Question

Approximation At some point, scientists are confronted with the recognition that some math problems do not have exact answers. This is very different than the math we learn in high school and college, which typically represents math as a construction that only has exact answers (2 + 2 = 4 and not any other number) What is the expected time of diffusion of biologically important molecules at different scales? There is no exact answer to a question like how long does it take for oxygen to diffuse across the respiratory membrane". Instead there are better answers and worse answers. The reason there isn't an exact answer is because 1. the question is about a system of particles that are in diffusion The motion of individual particles is random and the time an individual particle travels a certain net distance is a function of its individual history of elastic collisions with other particles. But we can compute expected (or the average) time for diffusion over a specified distance using a simple diffusion model (see below) 2. The rate of diffusion is a function of the medium such as pure water, air, cytosol, or lipid bilayer. The diffusion coefficient in the table below is measured using water as the medium but in the questions below the media might include cytosol, extracelular fluid, and phospholipid membrane, so the water-based coefficient will only give us a close (or approximate) answer 3. good enough value. The final reason is the one that makes students the most uncomfortable. There is no single, correct value for the distance for each of the questions below. Instead there are many values that are good enough for the purpose of this exercise. For example, if I ask a biologist what is the diameter of a bacterial cell?", I'll get the answer about 1 micron" True, different bactena differ in size - the smallest are about 02 um. For the purpose of understanding phenomenon that change radically over many orders of magnitude, as in this exercise (9 orders of magnitude or 1 billion times), any answer near 1 um (0.5 um 2 um) is good enough You use this sort of reasoning in #3 all the time. If someone asks me how long it takes to drive to work, I answer 20 minutes" Clearly it depends on the route that I take (and I take different routes depending on traffic), traffic levels, it get stuck waiting for a train, etc. But 20 minutes is good enough for whatever reason the person is asking. It doesn't matter if its 17 minutes or 23. the person has a pretty good sense of my commute time and the consequences of this: It's a short enough commute that I could go in and grab something if its important but not short enough that I would go in to grab something not too important. If I had a 5 minute walk to work. I'd go in and grab something not important If I had an hour commute, I'm not going to go in unless I plan to be there all day Thinking about diffusion quantitatively A simple formula to calculate the approximate time of diffusion (t) over a distance (x) is 2D where D is a diffusion coefficient. The symbol means "approximately equal to" Problems Use the diffusion time calculator to compute diffusion times for the following events. Each number has a question and a computation Write your answers to the questions in the answer window. Remember to include units with your distance and time and to think about units when you use the calculator 1. What is the width across a synaptic clef? Use this distance to compute the diffusion time for Na+ and Hemoglobin 2. What is the width across a plasma membrane? Use this distance to compute the diffusion time for 02 3. What is the width across of the respiratory membrane in the lung? Use this distance to compute the diffusion time for 02 4. What is the radius of a typical human cell? Use this distance to compute the diffusion time for 02 from the plasma membrane to a mitochondrion at the center of a cell 5. What is the radius of a beaker (similar to a jam jar)? Use this distance to compute the diffusion time for glucose from the center of the beaker to the edge 6. What is the distance from your hearto your quadriceps muscle. Use this distance to compute the diffusion time for O2 from your heart to skeletal muscle cells in your quadriceps 7. What is the distance across a typical classroom at USM. Use this distance to compute the diffusion time of glucose from the front to the back of the room

Answer 1

In this problem we will be using the given diffusion formula. Here we will find the width of the given thing and use it in the formula to find the diffusion time.

1] the width of synaptic cleft = 30nm , t =( 30 nm)^2 / 2D = 450/D nm^2

2] Width across plasma membrane = 10nm , t = (10nm)^2 /2D = 50/D nm^2

3] Width across the resperatory membrane in lungs = 0.5mm , t= (0.5mm)^2/2D = 0.125/D mm^2

4] The radius of a typical human cell = 10μm , t= (10μm)^2/2D = 50/D μm^2

5] the radius of beaker(100 mL ) is nearly taken as = 5 cm , t=(5cm)/2D = 12.5 /D cm^2