We have examined two physiological extremes with respect to concentration – how

Question

We have examined two physiological extremes with respect to concentration – how low levels of hormones amplify their signal, and the incredible compaction of DNA to fit 2 m of DNA into the nucleus of a single cell. In order to better appreciate and contrast these extremes answer the following questions:

A. Epinephrine, C9H13NO3, has a concentration of 10-10 M in circulating blood. Calculate the diameter of a round swimming pool with a water depth of 2.0 M that would be needed to dissolve 1.0 g (about a teaspoon) of epinephrine to a concentration equal to that in the blood?

B. Assuming the human genome has equal concentrations of each of the four nucleotides, what is the approximate mass of nucleotides that one would have to add to this pool to provide a concentration in the pool equivalent to the concentration of nucleotides in chromosomal DNA in the human nucleus of a typical cell?

Explanation / Answer

Que-1:

Under normal conditions, the human adrenal medulla secretes epinephrine (C9H13NO3) at a rate sufficient to maintain a concentration of 10-10 M in circulating blood. To appreciate what that concentration means, calculate the diameter of a round swimming pool, with a water depth of 2.0m that would be needed to dissolve 1.0 g (about 1 teaspoon) of epinephrine to a concentration equal to that in blood.

Epinephrine concentration given in blood -----> 10^- 10 M --> 10 ^ - 10 mol/L

Given molecular weight of epinephrine -------> 183.21 g/mol

Therefore, total mass of epinephrine (in grams) required for 10 ^ - 10 mol/L * 183.21 g/mol ---> 1.8 x 10^- 8 g/L

When considering “v” is the volume (Liter) required to dissolve 1.8 x 10^- 8 g/L = 1g/v

V = [1gram/1.8 x 10^- 8 g/L] ---> 5.5 x 10 ^7L ----> 5.5 x 10^10cm3   

When consider “r” ---> radius of the swimming pool whereas “h” ---> height of the water

V ---> volume of water is then v = r^2h (volume of a cylinder)

r^2----> (5.5 x 10^10) / 3.14(200 cm) ---> 8.8 x 10^7cm2

r = sqrt of 8.8 x 10^7cm2   ----> 9,400 cm or 94 m

Now, the diameter of swimming pool ---> 2r ---> 190m

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