Question

Stability of compounds in new drugs. Testing the metabolic stability of compounds used in drugs is the cornerstone of new drug discovery. Two important values computed from the testing phase are the fraction of compound unbound to plasma (fup) and the fraction of compound unbound to microsomes (fumic). A key formula for assessing stability assumes that the fup/fumic ratio is 1. Pharmacologists at Pfizer Global Research and Development investigated this phenomenon and reported the results in ACS Medicinal Chemistry Letters (Vol. 1, 2010). The fup/fumic ratio was determined for each of 416 drugs in the Pfizer database. An SPSS graph describing the fup/fumic ratios is shown below.

a. What type of graph is displayed?

b. What is the quantitative variable summarized in the graph?

c. Determine the proportion of fup/fumic ratios that fall above 1.

d. Determine the proportion of fup/fumic ratios that fall below .4

Short answer

a.) A histogram is a graphical depiction of a frequency distribution with ongoing classes that have been categorized.

b.) 0.03365

c.) 0.836538

Step-by-step solution

(a) Histogram

Ahistogramis a graphical depiction of a frequency distribution with ongoing classes that have been categorized. It is an area chart with foundations as well as intervals among class borders, including areas proportionate to frequencies in the respective classes. Because the base spans the spaces among class borders, all rectangles in these depictions are contiguous. Rectangular heights are equal to the matching frequency of related categories, while heights of dissimilar classes are proportionate to similar frequencies density.

(b) Summarized quantitative variable

Fup/fumic ratio evaluates the metabolism stability of medicinal molecules and is the foundation of novel medication development. The percentage of compound unbound to plasma (fup) as well as the fraction of compound unbound to microsomes (fum) are two crucial variables obtained during the testing stage (fumic).

(c) The proportion of fup/fumic ratios that fall above 1.

Proportion ratios that fall above 1:

$$\begin{gathered} =\frac{9+4+1}{416} \\ =\frac{14}{416} \\ =0.03365 \end{gathered}$$

(d) The proportion of fup/fumic ratios that fall below .4

Proportion ratios that fall below .4

$$\begin{gathered} =\frac{182+107+59}{416} \\ =\frac{348}{416} \\ =\text{0.836538} \end{gathered}$$