**4.1.1 Structures of HBP and MUP**

26 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

QM methods are also used in molecular docking. The application of QM methods to molecular docking was pioneered by Raha and Merz (2004), who developed a semiempirical QM-based scoring function and studied ion-mediated ligand binding processes. Their conclusion was that quantum chemical description is required for metal-containing systems, mainly because of poorly-defined atom types of metal atoms in most of the force field parameters, which cannot describe the interactions between a small molecule ligand

Applicability of QM methods to study ligand-protein system has been discussed in literature (Raha *et al.*, 2007, Stewart, 2007). As well as these successes, many examples of the failure of QM approaches have been demonstrated. However, it should be kept in mind that most of these studies were based on either DFT, or semi-empirical Hamiltonians, which do not describe van der Waals interactions and hydrogen bonding terms of ligand-protein interactions correctly. This is, indeed, a serious limitation of "fast", hence more popular QM methods. A straightforward way to solve this problem is to add additional correction terms to the QM energy. It has been demonstrated that the addition of the dispersion energy and corrections for hydrogen bonds improved the performance of semi-empirical QM methods dramatically (Rezac *et al.,* 2009). The recently developed PM6-DH2 method (Fanfrlik *et al.,* 2010) yields, to date, the most accurate results for non-covalent interactions among the semiempirical QM methods. For small non-covalent complexes, the results obtained were comparable to the high-level wave-function theory-based calculations within chemical

Another major bottleneck of QM methods applied to studying ligand-protein interactions thermodynamics is the size of the system. DFT can handle up to 150 atoms, highly-accurate methods such as coupled-clusters can handle a few tens of atoms and require very fast computers and long computing times. This limitation of the size of the systems that can be studied seriously compromises its usage in the study of ligand-protein thermodynamics. For instance, the usage of the linear scaling algorithm MOZYME (Stewart, 2009) based on the localised orbitals allows size increases to systems as large as 18 000 atoms and above, which allows calculation of very large ligand-protein complexes. Due to these developments QM methods have become, therefore, very useful for fast and highly accurate predictions of

An alternative approach is to use so-called divide-and-conquer (DIVCON) algorithm (Dixon and Merz, 1996, 1997). The principle is to divide a large system into many smaller subsystems, separately determine the electron density of each of these subsystems, and then to add the corresponding contributions from each subsystem in order to obtain the total

In the previous sections of this chapter, I briefly introduced the forces governing macromolecular associations and characterised methods commonly used to assess these contributions. Here, I will illustrate on several examples of 'real' ligand-protein systems and

Both histamine-binding protein (HBP) and mouse major urinary protein (MUP) are members of lipocalin family of proteins, so their overall structures are similar (Figure 4). The

and a metal ion in the active site of the protein.

accuracy (1 kcal/mol) (Rezac *et al.*, 2009).

ligand-protein interactions energetics.

the way how their binding thermodynamics is studied.

**4.1 Hydrophobic versus hydrophilic binding pocket: MUP and HBP** 

electron density and the energy.

**4. Examples** 

The structure of MUP was solved both by x-ray crystallography and solution NMR (Barratt *et al.*, 2005, Kuser *et al.*, 2001, Timm *et al.*, 2001). Several ligand-MUP complexes were studied, including long-chain alcohols, pyrazine derivatives, and pheromones as ligands. Regardless of the chemical nature of ligand, the protein structures are very similar to each other: the desolvated ligand, which occupies the central, hydrophobic binding pocket, causes very few conformational changes (Figure 4, left panel).

The crystal structure of HBP complexed with histamine revealed two binding sites for the ligand: one of them possessing considerably higher affinity than the other (Figure 4, right panel) (Syme *et al*., 2010). Therefore, in order to simplify the thermodynamic analysis of ligand binding, a mutant of HBP was designed. In this mutant, denoted as HBP-D24R, negatively charged aspartic acid D24 inside the "low" affinity site was replaced by larger and positively charged arginine. This abolished binding of ligand to the "low" affinity site.

Fig. 4. Crystal structures of MUP (left panel) and HBP (right panel). Both MUP and HBP are displayed with their ligands bound: octanediol (purple), and histamine (pink). Ligands are represented as VDW spheres. For MUP, superimposed structures of apo (blue) and holo (dark cyan) protein are showed, in order to display a lack of major conformational changes associated with ligand binding. For HBP, the second (low affinity) binding site is showed and coloured yellow.
