The binding of nonpolar groups of amino acid to hydrophobic sites in the interior of proteins is governed largely by hydrophobic interactions.

(a) Consider a family of hydrocarbons R-H. The hydrophobicity constants, \(\pi\), for \(\mathrm{R}=\mathrm{CH}_{3}\), \(\mathrm{CH}_{2} \mathrm{CH}_{3}\),\(\left(\mathrm{CH}_{2}\right)_{2} \mathrm{CH}_{3}\),\(\left(\mathrm{CH}_{2}\right)_{3} \mathrm{CH}_{3}\), and \(\left(\mathrm{CH}_{2}\right)_{4} \mathrm{CH}_{3}\) are, respectively, 0.5,1.0,1.5,2.0, and 2.5. Use these data to predict the \(\pi\) value for \(\left(\mathrm{CH}_{2}\right)_{6} \mathrm{CH}_{3}\).

(b) The equilibrium constants \(K_{I}\) for the dissociation of inhibitors (6) from the enzyme chymotrypsin were measured for different substituents R:

Plot \(\log K_{I}\) against \(\pi\). Does the plot suggest a linear relationship? If so, what are the slope and intercept to the \(\log K_{I}\) axis of the line that best fits the data?

(c) Predict the value of \(K_{\mathrm{I}}\) for the case R=H.

Text Transcription:

pi

R=CH_3

CH_2 CH_3

(CH_2)_2 CH_3

(CH_2)_3 CH_3

(CH_2)_4 CH_3

(CH_2)_6 CH_3

K_I

log K_I

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