Protein Engineering vol.10 no.12 pp.1363–1372, 1997
A fast estimate of electrostatic group contributions to the free
energy of protein-inhibitor binding
Ingo Muegge,‡ Holly Tao and Arieh Warshel1
Department of Chemistry, University of Southern California, Los Angeles,
CA 90089-1062, USA
1To
to have a rapid way of anticipating the effect of mutation
on both drug binding and catalysis.
Keywords: drug resistance/electrostatic fingerprint/endothiapepsin/group contributions/inhibitor binding
whom correspondence should be addressed
‡Present
address: Pharmaceutical Products Division, Abbott Laboratories,
Abbott Park, IL 60064-3500, USA
Dissecting ligand–protein binding free energies in individual contributions of protein residues (which are referred
to here as ‘group contributions’) is of significant
importance. For example, such contributions could help in
estimating the corresponding mutational effects and in
studies of drug resistance problems. However, the meaning
of group contributions is not always uniquely defined and
the approximations for rapid estimates of such contributions are not well developed. In this paper, the nature of
group contributions to binding free energy is examined,
focusing particularly on electrostatic contributions which
are expected to be well behaved. This analysis examines
different definitions of group contributions; the ‘relaxed’
group contributions that represent the change in binding
energy upon mutation of the given residue to glycine, and
the ‘non-relaxed’ group contributions that represent the
scaled Coulomb interaction between the given residue and
the ligand. Both contributions are defined and evaluated
by the linear response approximation (LRA) of the PDLD/
S method. The present analysis considers the binding of
pepstatin to endothiapepsin and 23 of its mutants as a
test case for a neutral ligand. The ‘non-relaxed’ group
contributions of 15 endothiapepsin residues show significant
peaks in the ‘electrostatic fingerprint’. The residues that
contribute to the electrostatic fingerprint are located in the
binding site of endothiapepsin. They include the aspartic
dyad (Asp32, Asp215) with adjacent residues and the flap
region. Twelve of these 15 residues have a heavy atom
distance of <3.75 Å to pepstatin. The contributions of 8 (10)
of these 12 residues can be reconciled with the calculated
‘relaxed’ group contributions where one allows the protein
and solvent (solvent only) to relax upon mutation of the
given residue to glycine. On the other hand, it was found
that residues at the second ‘solvation shell’ can have relaxed
contributions that are not captured by the non-relaxed
approach. Hence, whereas residues with significant nonrelaxed electrostatic contributions are likely to contribute
to binding, residues with small non-relaxed contributions
may still affect the binding energy. At any rate, it is
established here that even in the case of uncharged
inhibitors it is possible to use the non-relaxed electrostatic
fingerprint to detect ‘hot’ residues that are responsible for
binding. This is significant since some versions of the nonrelaxed approximation are faster by several orders of
magnitude than more rigorous approaches. The general
applicability of this approach is outlined, emphasizing its
potential in studies of drug resistance where it is crucial
© Oxford University Press
Introduction
The free energy of biological processes such as catalysis and
binding provides a correlation between structure and function
of proteins (e.g. Warshel, 1981b; Warshel and Åqvist, 1991;
Kollman, 1993). This is particularly true for electrostatic
energies (Warshel, 1981b) and decomposing the components
of such energies to the contributions of individual residues
can provide useful guidance for sequence–function relationships (e.g. Muegge et al., 1996). In principle, one can define
a thermodynamic cycle that decomposes the calculated property
into its group contributions in such a way that these
contributions add up to the total value. However, these group
contributions depend on the thermodynamic cycle used (e.g.
van Gunsteren and Mark, 1992). If one deals with n residues
one can create n! different thermodynamic cycles that add up
to the same total but each of them may yield different
group contributions. Nevertheless, the use of isolated energy
contributions to the total free energy and in particular electrostatic contributions is extremely useful, as demonstrated in
early studies (Warshel et al., 1986) and in more recent work
(e.g. Lee et al., 1992; Boresch and Karplus, 1995). Most
importantly, as argued by several workers (Åqvist et al., 1991;
Muegge et al., 1996), it is clearly possible and useful to define
a contribution by operational definition in terms of a real or
conceptual experiment. For example, it is very useful to
relate group contributions to mutation experiments. These
contributions can be linked to conformational changes and/or
changes of interaction energies between the ligand and its
environment (protein solvated in water). One of the most
reasonable and useful definitions of group contributions is the
change of a particular property upon mutation of the given
residue to glycine. Such group contributions and the proper
thermodynamic cycles can be used to generate all possible
mutations. Unfortunately, the calculation of the free energies
of mutations is very time consuming and can usually be done
for only a limited number of residues. Hence it is important
to search for effective approximations for the rapid evaluation
of group contributions. This is particularly needed in studying
drug resistance problems, where it is crucial to have a fast
way of estimating the effect of mutations on the binding of
proposed drugs.
In previous studies we developed several approximations
for obtaining group contributions. In particular, we examined
a ‘non-relaxed’ approach that considered the contribution of
the protein relaxation in an implicit way, using different
‘protein dielectric constants’ for charged and uncharged
residues (Muegge et al., 1996), and compared this approach in
some cases with the results obtained by the corresponding
1363
I.Muegge, H.Tao and A.Warshel
‘relaxed’ approaches. The motivation for the non-relaxed
approach is obvious: this approach can provide a fast screening
of the effect of mutations and locate ‘hot’ residues of significant
biological importance (Muegge et al., 1996). However, the
range of validity of using the non-relaxed group contributions
was not examined in a systematic way. This work presents
such an examination, considering as a test case the binding of
the inhibitor pepstatin to the aspartic proteinase endothiapepsin,
a system for which many structural and binding studies are
available (Workman and Burkitt, 1979; James et al., 1982;
Rich, 1985; Foundling et al., 1987; Cooper et al., 1989; Sali
et al., 1989; Rao et al., 1993a,b; Åqvist et al., 1994; Warshel
et al., 1994; Gomez and Freire, 1995). This system is also of
great interest in view of the fact that the HIV proteinase is
also an aspartic proteinase and studies of the mutations
of these enzymes can be useful in providing fundamental
understanding of drug resistance.
The next section describes the PDLD/S-LRA method and
its use in evaluating group contributions. The third section
compares the performances of the relaxed and non-relaxed
approaches for the case of the uncharged inhibitor pepstatin,
where approximate group contributions are not expected to be
highly accurate. It is illustrated that the non-relaxed approach
provides a reaonable but far from perfect approximation for
results of the relaxed approach. In the final section we discuss
the significance of our findings, pointing out that even a rough
approximation can be useful in studies of drug resistance
problems, where one needs very fast screening approaches.
Methods
PDLD/S-LRA calculations of binding free energies
The absolute energy of ligand binding to proteins can be
estimated in different ways. These include formally rigorous
approaches such as the free energy perturbation (FEP) method
(Warshel et al., 1988; Kollman, 1993) and the all-atom linear
response approximation (LRA) introduced in studies of
binding energies by Lee et al. (1992) and used effectively and
extensively by Åqvist and co-workers (Åqvist et al., 1994;
Åqvist and Hansson, 1996). More approximated and
significantly faster approaches which frequently focus on electrostatic energies are also effective (Bohm and Klebe, 1996).
These include the scaled protein dipole Langevin dipole
(PDLD/S) method (e.g. Lee et al., 1992) and other approaches
(e.g. Madura et al., 1996; Froloff et al., 1997). The present
work is formally based on a recent version of the PDLD/S
method that takes the protein reorganization into account
within the LRA framework. The implementation of the PDLD/
S-LRA method in calculations of binding free energies was
considered in several recent publications (e.g. Muegge et al.,
1996, 1997b) and here we will emphasize and clarify the main
points of this approach.
The absolute binding free energy is considered here using
the thermodynamic cycle of Figure 1. The inner cycle of the
figure (a, d, e, h) is the cycle considered by Lee et al. (1992)
in evaluating antibody antigen binding energies. It describes
elec ) to the absolute binding
the electrostatic contribution (∆G bind,l
free energy of a ligand (1) to a protein (p), where the
configurations of a protein–ligand complex are kept at a single
configuration (s) in the bound state and single configuration
(s9) at the dissociated state but the solvent is allowed to relax
at each step of the cycle. In this case, we can express the total
binding free energy as
1364
elec )
(∆G bind)s9→s 5 (∆G bind
s→s9 1 (∆G hyd 1 ∆G vdw 2 T∆S9)s→s9 (1)
w ) 1 (G bind )
5 (∆G pelec,l)s 2 (∆G elec,l
elec,l9 s9→s
s9
1 (∆G hyd 1 ∆G vdw 2 T∆S9)s9→s
where ( )s indicates that the corresponding form is evaluated
at a single configuration of the protein–ligand complex. The
term ∆G w
elec,l is the solvation energy of the ligand in water
(without the van der Waals and hydrophobic contributions),
∆G pelec,l is the change of the electrostatic contribution to the
solvation energy of the protein–ligand complex upon charging
the ligand (from an artificial uncharged state where all atomic
partial charges are set to zero to the state where all charges
including partial charges are switched on) and ∆G elec,l9 is the
electrostatic contribution to the binding free energy of the
uncharged ligand, l9. ∆G hyd and ∆G vdw are the hydrophobic
and van der Waals contributions to binding and 2T∆S9
represents the non-electrostatic entropic contribution which is
associated with the binding of the uncharged ligand.
The free energy of Equation 1 can be evaluated
conveniently by the semi-macroscopic PDLD/S model (e.g.
Lee et al., 1992), replacing the microscopic ∆G elec terms by
their semi-macroscopic counterparts. This is done by
considering the extra cycles (h, e, f, g) and (a, b, c, d)
where the ‘dielectric constant’ of the solvent around the
protein is changed from that of water, εw, to a value that
corresponds to the assumed protein ‘dielectric constant’, εin
(this parameter represents the implicit contribution of the
protein which will be considered below). The PDLD/S
contributions of the different steps in the cycles are
considered in detail elsewhere (Lee et al., 1992, 1993) and
they are also given in Figure 1. Since we deal with a single
protein–ligand configuration, we consider the sum of the
PDLD/S terms as an effective potential (a potential that
should be averaged to obtain the proper free energy) and write
(∆G pelec,l)s 5 U pelec,l 5
[
l1p – ∆G l91p )
(∆G sol
sol
( ε1
in
(
l
1∆G sol
1–
1
εin
)1 Vε
l
qµ
1
l
V intra
in
εin
[ ( )
( ) ]
w ) 5 Uw
(∆G elec,l
elec,l 5
s9
l
1∆G sol
1–
–
1
εin
l
(∆G sol
1
l
V intra
εin
]
1
εw
)
S
(2)
1 1
–
εin εw
S9
where ∆G sol denotes the electrostatic contribution to the
solvation free energy of the indicated group in water. To be
more precise, ∆G sol should be scaled by 1/(1–1/εw), but this
small correction is neglected here. V qµ is the electrostatic
interaction between the indicated groups in vacuum (this is a
l9 5 0.
standard PDLD notation) and in the present case Vqµ
V lintra is the intramolecular electrostatic interaction of the
ligand. Since the PDLD/S results obtained with a single
protein–ligand configuration cannot capture properly the effect
of the protein reorganization [see discussion in Sham et al.
(1997)] a more consistent treatment should involve the use of
Electrostatic group contributions to the free energy of protein–inhibitor binding
Fig. 1. Thermodynamic cycles for studies of the binding of a ligand (1) to a protein (p). The cycles consider only the electrostatic contributions to binding free
energies. This is done by changing the charges of the ligand from their actual value (black squares) to zero (cross-hatched squares). The figure only represents a
single configuration (s) for the complex state and a single configuration (s9) for the unbound state. The proper average over the configuration of the system, on
the charged and uncharged state of the ligand, is performed by the LRA approach as described in the text. The inner cycle (a, b, d, h) describes the binding
process on a macroscopic level. The outer cycles (a, d, c, b) and (h, e, f, g) are used to provide the semi-macroscopic estimates of the relevant electrostatic
energies. This is done by using the PDLD/S three steps cycle where the solvent ‘dieletric constant’ is changed from εw to εin, the ligand charges are changed and
finally the dielectric constant is changed back form εin to εw. The relevant PDLD/S energy contributions are given; more details about these evaluations are given
elsewhere (e.g. Lee et al., 1992).
the LRA or related approaches (e.g. Lee et al., 1992; Sham
et al., 1997). This approach provides a reasonable approximation for the actual free energy by using [see Lee et al.,
(1992)].
(3)
∆G pelec,l 5 12 〈U pelec,l 〉l91p 1 〈U pelec,l〉l1p
(
(
1
w
w
∆G w
elec,l 5 2 〈U elec,l 〉l9 1 〈U elec,l〉l
)
)
where , .l and , .l9 designate an MD average over a force
field that corresponds to the ligand in its charged and uncharged
form and , .l1p and , .l91p designate an MD average over
a force field of the ligand plus protein system where the bound
ligand is in its charged and uncharged forms, respectively. It
is important to realize that the average of Equation 3 is always
done where both contributions to the relevant Uelec are evaluated
at the same configurations. That is, the PDLD/S energies of
the charged and uncharged states are always evaluated at each
averaging step at the same structure, but these structures are
generated by MD simulations using the potential surface
of the charged and uncharged states. The free energy that
corresponds to the first two terms of Equation 1 is now
obtained from Equations 2 and 3 and is given by
p
p
w
∆G w→
elec,l 5 ∆G elec,l – ∆G elec,l
[〈
l91p→l1p )
™12 (∆G elec,l
〈
l91p→l1p )
1 (∆G elec,l
(4)
1
(
–
1
εin εw
1
(ε
–
in
1
εw
)
l9
l
1 ∆G sol
l
qµ
in
1
[(〈 〉 〈 〉 ) (
l
–12 ∆G sol
) 1 Vε 〉
l
l
V qµ
εin
1
εin
–
〉
l91p
]
l1p
1
εw
)
(〈 〉 1 〈∆G 〉 – 〈∆G 〉 – 〈∆G 〉 )
l
– ∆G sol
l1p
l
sol
( 1 – ε1 ) ] 1 ∆G
l91p
l
sol
l
l
sol
l9
l
intra
in
1365
I.Muegge, H.Tao and A.Warshel
where ∆G lintra is the contribution to the cycle due to structural
l . Here we use the fact that ∆G l9 5 0, since
relaxation of Vintra
sol
the hydrophobic term is evaluated separately. Also note that
∆G psol cancels out in the cycle. The last two terms of Equation
4 can be written as
[(〈 〉 〈 〉 ) (
l
l
–12 ∆G sol
1 ∆G sol
l
1–
l9
1
εw
)
(5)
(〈 〉 1 〈∆G 〉 ) (1 – ε )] 1 ∆G
l
– ∆G sol
l
sol
l1p
1
l91p
l
intra.
in
The present treatment keeps the ligand structure unchanged in
the cycles used to evaluate Equation 4 and evaluates the
energetics of its structural relaxation in water by a separate
microscopic step. Thus the last two terms in Equation 4 are
reduced to
–〈∆G lsol 〉l1p
( ε1 – ε1 )
in
w
l91p
p
–∆G bind
elec,l9 ™ (–〈∆G sol 〉l91p 1 〈∆G sol 〉l91p)
1
( ε – ε ) 1 ∆∆G prelax 1 ∆G l9relax
in
w
(6)
where we used the fact that the electrostatic contribution to
∆G l9sol is zero and we also used the lower cycle to obtain the
first two terms of Equation 6. The first three terms represent
the electrostatic contribution to the change in solvation energy
during the dissociation process when the ligand is held to its
configuration in the (l9 1 p) state, while ∆∆G prelax represents
the electrostatic effect of protein relaxation upon release of 19
and ∆G l9relax represents the corresponding effect of relaxation
of l9. Note also that the average of Equation 6 is not based on
a rigorous LRA procedure.
Now we can express the PDLD/S-LRA binding free energy as
(〈
〉〈
∆Gbind™ ∆G l1p
– ∆G psol
sol
〉 – 〈∆G 〉 )( ε1 – ε1 )
l
sol
l1p
in
(7)
w
〈 〉 ε1 – [(〈∆G 〉 – 〈∆G 〉 )
l
1 V qµ
l91p
sol
in
(〈
〉〈
l91p – ∆G p
– ∆G sol
sol
p
sol
l91p
l91p
〉)] ( ε1 – ε1 )
in
w
1∆∆G prelax 1 ∆G l9relax 1 ∆Ghyd 1 ∆Gvdw – T∆S9
where , . without subscript designates 1/2 (, .l1p 1 ,
.l91p) and where, as stated above, we evaluated the effect of
Vintra and ∆G l9relax in a separate cycle by constraining the ligand
to stay in its original configuration during the cycle of Figure 1.
Now the 2T∆S9 term does not include the entropic contributions
l
but only the translational and rotational
of ∆∆G prelax and ∆G relax
1366
[(〈 〉 〈 〉 ) (〈
∆G l91p
sol
l91p9
p
– ∆G sol
l91p
〉〈
– ∆Gl91p
– ∆Gpsol
sol
〉)] ( ε1 – ε1 ).
in
w
This approximation involves an overestimate of the change in
the electrostatic solvation of the protein upon displacement of
l9 (the final expression given a larger weight to ∆Gpsol than to
∆Gl1p
sol ). The validity of this approximation will be examined
elsewhere, but it has little consequence except in the present
case where we focus on mutations of neutral residues. Now we
end with our final expression:
1
1
p
l
∆Gbind ™ 〈∆G l1p
–
(8)
sol 〉 – 〈∆G sol 〉 – 〈∆G sol 〉l1p
εin εw
(
l 〉
1〈V qµ
Considering for simplicity the dissociation (d→e) rather than
the binding process (e→d) we may approximate the negative
bind term of Equation 1 by
of the 2∆G elec,l9
1
terms. We further simplify our treatment by assuming that most
p
of the effect of ∆∆G relax
is captured in the LRA treatment of
the uncharging process (a → d in Figure 1). This approximation
is further discussed in Muegge et al. (1998). We also make a
convenient approximation and neglect the term
)(
1
εin
)
l
1 ∆G relax
1 ∆Ghyd 1 ∆Gvdw – T∆S9
∆G hyd represents the hydrophobic term that estimates the relevant
surface area from the number of Langevin dipoles in the first
‘solvation shell’ and corrects it considering the local field of
each dipole (Lee et al., 1993). ∆G vdw is evaluated by assigning
van der Waals interaction terms to the Langevin dipoles (Lee
et al., 1993).
With regard to the term εin, it is important to realize that this
scaling constant is not related to the true local dielectric constant
of the protein but merely represents the contributions that are
not treated explicitly in the model (King et al., 1991). When all
contributions are treated explicitly in the case of the regular
PDLD treatment, then εin 5 1. When the protein-induced dipoles
are treated implicitly, as in the PDLD/S model, then εin 5 2.
Since the PDLD/S represents explicitly all contributions except
the induced dipoles, ideally εin 5 2 should be implemented.
However, experimentation with many test cases indicates that
more accurate results are obtained with εin ™ 4 (larger values
are needed if the protein reorganization is not taken into account
(Muegge et al., 1996; Sham et al., 1997). This is probably due
to the fact that most microscopic treatments do not fully converge
within the available stimulation time. In particular, it is possible
that the penetration of water molecules upon change of substrate
charges is not fully accounted for. It is also possible that the
simulations do not sample sufficiently large configurational
space, although the model involves averaging over configurations
generated by MD simulations with very reliable boundary
conditions and with a proper treatment of long-range effects by
the LRF approach (Lee and Warshel, 1992). The performance
of the PDLD/S approach in evaluation of electrostatic free
energies in general (e.g. pKa values, redox potentials, ion pair
energies) and binding free energies in particular has been well
established (Lee et al., 1993; Warshel et al., 1994; Muegge
et al., 1996; Sham et al., 1997). It was also shown that the
PDLD/S approach provided reasonable estimates of the effect
of mutation on the binding energy of highly charged ligands
(Muegge et al., 1996). The PDLD/S-LRA procedure is implemented in a fully automated way in the POLARIS program
package (Lee et al., 1993).
Electrostatic group contributions to the free energy of protein–inhibitor binding
Group contributions
The PDLD/S approach for calculations of absolute binding free
energies can also be useful in estimating the contributions of
individual residues to the binding process. A very useful
definition of these group contributions is the effect of ‘mutating’
the given residue to glycine, or alternatively of annihilating all
the residual charges of the given residue. Although these
definitions are not unique, they provide a ‘road map’ for the
location of ‘hot’ residues whose mutations are likely to change
the functional properties of the protein (Muegge et al., 1996).
This definition is also very useful in any attempt to generate all
possible mutations since the mutation A → B can always be
obtained by the thermodynamic cycle A → Gly, Gly→ B. The
difference between the calculated binding affinities of the wildtype and the glycine mutants are referred to here as the
‘relaxed group contributions’ of the mutated residue. These
group contributions involve the full relaxation of the protein
matrix as well as the surrounding water solvent upon mutation.
In particular, the steric reorganization caused by the truncation
of large side chains is explicitly included.
Since the evaluation of the relaxed group contributions is
time consuming, it is important to examine alternative treatments.
In particular, we note that the electrostatic contribution of the
ith residue to Equation 8 can be written as
(∆Gbind)i 5
V (i)
qµ
εin
1 〈∆G l1p
– ∆G psol 〉(i)
sol
(
1
εin
–
1
εw
)
(9)
where we designate (V lqµ)(i) by V (i)qµ. The ith contribution of
the solvation term represents the effect of the solvent in response
to turning off the residual charges of the ith residue. For nonionized residues the effect of the solvent around the protein is
expected to be small. Furthermore, for non-ionized residues the
effect of protein reorganization upon turning off the charges of
the ith residue is expected to be small and can be reasonably
represented by small εin. Thus we may try to use
[
]
∆∆G (i)
bind
unionized
™
〈
V (i)
qµ
εin
〉
(10)
This non-relaxed approximation, with εin 5 4, has been found
to be reasonable in the case of nucleotide binding in p21ras
(Muegge et al., 1996) and the ‘solvation’ of the heme in
cytochrome c (Muegge et al., 1997a). Obviously, Equation 9
and small εin provide a very poor approximation in the case of
ionized residues where the contribution from the solvation term
is enormous, leading to significant compensation of the Vqµ
term. Furthermore, as illustrated and argued repeatedly by
Warshel and co-workers (e.g., Warshel and Russell, 1984), the
combined effect of the solvent and protein relaxation leads to
almost complete compensation of the Vqµ term. This physics
can be best captured by simply using Coulomb’s law with a large
effective dielectric constant. That is, for the group contribution of
charged residues, it is very effective to use the seemingly simple
expression
[∆∆G ]
(i)
bind
ionized
™
〈 Vε 〉
(i)
qµ
(11)
eff
This approximation, with εeff 5 40, has been repeatedly validated
in studies of interactions between ionized residues and charged
ligands (e.g. Warshel and Åqvist, 1991; Muegge et al., 1996;
Sham et al., 1997, and references therein). In the case of
interactions between ionized residues and non-ionized ligands
the rules are less clear and here we use εeff 5 20 to scale the
charge–dipole interactions between the charged protein residue
and the neutral ligand.
Equations 3 and 4 can be further simplified by replacing the
average over Vqµ by Vqµ at the average structure of a single
equilibration run or just at the crystal structure. This non-relaxed
approach is several orders of magnitude faster than the PDLD/
S-LRA approach, which is in turn a few orders of magnitude
faster than the LRA and FEP approaches (Lee et al., 1992). Of
course, the non-relaxed approach is less reliable than the
more rigorous approaches and this work is mainly focused on
determining how much is traded in reliability for the price of a
faster method and on examining the optimum εeff for ionized
and non-ionized residues.
Equations 9 and 10 do not include the contributions from
∆G hyd, ∆G vdw and 2T∆S9. The first two contributions are less
sensitive to the detailed structure of the mutated residues and
can be estimated by simplified approaches. In particular, a single
evaluation of ∆G hyd and ∆G vdw by the PDLD/S approach is
sufficient except in the case of mutation to a large bulky residue,
which is likely to lead to large structural changes. The 2T∆S9
term is anyhow hard to estimate by any approach and it is
outside the scope of the present work. Hence the main uncertainty
in developing a practical non-relaxed model is how closely we
can come with Equations 8 and 9 to the more complete PDLD/
S treatment of ∆G elec
bind.
Results and discussion
The crystal structure of the aspartic proteinase endothiapepsin
complexed with the inhibitor pepstatin (Cooper et al., 1989)
was allowed to undergo a short molecular dynamics (MD)
relaxation of 5 ps at 300 K by using the program ENZYMIX
(Lee et al., 1993). The spherical inner part of the system with
radius 18.0 Å was constrained by a weak harmonic potential of
→
→
the form V9 5 ΣiA(r i – ri0)2, with A 5 1.0 kcal/mol. Å2. The
r.m.s. deviation of the relaxed structure from the crystal structure
was 0.7 Å on average. The binding energy of pepstatin to
endothiapepsin depends on the protonation states of the protein
(Gomez and Freire, 1995). Therefore, the proper choice of the
ionization states of the aspartic acids in the binding pocket is
important for reproducing a reasonable binding energy. In order
to determine the ionization state of the five most adjacent
aspartic acids of the inhibitor, we used the approach described
by Lee et al. (1993) and Sham et al. (1997). This was done
using the ‘titra_pH’ routine of the POLARIS program package
(Lee et al., 1992, 1993). If the probability of a group to be
charged at pH 7 was .50%, it was considered to be charged.
Our calculations indicated that three aspartic acids, Asp30,
Asp32 and Asp77, are ionized. This is in agreement with the
probable ionization state of the aspartic dyad (Asp32, Asp215).
It is usually assumed that Asp32 is charged and Asp215 is
uncharged at pH 3–7 (Bailey and Cooper, 1994). The calculations
involved the SCAAS polarization boundary conditions and the
local reaction field (LRF) method (Lee and Warshel, 1992) that
provides a very efficient way of solving the electrostatic longrange problem. The protein was embedded in a water sphere of
radius 20 Å surrounded by a shell with an outer radius of 24 Å
containing a Langevin grid and a continuum representation
beyond the 24 Å shell. A detailed description of how the
1367
I.Muegge, H.Tao and A.Warshel
Table I. Contributions to the overall binding free energy of pepstatin to
endothiapepsin
Energy contribution (kcal/mol)
Free energy terma
(l 1 p)
〈∆Vqµ / εin〉
〈 ∆G
〈 ∆G
〈 ∆G
〈 ∆G
p
solv,w
(
(
(
bind
elec
〉
l1p
solv,w
l
solv,w
〈∆G hyd〉
∆G calc
bind
∆G exp
bind
1
1
2
εw
εin
1
1
2
εw
εin
1
1
2
εw
εin
)〉
)〉
)〉
(l9 1 p)
223.42
217.18
2107.21
2104.48
216.85
217.09
2122.79
2119.26
9.01
14.69
225.87
214.0
214.0b
aSee Equation 8 and the text for the meaning and evaluation of the different
terms. The calculations used an optimum dielectric scaling, εin 5 2.9, that
was selected in order to reproduce the experimental binding energy.
bThe ‘perfect’ agreement between the calculated and observed ∆G
bind is
meaningless since it was obtained by adjusting εin (see the text). Using εin 5
4 gave ∆G bind 5 –17.6 kcal/mol.
ENZYMIX program treats different regions of the protein is
given elsewhere (Lee et al., 1993).
The simulations, needed to generate the PDLD/S-LRA results,
were performed for the wild-type structure and the 23 ‘mutants’,
starting from the state after the initial relaxation and decreased
the harmonic potential by using A 5 0.1 kcal/mol.Å2. Otherwise,
the MD simulations were performed using the same conditions
as described for the initial relaxation. The averaged r.m.s.
deviations varied between 0.4 and 0.5 Å.
The first step of the calculations involved PDLD/S-LRA
evaluation of the absolute free energy of binding of pepstatin
to endothiapepsin. This was done by generating four proteincomplex configurations, for both (l9 1 p) and (l 1 p), and
averaging the results according to Equation 8. The calculations,
which are summarized in Table I, neglected the contributions of
∆G vdw 2T∆S9. This neglect is not so relevant in the present
case since we do not focus on the actual value of the absolute
binding energy. In fact, resolving the real effect of 2T∆S9 is a
major challenge which is being addressed in our laboratory
using all-atom simulations, but it is outside the scope of the
present work. The contribution of ∆G vdw is positive when it
includes the interaction of the solvent with the ligand-free
proteins and it usually compensates for some of the negative
contribution of ∆G hyd. However, the exact compensation is
again outside the scope of the present work and it is simply
very easy to change the absolute value of ∆G bind by adjusting
εin. Hence all that is done here is to select an εin (εin 5 2.9)
that forces the calculated ∆G bind to reproduce the corresponding
observed value of 214.0 kcal/mol (Workman and Burkitt,
1979). This arbitrary selection was not meant to represent any
sophisticated scientific procedure of obtaining improved results
but merely a way of forcing the overall effect of all the protein
residues to reproduce the observed binding free energy (this
does not mean, of course, that the sum of the group contributions
will reproduce the observed binding energy of the native
enzyme). Using the standard value of εin 5 4 gave ∆G bind 5
–17.6 kcal/mol.
In the next step, we turn to the evaluation of the group
1368
contributions to the total inhibitor binding energy. Figure 2
shows the non-relaxed group contributions of every single
residue of endothiapepsin to pepstatin binding free energy. All
protein residues that are located in proximity to the inhibitor
(i.e. at least one non-hydrogen atom closer than 3 Å to a nonhydrogen atom of the inhibitor) are found to have significant
electrostatic contributions to the inhibitor binding. There are
three patches of groups that appear to be important in determining
the electrostatic fingerprint. The first group comprises residues
Asp12, Asp30, Asp32 and Gly34 and stretches along the convex
inhibitor side from Iva227 to Sta330. The second group of
residues, Ser74, Tyr75, Gly76, Asp77 and Gly78, fits nicely
into the groove-like concave side of the inhibitor between Sta330
and Sta332. The third group, comprising residues Asp215,
Gly217, Thr218 and Thr219, stretches almost parallel to the
first group along the same residues of the inhibitor. The three
regions found to be important using the non-relaxed approach
coincide with the functionally important motifs in the binding
site. The first and third regions provide a symmetrical hydrogen
bond network in the active site. They involve similar sequences
(Asp32, Thr33, Gly34, Ser35 and Asp215, Thr216, Gly217,
Thr218) and contain the aspartic dyad Asp32 and Asp215. The
second region (residues 74–83) forms the so-called flap region—
a highly flexible loop that controls binding and release of the
substrate. This flap region binds to the center part of the inhibitor
and covers the catalytic site. Figure 3 illustrates the location of
the inhibitor relative to the above-mentioned residues.
Fifteen residues are likely to be particularly important for
pepstatin binding as they show significant electrostatic peaks in
the electrostatic fingerprint of Figure 2. Twelve of these residues
that are located close to the inhibitor (heavy atom distance
,3.75 Å) were chosen as our benchmark and were mutated to
glycine. That is, the side chain of the given residue was replaced
by a hydrogen atom and the main chain conformation remained
unchanged. However, in the case of glycine residues in the wildtype sequence we created an artificial ‘mutant’ by annihilating all
residual charges of the glycine main chain, thereby forming an
uncharged glycine counterpart. The special procedure of mutating
Gly to its uncharged form allows one to evaluate the effect of
main-chain dipoles. Although such effects cannot be verified by
current experimental approaches, they clearly play a major role
in binding and catalysis (e.g. Muegge et al., 1996). The mutations
of the other residues to their uncharged form is also of interest
(e.g. Muegge et al., 1996), but in this work we focused on
actual mutations to Gly since this allows one to consider actual
steric effects in the relaxed model.
The generated mutant structures underwent an MD-relaxation
process responding to the change in structure and charge upon
mutation. This allows us to examine the explicit effect of the
relaxation of the protein matrix and the water solvent on the
contribution of the mutated residue to the binding of the inhibitor.
The corresponding PDLD/S results, obtained with the relaxed
(s 1 p relaxed) and non-relaxed approximations for the residues
whose closest distance to the inhibitor, is ,3.75 Å, are summarized in Table II. These residues represent the first ‘solvation
shell’ of the ligand and are expected to have the largest
contributions to the binding free energy. As can be seen from
Table II, for 8 out of 12 residues the s 1 p-relaxed group
contributions can be correlated to the non-relaxed group contributions. When we allowed only the solvent to relax and hold the
protein atoms fixed upon mutation (s-relaxed), we could reconcile
the relaxed (s-relaxed) and non-relaxed group contributions of
10 out of 12 residues. The most negative contribution is due to
Electrostatic group contributions to the free energy of protein–inhibitor binding
Fig. 2. Non-relaxed group contributions to pepstatin binding energy for every residue of endothiapepsin. The non-relaxed group contributions generate the
electrostatic ‘fingerprint’ of the protein-inhibitor interaction. εin 5 4 and εin 5 εeff 5 20 were chosen for uncharged and charged residues, respectively.
Fig. 3. Crystal structure of pepstatin bound to endothiapepsin. The pepstatin is
shown together with the residues that exhibit the largest group contributions
in the electrostatic fingerprint of Figure 2.
Gly76 (see Figure 2) and the same trend is obtained using the
relaxed approach. The same holds for the largest positive
contribution, which is due to Gly217. The effect calculated with
the non-relaxed approach could not reproduce the corresponding
relaxed results for four residues, Asp30, Gly34, Asp77 and
Thr219. The nearest contact between Asp30 and the inhibitor
is a methyl group of Sta330 at 3.5 Å. This residue neither
forms a hydrogen bond to pepstatin nor is it in other close
electrostatically important contact. Even though this residue is
charged, its non-relaxed group contribution is not very high.
The non-relaxed group contribution of Asp77 is relatively small
considering that it is a charged residue. Asp77 forms only a
weak hydrogen bond with its backbone to Val229. In the case
of Gly34 the hydrogen bond between the Gly34 oxygen and
the backbone nitrogen atom of Ala331 was weakened owing to
the uncharging of Gly34, and this forced Asp33 to move
closer to Ala331. This structural change led to an increase in
electrostatic interaction between the charged side chain of Asp33
and Ala331 and gave rise to an even slightly increased inhibitor
binding energy in the mutant relative to the wild-type. This
effect is opposite to that found in the non-relaxed calculations
that produced a negative contribution of Gly34. Although, in
the case of the Thr219→Gly mutation, Vqµ decreased by almost
2 kcal/mol, this effect was more than compensated for by an
increased solvation since this residue is exposed to the water
solvent. Furthermore, the entire side chain of Thr219 has contact
to Iva227 and Val228 and its truncation has an overall effect
on the conformation of the binding pocket and even the distant
stretch of residues 74–78 now binds more strongly than in the
wild-type. An interesting point that emerges from Table II is the
correlation between the performance of the non-relaxed approach
and the location of the given residue. It appears that the nonrelaxed approach correlates well with the solvent relaxed (srelaxed) results (obtained using Equation 3 without allowing for
protein reorganization) as long as the given residue is not fully
exposed to the solvent. Interestingly, for solvent-exposed residues
we found that the non-relaxed approach correlates better with
the results obtained by considering the relaxation of both the
1369
I.Muegge, H.Tao and A.Warshel
Table II. Group contributions to the binding free energy of pepstatin to endothiapepsin from residues witin the first ‘solvation shell’ of the inhibitora
Groupa
Original
structure
Average over
4 MD runs
Non-relaxed
20.47
20.89
21.95
21.43
22.95
0.17
22.28
20.39
21.32
0.18
20.54
21.60
Asp12
Asp30
Asp32
Gly34
Ser74
Tyr75
Gly76
Asp77
Asp215
Gly217
Thr218
Thr219
20.26
20.42
21.62
21.20
20.24
21.01
22.05
20.15
20.36
0.44
20.71
21.05
Average over 4 MD runs
s1p relaxedb
s relaxedc
SASAd
Locatione
20.26 (1)
0.79 (2)
21.55 (1)
0.14 (2)
21.16 (1)
21.33 (1)
23.95 (1)
0.42 (2)
23.19 (1)
2.29 (1)
21.66 (1)
1.19 (2)
20.06
2.32
21.92
21.08
20.04
20.38
20.54
20.12
20.12
1.05
20.03
20.67
20.25
20.15
20.10
20.30
20.60
20.20
20.40
20.35
20.20
20.70
20.45
20.65
s
b/s
b
b/s
s
s
s
s
b
b/s
b/s
b/s
(1)
(2)
(1)
(1)
(2)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
includes all endothiapepsin residues that have at least one heavy atom with a distance of ,3.75 Å to a heavy atom of pepstatin.
the results of the relaxed approach according to Equations 8 and 9. s1p indicates that solvent and protein are subject to structural relaxation upon
mutation (the solvent relaxation is automatically obtained by using the ∆G sol,w in Equation 9). Energies are given in kcal/mol. The table considers residues that
were found to have large electrostatic contributions in the non-relaxed approach of Figure 2. Asp30, Asp32 and Asp77 were charged. For the relaxed approach all
non-glycine residues were mutated to glycine replacing the side chain group by a hydrogen atom. In contrast, glycine residues were mutated to their uncharged
counterpart by annihilating the residual charges of the main chain atoms; however, both internal interactions and van der Waals interactions remained activated
during the MD-relaxation process of the mutant formed. The corresponding contributions were evaluated from Equation 2 using εin 5 2.9. The non-relaxed
contributions were evaluated using εin 5 4 and εin 5 εeff 5 20 for uncharged and charged residues, respectively. (1) and (–) designate agreement and
disagreement, respectively, between the given relaxed and non-relaxed results.
cOnly the solvent is allowed to relax. These results are obtained by using the relaxed approach and Equations 8 and 9 without taking the protein relaxation upon
mutation into account. (The protein atoms are held fixed upon mutation.)
dGroup contributions were calculated using the change in the solvent-accessible surface area upon ligand binding of each residue considered. Data taken from
Figure 7 of Gomez and Freire (1995).
eGroup located at the surface of the protein (s), buried in the protein matrix (b) or partly buried and partly exposed to the solvent (b/s).
aThis table
bThese are
Table III. Group contributions to the binding energy of pepstatin to
endothiapepsin from residues of the second ‘solvation shell’ of the inhibitora
Group
Original
structure
Average over
4 MD runs
Non-relaxed
Ala13
Ser35
Gly78
Leu128
Gln187
Ile213
Leu220
Tyr222
Phe275
Phe284
Ile297
0.00
20.43
20.22
0.08
0.37
0.01
20.12
20.10
20.08
0.00
0.10
0.00
0.18
20.26
20.09
0.32
0.02
20.07
20.03
20.04
0.00
0.01
Average over 4 MD runs
s1p relaxeda
SASAb
22.23
21.70
20.72
23.64
23.51
1.37
20.65
0.74
20.40
22.83
21.73
20.15
0.03
2
20.25
2
20.10
20.10
20.25
20.10
20.10
20.20
aResidues whose closest heavy atom distance to pepstatin is between 3.75 and
6 Å. Energies are given in kcal/mol. The non-relaxed contributions were
evaluated using εin 5 4. The relaxed group contributions were calculated
using εin 5 2.9. Asp30, Asp32 and Asp77 were charged.
bGroup contributions were calculated using the change in the solventaccessible surface area upon inhibitor binding of each residue considered.
Data taken from Figure 7 of Gomez and Freire (1995).
protein and the solvent (s 1 p) than with results obtained by
considering only solvent relaxation (s).
In addition to examining the effect of residues with large
electrostatic contribution, it is important to explore the effect of
other residues that are in close contact with the substrate. Such
an examination is summarized in Table III, which considers the
effect of mutated residues whose closest distance to the inhibitor
is between 3.75 and 6 Å. Table III indicates that residues which
lie in the second ‘solvation shell’ of the inhibitor may have
1370
significant relaxed contributions even if the corresponding nonrelaxed contributions are very small. All of these relaxed
contributions reflect ‘second-order’ conformational effects,
where the mutation of the given residue changes the positions
and orientations of residues that interact directly with the ligand.
Table III further indicates that Gly78, Gln187 and Ser35 have
a significant non-relaxed contribution to inhibitor binding. The
closest atom of Gln187 is located .5 Å away from the inhibitor,
yet this residue gives a positive contribution to the binding
energy (decrease of the binding affinity). Apparently, the Oε1
atom of this residue points directly towards the backbone oxygen
of Ala331. This electrostatic repulsion is responsible for the
positive contribution to binding found in Figure 2.
For a neutral ligand, only the interaction of the nearest protein
residues is electrostatically determined. That is, only for these
residues a qualitative agreement between the non-relaxed group
contributions and the relaxed group contributions could be
achieved (Table II). However, for charged ligands this agreement
can be reached even for residues that are located relatively far
from the ligand, as shown for the binding of highly charged
nucleotides in p21ras (Muegge et al., 1996).
The non-relaxed and relaxed group contributions to the
binding energy of pepstatin to endothiapepsin can be compared
with calculations of these contributions using an entirely different
approach. Gomez and Freire (1995) calculated the change of
solvent-accessible surface area (SASA) of endothiapepsin and
pepstatin upon complex formation and the enthalpic change is
then expressed by the sum over differently weighted SASA for
polar and non-polar atoms and a term for the effective enthalpy
of ionization. The results of Gomez and Freire [Figure 7 in
Gomez and Freire (1995)] are given in Tables I and II and can
be compared with our results. The SASA is an empirical
approach that involves several conceptual problems that can
Electrostatic group contributions to the free energy of protein–inhibitor binding
sometimes be absorbed into the parameters used. The main
problem is associated with the assumption that the enthalpic
contribution can be obtained by scaling the contributions of the
interacting atoms by the corresponding SASA. Unfortunately,
electrostatic interactions in protein interiors are not determined
by surface area but by local polarity (Warshel et al., 1984). For
example, if we consider a small polar ligand or in an extreme
case an ionizable group whose energy can be expressed in terms
of the energy of moving such a group from water to the protein
site (Warshel, 1981a; Yang et al., 1993), we find that this energy
is determined by the local polarity and cannot be scaled by
surface area considerations; otherwise it would have been
possible to calculate pKas of internal groups using surface area
considerations [see discussion in Warshel et al. (1984)]. The
contributions are classified only according to polar or non-polar
atom types. This means that very different hydrogen bonds such
as SH and OH will give the same contribution and the same
will be true for changes in the ligand that involves a replacement
of one polar group by another, in contrast to experimentally
observed differences in binding between different ligands [e.g.
see the series in Warshel et al. (1994)]. Finally, the SASA
approach scales the individual contributions so that they will
reproduce the total binding energy but the sum of the effect of
all mutations cannot (and should not) sum up to the observed
binding energy. Nevertheless, despite these and other conceptual
problems one would expect approaches that use effective potentials to be useful. This will be particularly true with models that
use effective group contributions such as the approach used in
folding studies (e.g. Levitt and Warshel, 1975). Such an approach
might sometimes be more accurate than fully microscopic
approaches as long as the microscopic approaches involve major
convergence problems. At any rate, the present study does not
try to assess the reliability of different approaches since this
will require comparison with mutation experiments (which are
outside the scope of this work) but rather an examination of the
ability of the non-relaxed approach to reproduce the relaxed
results.
Examination of Table II indicates that the larger contributions
obtained by the relaxed approach are also found by the nonrelaxed and SASA approaches. Residues in Table III contribute
significantly less in the non-relaxed and the SASA approaches.
However, there are some major differences in the results of both
methods. Although the SASA method is in principle capable of
identifying positive contributions to the binding energy, only
negative contributions were found. Especially Gly217, which
provides a positive contribution to the inhibitor binding in both
the relaxed and non-relaxed approaches, was found to provide
the most negative contribution in the SASA approach. While it
is encouraging that the SASA and the non-relaxed method
provide results of such a significant correlation for most of
residues considered, it is interesting to find out what caused the
misfit for Gly217. This question will be left, however, to
subsequent studies that consider actual mutation experiments.
Conclusion
This work examined the performance of the electrostatic
non-relaxed approach in detecting residues that contribute significantly to the binding free energy of a neutral ligand. The
binding of the neutral inhibitor pepstatin to endothiapepsin was
taken as a generic benchmark. A time-consuming mutational
analysis was performed for 23 residues within the first and
second ‘solvation shell’ of the ligand. A correlation between
the non-relaxed and solvent relaxed contributions was found for
10 out of 12 residues of the first ‘solvation shell’ (8 out of 12
correlated for the non-relaxed and the protein 1 solvent relaxed
approach). Hence it appears that looking for the peaks in
diagrams of the type presented in Figure 2 should help in
identifying the most important residues for inhibitor binding.
However, the non-relaxed contributions of residues that show
no significant peak and are not in contact with the inhibitor
might not be so informative, since mutations of such residues
may still lead to global conformational changes rather than to
a direct electrostatic effect. That is, the non-relaxed approach
cannot reproduce the results of the relaxed approach for neutral
residues which are in the second ‘solvation shell’ around the
inhibitor. The significance of this finding is not completely clear,
as it is almost certain that these calculated relaxed contributions
overestimate the actual effects (this point will be verified in the
future using observed mutation effects). Nevertheless, it is clear
that neutral residues in the second ‘solvation shell’ can contribute
by a second-order conformational effect (by pushing the first
‘solvation shell’ residues) and that this indirect effect cannot be
reproduced by the non-relaxed approach.
Our previous studies (Muegge et al., 1996) already demonstrated that the non-relaxed electrostatic group contributions are
useful for charged ligands. The present work demonstrated that
even for a neutral ligand this approach is useful although second
‘solvation shell’ residues with no electrostatic contribution that
contribute to binding cannot be screened effectively by the
current version of our approach. However, even here one can
design non-relaxed ways of estimating the coupling between
the second and first ‘solvation shells’ and thus for estimating
the effect of residues of the second ‘solvation shell’. Hence we
conclude that the use of the non-relaxed electrostatic fingerprint
can be useful for both charged and uncharged ligands. Obviously,
we must keep in mind that finding a small electrostatic contribution cannot be used to exclude the possibility that a mutation
of the corresponding residue will change the binding energy in
a significant way.
As should be obvious to the reader, we have not addressed
in this paper the relationship between the calculations and
experimental mutation studies. Not only are we not aware of such
results for the complex studied but, perhaps more importantly, the
paper addresses the theoretical yet practical question of how
justified it is to use part of the relaxed model in reproducing
the results of the ‘complete’ model. Since we find that the nonrelaxed approximation is valid for more than 70% of the residues
in the first ‘solvation shell’ (Table II), we believe that it is
justified to take advantage of this approach in fast screening
studies (see below).
One of the main reasons of our interest in the non-relaxed
approach is the need for very rapid computer-aided screening
approaches for fighting the drug-resistance problem. Here one
has to anticipate the effect of mutations that would reduce the
binding energy of a given drug while retaining catalytic activity
against the native substrate (Gulnik et al., 1995). The first step
in the development of an efficient method is our observation
that it is sufficient to have the information of mutating all
residues to Gly without the need to know the effect of each
residue to any other possible residue. That is, the effect of the
A→B mutation can be determined by the thermodynamic cycle
A→Gly, Gly→B. This idea (which is one of the reasons for
our definition of group contributions) reduces the order of the
computations needed that involves a single mutation from N3L
to N (where N is the number of residues in a given protein and
L is the number of naturally occurring amino acids). The second
1371
I.Muegge, H.Tao and A.Warshel
problem is, of course, the time needed to perform each computeraided mutation calculation. Here the non-relaxed approach takes
about 2 s of CPU time (on an SGI R8000 processor) for 100
amino acids whereas the fully relaxed approach takes about 50
days and a properly converging LRA study would probably take
a year for 100 amino acids. Of course, in principle the relaxed
approach is much more reliable but in many cases one can obtain
the correct trend by the non-relaxed approach. Furthermore, some
of the effects obtained here for the relaxed effect of non-polar
residues may reflect instability in the MD relaxation procedure.
Acknowledgements
This work was supported in part by ONR grant N00014-93-1-0967 and TobaccoRelated Disease Research Program grant 4RT-0002. I.M. gratefully acknowledges
support by a fellowship of the Deutsche Forschungsgemeinschaft (DFG).
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Received June 26, 1997; revised August 25, 1997; accepted September 18, 1997
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