From the
A new theoretical method for free energy calculations is used to
compute the absolute binding constants for
The glucose/galactose-binding protein (GBP)
The structure of GBP from Salmonella
typhimurium in complex with glucose was solved and refined at 2.4
Å resolution with an R factor of 15.8%
(1) . That
in complex with galactose has been refined to 1.7-Å resolution
with a conventional R factor of 19% and is essentially
identical
(2) . The overall structure of the protein is composed
of two similar domains, each consisting of a core of
In
addition to binding glucose and galactose as its name suggests, GBP is
able to bind some other sugars with good affinity: 0.04-2
µM glucose, 0.14-4 µM galactose,
3-12 µM 1-D-glyceryl-D-galactoside, 16
µM-1.3 mM methyl-
To understand better the origins of the tight binding and sugar
specificity of GBP, we have used a recently developed semiempirical
method for calculating binding energies that is based on molecular
dynamics (MD) simulations of the bound and free ligands
(11) .
This method was originally applied to the binding of various inhibitors
to endothiapepsin
(11) , and the present study also serves as an
additional check of the predictive power of the approach. Here we
report calculations of the binding of
The procedure for calculating binding free energies is that
described earlier by et al. (11) and will
be referred to here as the linear interaction energy (LIE)
approximation. With this method the free energy of binding for a given
compound is calculated as a linear combination of the differences in
the average ``ligand-solvent'' interaction energies between
the bound and free states of the ligand (we will use the term
``solvent'' to denote the entire surrounding medium, which
also then may include protein). That is, in order to evaluate the
absolute binding energy of a ligand to a host molecule two MD
simulations are carried out, one of the solvated ligand-host complex
and one of the ligand free in solution. The average interaction between
the ligand and its surroundings is calculated for each simulation and
its electrostatic and van der Waals components are weighted by
different factors:
On-line formulae not verified for accuracy
contains a summary of the average interaction
energies between the sugar molecules and their surrounding for the
cases where they are bound to the protein site and free in aqueous
solution. It can immediately be seen from the table that both the
electrostatic and van der Waals interactions are more favorable in the
protein than they are in water which, according to Equation 1, is
indicative of a negative free energy of binding. For glucose, the LIE
approximation as parametrized in Ref. 11 yields a value of
The high
affinity of GBP for glucose is quite impressive in view of the fact
that the ligand is a small neutral molecule. In contrast to other
systems with larger ligands or inhibitors, where it has been found that
a major portion of the binding strength stems from hydrophobic
interactions
(16, 11) , this does not seem to be the
case here. Instead we find that electrostatic interactions ( viz. hydrogen bonds) dominate the binding of glucose, although there is
also a significant contribution from nonpolar interactions with
especially Tyr
The reason for not
including crystallographic solvent molecules in the simulations above
is that, since one of the structures is known while the other is
unknown, taking water positions from the former may bias the
calculations. However, one should ask to what extent the inclusion of
these waters affects the energetics of glucose binding. Therefore, an
additional simulation of the glucose complex was carried out that
included x-ray waters. We then also decided to employ a recently
proposed method for treating long range electrostatic forces
(3) to examine the effect of using a 10-Å solvent-solvent
cutoff. This method uses a third-order expansion of the potential due
to groups outside of the regular cutoff and then updates this expansion
with a certain time interval (50 MD steps, in the present case). It is
then not applied to interactions involving the sugar, since they are
not subjected to any cutoff. While the effect of a cutoff on the
``solvation'' energetics of neutral compounds is only minor
it can cause severe overpolarization for charged systems
(22) .
The so-called local reaction field method
(3) has proven to be
very efficient for overcoming this problem
(3) .
The present study has addressed
the rather difficult problem of calculating absolute binding free
energies for two sugars that differ by a factor of about 1000 in their
affinity for GBP. We have found that the LIE approximation is able to
describe the binding energetics in a satisfactory way. While the
relative binding constant can also quite easily be evaluated by the
customary free energy perturbation approach, the absolute free energies
are much more difficult to obtain by that method. Since the ligands in
this case are neutral the effect of using a finite solvent-solvent
cutoff is not very pronounced. For charged ligands, however, one finds
the that cutoff effect is severe and that long range interactions must
be treated with great care.
The results
presented here demonstrate the important role of the charged groups in
the GBP receptor site for providing both the specificity and high
affinity for glucose. For such a small ligand, it is also difficult to
envisage how to achieve strong binding by van der Waals and
dipole-dipole interactions alone, since the magnitude of the former
will be limited by the size of the ligand and since the possible
dipole-dipole interactions (H-bonds) will to a large extent be
satisfied also in water. The use of charge-dipole interactions would
thus seem as a logical alternative, provided that the dielectric
constant associated with them can be kept low in the protein.
Furthermore, it seems clear that several such interactions are required
in order to achieve a high affinity. In this context, one may also
wonder to what extent the presence of these charged side chains affect
the equilibrium between the open and closed forms of the protein. Since
it is presumably this conformational change that constitutes the
activation (or signal) of the receptor, it is not inconceivable that
the role of the charged binding site residues is 2-fold, 1) to provide
strong binding and 2) to force the structure into the open
(unactivated) form in absence of ligand. The second effect could then
simply be the consequence of an otherwise unfavorable electrostatic
situation.
Energies are in kcal/mol and are averages over 250-ps simulations
except for the last entry for which the trajectories were 200 ps. The
superscripts p and w denote simulations with the
sugar bound to the protein site and free in solution, respectively. The
error bars are estimated from averaging of the first and second halves
of the MD trajectories. The upper and lower limits (see text) are given
for the experimental binding energies.
-D-glucose and
methyl-
-D-galactoside to the periplasmic
glucose/galactose receptor from Salmonella typhimurium. The
computer simulation results agree well with available experimental data
and make it possible to assess the sources of both the high affinity as
well as the specificity for glucose. It was found that the major
contribution to the binding energy comes from electrostatic
interactions and particularly hydrogen bonds of the charge-dipole type.
We also predict the structure of the complex with methyl-galactoside as
this has not yet been experimentally determined.
(
)
of Gram-negative bacteria is a member of a large family of
periplasmic proteins with roles in chemotaxis and transport. By virtue
of its high affinity for ligand (micromolar) and high concentration in
the periplasm (approaching millimolar after induction), it is able to
sequester sugar which appears in the environment, normally the lower
intestine, in transient bursts. Binding of sugar activates the protein,
after which it can bind to and activate the membrane components
directly responsible for transport of ligand or sensory information
across the inner membrane.
-sheet
enclosed by two layers of
-helices. These domains are connected by
a hinge made up of three segments of amino acid chain, with the
ligand-binding site residing in the cleft between the domains. Binding
of sugar occurs first to an open form, which subsequently closes to
bury the ligand almost completely.
(
)
-D-galactoside
(these seem to the most reliable K
values
and are extracted from Refs. 4-10). The relatively high affinity,
necessary for effective function, distinguishes the binding protein
from most carbohydrate-binding enzymes. GBP attains this high affinity
through a tightly coordinated combination of hydrogen bonding,
hydrophobic aromatic-sugar interactions, and a precise steric fit.
-D-glucose and
methyl-
-D-galactoside (Meg) to GBP.
G
=
11.2 ± 0.4
kcal/mol (K
= 0.006 µM).
The corresponding experimental value ranges from
9.1 kcal/mol
(equilibrium dialysis experiments, Ref. 8) to
10.1 kcal/mol
(kinetic fluorescence data, Ref. 9), and the simulations thus appear to
overestimate the binding strength in this case by a factor of
7-30. The calculated value for the free energy of binding for Meg
is
5.0 ± 0.6 kcal/mol (K
= 200 µM) which is within the experimentally
measured range of
G
(
4.1 to
6.5 kcal/mol). It should again be noted here that there are
fairly large and probably legitimate differences between different
experimental estimates of the sugar dissociation constants
(4, 5, 6, 7, 8, 9, 10) .
We can, however, say that LIE results are in reasonable agreement with
the measured binding data both with respect to the absolute binding
energy as well as the differential binding of the two sugars although
the affinity for glucose might be somewhat overestimated.
and Trp
. Similar conclusions
have been drawn by Quiocho and co-workers
(17) , in the case of
L-arabinose-binding protein, based on binding studies of
various galactose analogues. By comparing the average potential acting
on the dipolar groups of glucose in water and in GBP, one finds that
the C-1, C-2, and C-3 hydroxyl groups have particularily favorable
interactions in the protein. These three hydroxyls form a
hydrogen-bonded network with the charged side chains of
Asp
, Arg
, and Asp
in the
receptor site (Fig. 1 A). It is also at two of these
hydroxyl sites ( C- 1 and C- 2) that
the largest loss of interaction energy is found for the Meg ligand.
While the extra methyl group can be easily accommodated by protein, it
enforces a rotation by some 20 degrees of the sugar (in the plane of
the ring) according to the average MD structure
(Fig. 1 B). This causes the O-1
Asp
hydrogen bond to break and H-bonds between Arg
and
O-1 as well as O-2 to be weakened. The C-3 hydroxyl group H-bond to
Asp
switches to Asp
by the very same
rotation, but maintains a strong interaction. One can also note here
that the C-4 hydroxyl maintains its H-bond to Asp
without
loss of interaction energy, despite its axial configuration in Meg.
That the epimeric configuration around the C-4 carbon is only of minor
importance for binding is also suggested by the similar affinities of
GBP for glucose and galactose. However, our results indicate that the
protein framework of charged groups (in particular) provides the basic
element for specificity that does not tolerate rearrangement of the
H-bond pattern. In this context, it is interesting to note that
charge-dipole interactions seem to be very effective in establishing
strong binding, as evidenced also by several other proteins
(18, 19) . A reason for this is probably that the
``dielectric constants'' for such interactions can be kept
fairly low inside proteins, which is not always the case for
charge-charge interactions
(20) . It is also clear that a
quantitative modeling of this type of interactions that involve charged
(protein) groups requires careful parametrization of the force field
against solvation free energies
(21, 22) , and it seems
that the present force field does quite well in this respect.
Figure 1:
A, stereo view of the
average MD structure of the GBP-glucose complex ( thick lines)
superimposed on the crystal structure ( thin lines, Ref. 1).
Water positions are indicated by solid spheres ( large = MD, small = x-ray). No crystal waters
were included in the simulation, and the extra water molecule observed
in the MD structure can be as the lower rightmost one in the picture.
B, stereo view of the average MD structure of the GBPMeg
complex ( thin lines, small spheres) superimposed on
the average MD structure of the glucose complex ( thick lines,
large spheres). C, stereo view of the average MD
structure of the GBP
glucose complex, from the simulation including
crystal waters, superimposed on the corresponding x-ray structure
(structure representations as in
A).
The
structural agreement between the average MD structures and the
experimental one is remarkably good. The root-mean-square coordinate
deviation with respect to the x-ray complex of GBP-glucose is 0.56
Å for protein atoms within an 8 Å sphere of the sugar C-5
carbon, for the average MD glucose structure, and 0.68 Å between
the average Meg structure and the model built one. We also find that
the MD water positions agree very well with the experimental ones
(Fig. 1 A) although crystallographic waters were not
included in our starting structure. In particular, the position of the
crucial water molecule interacting with O-3 and O-4
(1, 2) is reproduced by the simulations. There is, however, one
additional water molecule observed in the MD structure in the vicinity
of the C-1 hydroxyl group that is not present in the crystal. In this
position the experimental structure does has a cavity which might be
able to accomodate a water molecule although no electron density is
observed in the refined structure. In fact, the newly determined
crystal structure of the closed ligand-free form of GBP has a water
molecule in this very same position
(23) .
(
)
It was applied here both in the protein simulation that
included crystal waters as well as in an additional simulation of the
free ligand, to allow for a consistent evaluation of the corresponding
binding energy. The results of these simulations are also summarized in
. Encouragingly, we find here that the resulting value of
G
=
11.2 ± 0.6
kcal/mol is identical to that previously obtained. It can, however, be
noted that the electrostatic binding contribution drops by 0.4 kcal/mol
and is compensated by a corresponding increase in the hydrophobic
contribution. In view of this result, it would thus appear that the
possible presence of a water molecule near O-1 is not of major
importance for the binding energetics. Fig. 1 C shows a
comparison of the average MD structure to the x-ray one for the
simulation including crystal waters.
(
)
This problem is
also quite independent of the method used for calculating free
energies. As far the LIE method is concerned it assumes in its present
form (Equation 1) that the linear response approximation for the
electrostatic part is valid, which might not always be the case
(11) . Therefore, with more simulation data at hand it could be
useful to treat also the electrostatic coefficient as an empirical one,
but such considerations are left for future work.
Table:
Average MD interaction energies for bound and
free sugars and calculated and observed free energies of binding
-D-galactoside; LIE, Linear interaction energy;
©1995 by The American Society for Biochemistry and Molecular Biology, Inc.