MathBench > Cellular Processes

Diffusion: Fick's 2nd Law

You need a lot of macrophages - or one smart one!


It would take about an hour and a half for the macrophage to meet with and devour the hapless virus. Except that the macrophage does not travel in a straight line. Instead it goes in a variety of random-looking directions, resulting in a diffusion coefficient of 11 micrometres 2 / minute. Therefore, the real time to viral annihilation is more like:

Assuming that the macrophages movement is similar to diffusion, how long will it take the macophage to reach the virus (on average)?

D = 11 µm2/min. Distance = 300 µm

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I think I have the answer: About 3 days.

 

You might say that this calculation is not realistic – even a macrophage does not move completely at random. You would be right, the macrophage can home in on the virus to some extent (called chemotaxis). Nevertheless, this simple model points out something important:

acornsAs it happens, the answer in this case is a little of both.

There are many other systems, particularly in ecology, that use diffusion as a simple model of organismal movement.

The organisms modelled include forests (even though the trees don’t move the forest will “move” via seed dispersal), insects, and even larger animals like rabbits. Diffusion is one way that biologists are looking at the likely effects of large-scale stressors like global warming – can oak trees disperse north fast enough to escape the pressures of a warmer world? However, these models are mathematically more complicated than the diffusion we have been talking about: the organisms do not only move around, they also reproduce.