**4.3 Enthalpy-entropy compensation revisited: bovine carbonic anhydrase II**

In studies on the thermodynamics of ligand-protein interactions, it is usually assumed that the bound ligand is fixed in the binding site. However, there is little direct experimental evidence for this assumption, and in the case of binding of p-substituted benzenesulfonamide inhibitors to bovine carbonic anhydrase II (BCA II), the observed thermodynamic binding signature assessed by ITC measurements leads indirectly to the conclusion that the bound ligands retain a considerable degree of flexibility (Krishnamurthy *et al.*, 2006).

BCAII and its binding to a large panel of ligands was reported in literature as a classic example of enthalpy-entropy compensation. Whitesides and his coworkers studied these interactions for a series of *p*-(glycine)*n*-substituted benzenesulfonamides (where n = 1-5) and found almost perfect enthalpy-entropy compensation across the series: as demonstrated by ITC measurements, the enthalpy of binding became less favorable and the entropy more favorable with increasing chain length. Changes in heat capacity were independent of chain length, which indicated that the observed changes in binding thermodynamic signatures across the series cannot be explained on the basis of the classical hydrophobic effect. In addition, strong evidence exists that these thermodynamic signatures are not driven by solvent effects (Syme *et al.*, 2010). To explain the observed data, a model was proposed, which assumed the increased mobility of ligand upon the chain length growth. Such increased flexibility of the bound ligand (favourable entropic contribution) would be compensated by a decreased number of direct ligand-protein contacts (unfavourable enthalpic contribution).

Such an increase in mobility of the ligand can be readily probed by 15N NMR relaxation measurements and computational studies. Thus, we investigated these using a combination of the solution NMR and MD simulations. Two series of ligands were studied: The first

penalty arising from loss in degrees of freedom of the galactose hydroxyl rotors alone is likely to be ~30 kJ/mol (Lundquist and Toone, 2002). Another contribution arises from the solvation effects. As calculated by means of QM/COSMO approach, desolvation energy of galactose is +87.6 kJ/mol (at 300 K), which is a significant unfavourable contribution

It is known that the ABP binding site contains a significant number of tightly bound water molecules, which maintain the structure of the binding site and play a role in governing the specificity of ligand binding (Quiocho, 1993). Examination of the structures of ABP in complex with its ligands (galactose, fucose, and arabinose) revealed some 15 crystallographically resolved and structurally conserved water molecules within the binding site (MacRaild *et al.*, 2007). Dunitz (1994) estimated the maximal entropic cost of confinement of a single water molecule to 8 kJ/mol. Even if the cost of confinement of the water molecules in the binding site of ABP is lower than this maximal value, the overall cost

All these amount to unfavourable entropic contribution of galactose-ABP binding. However, the entropy of galactose-ABP interactions is much lower than the sum of these

2004). Observed discrepancy can be explained in terms of favourable contribution of protein dynamics to the entropy of galactose-ABP interactions, which was observed by NMR

In studies on the thermodynamics of ligand-protein interactions, it is usually assumed that the bound ligand is fixed in the binding site. However, there is little direct experimental evidence for this assumption, and in the case of binding of p-substituted benzenesulfonamide inhibitors to bovine carbonic anhydrase II (BCA II), the observed thermodynamic binding signature assessed by ITC measurements leads indirectly to the conclusion that the bound ligands retain a considerable degree of flexibility (Krishnamurthy

BCAII and its binding to a large panel of ligands was reported in literature as a classic example of enthalpy-entropy compensation. Whitesides and his coworkers studied these interactions for a series of *p*-(glycine)*n*-substituted benzenesulfonamides (where n = 1-5) and found almost perfect enthalpy-entropy compensation across the series: as demonstrated by ITC measurements, the enthalpy of binding became less favorable and the entropy more favorable with increasing chain length. Changes in heat capacity were independent of chain length, which indicated that the observed changes in binding thermodynamic signatures across the series cannot be explained on the basis of the classical hydrophobic effect. In addition, strong evidence exists that these thermodynamic signatures are not driven by solvent effects (Syme *et al.*, 2010). To explain the observed data, a model was proposed, which assumed the increased mobility of ligand upon the chain length growth. Such increased flexibility of the bound ligand (favourable entropic contribution) would be compensated by a decreased number of direct ligand-protein contacts (unfavourable

Such an increase in mobility of the ligand can be readily probed by 15N NMR relaxation measurements and computational studies. Thus, we investigated these using a combination of the solution NMR and MD simulations. Two series of ligands were studied: The first

amounts to –61 kJ/mol at 308 K (Daranas *et al.*,

**4.3 Enthalpy-entropy compensation revisited: bovine carbonic anhydrase II** 

(Bronowska and Homans, unpublished data).

contributions: as measured by ITC the <sup>0</sup> *T S*

measurements and MD simulations.

*et al.*, 2006).

enthalpic contribution).

of confining these water molecules in the binding site will be vast.

(series 1) consisted of six ligands with different chain lengths (*n =* 1-6), isotopically 15N labeled at the terminal amide, whereas the second (series 2) comprised six ligands with the same chain length (*n =* 6), but isotopically 15N -labeled at a single amide at each position *n*. The ligands bound at the BCAII binding site are shown in Figure 10.

Fig. 10. The binding of investigated benzenesulfonamides to BCAII. The protein backbone is coloured cyan, with three histidines (yellow) coordinating zinc atom (dark blue dot) displayed. The ligand is showed, with glycine side chains represented as VDW spheres and coloured as follows: n=1 – purple, n=2 – red, n=3 – orange, n=4 – bright yellow, n=5 – dark green, and n=6 – blue.

Contrary to expectation, we found that the observed thermodynamic binding signature could not be explained by residual ligand dynamics in the bound state, but rather results from the indirect influence of ligand chain length on protein dynamics.

Chemical shift changes on ligand binding were monitored by simple one-dimensional 1H, 15N HSQC spectra. It was possible, since each ligand was selectively 15N -labeled. The results (Figure 11) indicated that residues proximal to the aromatic moiety of ligand show substantial changes in chemical shift, whereas residues more distant to the aromatic moiety show much smaller changes. The former is indicative of interactions with the protein, while the latter suggests less substantive interactions with the protein by these more distant residues.

Fig. 11. Observed chemical shift differences between free ligands and ligand-BCAII complexes, for both series of ligands, plotted against the number of glycine residues (n from 1 to 6) in the side chain (Stoeckmann *et al.*, 2008).

Comparing these results with ITC data by Krishnamurthy *et al*. (2006), it is clear that a poor correlation exists between the change in ligand conformational entropy determined from NMR relaxation studies and the entropies of binding derived from ITC (Figure 14, middle panel). It indicates that a model based on increased dynamics of the ligand in the bound state is not a plausible explanation for the observed thermodynamic binding data. This is not entirely unexpected since the ITC values are global parameters, which include contributions not only from the ligand, but from protein and solvent as well. However, the role of solvation is unlikely to be the driving one in the case of ligand-BCAII binding – for

Gly chain length (Stoeckmann *et al*., 2008). Second, these values are fairly small: around 80 J/mol/K. Finally, ligands are not fully desolvated upon the binding event: more distal residues extend beyond the binding pocket and they interact with water molecules. The observed increase in entropy with respect to the ligand chain length is approximately linear,

It was hoped that assessment of the protein contribution would shed light on the observed binding signature. To achieve this, MD simulations of both series of ligands in complexes with BCAII were performed (Stoeckmann *et al.*, 2008). In order to validate the methodology, generalised order parameters for ligand amide vectors were calculated from the trajectory and compared to NMR data. These MD trajectories were then used to probe the influence of ligand binding on protein dynamics. Specifically, <sup>2</sup> *S* values for backbone amide bond vectors, side chain terminal heavy-atom bond vectors, and corresponding conformational

The results obtained showed that the aromatic moiety became correspondingly more rigid with respect to series 1 ligand chain length. This was consistent with the NMR data showing that addition of successive glycine residues decreased the dynamics of the preceding units. Moreover, we observed the trend of increased dynamics of protein residue side chains with respect to ligand chain length (Table 2). This counter-intuitive observation that ligand binding increases protein dynamics has been observed in a number of ligand-protein

Residues Gly2-Gly1 Gly3-Gly2 Gly4-Gly3 Gly5-Gly4 Gly6-Gly5 Biding site 4.37 ± 1.1 5.28 ± 1.2 4.33 ± 1.0 3.11 ± 1.0 6.04 ± 1.3 Whole protein 14.9 ± 1.7 4.6 ± 1.8 5.5 ± 2.2 9.9 ± 2.4 8.4 ± 2.5

systems, including ABP, which was described in the previous section of this chapter.

Table 2. Differences in per-residue entropies quantified as TDS (in kJ/mol at temperature 300 K) for residues in the binding pocket of BCAII as well as for the whole BCAII protein. Displayed differences are result of changing side chain length of the ligand (Glyn – Glyn-1). Summarising, our results suggest that the enthalpy-entropy compensation observed for binding of ArGly*n*O- ligands to BCA II derives principally from an increase in protein dynamics, rather than ligand dynamics, with respect to the ligand chain length. Krishnamurthy and his coworkers showed that enthalpy-entropy compensation was observed for a range of BCAII ligands, whose structurally distinct chain types gave similar thermodynamic signatures (Krishnamurthy *et al.*, 2006). This suggests that a common process is underway that is unlikely to be related to specific interactions between the chain

*Cp* values for the interaction determined by ITC are independent of

three reasons. First,

which argues against a significant solvation contribution.

entropies were calculated for each complex with series 1 ligands.

In order to obtain a more detailed picture of ligand dynamics in the bound state, 15N NMR relaxation data (*R*1, *R*2, NOE) were measured for each series of ligands. The results obtained showed that the ligand chain became more dynamic as *n* increased. However, there were substantial differences between series 1 and 2 ligands: series 1 ligands were much more dynamic for small *n* values, while in case of series 2 ligands, the three residues nearest the aromatic ring adopted slow dynamic motions, whereas the three residues distal to the aromatic ring adopted faster dynamics similar to series 1 ligands.

The relaxation data were analysed using the Lipari-Szabo model-free approach (1982) and the 'fast' dynamics was quantified by means of generalised order parameters. The entropic contributions arising from these 'fast' motions were assessed from <sup>2</sup> *S* parameters using the relation derived by Yang and Kay (1996).

The order parameters of all ligand Gly residues in both series were much smaller than those of backbone residues within protein, indicating a comparatively high mobility of the ligand chain. The first two residues of the ligand were relatively immobile adjacent to the aromatic ring and are engaged in direct interactions with the protein, whereas the last four Gly residues were significantly more mobile, with <sup>2</sup> *S* values indicating motions being unrestricted by BCAII protein. From <sup>2</sup> *S* values, the entropic contribution to ligand-BCAII binding arising from each Gly residue, could be obtained. These data are shown in Figure 12.

Fig. 12. Top panel: order parameters for backbone amide (N-H) bond vectors for ligand series 1 (white) and 2 (black), obtained from NMR relaxation measurements. Middle panel: Derived entropy differences for series 1 ligands (white) compared to entropies of binding obtained from ITC measurements (black) (Krishnamurthy *et al.*, 2006). Bottom panel: Entropy differences for series 2 ligands (per N-H bond vector), obtained by NMR.

In order to obtain a more detailed picture of ligand dynamics in the bound state, 15N NMR relaxation data (*R*1, *R*2, NOE) were measured for each series of ligands. The results obtained showed that the ligand chain became more dynamic as *n* increased. However, there were substantial differences between series 1 and 2 ligands: series 1 ligands were much more dynamic for small *n* values, while in case of series 2 ligands, the three residues nearest the aromatic ring adopted slow dynamic motions, whereas the three residues distal to the

The relaxation data were analysed using the Lipari-Szabo model-free approach (1982) and the 'fast' dynamics was quantified by means of generalised order parameters. The entropic contributions arising from these 'fast' motions were assessed from <sup>2</sup> *S* parameters using the

The order parameters of all ligand Gly residues in both series were much smaller than those of backbone residues within protein, indicating a comparatively high mobility of the ligand chain. The first two residues of the ligand were relatively immobile adjacent to the aromatic ring and are engaged in direct interactions with the protein, whereas the last four Gly residues were significantly more mobile, with <sup>2</sup> *S* values indicating motions being unrestricted by BCAII protein. From <sup>2</sup> *S* values, the entropic contribution to ligand-BCAII binding arising

aromatic ring adopted faster dynamics similar to series 1 ligands.

from each Gly residue, could be obtained. These data are shown in Figure 12.

Fig. 12. Top panel: order parameters for backbone amide (N-H) bond vectors for ligand series 1 (white) and 2 (black), obtained from NMR relaxation measurements. Middle panel: Derived entropy differences for series 1 ligands (white) compared to entropies of binding obtained from ITC measurements (black) (Krishnamurthy *et al.*, 2006). Bottom panel: Entropy differences for series 2 ligands (per N-H bond vector), obtained by NMR.

relation derived by Yang and Kay (1996).

Comparing these results with ITC data by Krishnamurthy *et al*. (2006), it is clear that a poor correlation exists between the change in ligand conformational entropy determined from NMR relaxation studies and the entropies of binding derived from ITC (Figure 14, middle panel). It indicates that a model based on increased dynamics of the ligand in the bound state is not a plausible explanation for the observed thermodynamic binding data. This is not entirely unexpected since the ITC values are global parameters, which include contributions not only from the ligand, but from protein and solvent as well. However, the role of solvation is unlikely to be the driving one in the case of ligand-BCAII binding – for three reasons. First, *Cp* values for the interaction determined by ITC are independent of Gly chain length (Stoeckmann *et al*., 2008). Second, these values are fairly small: around 80 J/mol/K. Finally, ligands are not fully desolvated upon the binding event: more distal residues extend beyond the binding pocket and they interact with water molecules. The observed increase in entropy with respect to the ligand chain length is approximately linear, which argues against a significant solvation contribution.

It was hoped that assessment of the protein contribution would shed light on the observed binding signature. To achieve this, MD simulations of both series of ligands in complexes with BCAII were performed (Stoeckmann *et al.*, 2008). In order to validate the methodology, generalised order parameters for ligand amide vectors were calculated from the trajectory and compared to NMR data. These MD trajectories were then used to probe the influence of ligand binding on protein dynamics. Specifically, <sup>2</sup> *S* values for backbone amide bond vectors, side chain terminal heavy-atom bond vectors, and corresponding conformational entropies were calculated for each complex with series 1 ligands.

The results obtained showed that the aromatic moiety became correspondingly more rigid with respect to series 1 ligand chain length. This was consistent with the NMR data showing that addition of successive glycine residues decreased the dynamics of the preceding units. Moreover, we observed the trend of increased dynamics of protein residue side chains with respect to ligand chain length (Table 2). This counter-intuitive observation that ligand binding increases protein dynamics has been observed in a number of ligand-protein systems, including ABP, which was described in the previous section of this chapter.


Table 2. Differences in per-residue entropies quantified as TDS (in kJ/mol at temperature 300 K) for residues in the binding pocket of BCAII as well as for the whole BCAII protein. Displayed differences are result of changing side chain length of the ligand (Glyn – Glyn-1).

Summarising, our results suggest that the enthalpy-entropy compensation observed for binding of ArGly*n*O- ligands to BCA II derives principally from an increase in protein dynamics, rather than ligand dynamics, with respect to the ligand chain length. Krishnamurthy and his coworkers showed that enthalpy-entropy compensation was observed for a range of BCAII ligands, whose structurally distinct chain types gave similar thermodynamic signatures (Krishnamurthy *et al.*, 2006). This suggests that a common process is underway that is unlikely to be related to specific interactions between the chain

should be emphasised that the overall shape of the free energy landscape controls the binding free energy. This shape is affected by the depth and width of the local minima, and the height and breadth of the energy barriers. The factors that shape that landscape include intrinsic entropic contributions of both interacting partners, ligand poses, protein conformations, solvent effects, and protonation states. Computational and experimental approaches combined together can provide insight into this crucial but otherwise hidden landscape, which is pivotal not only to understand the origin of each contribution and its

I would like to thank my collaborators and coauthors of my publications: Steve Homans, Chris MacRaild, Arnout Kalverda, Liz Barratt, Bruce Turnbull, Antonio Hernandez Daranas, Neil Syme, Caitriona Dennis, Dave Evans, Natalia Shimokhina, Pavel Hobza, Jindra Fanfrlik, Honza Rezac, Honza Konvalinka, Jiri Vondrasek, Jiri Cerny, Henning Stoeckmann, Stuart Warriner, Rebecca Wade, and Frauke Gräter. I also would like to thank for the financial support: BBSRC (United Kingdom), DAAD (Germany), DFG (Germany), Heidelberg Institute for Theoretical Sciences, and University of Heidelberg, Germany.

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role in the binding event, but which can allow a truly rational molecular design.

**6. Acknowledgements** 

**7. References** 

11827-34.

pp. 994-1003.

4309–4312.

and the protein. In our study, we demonstrated an increase in protein dynamics upon binding longer-chained ligands. This observation provides an explanation for the enthalpyentropy compensation across these structurally distinct ligands.
