Entropic freedom

An early treatment of the problem of calculating effective concentrations was to consider the concentration of an intramolecular group to be approximately the same as that of water in aqueous solution, since a molecule in solution is completely surrounded by water.22 This gives an upper limit of 55 M for effective concentration, equivalent to 34 J/deg/mol (8 cal/deg/mol) of entropy. That figure does represent the probability of two molecules being next to each other in solution. But, as soon as the two molecules are tightly linked, there is a large loss of entropy. A loose transition state may, perhaps, be interpreted as two molecules that are in close juxtaposition but that retain considerable entropic freedom. 

Although immobilization of proteins by amine coupling does not usually inhibit the entropic freedom of macromolecules or significantly change their interaction properties [54], it is nevertheless desirable to present a protein to its binding partner in a directed and uniform orientation. This may be achieved by chemically modifying a specific region of the protein in solution... 

The entropic hypothesis seems at first sight to gain strong support from experiments with model compounds of the type listed in Table 9.1. These compounds show a huge rate acceleration when the number of degrees of freedom (i.e., rotation around different bonds) is restricted. Such model compounds have been used repeatedly in attempts to estimate entropic effects in enzyme catalysis. Unfortunately, the information from the available model compounds is not directly transferable to the relevant enzymatic reaction since the observed changes in rate constant reflect interrelated factors (e.g., strain and entropy), which cannot be separated in a unique way by simple experiments. Apparently, model compounds do provide very useful means for verification and calibration of reaction-potential surfaces... 

Hence the reduction in entropy (A5 > that results from loss of rotational and translational freedom leads to a more positive (unfavorable) value of AG. The enthaplic and entropic components of AGto, and AG, st can be determined from the temperature dependence of kcM and of kcJKs, respectively, from the Arrhenius equation... 

As shown in Figure 6, the solvent molecules tend to be ordered around the molecules and when the protein and the ligand bind, several of these molecules are liberated and become disordered (entropic effect). Therefore, upon complex formation water molecules are released, receptor and ligand lose degrees of freedom and the interaction between the ligand and the receptor is calculated. 

Besides the energy factors, defined by the close-packing principle, entropic factors are also involved in determining the mode of packing of molecules. A molecule in a crystal tends to maintain part of its symmetry elements, provided that this does not cause a serious loss of density. In a more symmetric position a molecule has a greater freedom of vibration, that is, the structure corresponds to a wider energy minimum.126... 

Two phenomena have to be taken into account in order to make the pre-vioiiK Irciitmcnl of an isolated solute applionhie to the present situation. First, one must consider the strength of the interaction between E and B in the absence of any solvent effects. Second, an additional entropic term must be introduced because B, and consequently EB, are bonded so that the complex has restricted translational freedom at the surface. We will neglect, however, the latter effect because its contribution to the free energy of binding is expected to be small, i.e., not more than a few hundred calories per mole. Moreover, the entropic contributions for both species B and EB should be nearly identical and cancel when the individual terms are summed. 

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