©1995 by The American Society for Biochemistry and Molecular Biology, Inc.
Sugar Recognition by a Glucose/Galactose Receptor
EVALUATION OF BINDING ENERGETICS FROM MOLECULAR DYNAMICS SIMULATIONS (*)

Johan , Sherry L. Mowbray

From the (1) Department of Molecular Biology, Uppsala Biomedical Centre, Box 590, S-75124 Uppsala, Sweden

ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS AND DISCUSSION
FOOTNOTES
REFERENCES

ABSTRACT

A new theoretical method for free energy calculations is used to compute the absolute binding constants for -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.


INTRODUCTION

The glucose/galactose-binding protein (GBP)() 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.

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 -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.()

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--D-galactoside (these seem to the most reliable Kvalues 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.

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 -D-glucose and methyl--D-galactoside (Meg) to GBP.


MATERIALS AND METHODS

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


RESULTS AND DISCUSSION

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 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.

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 Tyrand 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 Aspin 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-1Asphydrogen bond to break and H-bonds between Argand O-1 as well as O-2 to be weakened. The C-3 hydroxyl group H-bond to Aspswitches to Aspby the very same rotation, but maintains a strong interaction. One can also note here that the C-4 hydroxyl maintains its H-bond to Aspwithout 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 GBPglucose 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) .

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) .() 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.

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.() 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.

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.

  
Table: Average MD interaction energies for bound and free sugars and calculated and observed free energies of binding

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.



FOOTNOTES

*
This work was supported by grants from the Swedish Natural Science Research Council (NFR). The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore by hereby marked `` advertisement'' in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

The abbreviations used are: GBP, glucose/galactose-binding protein; MD, molecular dynamics; Meg, methyl--D-galactoside; LIE, Linear interaction energy;

B. Shilton and S. L. Mowbray, manuscript in preparation.

J. , unpublished data.

T. Hansson and J. , manuscript in preparation.


REFERENCES
  1. Mowbray, S. L., Smith, R. D., and Cole, L. B. (1990) Receptor 1, 41-54 [Medline] [Order article via Infotrieve]
  2. Zou, J., and Mowbray, S. L. (1993) J. Mol. Biol. 233, 739-752 [CrossRef][Medline] [Order article via Infotrieve]
  3. Lee, F. S, and Warshel, A. (1992) J. Chem. Phys. 97, 3100-3107 [CrossRef]
  4. Anraku, Y. (1968) J. Biol. Chem. 243, 3116-3122 [Abstract/Free Full Text]
  5. Boos, W. (1969) Eur. J. Biochem. 10, 66-73 [Medline] [Order article via Infotrieve]
  6. Hazelbauer, G. L., and Adler, J. (1971) Natl. New Biol. 230, 101-104
  7. Rotman, B., and Ellis, J. H., Jr. (1972) J. Bacteriol. 111, 791-796 [Medline] [Order article via Infotrieve]
  8. Zukin, R. S., Strange, P. G., Heavey, L. R., and Koshland, D. E., Jr. (1977) Biochemistry 16, 381-386 [Medline] [Order article via Infotrieve]
  9. Miller, D. M., Olson, J. S., and Quiocho, F. A. (1980) J. Biol. Chem. 255, 2465-2471 [Free Full Text]
  10. Richarme, G., and Kepes, G. (1983) Biochim. Biophys. Acta 742, 16-24
  11. , J. Medina, C., and Samuelsson, J.-E. (1994) Prot. Eng. 7, 385-391 [Abstract]
  12. Straatsma, T. P., and McCammon, J. A. (1992) Ann. Rev. Phys. Chem. 43, 407-435 [CrossRef]
  13. , J., Fothergill, M., and Warshel, A. (1993) J. Am. Chem. Soc. 115, 631-635
  14. Warshel, A., and Creighton, S. (1989) in Computer Simulation of Biomolecular Systems (van Gunsteren, W. F., and Weiner, P. K., eds) pp. 120-138, ESCOM, Leiden, The Netherlands
  15. van Gunsteren, W. F., and Berendsen, H. J. C. (1987) Groningen Molecular Simulation (GROMOS) Library Manual, Biomos BV, Nijenborgh 16, Groningen, The Netherlands
  16. Miyamoto, S., and Kollman, P. A. (1993) Proc. Natl. Acad. Sci. U. S. A. 90, 8402-8406 [Abstract/Free Full Text]
  17. Vermersch, P. S., Tesmer, J. J. G., and Quiocho, F. A. (1992) J. Mol. Biol. 226, 923-929 [Medline] [Order article via Infotrieve]
  18. Pflugrath, J. W., and Quiocho, F. A. (1985) Nature 314, 257-260 [Medline] [Order article via Infotrieve]
  19. Luecke, H., and Quiocho, F. A. (1990) Nature 347, 402-406 [CrossRef][Medline] [Order article via Infotrieve]
  20. Warshel, A., and , J. (1991) Ann. Rev. Biophys. Biophys. Chem. 20, 267-298 [CrossRef][Medline] [Order article via Infotrieve]
  21. , J. (1990) J. Phys. Chem. 94, 8021-8024
  22. , J. (1994) J. Phys. Chem. 98, 8253-8255
  23. Flocco, M. M., and Mowbray, S. L. (1994) J. Biol. Chem. 269, 8931-8936 [Abstract/Free Full Text]

©1995 by The American Society for Biochemistry and Molecular Biology, Inc.