Translational and rotational entropy

Murray, C.W. and Verdonk, M.L The consequences of translational and rotational entropy lost by small molecules on binding to proteins. 

Andrews et al. (1984) have adopted a semi-empirical approach to the calculation of binding energy. They fix the loss of translational and rotational entropy in any drug-receptor association to be 14 kcal/mol (the Williams ACj+r term) and partition binding energy AG (defined as a -t-ve quantity) according to equation (11) ... 

The entropy of a molecule is composed of the sum of its translational, rotational, and internal entropies. The translational and rotational entropies may be precisely calculated for the molecule in the gas phase from its mass and geometry. The entropy of the vibrations may be calculated from their frequencies, and the entropy of the internal rotations from the energy barriers to rotation. 

The formation of the transition state AB leads to the loss of translational and rotational entropy as described above, although there are some compensating gains in internal rotation and vibration. The intramolecular cyclization in equation 2.23 involves the loss of only some entropy of internal rotation. 

A related phenomenon is that the binding of a dimer X—Y to an enzyme may be far greater than expected from the binding of X and Y separately, because the dimer loses only one set of translational and rotational entropies overall. 

Indeed, this is a case of complex additivity of binding energies, a phenomenon commonly seen in biological systems [35, 36]. Jencks has attributed the complex additivity in many systems to changes in translational and rotational entropy [36]. For example, the two complexing chromophores of the molecular tweezers are covalently connected. This means that the enthalpy of the second 7t-stacking interaction comes without paying the translational and rotation entropy price a second time. 

Table X1I.3. Translational and Rotational Entropies at 300 K AND 1 Atm of Some Transition Complexes...

For bimolecular reactions (i.e. where the reactant is two separate molecules) and contribute a constant —4 RT. The translational and rotational entropy changes are substantially negative, —30 to —50 e.u., due to the fact that there arc six translational and six rotational modes in the reactants but only three of each at the TS. The six remaining degrees of freedom are transformed into the reaction coordinate and five new vibrations at the TS. These additional vibrations usually make a few kcal/mol... 

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