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

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:

Now; if a message is passed through a ion, From studies; we know that these ions are infinitesimally smaller in size in the channels.

Also the information being carried through the 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 =

=

= 1570.8 micrometers

Now;the time taken can now be calculated as:

a gas, having a molecular weight of 13 kg/kmol and a kinematic viscosity of 0.25 cm2/s, flows through a pipe 0.25 m internal diameter and 5 km long at the rate of 0.4 m3/s and is delivered at atmospheric pressure.