Diffusion is the enemy of life. This is because diffusion causes small particles to spread out, and for aggregates of particles to dissipate. Thus, in order to be alive and maintain its structure, an organism must have ways to counteract the constant tendency of things to spread out. And indeed they do. Plants, for example, are able to harness the energy of the sun to convert carbon dioxide and water into high energy compounds such as carbohydrates. These high energy compounds are then carefully deconstructed by living organisms to do work moving things around and building and repairing their structures. In this way, living things are able to combat the tendency of structures to dissipate and fall apart.
However, living organisms do much more than simply counteract diffusion; they actually exploit it for specific purposes. That is, they expend energy to concentrate molecules and then use the fact that molecules move by diffusion down their concentration gradient to do useful things. How do they do this? The short answer is that they couple diffusion with appropriate chemical reactions and are thereby able to exploit the inherent diffusive motion of molecules. Indeed, many of the processes that take place in living cells can be described as the interaction of reacting and diffusing chemical species. This realization has led to the mathematical description of many interesting biological processes and this in turn has led to an increased understanding of how biological systems work.
In this talk, I give several examples of the ways that cells use diffusion to their advantage, and describe the equations that model these processes. In particular, I will describe how molecular diffusion and reaction are used to make signals, to create functional aggregates, to take a census, and to make length measurements.
In this way, I hope to convince you that living organisms have made diffusion their friend, not their enemy, and in the process, demonstrate the importance of understanding the solutions of the equations governing diffusion-reaction processes.
Note: This is a pre-recorded MBI (Mathematical Biosciences Institute in Columbus, OH) Colloquium