**4.1.5 Molecular dynamics (MD) simulations**

MD simulations were used to examine the solvation of the binding pocket of MUP and HBP. The MUP binding pocket was found virtually devoid of water, even without any ligand bound (Barratt *et al.*, 2006). Even if water molecules were artificially "forced in" at the beginning of the MD simulation, they did not remain inside the pocket. This observation contributed to the explanation of the unexpected thermodynamic signature of the ligand binding to MUP, measured by ITC.

An average of five to six water molecules is observed in the binding pocket of HBP over the simulation time in the absence of ligand. Analysis of the diffusion and rotational correlation functions of these solvent molecules suggested that their dynamic behaviour was very similar to those of bulk water (Syme *et al.*, 2010), which suggests that the return of these water molecules to bulk solution on ligand binding would not offer any significant contribution to the binding entropy.

For HBP, side chain entropies were computed from the MD simulation. Moreover, as a test of the robustness of these simulations, backbone amide entropy changes were calculated from the MD simulation and compared to NMR data. The comparison was very favourable (16.4 ± 1.0 kJ/mol versus 12.4 ± 9.8 kJ/mol), which raised confidence in the applied methodology. Contribution from the protein side chains was estimated at +17.4± 1.8 kJ/mol (Syme *et al.,* 2010). Taken together, these data strongly indicate an overall increase in entropy on ligand binding. This observation, although counter-intuitive, it is not without precedent in the literature (MacRaild *et al.*, 2007, Stoeckmann *et al.*, 2008).

MD simulations were also used to estimate the entropic contributions from the ligand. A contribution from the loss in vibrational degrees of freedom of histamine on binding to HBP was estimated using the Schlitter's method (Schlitter, 1993), leading to an unfavorable contribution of 22 2.4 kJ/mol.

In addition to this contribution, there was an assumption that internal degrees of freedom of the ligand are heavily constrained upon binding. The unfavorable contribution from the three relevant internal degrees of freedom of histamine amounted to -12 kJ/mol (Lundquist *et al.*, 2000). In addition, the entropic contribution from the loss of translational and rotational degrees of freedom of the ligand depends on the logarithm of the molecular mass, and on the basis of earlier work this represents an unfavorable contribution that can be estimated as -25 kJ/mol (Turnbull *et al.*, 2004).

### **4.1.6 Solvation thermodynamics estimation**

For MUP ligands, it was possible to measure their solvation free energies directly, using the water/vapor partitioning experiments (Shimokhina *et al.*, 2006). For histamine, experimental measurements could not be done due to non-volatility of histamine, and hence the ligand free solvation energies were calculated quantum-chemically, using the COSMO model (Klamt and Schüürmann, 1993). Prior to running calculations, the ligand was optimised using *ab initio* QM calculations (RFH/6-31G\* basis set). The optimised structure was

For both HBP and MUP, both positive and negative changes in local backbone entropy were observed. Entropy changes were not restricted to the binding pocket but were dispersed

was close to the error value, i.e., an overall change in backbone entropy that was not

MD simulations were used to examine the solvation of the binding pocket of MUP and HBP. The MUP binding pocket was found virtually devoid of water, even without any ligand bound (Barratt *et al.*, 2006). Even if water molecules were artificially "forced in" at the beginning of the MD simulation, they did not remain inside the pocket. This observation contributed to the explanation of the unexpected thermodynamic signature of the ligand

An average of five to six water molecules is observed in the binding pocket of HBP over the simulation time in the absence of ligand. Analysis of the diffusion and rotational correlation functions of these solvent molecules suggested that their dynamic behaviour was very similar to those of bulk water (Syme *et al.*, 2010), which suggests that the return of these water molecules to bulk solution on ligand binding would not offer any significant

For HBP, side chain entropies were computed from the MD simulation. Moreover, as a test of the robustness of these simulations, backbone amide entropy changes were calculated from the MD simulation and compared to NMR data. The comparison was very favourable (16.4 ± 1.0 kJ/mol versus 12.4 ± 9.8 kJ/mol), which raised confidence in the applied methodology. Contribution from the protein side chains was estimated at +17.4± 1.8 kJ/mol (Syme *et al.,* 2010). Taken together, these data strongly indicate an overall increase in entropy on ligand binding. This observation, although counter-intuitive, it is not without

MD simulations were also used to estimate the entropic contributions from the ligand. A contribution from the loss in vibrational degrees of freedom of histamine on binding to HBP was estimated using the Schlitter's method (Schlitter, 1993), leading to an unfavorable

In addition to this contribution, there was an assumption that internal degrees of freedom of the ligand are heavily constrained upon binding. The unfavorable contribution from the three relevant internal degrees of freedom of histamine amounted to -12 kJ/mol (Lundquist *et al.*, 2000). In addition, the entropic contribution from the loss of translational and rotational degrees of freedom of the ligand depends on the logarithm of the molecular mass, and on the basis of earlier work this represents an unfavorable contribution that can

For MUP ligands, it was possible to measure their solvation free energies directly, using the water/vapor partitioning experiments (Shimokhina *et al.*, 2006). For histamine, experimental measurements could not be done due to non-volatility of histamine, and hence the ligand free solvation energies were calculated quantum-chemically, using the COSMO model (Klamt and Schüürmann, 1993). Prior to running calculations, the ligand was optimised using *ab initio* QM calculations (RFH/6-31G\* basis set). The optimised structure was

precedent in the literature (MacRaild *et al.*, 2007, Stoeckmann *et al.*, 2008).

summed over backbone amides

over the protein (Figure 6). For HBP as well as MUP, *T S*

statistically different from zero (Syme *et al.*, 2010).

**4.1.5 Molecular dynamics (MD) simulations** 

binding to MUP, measured by ITC.

contribution to the binding entropy.

contribution of 22 2.4 kJ/mol.

be estimated as -25 kJ/mol (Turnbull *et al.*, 2004).

**4.1.6 Solvation thermodynamics estimation** 

subjected to COSMO calculations at three different temperature settings (270, 300, and 330 K) in order to extract the enthalpic and entropic contributions to the free energy of solvation, using the finite-difference approach. The approximation used therein was based on the assumption that the heat capacity is constant over a certain range of temperatures near the target temperature, *T*. In the case of solute molecules solvated in water, this approximation usually holds near room temperature for temperature ranges (denoted as *T*) as wide as 50 K. Using the finite-difference approximation, the entropy can be approximated at the target temperature as in equation (11):

$$\Delta \mathbf{S}(T) = -\left(\frac{\Delta \mathbf{G}(T + \Delta T) - \Delta \mathbf{G}(T - \Delta T)}{2\Delta T}\right) \tag{11}$$

where *S T*( ) denotes entropy at the target temperature, *G T*( ) is the free energy of solvation energy, and *T* is the temperature difference. For the calculations presented here *T* was 30 K.

Obviously, it was very difficult to assess the accuracy of such calculations, but the experimental solvation thermodynamics of two related "fragments" of histamine have been reported (Cabani *et al.*, 1981). Comparison (Table 1) shows that the solvation free energies are reproduced very well, and the solvation entropies and enthalpies reasonably well (for *n*propylamine) compared with experiment, which lends some confidence in the computed values for histamine.


Table 1. Solvation parameters: free energy, enthalpy, and entropy at temperature 300 K for histamine and related ligands. All values are given in kJ/mol. Experimental values (exp) are taken from Cabani *et al.* (1981).
