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J. Phys. Chem. 1996, 100, 2528-2534
Free Energy Simulation Studies of the Binding Specificity of Mannose-Binding Protein G. Liang,† R. K. Schmidt,† H.-A. Yu,*,‡ D. A. Cumming,‡ and J. W. Brady*,† Department of Food Science, Stocking Hall, Cornell UniVersity, Ithaca, New York 14853, and Genetics Institute, Inc., 87 Cambridge Park DriVe, Cambridge, Massachusetts 02140 ReceiVed: September 29, 1995; In Final Form: December 20, 1995X
Free energy simulations and standard molecular mechanics calculations have been used to examine the binding specificity of the C-type lectin rat mannose-binding protein. This protein, which is important in inflammation and immunoglobin-independent immune response, recognizes and binds to mannose and high-mannose oligosaccharides but not to galactose. Molecular dynamics simulations were used to estimate the free energy difference between these two sugars in aqueous solution and in the binding site of the protein. While the simulations found mannose to be favored over galactose, interactions with the solvent tended to favor galactose. The calculated binding free energy difference for these two sugars to MBP was 3.1 kcal/mol favoring mannose, approximately twice the experimental value. An estimate of the resolution into components found that enthalpy favored mannose but that entropy favored galactose, a reversal of the situation in solution. From standard MD simulations, the galactose was found to rotate in the binding site away from the mannose orientation found in crystallographic studies.
Introduction Lectins are widespread globular proteins, first identified from plants, which bind carbohydrates with a high degree of configurational specificity.1,2 While their function in plants is not completely clear, their configurational selectivity in vitro has been widely exploited in biological and medical research for a variety of purposes. The stereochemical selectivity of lectins not only is of practical importance but also is interesting as a model for many carbohydrate-mediated interactions in molecular recognition. A number of animal lectins are also now known which serve in molecular recognition functions.3 Most mammalian lectins belong to one of three broad categories: the P-type lectins which bind mannose 6-phosphate; the free thiolcontaining S-type lectins; and the extracellular, calciumdependent C-type lectins. One important family of C-type lectins includes the L-, P-, and E-selectins.4 Selectins are surface glycoproteins present in leukocytes, platelets, and endothelial cells. Their recognition of cell-specific carbohydrate ligands plays an essential role in cell adhesion events that underlie leukocyte extravasation to the site of injury during inflammation. As such, selectins are an important component in host defense and have attracted widespread interest as targets for the development of antiinflammatory drugs. Another important class of C-type serum lectins in mammals consists of the mannose-binding proteins (MBPs) which function in the immunoglobin-independent acute response to infection.5 These proteins bind selectively to high-mannose cell-surface oligosaccharides found in the cell walls of bacterial and fungal pathogens but not in mammalian cells, marking them for destruction by complement fixation or by opsonization.6 MBPs consist of at least two domains; a globular carbohydrate recognition domain (CRD) which binds to mannose, and a long nonglobular collagen-like domain; proteins of this type are sometimes referred to as collectins. The crystal structures of the CRD of human MBP7 and E-selectin8 have recently been determined to high resolution using X-ray crystallography. In †
Cornell University. Genetics Institute, Inc. * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, February 1, 1996. ‡
0022-3654/96/20100-2528$12.00/0
addition, high-resolution structures of the homologous rat MBP have been reported both for the uncomplexed form9 and for the protein bound to an oligosaccharide ligand.10 MBP contains two calcium ions as integral parts of its structure which are essential to its function; the absence of these ions abolishes the ligand-binding capability of MBP. The molecular features responsible for this intimate coupling of structure and function by calcium ions were nicely revealed by the crystal structure of the rat protein complex. It was determined that one of the calcium ions (#2 in the nomenclature of the crystallographic study) is directly coordinated to two of the hydroxyl groups of the mannose ring in the binding site,10 in contrast to the situation in many plant C-type lectins such as concanavalin A and its homologues. In the structure of the wild-type MBP, the mannose ligand makes several specific interactions with protein residues and the calcium ion. In particular, the O3 and O4 hydroxyl groups are directly bound to the ion as part of its coordination sphere, while the side chains of various residues interact both with these hydroxyl groups and the calcium ion so as to restrict the orientational freedom of the sugar and position it precisely in the binding site. The protein will also bind a third calcium ion in a specific site, but this ion is not essential for activity. Because of the importance of MBP in inflammation and the immune response, it would be most desirable to learn how to manipulate its specificity and how to design competitive inhibitors and substrate analogues. This goal in turn would be facilitated by a quantitative model for the contributions of various interactions to the total binding energy as a function of ligand stereochemistry. In addition to the crystallographic studies, MBP has also been the subject of several physicochemical and mutagenesis studies. In particular, Drickamer has measured the binding affinities of simple sugars for the wildtype protein and has reported that the specificity of the rat lectin can be changed from mannose to galactose through two simultaneous point mutations in the combining site.11 The availability of these results, along with the high-resolution structural information, makes this an excellent system for theoretical studies. We report here molecular dynamics (MD) free energy calculations of the difference in binding affinity of the wild© 1996 American Chemical Society
Binding Specificity of Mannose-Binding Protein
Figure 1. (a) R-D-mannopyranose; (b) R-D-galactopyranose.
type rat MBP for the two monosaccharide sugars D-mannose and D-galactose and use conventional MD simulations and conformational energy analysis to help provide a qualitative explanation for the results. Recent simulations of this type have been used to analyze the energy differences between anomeric forms for the sugars glucose12 and xylose13 in aqueous solution in terms of the structural differences between these two isomers and the way in which they interact with solvent water molecules. In addition, such studies have been widely used in recent years to calculate differences in binding affinities of proteins for different ligands14 and the differences in binding affinities of mutant proteins for a common ligand.15 Similar free energy calculations have been applied to the study of binding specificity in L-arabinose-binding protein and its mutants.16 Standard MD simulations have also recently been used to study the differences in thermal fluctuations in MBP resulting from the binding of a third calcium to the protein.17 The development of useful theoretical models of this type would be of considerable utility in understanding the specificity of MBP and in designing new mutants of this protein. Methods In the present study a series of standard MD simulations and free energy perturbation calculations were carried out using the molecular mechanics program CHARMM.18,19 Free energy perturbation simulations were conducted in which so-called “computer alchemy” methods were used to gradually transform an R-D-mannopyranose molecule into R-D-galactopyranose (Figure 1) in aqueous solution and in the binding site of the CRD of rat MBP. In addition, to assist in the analysis of the results, standard MD simulations of the two sugars in aqueous solution and in the protein binding site were conducted. The results of these simulations were compared to conventional conformational energy minimization analyses of the sugars and their complexes with the protein. The protein potential energy
J. Phys. Chem., Vol. 100, No. 7, 1996 2529 was calculated using the recently developed CHARMM23 force field,20 and the energy of the sugar molecules was calculated using a provisional CHARMM-type carbohydrate force field.21 Water molecules were modeled using the TIP3P energy function.22 One goal of these studies was to characterize the ability of presently available force fields and simulation protocols to model C-type lectin systems and to suggest directions for improvement, such as needed revisions of the force field. The standard MD simulations of D-mannose and D-galactose in solution were started by superimposing the lowest energy pyranoid structure for the R anomer of each sugar onto a previously equilibrated cubic box of water, removing any overlapping solvent molecules. The box length was adjusted to 18.4987 Å to give a density of 1.015 g/cm3. Periodic boundary conditions were employed, and nonbonded interactions were made to go to zero at long ranges through the application on a neutral group basis of a switching function which smoothly tapered the interactions to zero between 6.0 and 8.0 Å. Both simulations were equilibrated for 20 ps, with periodic adjustment of the atomic velocities if needed to maintain the desired temperature, followed by 500 ps of further dynamics. Trajectories were numerically integrated using a Verlet integration scheme23 with a step size of 1 fs, and bond lengths for those bonds involving hydrogen atoms were kept fixed using the SHAKE constraint algorithm.24 Because of the large size of the protein-sugar complex, it is too costly to apply a comparable approach to the solvation of this system, in which the complex would be immersed in a very large cubic box of water, with the application of periodic boundary conditions. Since the interactions of interest in carbohydrate discrimination are likely to be somewhat localized in the binding site vicinity, a spherical stochastic-boundary Langevin system25 was constructed around the sugar ligand. An 18 Å sphere of water was placed around calcium ion number two (the binding center between mannose and MBP), with the sphere of sufficient size as to contain several layers of solvent molecules. Those solvent molecules which overlapped with the sugar or protein were removed. Those protein atoms more than 18 Å from the calcium ion number two were kept fixed, and the water molecules were constrained to remain within the sphere through the use of a constraining potential, as has often been done in previous simulations of this type.12,13,25 Atoms between 14 and 18 Å were governed by Langevin equations of motion, while all atoms less than 14 Å from the center moved according to Newtonian dynamics. Long-range interactions were truncated on an atom-by-atom basis through the use of the CHARMM shifting function with a cutoff of 12 Å. Previous studies have demonstrated that this cutoff distance is sufficient to reduce the artifacts of this procedure and give results similar to those calculated using switching functions applied on a neutral group basis.26 This method of terminating long-range interactions was required by the free energy perturbation studies described below, which complicate the division of the sugar molecules into neutral groups. In the free energy simulations, a coupling parameter approach19 was used to transform mannose into galactose in a series of calculations for different values of the parameter λ, using an equation of the form
Eλ ) λEgal + (1 - λ)Eman
(1)
In these simulations, both sugar molecules are simultaneously present, with both equatorial and axial aliphatic protons and hydroxyl groups present on the C2 and C4 positions. The degree to which each “mutated” group contributes to the total energy is determined by λ, which transforms the sugar from
2530 J. Phys. Chem., Vol. 100, No. 7, 1996
Liang et al.
mannose to galactose as λ varies from 0 to 1. While these simulations do not correspond to any physical system, they define a path between the two physical end points as a series of steps for which the free energy difference between each can be calculated from a perturbation equation of the form
G1 - G0 ) -kT ln 〈exp[-β(E1 - E0)]〉0
(2)
Since free energy is a state function, the total difference between the two physical end points can be calculated from the total difference for the individual steps: N
∆G ) ∑∆Gi
(3)
i)1
This approach has recently been used to model the anomeric equilibrium in D-glucose and D-xylose in solution. In the solution simulations, the initial structure of the sugar was the lowest energy geometry for mannose using the CHARMM energy function as determined by energy minimization. For simulations of the sugar-protein complex, the crystal structure of the MBP-mannose complex, using only residue 9 of the oligosaccharide found in the binding site of the crystal structure, was taken as the starting geometry.10 For both types of simulations the spherical stochastic boundary method described above was used. A series of seven intermediate values of λ were used at 0.04, 0.1, 0.3, 0.5, 0.7, 0.9, and 0.96, as in our previous studies of xylose.13 For each λ value, the system was equilibrated for 10 ps followed by a further 50 ps of dynamics used for analysis. Each simulation was kept at a temperature of 300 ( 2 K. The free energy changes were calculated both by direct exponential averaging and by thermodynamic integration. The calculation of the difference in binding affinities must take into account the fact that the two sugars do not have the same free energy in aqueous solution, as well as the difficulty of directly estimating the free energy change associated with the substantial, nonperturbative changes involved with taking a sugar out of solution and putting it in the binding site, desolvating both in the process. The total difference in binding affinities for the two sugars, ∆∆Gb, can be calculated from a thermodynamic cycle of the type:19 P + L1
∆G1
∆G3
P + L2
PL1 ∆G4
∆G2
(4)
PL2
In this scheme, ∆G1 and ∆G2 are the free energy differences for the binding of the two sugar ligands to the protein, and ∆G3 and ∆G4 are the free energy changes for the nonphysical processes of transforming D-mannose into D-galactose in solution and in the protein binding site, respectively. Since free energy is a state function, the difference in the binding energies of the two ligands can be written as
∆∆Gb ) ∆G2 - ∆G1 ) ∆G4 - ∆G3
(5)
While it is difficult to obtain the quantities ∆G1 and ∆G2 from MD calculations, estimation of the free energy difference associated with the change in sugar structure going from mannose to galactose, both in solution and in the protein binding site, is tractable using the perturbative mutation pathway described above, thus allowing the calculation of ∆∆Gb. Results and Discussion Solution Energy Difference. Figure 2 displays the change
Figure 2. Free energy for the “mutation” of a R-D-mannopyranose into R-D-galactopyranose in aqueous solution (circles) and in the protein binding site (squares) as a function of the coupling parameter λ.
in free energy for the transformation from mannose to galactose in aqueous solution as a function of the coupling parameter λ. The free energy change in solution favors mannose by 2.4 kcal/ mol. The corresponding free energy difference for the transformation in vacuum is 4.01 kcal/mol, implying that hydration favors galactose. However, direct averaging of the total interaction energy and its components from the standard MD simulations of the two sugars in aqueous solution finds that the internal energy in these simulations favors mannose by only 0.31 kcal/mol in solution. Also, the energy difference between the lowest energy-minimized conformations in vacuo for each molecule favors mannose by 0.36 kcal/mol, and the energy difference between the two molecules averaged over standard MD trajectories in vacuum favors mannose by 0.79 kcal/mol. The discrepancies in the magnitudes of the preferences for mannose between the free energy simulations and the standard MD simulations apparently result in part from different distributions of primary alcohol conformations between the two types of simulations (see below), since the internal energies of the sugar molecules are a strong function of this orientation. Because the standard simulations were longer, they experienced more transitions in these primary alcohol groups and thus probably provide a better estimate of this internal energy component. It should be noted that the total internal energies of the two sugars cannot be compared experimentally. Also, unlike the case in our previous studies,12,13 the total energy difference between the two sugars in solution cannot be compared to experimental solubilities, since they are not able to interconvert as the anomeric forms can. Furthermore, the two crystals have different, unknown lattice energies and cannot be conveniently put into the vapor phase due to their extensive hydrogen bonding. As can be seen from Table 1, the interaction energy between the sugars and the solvent molecules in the standard MD simulations favors galactose by 3.71 kcal/mol, indicating that this sugar is better hydrated than mannose, which is consistent with the results of the free energy simulation. This stronger interaction of the galactose molecule with solvent water is also consistent with the direct analysis of the hydrogen bonding pattern of each sugar with water. Table 2 lists the mean number of hydrogen bonds to solvent made by each hydroxyl group of the sugar molecules as calculated using geometric criteria. In this analysis a water molecule was considered to be hydrogen bonded to the hydroxyl group if the oxygen-oxygen distance was less than 3.4 Å and the O-H‚‚‚O angle was 120° or greater. As can be seen, the galactose makes 0.46 more hydrogen bonds to solvent than the mannose does, which would be consistent with a stronger total interaction energy with the solvent. However, unlike the situation with the anomeric equilibrium in
Binding Specificity of Mannose-Binding Protein
J. Phys. Chem., Vol. 100, No. 7, 1996 2531
TABLE 1 Free Energy Simulations ∆A ∆H ∆S -T∆S (kcal/mol) (kcal/mol) (kcal/mol/degree) (kcal/mol) in solution in vacuum in MBP binding site
-14.7 4.2 41.5
2.4 4.0 5.5
-0.058 0.00073 0.12
17.4 -0.2 -36.6
Standard MD Simulations ∆E total
solute-solute solute-solvent solvent-solvent
in solution -0.89 in vacuum 0.79
0.31
-3.71
2.51
TABLE 2: Number of Hydrogen Bonds to Solvent O1 O2 O3 O4 O5 O6 total
mannose
galactose
difference
2.29 2.53 2.58 2.36 0.74 2.74 13.24
2.39 2.72 2.58 2.46 0.74 2.81 13.70
0.10 0.19 0.00 0.10 0.00 0.07 0.46
glucose and xylose, in which a similar increased amount of solvent hydrogen bonding for the preferred anomeric form was found to arise entirely from one hydroxyl group,13 in the present case the total difference is the result of small differences at several of the hydroxyl groups. Although the length of the simulations and experience with the previous sugar simulations suggest that this difference is real rather than statistical noise, no obvious qualitative explanation for its origin is apparent. It is interesting, however, that much of the difference between the hydrogen bonding for these two sugars is at the O2 and O4 hydroxyl groups, which are of course the positions of stereochemical difference between the isomers. Estimates of the resolution of this free energy difference into enthalpy and entropy components27 (Table 1) suffer from large uncertainties, but the trends indicate that a significant enthalpy component favors galactose while an even larger entropy term favors the mannose. Such a distribution would seem to be qualitatively reasonable in view of the stronger hydration interactions of the galactose. Presumably the increased hydrogen bonding to solvent results in an increase in the localization of the water molecules and thus a lower entropy, while this larger number of hydrogen bonds would imply an enthalpy contribution favoring galactose. The primary alcohol groups of the sugars made several transitions during the standard simulations. In the mannose simulation, this exocyclic group started in the TG conformation but made a transition to the GT conformational shortly after the beginning of the data collection period and then subsequently three times rotated back to the TG conformation followed by a return to GT each time, for a total of seven transitions. The conformation of this group was GT 40.4% of the simulation time and TG 59.6% of the time. No transitions to the GG conformation occurred during the simulation. In the galactose simulation, nine transitions in this angle occurred, and the distribution of conformations was 12.7% GT, 7.8% GG, and 79.6% TG. The simulation began with this group in the GG conformation since this geometry was found to have the lowest energy in vacuum minimizations, but the primary alcohol remained in this conformation for only around 4 ps before rotating to TG. It did not subsequently return to the GG conformation during the simulation.
Figure 3. Stereo view of the residues in the binding site of the crystal structure of MBP bound to a mannose ligand. This figure was prepared using the program MOLSCRIPT.32
The carbohydrate potential energy function used here is known to disproportionately disfavor GT orientations due to the repulsive (1-4) interactions of the O4 and O6 oxygen atoms, which are greater in the gauche conformations (GT and GG) than in the trans TG conformation. As a result, this potential energy function produces a TG population which is also too large compared to experiment in the case of glucose. NMR NOE data are available for galactose which suggest that in aqueous solution the distribution of this primary alcohol conformation is 61% GT, 18% GG, and 21% TG.28 From the crystal structure of the oligosaccharide-lectin complex, it would appear that the primary alcohol groups play little role in the binding of the sugars to the protein, since they point away from the protein into the solvent and make hydrogen bonds to solvent molecules. However, the orientation of this group has a substantial effect on the total internal energy of the sugar through the interaction of its dipole with the rest of the molecule and can thus affect total relative energies since this effect varies from one sugar to the next. Energy Difference in the Protein Binding Site. From the free energy simulation of the transformation in the protein binding site, mannose binding is favored by 5.5 kcal/mol (Figure 2). Subtracting the change in solution (eq 5) gives a difference in binding free energy ∆∆Gb for the two sugars of 3.1 kcal/ mol favoring the mannose binding. This strong preference for mannose is in qualitative agreement with experiment; Drickamer has reported using a competition assay to determine that mannose binds with a 14-fold higher affinity than galactose (Ki of 7.2 versus 100 mM), corresponding to a free energy difference at room temperature of 1.6 kcal/mol favoring mannose. The present simulations correctly predict the strong preference for mannose but overestimate this energy by a factor of 2. The close match of the MBP binding site to the mannose stereochemistry, as described from the crystal structure by Weis et al., is accomplished through the strategic positioning of several residues. Five side-chain oxygen atoms from Glu 185, Glu 193, Asn 187, Asn 205, and Asp 206, and one main-chain peptide carbonyl oxygen from Asp 206, are positioned to coordinate with calcium 2 (Figure 3). The binding of the mannose substrate is achieved through direct coordination of its O3 and O4 hydroxyl oxygen atoms to the same calcium ion, completing the compact but irregular coordination shell of this ion. The strong interaction of the oxygen atoms of these residues with the calcium also places their noncoordinated hydrogen-bonding atoms precisely in position to fully satisfy the hydrogen-bonding capacity of the O3 and O4 hydroxyls of mannose, making it difficult for them to interact favorably with sugars of different stereochemistry. For example, the mannose
2532 J. Phys. Chem., Vol. 100, No. 7, 1996
Figure 4. Stereoview of the final structure from the free energy “mutation” of mannose to galactose, illustrating the binding site residues and the rotated orientation of the galactose ligand. The original orientation of the mannose ligand in the crystal structure is also illustrated, but displaced outward from the binding site for clarity.
O4 hydroxyl group, in addition to coordinating to the calcium ion, is capable of making a hydrogen bond as a donor with the free oxygen atom of Glu 193 and acts as an acceptor in a hydrogen bond with an amide proton of Asn 205. Similarly, mannose O3 makes a hydrogen bond as a donor with the free side-chain oxygen of Glu 185 and a polar proton of Asn 187 makes a hydrogen bond as a donor to the axial O2 hydroxyl oxygen. All of these interactions are stable in the standard MD simulations of the protein-mannose complex, and the average structure deviates little from the crystal structure, with an rms drift for the atomic positions in the complex of only 1.11 Å. While the O3 interactions would be essentially the same for a galactose substrate bound in this site in the same orientation, the axial configuration of the O4 hydroxyl group would prevent it from hydrogen bonding to Asn 205, where the distance to the proton of this residue would increase to 3.15 Å in the minimized structure from the 1.73 Å found in the mannose complex crystal structure. The high complementarity of the binding site structure with the mannose stereochemistry explains the specificity shift observed by Drickamer in mutagenesis experiments. The socalled QPD double mutant, in which Glu 185 is changed to Gln and Asn 187 is changed to Asp, will bind to galactose but not to mannose. Presumably, in such a mutant, Asn 185 can make a hydrogen bond as a donor to O2 if it is equatorial, as in galactose, but is too far away for such a bond to mannose, while the O3 hydroxyl group would then donate its proton in a hydrogen bond to the free oxygen of Asp 187. This latter interaction is necessary in order to replace the hydrogen bond lost to the 185 residue, explaining the necessity of the double mutant. Significantly, during the course of the transformation from mannose to galactose in the free energy simulation, the sugar ring rotates by almost 90°, indicating that galactose prefers to bind in this site with a different orientation. In the final coordinate set of the transformation simulation, the O3 and O4 hydroxyls remain tightly coordinated to the calcium 2 ion, but the remainder of the ring has pivoted in order to maximize interactions with the Asn 205 side chain, whose oxygen atom is closely hydrogen bonded as an acceptor to both the O2 and O3 hydroxyl groups in the galactose (Figure 4). The galactose makes no other close hydrogen bonds to protein groups, although the coordination of the O3 and O4 hydroxyl groups to the calcium is as close as in the mannose complex. Apart from making these bonds, a principal reason for the rotation would appear to be the need to relieve unfavorable O-O interactions between the O2 hydroxyl group and Glu 185, since
Liang et al.
Figure 5. Stereoview of the final structure from the standard MD simulation of galactose in the binding site. The original orientation of the mannose ligand in the crystal structure is also illustrated but displaced outward from the binding site for clarity.
in the final structure this hydroxyl group is pointing its proton at one of the oxygen atoms of Glu 185. The rotation of the galactose in the binding site does not appear to be an artifact of the physically unrealistic mutation simulation, since 120 ps of standard MD simulations of the galactose complex starting from this final structure of the free energy simulation produced a small lateral drift in the ring position but no tendency for it to rotate back to the mannose orientation. To further test the tendency for a galactose to shift in the binding site, an additional standard MD simulation was performed in which the mannose substrate in the crystal structure was simply converted to a galactose, followed by 20 ps of equilibration and 100 ps of further dynamics. Again the sugar rotated in the binding site to a position almost perpendicular to its starting position. However, the final orientation in this simulation, illustrated in Figure 5, was not only different from that in the crystal structure but also different from that seen in the free energy simulation described above. In this new geometry, the galactose is only coordinated to the calcium through the O4 hydroxyl group, since the O3 hydroxyl has rotated its hydrogen such that it is closer to the calcium ion than the oxygen is. This seemingly unfavorable arrangement is maintained because this geometry allows it to make a bifurcated hydrogen bond with both oxygens of the charged Glu 185 group. The oxygen of the O3 hydroxyl makes a hydrogen bond as an acceptor with the polar proton of Asn 205. The O2 hydroxyl group is also hydrogen bonded as a donor to Glu 185, and O4, which is still coordinated to the calcium 2, is hydrogen bonded as a donor to Glu 193, as is O6. The rotation of the galactose in the binding site in this second simulation further confirms that the binding specificity is apparently reduced for this sugar, while the differences between this binding scheme and that described above indicate that there may not be a single binding mode for galactose in the active site, as might be expected if it is more weakly bound. An estimate of the breakdown into components of the free energy difference27 for the mannose and galactose binding is revealing. The 5.5 kcal/mol difference in binding energy results from the rough cancellation of a large enthalpy difference favoring the mannose and a large entropy term favoring the galactose. This represents a reversal of the situation in aqueous solution. A qualitative explanation for this difference might be that the binding site for the mannose is so closely tailored to its stereochemistry, and the binding to the calcium and the acid and asparagine groups is so tight that the sugar is constrained from making significant fluctuations in its position, leading to a low entropy and a strong interaction enthalpy. The galactose is much less tightly bound, so it has much greater
Binding Specificity of Mannose-Binding Protein mobility in the binding site, leading to a weaker interaction enthalpy and a larger entropy. The possibility of a number of weakly bound states for the galactose complex could contribute to the difference between the calculated and experimental binding energies. Apparently not all of the substrate discrimination arises from direct hydrogen-bonding interactions. Analysis of the conformational energy components for the minimized crystal structure complexed with mannose and a similar minimized complex with galactose where the sugar is not rotated but bound in the mannose orientation, revealed that the Glu 185 residue makes a large contribution to the preference for mannose binding, even though it is directly hydrogen bonded only to the O3 hydroxyl groups of the sugars, which has the same configuration in both molecules. However, the galactose molecule, with the equatorial C2 hydroxyl group, has its O2 oxygen atom 1.12 Å closer to the OE2 atom of Glu 185, increasing its repulsive energy contribution, while its hydrogen atom is apparently unable to rotate so as to point at this negatively charged atom because of the presence of the positively charged -amino group of Lys 182. Although in our simulation only monosaccharides were used, there exists experimental evidence that this Lys is important in carbohydrate-lectin recognition. In the crystal structure of the oligomannose/MBP complex, Lys 182 makes a hydrogen bond to the O3 and O4 hydroxyls of the mannose linked to the calcium-coordinating mannose. It was also found to be an important determinant of the carbohydrate specificity in E-selectin. Kogan et al. have reported that by mutating the topologically equivalent Ala 77 in the lectin domain of E-selectin to Lys, the mutant protein will bind oligomannose preferentially.29 Conclusions Given the limitations of the simulation design, it is interesting and encouraging that the results are both qualitatively correct and in reasonable quantitative agreement with experiment. The significant rotation of the galactose sugar ring from the position occupied by the mannose ring in the crystal structure, while very interesting, is not necessarily a surprising result. In fact, it must represent a special case of a more general problem which might arise in such free energy calculations when comparing the binding affinities of two species, one of which has a greatly reduced affinity, in both the absolute and relative sense, for the binding site. In such a situation, it is quite reasonable that the sugar might shift in the binding site or drift away from it altogether during the course of a simulation of sufficient length. In a case where the sugar has no real affinity for the binding site and would prefer to be fully solvated instead, the stepwise perturbative approach used here will not work. An even more difficult case to model would arise if a residual binding affinity remained, but of such low magnitude that the binding took place at an alternate site or nonspecifically at a number of places on the surface. In the present situation, the direct coordination of the calcium ion to the sugars is sufficiently strong to keep even the galactose ring in the same general binding site, without allowing it to drift away, but the orientation shifts, along with the overall strength of the interaction. It would be most interesting to determine whether galactose can be cocrystallized with MBP in usefully diffracting single crystals, and if so, whether the position of the ligand in the crystal structure is similar to those predicted from the present studies. Presumably the lower affinity of galactose for the protein would make this experiment difficult. Another limitation of the present studies is that only one anomeric configuration was considered. In each simulation only
J. Phys. Chem., Vol. 100, No. 7, 1996 2533 the alpha anomer of the sugar was modeled, although in an aqueous environment an equilibrium exists with significant amounts of each form present. Complicating the analysis, these forms have different internal energies and different interaction energies with aqueous solvent, and could easily have different energies of interaction with the protein. In addition, the two monosaccharides have different equilibrium ratios of the two forms;30 in D-mannose, the ratio is 67% R and 33% β, while D-galactose has almost the exact opposite ratio, with 32% R, 64% β, and 4% furanoid tautomers at 20 °C. In the oligosaccharide ligand of the crystal structure the (1 f 2) linkage between the complexed MAN9 and MAN6 sugar rings has the R configuration, but there are no close contacts that would prevent the β anomer of the free monosaccharide from binding since this hydroxyl sticks out into the solvent. An important reason for undertaking these simulations was to determine how successfully this system could be modeled using currently available potential energy functions and simulation protocols and to provide information to guide in the revision of the potential energy functions. The present protein parameters have been extensively tested and have been shown to model protein conformational dynamics quite satisfactorily. The carbohydrate force field, however, suffers from several known limitations, as well as from being developed for an older form of the CHARMM energy function, which, for example, treated torsional terms differently. Among its more important problems are the inability to correctly represent the torsional behavior of the primary alcohols,31 a hydroxyl rotation barrier which apparently allows these groups to rotate too facilely, and a poor representation of the bond lengths and angles at the anomeric center. In addition, for disaccharides, there is no attempt to include the so-called exo-anomeric rotational energy term. An extensive reparameterization of the energy function for pyranoid carbohydrates is underway in this laboratory to correct these and other problems while improving the vibrational behavior of the molecules. In particular, experimental and ab initio data have been used to revise the terms contributing to the troublesome primary alcohol conformation. However, the question of how to treat the ion-sugar interactions is more difficult than the development of a general parameter set. The direct interaction of a highly charged ion with the sugar hydroxyl groups must surely result in a significant polarization of the hydroxyl chemical bonds involved, and a substantial redistribution of electronic density in the molecule, potentially affecting the relative intramolecular energies of stereoisomers and the strength of their binding to the ion/protein binding site. Ab initio calculations of the interactions of such ions with model compounds are being undertaken, but the possibility that such interactions might be strongly dependent upon geometry and sugar configuration may complicate the refinement of potential parameters. References and Notes (1) Sharon, N. Lectins; Chapman and Hall: London, 1989. (2) Lis, H.; Sharon, N. Curr. Opinion Struct. Biol. 1991, 1, 741. (3) Drickamer, K. J. Biol. Chem. 1988, 263, 9557. (4) Lasky, L. A. Science 1992, 258, 964. (5) Ikeda, K.; Sannoh, T.; Kawasaki, N.; Kawasaki, T.; Yamashina, I. J. Biol. Chem. 1987, 262, 7451. (6) Ezekowitz, R. A. B.; Day, L. E.; Herman, G. A. J. Exp. Med. 1988, 167, 1034. (7) Sheriff, S.; Chang, C. Y. Y.; Ezekowitz, R. A. B. Nature Struct. Biol. 1994, 1, 789. (8) Graves, B. J.; Crowther, R. L.; Chandran, C.; Rumberger, J. M.; Li, S.; Huang, K.-S.; Presky, D. H.; Familletti, P. C.; Wolitzky, B. A.; Burns, D. K. Nature 1994, 367, 532. (9) Weis, W. I.; Kahn, R.; Fourme, R.; Drickamer, K.; Hendrickson, W. A. Science 1991, 254, 1608.
2534 J. Phys. Chem., Vol. 100, No. 7, 1996 (10) Weis, W. I.; Drickamer, K.; Hendrickson, W. A. Nature 1992, 360, 127. (11) Drickamer, K. Nature 1992, 360, 183. (12) Ha, S.; Gao, J.; Tidor, B.; Brady, J. W.; Karplus, M. J. Am. Chem. Soc. 1991, 113, 1553. (13) Schmidt, R. K.; Karplus, M.; Brady, J. W. J. Am. Chem. Soc., in press. (14) Rao, B. G.; Tilton, R. F.; Singh, U. C. J. Am. Chem. Soc. 1992, 114, 4447. (15) Daggett, V.; Brown, F.; Kollman, P. J. Am. Chem. Soc. 1989, 111, 8247. (16) Zacharias, M.; Straatsma, T. P.; McCammon, J. A. Biochemistry 1993, 32, 7428. (17) Harte, Jr., W. E.; Bajorath, J. J. Am. Chem. Soc. 1994, 116, 10394. (18) Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M. J. Comput. Chem. 1993, 4, 187. (19) Brooks, C. L.; Karplus, M.; Pettitt, B. M. Proteins: A Theoretical PerspectiVe of Dynamics, Structure, and Thermodynamics; AdV. Chem. Phys. Wiley-Interscience: New York, 1988; Vol. LXXI. (20) MacKerell, A. D.; Karplus, M.; et al., manuscript in preparation. (21) Ha, S. N., Giammona, A., Field, M., Brady, J. W. Carbohydr. Res. 1988, 180, 207.
Liang et al. (22) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926. (23) Verlet, L. Phys. ReV. 1967, 159, 98. (24) van Gunsteren, W. F.; Berendsen, H. J. C. Mol. Phys. 1977, 34, 1311. (25) Brunger, A. T.; Brooks, C. L.; Karplus, M. Proc. Natl. Acad. Sci. U.S.A. 1985, 82, 8458. (26) Tasaki, K.; McDonald, S.; Brady, J. W. J. Comput. Chem. 1993, 14, 278. (27) Fleishman, S. H.; Brooks, C. L. J. Chem. Phys. 1987, 87, 3029. (28) Ohrui, H.; Nishida, Y.; Higuchi, H.; Hori, T.; Meguro, H. Can. J. Chem. 1987, 64, 1145; Nishida, Y.; Hori, H.; Ohrui, H.; Meguro, H. J. Carbohydr. Chem. 1988, 7, 239. (29) Kogan, T. P.; Revelle, B. M.; Tapp, S.; Scott, D.; Beck, P. J. J. Biol. Chem. 1995, 270, 14047. (30) Shallenberger, R. S. AdVanced Sugar Chemistry; AVI Publishing Co.: Westport, CT, 1982. (31) Brady, J. W. J. Am. Chem. Soc. 1989, 111, 5155. (32) Kraulis, P. J. J. Appl. Crystallogr. 1991, 24, 946.
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