**1. Introduction**

764 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

[53] M.M. Nassar, K.T. Ewida, E.E. Ebrahiem, Y.H. Magdy and M.H. Mheaedi, Adsorption

[54] Nacèra Yeddou, Aicha Bensmaili, Equilibrium and kinetic modeling of iron adsorption

[55] W. S. Wan Ngah, S. Ab Ghani and A. Kamari, Bioresource Technology Volume 96,

[56] Peniche-Covas, C., Alvarez, L.W., Arguelles-Monal, W., 1992. The adsorption of

[57] O. Sirichote, W. Innajitara, L. Chuenchom, D. Chunchit and K. Naweekan. Song

[58] Uchida, M., Shinohara, O., Ito, S., Kawasaki, N., Nakamura, T. and Tanada, S. 2000.

[59] C.Y. Abasi , A.A. Abia and J.C. Igwe, Environmental Research Journal, 5(3), 2011, Page

[60] Y. S. Ho, C. T. Huang, H. W. Huang, equlibrium sorption isotherm for metal ions on

[61] B. A. Shah, A. V. Shah, R. R> Singh, Sorption isotherms and kinatics of chrmoium

[62] a) M. Horsfall, A.I. Spiff, A.A. Abia, studies the influence of mercaptoacetic acid

kinetic and equilibrium studies. Environ. Pollution, 142 (2006) 264-273.

Reduction of iron(III) ion by activated carbon fiber. J. Colloid Interface Sci. 224: 347-

uptake from watewater using natural sorpbent materails. Intern. J. Environ. Sci.

(MAA) modification of cassava (Manihot esculenta cranz) waste biomass on the adsorption of Cu2+ and Cd2+ from aqueous solution. Bull Korean Chem. Soc. 25 (2004) 969-976. b) P. Loderio, J,L. Barriada, R. Herrero, M.E. Sastre-Vicente, The marine macroalge crstoserira baccata as biosorbent for Cd(II) and Pb(II) removal:

mercuric ions by chitosan. J. Appl. Polym. Sci. 46, 1147–1150.

klanakarin J. Sci. Technol., 2002, 24(2) : 235-242.

tree fern. Process biochem, 37 (2002) 1421-1430.

of iron and manganese ions using low-cost materials as adsorbents, Adsorp. Sci.

by eggshells in a batch system: effect of temperature, Desalination 206 (2007) 127–

[52] A. Edwin Vasu, E-Journal of Chemistry, 5:1, (2008) 1-9.

Technol., 22(1) (2004) 25–37.

Issue 4, March 2005, Pages 443-450.

134.

350.

No.: 104-113.

Technology. 6, (2009) 77-90.

A non-covalent interaction is a kind of chemical bond, typically between macromolecules, that involves dispersed variations of electromagnetic interactions (Alberts *et al.* 1994; Connors & Mecozzi 2010). Non-covalent interactions are individually weak as compared with covalent bonds, but their net strength is higher than the sum of that of the individual interactions. There are few drugs that bind irreversibly to their targets, in pharmacology, most drugs establish non-covalent interactions with their target molecules (usually proteins).

From a chemical point of view, the affinity constant (Ka) is a very useful measurement for the study of binding reactions as it provides much information about the mechanism. In many cases some chemical or physical properties of ligand or target change with the interaction between them, these changes might help to measure binding constants. It is important to establish the stoichiometry of the complex to be sure that the constants are accurately calculated. From the affinity constants measured it is possible to calculate the standard thermodynamic quantities for the binding reaction: free-energy (ΔG), enthalpy (ΔH) and entropy (ΔS).

Our group has already demonstrated that, in some cases, binding affinity measurements are very helpful for the optimization of ligand binding as it can be determined the contribution of every single chemical modification of the ligand to the binding affinity (Buey *et al.* 2004; Matesanz *et al.* 2008)

One of the objectives of drug development is the search of new or modified compounds with improved properties such as better potency, higher selectivity, better pharmacokinetics or superior drug resistance profiles. An important goal in this objective is the optimization of drugs binding affinity towards their targets, as binding affinity is directly related to potency (Ruben *et al.* 2006). Moreover, it has been shown that extremely high affinity drugs reflect as well changes in other properties like selectivity (Ohtaka *et al.* 2004; Ohtaka & Freire 2005) or resistance overcoming ability (Matesanz *et al.* 2008).

Examples of the importance of ligand affinity in drug optimization can be observed in the development of HIV-1 protease inhibitors and statins (cholesterol lowering drugs) over the years as remarked in (Freire 2008).

In this chapter we will study the nature of non-covalent interations and the concept of binding constant for these interactions. Examples of methodologies to measure binding constants of small ligands to macromolecules will be introduced and we will emphasize the

Thermodynamics as a Tool for the Optimization of Drug Binding 767

Van der Waals forces are short range attractive forces between chemical groups in contact. The forces are caused by slight charge displacements. The distribution of electronic charge around an atom changes with time. At any moment, the charge distribution is not perfectly symmetric. This transient asymmetry in the electronic charge around an atom induces a complementary asymmetry in the electron distribution around its neighboring atoms. These induced dipole effects give rise to the so called van der Waals interactions, also known as dispersion forces. The attraction between two atoms increases as they come closer to each other, until they are separated by the so called van der Waals contact distance. At a shorter distance, very strong repulsive forces become dominant because the outer electron clouds overlap. The van der Waals radius of an atom is defined where the net force between two atoms is zero. The van der Waals potential is then best described as a balance between

Van der Waals forces are non-directional. Energies associated with them are quite small; typical interactions contribute from 2 to 4 kJ/mol per atom pair. However, when the surfaces of two large molecules come together, a large number of atoms are in van der

A hydrogen bond is an interaction between a proton donor group (a hydrogen atom covalently bound to an electronegative atom -e.g. F, O, N, S-) and a proton acceptor atom (another electronegative atom). It is a very important interaction responsible for the structure and properties of water, as well as the structure and properties of biological macromolecules (e.g. hydrogen bonds are responsible of specific base-pair formation in the

Hydrogen bonds are fundamentally electrostatic interactions. The relatively electronegative atom to which the hydrogen atom is covalently bonded pulls electron density away from the hydrogen atom so that it develops a partial positive charge (δ+). Thus, it can interact with an

interaction is more than just an ionic or dipole-dipole interaction between the donor and the acceptor groups. Here, the distance between the hydrogen and acceptor atoms is less than

Hydrogen bonds are directional toward the electronegative atom. The strongest hydrogen bonds have a tendency to be approximately straight, such that the proton donor group, the hydrogen atom, and the acceptor atom lie along a straight line, with significant weakening of the interaction if they are not colinear. They are somewhat longer than are covalent bonds. Hydrogen bonds are constantly being made and remade. Their half-life is about 10 seconds. These bonds have only 5% or so of the strength of covalent bonds. They have energies of 5-15 kJ/mol compared with approximately 420 kJ/mol for a carbon-hydrogen covalent bond. However, when many hydrogen bonds can form between two molecules (or parts of the same molecule), the resulting union can be sufficiently strong as to be quite stable. Examples of multiple hydrogen bonds are widely found in biological systems, they hold secondary structures of polypeptides, help in binding of enzymes to their substrate or antibodies to their antigen, help also transcription factors bind to each other or to DNA.

Hydrophobic interactions result when non-polar molecules are in a polar solvent (e.g. water). The non-polar molecules group together to exclude water so that they minimize the

) through an electrostatic interaction. However, this

Waals contact, and the net effect, summed over many atom pairs, can be substantial.

**2.1.2 Van der Waals forces** 

attraction and repulsion.

**2.1.3 Hydrogen bonds** 

DNA double helix).

atom having a partial negative charge (δ-

**2.1.4 Hydrophobic interactions** 

the sum of their respective van der Waals radii.

need to determine the stoichiometry of the studied system to calculate accurately the constants. Once the thermodynamic concepts were introduced, we will show the use of these kind of studies for the optimization of drug binding to its target. We will detail the role of single chemical modifications in the molecule of study to modulate its binding affinity, and the way to quantify these changes. We will finally further discuss how the selection of the best sustituents can result in the optimization of binding.
