Understanding Molecular Motion: Diffusion of Phospholipids in Bacteria

[SUchica10]

Within a monolayer phospholipid molecules exchange places with their neighbors every 10^-7 seconds. It takes about 1 second for a phospholipid to diffuse from one end of the bacterium to the other, a distance of about 2 micrometers.

A) Are these numbers in agreement? Assume that the diameter of a phospholipid head is 0.5 nm. Explain why or why not.

B) To gain an appreciation for the speed of molecular motions, assume that a lipid molecule is the size of a ping pong ball (4 cm diameter) and that the floor of your living room (6 m by 6 m) is covered wall to wall in a monolayer of balls. If two neighboring balls exchanged positions every 10^-7 seconds how fast would they be moving in km/h? How long would it take for a ball to move from one end of the room to another?

I am not sure where to begin with these and what type of equations to use. If anyone can at least help me begin thatd be greatly appreciated!

 

[berkeman]

Well at least part B is straightforward algebra. A ping-pong ball moves 4cm every 0.1us. What is that velocity in units of km/hr? At that speed, how long does it take for a ball to travel the 6m to go from wall-to-wall?

Then I guess you're supposed to use a similar analysis to check the numbers for the biological dimension case in part A. Does that help?

 

[m2003]

A) The numbers provided are in agreement. To determine this, we can use the equation v = d/t, where v is the velocity, d is the distance, and t is the time. In this case, the distance is 2 micrometers (2 x 10^-6 meters) and the time is 10^-7 seconds. Plugging these values into the equation, we get v = (2 x 10^-6 m) / (10^-7 s) = 20 m/s. This is equivalent to the speed of sound in air, which is a reasonable speed for molecular motion. Additionally, the diameter of a phospholipid head is 0.5 nm (5 x 10^-10 meters), which is much smaller than the distance of 2 micrometers. This means that the phospholipid molecules have enough room to move and exchange places with their neighbors within the given time frame.

B) To determine the speed of the lipid molecules in km/h, we first need to convert the distance of 6 m to km (1 km = 1000 m), which gives us 0.006 km. Then, using the same equation v = d/t, we can calculate the velocity of the molecules as v = (0.006 km) / (10^-7 s) = 6 x 10^4 km/h. This is an incredibly high speed, which is expected due to the large size of the ping pong ball compared to the distance being covered. To determine the time it would take for a ball to move from one end of the room to the other, we can rearrange the equation to t = d/v, where t is the time, d is the distance, and v is the velocity. Plugging in the values, we get t = (0.006 km) / (6 x 10^4 km/h) = 1 x 10^-7 hours. This is equivalent to 0.36 seconds, which is incredibly fast. This demonstrates the incredible speed at which molecular motion occurs in comparison to our everyday experiences.