necessarily contributing more to stability than a surfaceexposed salt bridge.
In concluding this section on the pKa approach we note that
knowledge of pKa shifts is necessary to establish whether or
not charged groups add to stability when compared with uncharged groups. pKa values give direct insight into the electrostatic forces between ionizable side chains. The lower the
value of pKaF compared to pKaU , the more the deprotonated
group (charged acidic or uncharged basic residue) is stabilizing the folded protein. However, this is a relative energy
contribution of charges. Knowledge of pKas is not sufficient to
establish the net (or absolute) free energy contribution of
charges, of which we have seen that it results mainly from the
balance between favorable direct free energies of interaction
between charges and unfavorable desolvation penalties, the
contributions from background interactions being often small
and either favorable or unfavorable.
THE MUTATION APPROACH:
ASSESSING ELECTROSTATIC
INTERACTIONS FROM MUTATIONS
There are numerous reports about the mutation of residues
involved in salt bridges. In the vast majority of examples,
removing a charge by mutation destabilizes the protein.
Taken at face value this would mean that most salt bridges
are stabilizing, which is obviously wrong. The loss of free
energy from mutation cannot be equated with the loss of salt
bridge energy. The reason is simple. Even in the case of the
least invasive mutation of, for example, glutamic acid to
glutamine, desolvation of the carboxylate group differs from
desolvation of the isosteric, uncharged amide group. Also,
the amide group may undergo new background interactions
that are absent in the original protein, for example new Hbonds. The situation is much more serious when the charged
residue is mutated to Ala or even to a residue of opposite
charge, as is often done. If we take as an example the
mutation Glu ! Ala, the electrostatic interaction is removed
but so is the H-bonding capability of uncharged Glu. Solvent
and van der Waals interactions are lost and new ones are
formed. Space is created which may permit other groups of
the protein to repack, and so forth. In short, it is not possible
to remove the charge–charge interaction of interest and not
to alter other interactions or introduce new ones. Thus,
individual mutations cannot provide quantitative information about the free energy of a salt bridge. Still, mutations
can give valuable qualitative information. For example, in
the case of the salt bridges Glu15–Lys200 and Glu22–Arg270
of the leucine zipper ABSS, it could be shown by mutation of
Lys200 to isosteric norleucine (Nle) and of Arg270 to
Copyright # 2004 John Wiley & Sons, Ltd.
isosteric norvaline (Nva) that both salt bridges are indeed
present even so they destabilize the coiled coil conformation
(Marti and Bosshard, 2003). In the salt bridge Glu15–Lys200
to which the charged Glu contributes favorably, charge–
charge interaction is lost if the salt bridge is mutated to
Glu15–Nle200 . Indeed, pKaF of Glu15 is significantly higher
in the mutant, a clear indication of the presence of the salt
bridge. Similarly, if there were no salt bridge between Glu22
and Arg270 , the pKaF of Glu22 should not increase in the
mutant Glu22–Nva270 . However, the experiment showed
pKaF of 5.45 for the mutant as compared to 4.86 for the wildtype. This clearly indicates that the salt bridge Glu22–
Arg270 does exist despite that charged Glu22 is in fact
destabilizing the coiled coil structure. Again, a destabilizing
charge is no evidence against a salt bridge.
Double mutant cycles yield the coupling free energy
of salt bridges
Combining mutations in a double mutant cycle provides an
elegant way to obtain quantitative information about the
stability contribution of a salt bridge (Carter, 1984; Ackers
and Smith, 1985; Horovitz et al., 1990; Serrano et al., 1990;
Krylov et al., 1998). If two charged residues are not
interacting with each other, then the change in protein
stability resulting from the removal of both charges by
mutation will be equal to the sum of the stability changes
seen with the two single mutations. By contrast, if the two
charges are interacting with each other, the change in
stability of the double mutant will not be the sum of the
changes of the two single mutants.
A double mutant cycle yields the so-called coupling
free energy of a salt bridge. The principle is shown in
the example of Fig. 10. The cycle comprises the two
single mutations Glu ! Ala and Lys ! Ala and the
double mutation Glu/Lys ! Ala/Ala. If the mutated residues
are interacting with each other, the effect of substituting one
Figure 10. Determination of the coupling free energy of a salt
bridge by a double mutant cycle. See the text for detailed
discussion.
J. Mol. Recognit. 2004; 17: 1–16
PROTEIN STABILIZATION BY SALT BRIDGES
residue will depend on the substitution of the other residue.
The free energies of the two mutations are coupled:
Gwt!m1 6¼ Gm2!dm and Gwt!m2 6¼ Gm1!dm .
The coupling free energy is defined as:
Gijcoupling ¼ Gwt!dm Gwt!m1 Gwt!m2
ð7aÞ
From Fig. 10 it follows that eqn (7a) can also be written
as: Gijcoupling ¼ ðGdm Gwt Þ ðGm1 Gwt Þ
ðGm2 Gwt Þ which simplifies to:
Gijcoupling ¼ Gdm Gm1 Gm2 þ Gwt
ð7bÞ
Hence, to determine the coupling free energy of a salt bridge
according to eqn (7b), the free energy of unfolding, GU,
has to be determined for the wild-type protein, the two
single mutants and the double mutant.
The double mutant cycle is designed to cancel all effects
except those from the direct interaction between the two
mutated residues. In the example of Fig. 10, the mutation
Glu ! Ala removes desolvation and background effects of
Glu, the mutation Lys ! Ala removes the corresponding
effects of Lys. All the indirect effects for both residues are
removed in the double mutant Glu/Lys ! Ala/Ala. According to eqn (7b), the indirect effects are first subtracted for
each residue (Gm1 Gm2 ) and then added back again
by (þGwt ). Hence, in an ideal double mutant cycle the
coupling free energy is due only to the direct interaction
between the mutated residues. In the case of a salt bridge, it
is the direct charge–charge interaction and, perhaps, other
direct interactions (i.e. van der Waals interactions between
atoms of the side chains carrying the charges). Hence, in the
, assuming
ideal case, Gijcoupling should equal Gbridge
U
all other interactions and, especially desolvation of the
charges, are being cancelled. However, such cancellation
requires that all interactions are simply additive from the
single to the double mutation, that there is no significant
change of conformation caused by either mutation alone,
and that the mutations do not significantly change the
unfolded state. If these conditions are not met, the coupling
free energy, Gijcoupling , differs from the direct interaction
free energy between the groups of a salt bridge. Particularly
in the case of a strongly interacting ion pair maintaining van
der Waals contact, the mutational change in desolvation
energy in presence and absence of the ion pairing partner
may be large. The coupling energy term is then written as
Gi;desolv
Gj;desolv
Gijcoupling ¼ Gbridge
U
U
U
ð7cÞ
are the changes in desolvation energy of
where Gdesolv
U
the residues after mutation of the salt bridge partners. That
is the indirect energy contribution that is
means, Gdesolv
U
not canceled by the double mutation cycle and that is likely
due to larger exposedness to solvent in absence of the
partner residue (Serrano et al., 1990).
Examples of coupling free energies from double mutant
cycles. A test of the validity of the above assumptions in
double mutant cycles is to perform multiple mutations for
each group. For example, the coupling free energy of the salt
Copyright # 2004 John Wiley & Sons, Ltd.
11
bridge Glu–Lys of Fig. 10 should be determined not only for
mutations to Ala but also for mutations to Gln, Leu, etc. If
the same coupling free energy is found for each type of
mutation, all interactions are simply additive and there are
no mutation-induced conformational changes (or the
changes are the same for all mutations, which is very
unlikely). Only rarely has such rigorous testing been performed for a double mutant cycle. A very recent example is
a study on the partially surface-located salt bridge between
the N-terminal amino group and the side chain of Asp23 in
ribosomal protein L9. The coupling free energy of this ionic
interaction ranged from 2.9 to 7.1 kJ/mol, depending on
the set of different mutants used in the double mutant cycle
(Luisi et al., 2003). This observation, together with discrepancies between experimental and computed mutations,
indicates that assumptions frequently used to interpret
double mutant cycles may not always be adequate.
In the case of the salt bridge His31–Asp70 of T4
lysozyme, the coupling free energy is about 16–20 kJ/mol
(Anderson et al., 1990; Dong and Zhou, 2002). Is this
energy equivalent to the free energy of interaction between
? As disthe salt bridge partners: Gijcoupling ¼ Gbridge
U
cussed above, the maximum free energy obtained by the pKa
approach [19 kJ/mol based on published pKa shifts,
only if the indirect terms
Fig. 5(A)] is equal to Gbridge
U
are negligible. If this is not the case and the indirect
desolvation and background energy contributions are unis larger
favorable, it follows from eqn (6a) that Gbridge
U
than 19 kJ/mol. This is likely to be the case in view of the
fact that the desolvation term is always unfavorable and
usually dominates over the relatively small background
interaction term (Kumar and Nussinov, 1999). Thus, the
reported coupling free energy of 16–20 kJ/mol obtained by
the mutation approach probably underestimates the direct
. In general, the coupling
interaction free energy, Gbridge
U
free energy of a salt bridge, Gijcoupling , is smaller then the
direct interaction free energy, Gijbridge , whenever the
indirect terms are unfavorable and not fully compensated
by the double mutant cycle. On the other hand, Gijcoupling
tends to be larger than the net (or absolute) free energy
contribution of the salt bridge, GijU , defined by eqn (3),
since unfavorable indirect energy contributions are at least
partly compensated by the double mutant cycle.
In the case of interhelical salt bridges of leucine zippers,
extensive double mutant cycle analyses in a host-guest
system has provided mean values of coupling free energies
of 2.1–2.5 kJ/mol (Glu–Lys and Glu–Arg) and of 3.3 kJ/
mol for repulsive Glu–Glu interactions (Krylov et al., 1998).
These values are very unlikely to correspond to the mean
direct interaction free energy of interhelical salt bridges
) since indirect effects from desolvation
(mean Gbridge
U
and background interactions in coiled coils are non-zero.
of seven salt
The computed mean value of Gbridge
U
bridges in a heterodimeric leucine zipper is 9 kJ/mol (Kumar
and Nussinov, 2000), significantly larger than the mean
experimental coupling free energy reported by Krylov
et al. (1998). This indicates that context-dependent interactions introduced by the mutations did not cancel in the
double mutant cycle analyses. A striking example of context-dependent effects is the Lys11–Glu34 salt bridge of
ubiquitin. The coupling free energy of this salt bridge is 3.5–
3.7 kJ/mol and has been deduced from three different and
J. Mol. Recognit. 2004; 17: 1–16
12
H. R. BOSSHARD ET AL.
independent double mutations (Makhatadze et al., 2003).
One would expect that such a rigorous double mutant cycle
analysis should have canceled all the indirect effects and
that the above coupling free energy should equal the direct
. As a further test, the
interaction free energy Gbridge
U
orientation of the salt bridge was reversed from Lys11–
Glu34 to Glu11–Lys34: The coupling free energy was again
3.8 kJ/mol, the same within error as for the wild-type salt
bridge. Obviously, this salt bridge of ubiquitin exhibits the
same coupling free energy in both orientations. However,
the global stabilities (GU) of wild-type ubiquitin and of the
mutant with the reversed salt bridge differ by 2.2 kJ/mol, the
wild-type protein being less stable. This is a striking
example of a context-dependent effect, which was not
revealed by double mutant cycle analysis. There have to
be different long-range interactions in the two proteins
depending on the orientation of the salt bridge even so
either salt bridge apparently stabilizes the protein to the
same extent.
In concluding this section on the mutation approach, we
note that double mutant cycles provide valuable information
about the strength of salt bridges in terms of the coupling
free energies. It currently is the only experimental approach
to obtain a semi-quantitative estimate of the free energy of
pairwise charge–charge interaction (Horovitz, 1996). Under
optimal conditions, particularly for well isolated salt
bridges, the coupling free energy is similar to the direct
interaction free energy between salt bridge charges. However, this has only rarely been rigorously tested. Much like
the pKa approach, the mutation approach does not yield the
net free energy contribution of a salt bridge.
THE COMPUTATION APPROACH
Computation of electrostatic forces in proteins has a long
history. Theoretical modeling is focused on the prediction of
measurable properties such as redox potentials and pKa
values, which are modulated by electrostatic effects. Protein
electrostatics is currently still intractable by quantum-mechanical methods because of the size of proteins and the
large number of charges involved. pKas of single residues
have been calculated by the quantum-mechanical description of the residue of interest in combination with a
molecular mechanics description of the rest of the protein
and a mean field approximation of the solvent (Lim et al.,
1991; Li et al., 2002). The most rigorous microscopic
models treat the protein–solvent system as a collection of
atoms with all atomic partial charges and polarizabilities
explicitly considered (Warshel and Russell, 1984; Kollman,
1993). In the potential energy function, electrostatic interactions are described by Coulomb’s law for charges and by
related expressions for multipoles. If the potential function
is accurate and if the dynamics of the system is reliably
taken into account by molecular dynamics or Monte Carlo
dynamics, a precise description of electrostatic properties is
achieved. Truly microscopic models usually suffer from
insufficient sampling, from convergence problems due to
the long range nature of electrostatic forces, as well as from
some inconsistencies arising from the fact that electronic
polarizability is not explicitly considered. Semi-macroscopic approaches present an alternative [dipolar models
Copyright # 2004 John Wiley & Sons, Ltd.
(Florian and Warshel, 1997; Papazyan and Warshel, 1997)].
The protein is treated at the molecular level by classical
force fields. The surrounding solvent is modeled by
Brownian or Langevin dipoles fixed in space. On a further
level of simplification, macroscopic methods (often referred
to as continuum methods) represent the protein as a low
dielectric medium in which the charges of ionizable groups
and the partial charges of permanent dipoles are assigned to
the corresponding atoms according to the three-dimensional
structure of the protein. The solvent is represented as a high
dielectric medium and mobile ions are taken into account
through the ionic strength. Because of the complex shape of
proteins, charges are mapped on a three-dimensional lattice
and values for the dielectric constant and ionic strength are
assigned to each lattice point. The Poisson–Boltzmann
equation is numerically solved according to an iterative
scheme to estimate the electrostatic potential at each lattice
point (Warwicker and Watson, 1982; Bashford and Karplus,
1990; Honig et al., 1993).
Prediction of the electrostatic free energy contribution to
protein stability, including the contribution of salt bridges,
requires precise calculation of the protonation equilibria of
individual titratable groups, which means calculation of
pKas. Microscopic and macroscopic approaches have been
successfully used for this purpose. Continuum methods
enjoy growing popularity because of computational simplicity and the need for only few parameters. However, the
accuracy of pKa calculation by the continuum method
critically depends on several factors. First, the uniform
dielectric constant assigned to the protein interior is an
empirical parameter and its ‘correct’ value is not known
(Schutz and Warshel, 2001; Simonson, 2001). Moreover, it is
unlikely that the dielectric properties of proteins are uniform
throughout the whole molecule. Values between 2.5 and 4
are often used, but better agreement between calculated and
measured pKas of surface-located groups is achieved with
dielectric constants of 10–20 (Antosiewicz et al., 1994). The
pKa of solvent-exposed residues can be well reproduced
using a dielectric constant of 80, whereas for desolvated
residues a dielectric constant of 15 yields more accurate pKa
values (Demchuk and Wade, 1996). It was attempted to solve
the problem by calculating local dielectric constants or by
introducing position-dependent dielectric constants (Sharp
et al., 1992; Voges and Karshikoff, 1998; Simonson, 2001).
Second, the method is based on a rigid body approximation
of the protein, the calculations being performed on X-ray
structures or single NMR conformers of proteins. This does
not sufficiently account for the conformational fluctuations
of proteins at the local and global scale. A possible solution
is to average the calculations over an ensemble of relevant
structures, that is side chain rotamer libraries, NMR ensembles or ensembles generated by Monte Carlo sampling or
unconstrained molecular dynamics simulations (You and
Bashford, 1995; Antosiewicz et al., 1996; Alexov and
Gunner, 1997; van Vlijmen et al., 1998; Gorfe et al.,
2002). Third, electrostatic effects arising from conformational changes caused by protonation and deprotonation
cannot be captured by the rigid body treatment of a structure
that has been solved at a fixed pH (Spassov and Bashford,
1999). Finally, the existence of tautomeric states (e.g. for
protonated Glu or Asp and for deprotonated His) has to be
taken into account either by statistical-mechanical treatment
J. Mol. Recognit. 2004; 17: 1–16
PROTEIN STABILIZATION BY SALT BRIDGES
or by optimizing the hydrogen-bond network (Koumanov
et al., 2001a; Nielsen and Vriend, 2001). All these limitations have prompted for extensive theoretical work and
elegant solutions have been proposed.
With regard to salt bridges, the attractiveness of the
computation approach lies in the opportunity to calculate
the net free energy of a salt bridge, to compute the direct and
indirect components of the net free energy, and to perform
any kind of mutation in silico. For example, both charges
can be removed at the same time by making the groups
nonpolar without changing their chemical structure and
without affecting the protein conformation. Similarly, any
type of experimental double mutant cycle analysis can be
mimicked by computation. The vast data base of protein
structures can be mined to obtain information on hundreds
of salt bridges in order to classify salt bridges according to
location and geometry. However, few generalizations can be
made. For example, there is no obvious difference between
surface-located and buried salt bridges insofar as both can
be stabilizing or destabilizing (Kumar and Nussinov, 1999;
Kajander et al., 2000). It seems, however, that to bury a salt
bridge in the protein interior is costly and that, therefore,
replacing buried salt bridges by hydrophobic, preferably
isosteric residues is favorable (Hendsch and Tidor, 1994;
Waldburger et al., 1995). When compared with computed
hydrophobic and isosteric mutations, most salt bridges seem
to be destabilizing (Hendsch and Tidor, 1994; Xiao and
Honig, 1999). However, this conclusion largely depends on
the selection of the salt bridges used in the calculation
(Kumar and Nussinov, 1999) and on the definition of the
dielectric boundary conditions (Dong and Zhou, 2002).
Electrostatic interactions tend to oppose the association of
proteins (Sharp, 1996; Hendsch and Tidor, 1999) and of
protein with DNA (Misra et al., 1994).
A detailed discussion of the computation approach is
beyond the scope of this review. Excellent research papers
and reviews cover the details (Gilson and Honig, 1988;
Bashford and Karplus, 1990, 1991; Nicholls and Honig,
1991; Yang et al., 1993; Yang and Honig, 1993; Hendsch
and Tidor, 1994; Karshikoff, 1995; Kumar and Nussinov,
1999).
ELECTROSTATIC INTERACTIONS
IN THE DENATURED STATE
Experimental and computational approaches to estimate the
energetic contribution of salt bridges are based on thermodynamic cycles involving the unfolded state [eqns (2) and
(3), Figs 2 and 4]. Throughout the preceding discussion all
effects of salt bridges have been implicitly attributed to the
folded protein. This is a reasonable but not a necessary
assumption. The denatured protein is produced by the
addition of chemical denaturants or by heat and constitutes
a large ensemble of states in rapid equilibrium. Residual
electrostatic interactions may occur in some members of
this ensemble since secondary and tertiary contacts may be
retained. Indeed, the importance of electrostatic effects in
the denatured state has been demonstrated experimentally
and predicted by computation (Oliveberg et al., 1995;
Swint-Kruse and Robertson, 1995; Tan et al., 1995; Khare
et al., 1997; Schaefer et al., 1997; Elcock et al., 1999;
Copyright # 2004 John Wiley & Sons, Ltd.
13
Warwicker, 1999; Kundrotas and Karshikoff, 2002a,b).
Because the structural and thermodynamic properties of
the denatured state are poorly characterized, it is widely
assumed that side chain pKas of denatured proteins correspond to side chain pKas of small model compounds (e.g.
the pKa of Ac-Glu-amide is taken as the side chain pKa of
Glu in an unfolded protein). However, in a number of
studies, pKa values of acidic residues of denatured proteins
have been found to be depressed relative to the pKas of
freely accessible and well solvated model compounds
(Oliveberg et al., 1995; Swint-Kruse and Robertson, 1995;
Tan et al., 1995; Elcock et al., 1999; Kuhlman et al., 1999;
Whitten and Garcia-Moreno, 2000). This is a clear indication of residual and mainly local electrostatic interactions
between ionizable residues in the unfolded state. Electrostatic properties of the denatured state have been considered
in several computational studies dealing with the energetic
effect of salt bridges and with pH-dependent protein stability in general (Schaefer et al., 1997; Elcock et al., 1999;
Warwicker, 1999; Kundrotas and Karshikoff, 2002b; Zhou,
2002). Taken together, one is forced to conclude that
energetic contributions of salt bridges are also caused in
part by electrostatic interactions in the denatured state.
CONCLUDING REMARKS
There have been innumerable attempts to determine the
energy of salt bridges since the first measurement of the
‘strength’ of a salt bridge in chymotrypsin (Fersht, 1971).
Good computational methods permit to calculate the net
free energy of salt bridges based on high resolution protein
structures. However, the actual experiment remains the
benchmark. Therefore, our aim has been to compare the
merits and shortcomings of the two experimental methods
presently in use, the pKa approach and the mutation approach. The following points have been raised and
discussed:
(1) The free energy of unfolding of a salt bridge is defined
as a difference of differences. It is the change in the free
energy between the unfolded and the folded protein,
once with and once without the salt bridge [eqn (3)].
This difference is thermodynamically related to the
change of pKa of the ionizable groups in the unfolded
and folded protein [eqn (4c)].
(2) The net free energy contribution of a salt bridge is
composed of direct and indirect components. The direct
component comprises of the direct charge–charge inter, which are dominated by the single
actions, Gbridge
U
direct interaction between the oppositely charged
groups of the salt bridge; but interactions with other
. The indirect
nearby charges may also add to Gbridge
U
component comprises of desolvation and background
þ Gbackgrd
. Desolvation is
interactions, Gdesolv
U
U
unfavorable if the charges are buried and immobilized
in the folded protein. Background interactions with
permanent dipoles can be favorable or unfavorable.
The summed indirect effects tend to be unfavorable
since they are dominated by desolvation.
(3) The pKa approach provides the electrostatic contribution of charged groups relative to the corresponding
J. Mol. Recognit. 2004; 17: 1–16
14
H. R. BOSSHARD ET AL.
uncharged groups. This is the free energy gained or lost
when the groups involved in a salt bridge are being
charged. In other words, it is the free energy change
relative to a standard pH of 0 or 14 at which acidic and
basic groups, respectively, are uncharged. The pKa
approach cannot provide the net free energy of a salt
bridge. Only under the (rare) circumstances where there
is almost no desolvation and no change of background
interaction is the net free energy of the salt bridge
equivalent to the free energy deduced from pKa shifts.
(4) The mutation approach provides the coupling free
energy, Gijcoupling , between the charges of a salt
bridge with the help of a double mutant cycle. Indirect
effects from desolvation and change of background
interactions as well as context-dependent changes introduced by the mutations are assumed to be canceled in
the double mutant cycle. This assumption is very
difficult to test rigorously. Therefore, the coupling free
energy, Gijcoupling , is rarely equivalent but mostly
smaller than the direct charge–charge interaction en, yet larger than the net free energy
ergy, Gbridge
U
contribution of the salt bridge, GijU . Hence, the
coupling free energy is a valuable yet only approximate
measure of the ‘net strength’ of a salt bridge.
(5) The computation approach, which we have not discussed
in detail, allows to calculate the net free energy of a salt
bridge, including its decomposition into direct and
indirect components. However, the precision of computational results strongly depends on the quality of
structural data and on parameterizations such as the
definition of the electrostatic boundary conditions.
Therefore, results can be ambiguous. Even for structurally very obvious salt bridges (such as the one in T4
lysozyme we have used as an example) it still is very
difficult to assess the net contribution to protein stability.
Finally, we may ask why nature has kept salt bridges as
distinctive features of proteins? It has been speculated that
the burial of charges is a means to reduce protein stability. A
hydrophobic core of a large protein may give too much
stability if not destabilized by electrostatic interactions and
repulsions (Kajander et al., 2000). Though many salt
bridges may destabilize proteins with respect to the unfolded state, they are not necessarily more destabilizing than
other sequences compatible with the native structure. Also,
surface charges help to solubilize proteins in the aqueous
environment of the cell. To counterbalance repulsion,
charges should be of opposite sign. Indeed, significantly
more residues of opposite charge than like charge are found
within 4 Å charge–charge distance (Barlow and Thornton,
1983). Interestingly, salt bridges are more abundant and salt
bridge networks are more optimized in proteins from
hyperthermophiles than in thermophilic and mesophilic
homologues (Karshikoff and Ladenstein, 2001). It has
been argued that salt bridges are more stabilizing at high
temperatures because the unfavorable hydration entropy of
polar groups and the dielectric constant of water decrease
with temperature (Elcock, 1998). Salt bridges may increase
the specificity of folding because there are only few ways of
packing charged groups in a protein while there are many
ways of energetically equivalent packing of hydrophobic
groups (Wimley et al., 1996; Kajander et al., 2000). Also,
charged groups can create a suitable electrostatic environment for enzyme catalysis, protein–ligand binding and
formation of macromolecular assemblies. In summary,
electrostatic interactions, and salt bridges in particular, are
very important contributors to the structure and function of
proteins. Though it may not be easy, improving the experimental and computational means for measuring electrostatic
interactions remains a worthwhile endeavor. The more so if
we aim at modifying and improving the properties of
proteins for application in biotechnology.
Acknowledgements
We thank Alemajehu Gorfe, Andrey Karshikoff, Heinz Rüterjans and Jim
Warwicker for many helpful discussions.
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