Sunday, February 24, 2008

From birds and fish to cells [*]

A physicist’s view of collective transport in biological systems

Let me motivate what I want to say today with a couple of videos. First up, an amateur video of a flock of starlings in Scotland.

Or see this one, where the flock cohesively responds to a predator. A Starling is a small bird, shown in the picture alongside, about the size and shape of a “myna” if you are familiar with it. They fly in flocks that do amazing things as a collective entity as you just saw in the above example. Understanding how they do this is field of active research as indicated by this cover of the October issue of Physics Today. I will tell you a little bit about how they do that subsequently. But you might say to me, “They are birds, and they have brains, albeit “bird brains”, so they see, process that information somehow and do stuff. Why would a physicist concern herself with that?” So, to make my point even more clear, let me show you one more video.

video

This one is a microscopic movie of a bacterial swarm (obtained from here). Do you see the complex flow patterns they exhibit? These guys clearly do not have brains. It might be that this rich collective behavior originates in more chemistry than physics, but clearly not biology. And to make my point that it is indeed just physics, I ask you to look at this other video (obtained from here)

videoDo you see the similarity in the flow pattern to that seen in the bacteria? Can you guess what you are looking at? It is just a vibrated monolayer of some centimeter long metal rods! Whatever is going on here is clearly just physics. Moreover, one can mathematically represent the motion of the bacteria/birds and those of the rods by the same set of equations! What I want to do in the rest of this post is to give you a flavor of some of the physics behind these and other collective phenomena in biological systems.

When looking at fish schools or bird flocks, the first postulate that comes to mind is that the phenomenon is “follow the leader”, with one bird/fish doing its own thing, and the others following. But as stated above, the things that birds/fish do is “mathematically similar” to what the bacteria do. So “follow the leader” seems an unlikely scenario. The logical next question to ask would be, “What are the minimal rules that can give rise to this kind of behavior?” We have known the answer to this question for a while now [1]. The rules are the following – Each member of the flock does each of three things a) Alignment : Adjust my direction of motion so that I am going in the same direction as my neighbors, b) Velocity matching : I adjust my speed so that I am going with the same speed as my neighbors c) Cohesion : I try to keep the distance from my neighbors the same at all times. With these basic rules and simple boundary conditions for entities at the edge of the flock, like “If there is food, turn towards it” and “If there is danger, turn away from it”, most of the complex patterns exhibited by these groups of organisms can be reproduced!

But these are just rules. So, the next question to ask would be, “Can these rules come about from just physical interactions?” Let us ignore the boundary conditions associated with food/predator for the moment, they clearly are chemistry and other higher processes and focus on the bulk flocking rules. What is a unifying thing between the birds, the fish the bacteria and so on? What they are, are objects that have a non-spherical shape that actively move through a medium (air/water etc.). Now what does that mean? They exert a force on the medium [2]. The medium responds, i.e., the fact that my bird/fish/bacterium is pushing on the fluid induces a flow in the fluid itself. This response now propagates through the fluid. So, a bird/fish/bacterium that is elsewhere will feel this change in the fluid, in terms of the local flow field and pressure gradients. And it will adjust its own force on the fluid accordingly, and this whole things feeds back to the other entities in the flock. This phenomenon is called hydrodynamic interaction. And this is the dominant interaction that produces the three aspects of flocks that is listed in the previous paragraph!

Further, I want to make the case that this quest for minimal mechanisms for collective behavior is not just restricted to animal group behavior on the different scales encompassed from birds to bacteria. For this, see the famous video below.

This is a video of a neutrophil chasing a bacterium and then gobbling it, the immune system of your body at work. I know what you are thinking, “This is one cell chasing one bacterium and the primary thing at play here is chemotaxis, so what is collective about this?” The collective aspect lies in how the cell crawls, i.e., at the sub-cellular scale. The interplay between membrane fluctuations, the stresses in the actin-microtubule network that makes up the cytoskeleton of the cell, the interaction of this network stress with the medium that the cell is in and many other things go into understanding how the cell crawls. The mathematical paradigm and the physics aspects of this question are not so different from those one uses to address animal group behavior we considered earlier! But for now, this is just a teaser. A separate post on this to follow later.

[*] Cross posted from my personal blog, where this really belongs. Will write a really SC post in a couple of weeks

[1] Actually the first instance in literature was in the context of an algorithm for computer graphics, available here.

[2] If we want to be careful, then clearly third law tells us that the swimmer must at least be a force dipole. Since there is no mathematics displayed here, I fudge this point.