MathBench > Cellular Processes

Diffusion

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


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

Assuming that the phages movement is similar to diffusion, how long will it take the phage 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.

 

Three days is too long to wait around getting rid of a cold!

You might say that this calculation is not realistic – even a phage does not move completely at random. And you would be right, the phage 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 modeled include trees (which “move” via seed dispersal), insects, and even larger animals like muskrats. 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.