Answer:
a) the diffusion length = 1000 micrometers;
so if the diffusion co-efficient is also known or given; we can therefore deduce the time taken( i.e how long it would take for a message to reach from one side of the cell to the other).
b) We need to be given the data value concerning the diffusion coefficient of the protein.
c) 1.234 × 10⁷ seconds
Explanation:
a)
In a controlled transportation that occurs in diffusion; the time taken can be expressed as:
[tex]time (t) = \frac{diffusion length^2}{diffusion co-efficient }[/tex]
Now; if a message is passed through a [tex]Ca^{2+}[/tex] ion, From studies; we know that these [tex]Ca^{2+}[/tex] ions are infinitesimally smaller in size in the [tex]Ca^{2+}[/tex] channels.
Also the information being carried through the [tex]Ca^{2+}[/tex] ions are bound to be transported diagonally across the cell.
However; the diffusion length = 1000 micrometers;
so if the diffusion co-efficient is also known or given; we can therefore deduce the time taken( i.e how long it would take for a message to reach from one side of the cell to the other).
b) Since; we don't know the information concerning the diffusion coefficient of the protein, then it is quite not possible to determine how long it would take for a message to be transmitted through the diffusion of a small protein.
c) Here; we are given the value of the diffusion coefficient to be = 0.2 micrometer²/seconds
In a transmembrane protein; the diffusion length is half the circumference of the cell which is = [tex]\pi*r[/tex]
= [tex]\pi * \frac{1000}{2}[/tex]
= 1570.8 micrometers
Now;the time taken can now be calculated as:
[tex]time (t) = \frac{diffusion length^2}{diffusion co-efficient }[/tex]
[tex]time (t) = \frac{(1570.8)^2}{0.2 }[/tex]
[tex]time (t) =1.234*10^7 seconds[/tex]
