Interaction of Sweet-Tasting Molecules with Taste Receptors Many compounds taste sweet to humans. Sweet taste results when a molecule binds to the sweet receptor, one type of taste receptor, on the surface of certain tongue cells. The stronger the binding, the lower the concentration required to saturate the receptor and the sweeter a given concentration of that substance tastes. The standard free-energy change, $\Delta G^{\circ},$ of the binding reaction between a sweet molecule and a sweet receptor can be measured in kilojoules or kilocalories per mole.
Sweet taste can be quantificd in units of "molar relative sweetness" (MRS), a measure that compares the sweetness of a substance to the sweetness of sucrose. For example, saccharin has an MRS of $161 ;$ this means that saccharin is 161 times sweeter than sucrose. In practical terms, this is measured by asking human subjects to compare the sweetness of solutions containing different concentrations of each compound. Sucrose and saccharin taste equally sweet when sucrose is at a concentration 161 times higher than that of saccharin.
(a) What is the relationship between MRS and the $\Delta G^{\circ}$ of the binding reaction? Specifically, would a more negative $\Delta G^{\circ}$ correspond to a higher or lower MRS? Explain your reasoning.
Shown below are the structures of 10 compounds, all of which taste sweet to humans. The MRS and $\Delta G^{\circ}$ for binding to the sweet receptor are given for each substance.
Morini, Bassoli, and Temussi ( 2005 ) used computer-based methods (often referred to as "in silico" methods) to model the binding of sweet molecules to the sweet receptor.
(b) Why is it useful to have a computer model to predict the sweetness of molecules, instead of a human- or animal-based taste assay?
In earlier work, Schallenberger and Acree (1967) had suggested that all sweet molecules include an "AH-B" structural group, in which "A and B are clectroncgative atoms scparated by a distance of greater than $2.5 \AA[0.25 \mathrm{nm}]$ but less than $4 \AA[0.4 \mathrm{nm}] . \mathrm{H}$
is a hydrogen atom attached to one of the electronegative atoms by a covalent bond."
(c) Given that the length of a "typical" single bond is about 0.15 nm, identify the AH-B group(s) in each of the molecules shown above.
(d) Based on your findings from (c), give two objections to the statement that "molecules containing an AH-B structure will taste sweet."
(c) For two of the molecules shown here, the AH-B model can be used to explain the difference in MRS and $\Delta G^{\circ} .$ Which two molecules are these, and how would you use them
to support the AH-B model?
(f) Several of the molecules have closely related structures but very different MRS and $\Delta G^{\circ}$ values. Give two such examples, and use these to argue that the AH-B model is unable
to explain the observed differences in sweetness. In their computer-modeling study, Morini and coauthors used the three-dimensional structure of the sweet receptor and a molecular dynamics modeling program called GRAMM to predict the $\Delta G^{\circ}$ of binding of sweet molecules to the sweet receptor. First, they "trained" their model- -that is, they refined the parameters so that the $\Delta G^{\circ}$ values predicted by the model matched the known $\Delta G^{\circ}$ values for one set of sweet molecules (the "training set"). They then "tested" the model by asking it to predict the $\Delta G^{\circ}$ values for a new set of molecules (the "test set").
(g) Why did Morini and colleagues need to test their model against a different set of molecules from the set it was trained on?
(h) The researchers found that the predicted $\Delta G^{\circ}$ values for the test set differed from the actual values by, on average, $1.3 \mathrm{kcal} / \mathrm{mol}$. Using the values given with the molecular structures, estimate the resulting error in MRS values.
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