I am sure many have heard the old physics joke regarding modeling a
horse as a sphere to make the math easier, and while funny, it is often
very true. In order to fully simulate a system accurately,
you would need to get down and solve the quantum mechanical equations
that define each and every atom in the system… This quickly
becomes intractable, even in systems with a few electrons.
This becomes exactly impossible when you start to discuss
systems on the size of cells. So, in order to get around this,
physicists (and engineers and mathematicians) come up with simplified
models to make the math easier, but hopefully capture the important
physics of the system. This brings to mind a quote posted* in
my last simulation write up that is attributed to Prof. George E. P.
"All models are wrong, but some are useful."
Very, very true words. A model need not have every last detail included to be useful or to help us learn from it.
Recent work from the Max Planck Institute of Colloids and Interfaces in Potsdam and at the University of Heidelberg has illustrated this very nicely. Researchers there set out to study cell adhesion in blood vessels. Even with a lifetime of work, one can not fully model all the interactions that occur within a cell, or between a cell and the vessel wall. Instead they choose to use a simplified model of a cell, one that resembles a porcupine, to simulate this complex system. In the process, they identified what are key parameters for cellular adhesion.
Blood is the highway system of our bodies: it transports cells throughout the body via hydrodynamic forces resulting from our pumping heart. But these forces do not tell a cell where to exit; this is left to specific groups of specialized molecules called receptors that exist on the cellular surface. Receptor molecules work on a lock-and-key principle, e.g. the receptors on a certain cell will only fit into the receptors on its destination tissue, which ensures that the cell ends up where needed. The research team sought to understand what is most important physics in this process, what is it that causes cells to stick? This sticking process is critical in many biological applications. Malaria-infected red blood cells will stick to vessel walls to avoid destruction by the spleen, and white blood cells attach themselves at certain points to help fight off foreign bodies in adjacent tissues; therefore understanding the underlying physical mechanism is an important first step in exploiting it to our advantage.
By modeling the cell as a sphere with sticky knobs randomly placed on its surface, and the tissue as a plane with an even arrangement of similar sticky knobs, the researchers modeled the hydrodynamic flow of cells passing over this surface to see what stuck. It was found that higher flow lead to a higher number of cells sticking to the surface, since the increased flow would allow them to find a matching receptor on the surface more quickly. They found that increasing the receptor density on the cell itself increased the adhesion, but only to a point. The team found that beyond a few hundred receptors per cell, there was little gain in adhesion; this was because the receptor's effective areas would overlap each other due to the random thermal vibrations present in the system. Similar results were seen in the when the size of the adhesion areas was increased for similar reasons.
What was found to have a surprising effect on the adhesive properties was the height of the receptor knobs. The simulations showed that cells would have a large increase in adhesion rate from only a small increase in the height of the knobs. This phenomena is seen in nature as well: both white blood cells and malaria use this "porcupine spine" mechanism. What the researchers discovered is that this may not be limited to just a few systems, but rather is a feature of many other biological systems that exhibit similar behavior. This works emphasizes a point I made in a earlier article—we are living in interesting times, where experiments and simulations are now looking at the same thing, each bringing new information to light and helping advance science even more. No longer do advances in computational chemistry|biology|material science|engineering mean a trivial bit of information, but a real step forward in our scientific understanding of a system. This is just one of the latest examples of it.
*Thanks to rx_MD for posting Dr. Box's quote