Hairs

Suppose the length of the hair is affected by only the α-keratin synthesis, which is the major component. This synthesis takes place in the epithelial cells of the hair bulb. The structure of α-keratin is made up of α-helix for the 3.6 amino acid residues in one revolution. Each turn increases the α-helix of 5.7 Å. During the synthesis of the α-keratin per second, on average, 30 formed peptide bonds.

A)

What is the rate of hair growth in mm in one day?
The result round to three decimal places [mm/day]

B)

How many days will clone hair length 4.9 cm when the initial length was 3.5 mm?

Correct answer:

s =  0.41 mm/d
t =  110.9 d

Step-by-step explanation:

$$\begin{gathered} t_1=24\text{h}\to \text{s}=24\cdot 3600\text{s}=86400\text{s} \\ {v}_1=30/3.6\cdot 5.7\cdot 10^{-7}\doteq 4.75\cdot 10^{-6}\text{mm/s} \\ s=v_1\cdot t_1=4.75\cdot 10^{-6}\cdot 86400=0.41\text{mm/d} \end{gathered}$$

$$\begin{gathered} s_2=10\cdot 4.9-3.5=45.5\text{mm} \\ t=s_2/s=45.5/0.4104=110.9\text{d} \end{gathered}$$

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