Biochemistry. In 1913, biochemists Leonor Michaelis and Maude Menten proposed the rational...

Biochemistry. In 1913, biochemists Leonor Michaelis and Maude Menten proposed the rational function model (see figure)

for the velocity of the enzymatic reaction v, where s is the substrate concentration. The constants Vmax and KM are determined from experimental data.

(A) Show that .

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(B) Show that .

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(C) Table 1* lists data for the substrate saccharose treated with an enzyme.

Plot the points in Table 1 on graph paper and estimate Vmax to the nearest integer. To estimate KM, add the horizontal line to your graph, connect successive points on the graph with straight-line segments, and estimate the value of s (to the nearest multiple of 10) that satisfies .

Table 1

s	v
5.2	0.866
10.4	1.466
20.8	2.114
41.6	2.666
83.3	3.236
167	3.636
333	3.636

*Michaelis and Menten (1913) Biochem. Z. 49, 333–369.

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(D) Use the constants Vmax and KM from part (C) to form a Michaelis–Menten function for the data in Table 1.

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(E) Use the function from part (D) to estimate the velocity of the enzyme reaction when the saccharose is 15 and to estimate the saccharose when the velocity is 3.