Question

The Xenopus laevis oocyte is roughly 1mm in diameter. After fertilization, it undergoes mitosis, a process requiring the coordination of proteins at various locations within the large cell.
a) If this event were coordinated by diffusion alone, estimate how long it would take for a message to reach from one side of the cell to the other if it was passed through a Ca2+ ion?
b) How long would it take for a message to be transmitted through the diffusion of a small protein?
c) How long would it take if the message to reach the other side of the cell if it were carried on a transmembrane protein with diffusion coefficient of 0.2

Answer 1

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:

$time (t) = \frac{diffusion length^2}{diffusion co-efficient }$

Now; if a message is passed through a $Ca^{2+}$ ion, From studies; we know that these $Ca^{2+}$ ions are infinitesimally smaller in size in the $Ca^{2+}$ channels.

Also the information being carried through the $Ca^{2+}$ 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 = $\pi*r$

= $\pi * \frac{1000}{2}$

= 1570.8 micrometers

Now;the time taken can now be calculated as:

$time (t) = \frac{diffusion length^2}{diffusion co-efficient }$

$time (t) = \frac{(1570.8)^2}{0.2 }$

$time (t) =1.234*10^7 seconds$