Partitioning Of Ag

The driving forces for ligand-protein recognition are electrostatic interactions (ion-ion, ion-dipole, and dipole-dipole), lipophilicity/hydrophobicity, and shape complementarity. In order to understand the nature and the relative contributions of the different forces it is an useful approximation to partition AG into a sum of free energy contributions, as shown in Equation 1.5. Several different partitioning schemes have been proposed in the literature. The partition used here is essentially that suggested by Williams on the basis of studies by Page and Jencks (see Further Readings).

AG = AGtransl+rot + AGconf + AGpolar + AGhydrophob + AGvdW (1.5)

• AGtransl+rot accounts for the restrictions of translational movements (movements in x-, y-, and z-directions) and restrictions of rotations (about the x-, y-, and z-axes) of the "whole" molecule from the unbound to the bound state.

• AGconf is the difference in the conformational free energies between the unbound and bound states due to conformational restrictions in the ligand-protein complex.

• AGpolar is the free energy change due to interactions of polar functional groups in the binding cavity of the protein.

• AGhydrophob accounts for the binding free energy due to the hydrophobic effect.

• AGvdW gives the difference in free energy due to van der Waals (vdW) interactions in the bound and unbound states.

In the following sections, the different terms in Equation 1.5 and their magnitudes will be discussed in more detail and illustrated in terms of ligand-protein recognition.

1.3.1 Agtrans|+rot—The Freezing of the Overall Molecular Motion

Outside the binding cavity in the protein, the ligand tumbles freely in the aqueous solution through rotations and translations of the entire molecule. Since the freedom of translation and rotation in the binding cavity becomes severely restricted through formation of the ligand-protein complex, these motions to a large extent become frozen (i.e., three rotational and three translational degrees of freedom are lost). In terms of thermodynamics this leads to a decrease in entropy resulting in a more negative AS and consequently a more negative TAS. According to Equation 1.3 this gives a more positive AG. Thus, the loss of freedom of translation and rotation opposes binding and AGtransl+rot is a free energy cost, which must be overcome by the favorable binding forces to make the formation of a ligand-protein complex possible. The magnitude of this free energy cost has been much debated in the literature. Explicit calculations show that it varies only slightly with molecular weight, but an important problem for the estimation of AGtransl+rot is that it depends on the "tightness" of the ligand-protein complex. A tighter complex leads to a greater loss of freedom of movement and thus to a more negative TAS. Most estimates of AGtransl+rot range from 12 kJ/mol for a "loose" complex to 45 kJ/mol for a tightly bound complex. Whatever the exact magnitude of AGtransl+rot is in a particular case, it is a very significant energy to overcome by the favorable binding forces. Consider a ligand with an affinity (K) of 1 nM corresponding to AG of -53.4 kJ/mol at 310 K (Section 1.2). In order to end up with this free energy difference between the bound and unbound states, the favorable binding forces must produce not only 53.4 kJ/mol of ligand-protein binding energy but in addition 12-45 kJ/mol of free energy is required to make the association possible. It should be noted that this free energy cost of ligand-protein association is always present and cannot be reduced by ligand design. However, the exact value of AGtransl+rot is only important for predictions of "absolute" AG values. To a first approximation it cancels out when comparing the affinities of different ligands to the same receptor.

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