**4.2.2 Molecular dynamics (MD) study**

To confirm and further explore NMR relaxation result, we performed MD simulations of ABP in complex with galactose and its unbound state. In order to make a direct comparison between the observed order parameters and the simulations, backbone amide order parameters were calculated from the MD trajectory (MacRaild et al., 2007). A very good agreement between measured and calculated order parameters was observed, albeit with a small tendency for the simulation to underestimate the experimental values. The calculated changes in order parameter upon ligand binding reproduced the changes measured by NMR excellently, showing an approximately uniform decrease in order parameter (and, hence, increase of dynamics) upon galactose binding across the protein.

To understand the thermodynamic implications of the observed changes in dynamics, we employed the relationship between Lipari–Szabo order parameters <sup>2</sup> ( ) *S* and conformational entropy derived by Yang and Kay (1996).

In addition to generalised order parameters, we observed significant increase in backbone dynamics in the complex as compared with the apo protein by several other measures. RMS deviations from the average structure were significantly larger for the galactose-ABP complex than for apo-ABP. Fluctuations of backbone heavy-atom positions across the trajectory were generally larger in the complex than in the apo protein.

As well as validating the experimental results, the MD simulations revealed details of dynamic changes in regions that could not be measured experimentally. Importantly, the simulations revealed complex changes in the dynamics of the ABP binding site: counterintuitively, several residues in the binding site showed increase in flexibility upon binding, which was consistent with the trend seen throughout the rest of the protein. Other binding site residues displayed a decrease in flexibility, more in keeping with the intuitive expectation that ligand binding will reduce the conformational freedom of binding site residues (Figure 9).

The total entropy alters due to changes in the pico- to nanosecond motion upon galactose binding, estimated from MD simulations and NMR results, was 610(± 120) J/mol K, which gives *T S*188( 37) kJ/mol at 308 K. Clearly, this latter value is overestimated, as the

Full sets of 15N relaxation measurements were made for ABP in its apo form and in complex with D-galactose, L-arabinose and D-fucose. The analysis of these measurements, assessed by means of Lipari–Szabo model-free approach (1982), allowed for extraction of the information on the extent of 'fast' (ps-ns time scale) motion of the protein backbone and 15N-containing side chains. Differences in Lipari-Szabo generalised order parameters ( <sup>2</sup> *S* ) between apo- and holo-ABP and were interpreted in terms of changes in dynamics accompanying the binding event. Thus, observed dynamic changes could be related to binding thermodynamics by means of the relationship between changes in order parameters derived from NMR relaxation and changes in conformational entropy. Because <sup>2</sup> *S* parameters are specific to individual bond vectors, the described approach offered an unprecedented degree of structural resolution in thermodynamic analysis of protein

Surprisingly, generalised order parameters for apo ABP were, in general, larger than for the ABP–galactose complex. This suggests that 'fast' (pico- to nanosecond time scale) motions

To confirm and further explore NMR relaxation result, we performed MD simulations of ABP in complex with galactose and its unbound state. In order to make a direct comparison between the observed order parameters and the simulations, backbone amide order parameters were calculated from the MD trajectory (MacRaild et al., 2007). A very good agreement between measured and calculated order parameters was observed, albeit with a small tendency for the simulation to underestimate the experimental values. The calculated changes in order parameter upon ligand binding reproduced the changes measured by NMR excellently, showing an approximately uniform decrease in order parameter (and,

To understand the thermodynamic implications of the observed changes in dynamics, we employed the relationship between Lipari–Szabo order parameters <sup>2</sup> ( ) *S* and conformational

In addition to generalised order parameters, we observed significant increase in backbone dynamics in the complex as compared with the apo protein by several other measures. RMS deviations from the average structure were significantly larger for the galactose-ABP complex than for apo-ABP. Fluctuations of backbone heavy-atom positions across the

As well as validating the experimental results, the MD simulations revealed details of dynamic changes in regions that could not be measured experimentally. Importantly, the simulations revealed complex changes in the dynamics of the ABP binding site: counterintuitively, several residues in the binding site showed increase in flexibility upon binding, which was consistent with the trend seen throughout the rest of the protein. Other binding site residues displayed a decrease in flexibility, more in keeping with the intuitive expectation that ligand binding will reduce the conformational freedom of binding site

The total entropy alters due to changes in the pico- to nanosecond motion upon galactose binding, estimated from MD simulations and NMR results, was 610(± 120) J/mol K, which

188( 37) kJ/mol at 308 K. Clearly, this latter value is overestimated, as the

are more extensive in the ligand-protein complex than in the unbound protein.

hence, increase of dynamics) upon galactose binding across the protein.

trajectory were generally larger in the complex than in the apo protein.

function.

**4.2.2 Molecular dynamics (MD) study** 

entropy derived by Yang and Kay (1996).

residues (Figure 9).

gives *T S*

assumption of un-correlated motion is not likely to hold for all residues of the protein. It is evident, however, that the entropy change associated with changes in 'fast' dynamics contributes favourably to the free energy of binding. As the result, it allows the reduction of the unfavourable entropic contribution associated with ligand binding.

Fig. 9. Backbone amide order parameters for apo-ABP and galactose-ABP complex. <sup>2</sup> *S* order parameters were obtained by NMR relaxation measurements (red dots) and MD simulations (black lines). Data obtained for apo-ABP are showed in panel (a), while results for galactose-ABP complex are displayed in panel (b). Panel (c) shows changes in order parameters induced by galactose binding to ABP, with protein secondary structure elements displayed above. The N-domain of ABP is coloured is yellow, the C-domain is coloured blue, and the hinge region is coloured red. Residues interacting with the ligand are coloured cyan. This colouring scheme is consistent with colouring in Figure 10. (figure taken from MacRaild *et al.,* 2007)

### **4.2.3 Origins of entropic costs of binding**

We investigated the origin of the large and unfavourable entropic contribution to the binding free energy of galactose-ABP, observed by ITC (Daranas *et al.*, 2004), in terms of the different contributions.

It is clear that formation of a ligand-protein complex will involve the loss of entropy associated with constraining the translational and rotational degrees of freedom of one binding partner with respect to the other. The magnitude of these unfavourable contributions to the ligand-protein interaction can be approximated. In the case of galactose-ABP interactions, we took an estimate of the loss of ligand translational and rotational entropy from the work by Turnbull *et al* (2004) and Lundquist and his coworkers (Lundquist and Toone, 2002), which gave at approximately 25 kJ/mol for the free energy penalty.

It is assumed that the bound ligand will experience a loss of entropy reflecting the loss of conformational flexibility of the ligand in solution. On the assumption that conformational degrees of freedom are substantially restricted upon ligand-protein binding, the entropic

(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*.

Fig. 10. The binding of investigated benzenesulfonamides to BCAII. The protein backbone is

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

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

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

suggests less substantive interactions with the protein by these more distant residues.

Fig. 11. Observed chemical shift differences between free ligands and ligand-BCAII

1 to 6) in the side chain (Stoeckmann *et al.*, 2008).

complexes, for both series of ligands, plotted against the number of glycine residues (n from

from the indirect influence of ligand chain length on protein dynamics.

green, and n=6 – blue.

The ligands bound at the BCAII binding site are shown in Figure 10.

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 (Bronowska and Homans, unpublished data).

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

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 contributions: as measured by ITC the <sup>0</sup> *T S* amounts to –61 kJ/mol at 308 K (Daranas *et al.*, 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 measurements and MD simulations.
