Livin’ la Vida Micro
LIVING AT MICRO SCALE: The Unexpected Physics of Being Small. David B. Dusenbery. xxxii + 416 pp. Harvard University Press, 2009. $49.95.
Billions of years of evolution have shaped the strategies that microorganisms use for locomotion and feeding. Although evolution of successful biological strategies is driven by competition among organisms or by changes in the environment, all strategies must respect the constraints of physics. By studying the distinctive physics of the “micro world”—a realm invisible to the naked eye, made up of objects smaller than about 0.1 millimeter—one may determine what strategies are possible for microorganisms and which of those are optimal. David Dusenbery’s book Living at Micro Scale does an excellent job of explaining the physics that is relevant at this scale and, later in the book, how this physics affects the behavior of microorganisms.
As Dusenbery makes clear, the physics of the micro world is different from the familiar physics of our everyday experience. An important theme is that water is effectively very viscous at the micro scale, which may seem counterintuitive, given that viscosity is a material property. But it turns out that the characteristic length and velocity scales of a flow are important for determining whether that flow is viscous.
For example, the viscosity of air is not something we usually notice, but if you were to try breathing through a straw and then replacing that straw with a series of thinner ones, you would find it increasingly difficult to breathe. This reflects the fact that the narrower the straw is, the more important viscous forces become.
To determine quantitatively whether viscous effects are significant, you must measure them against something else. The natural comparison to make is between the typical viscous forces acting on a body and the inertial forces required to cause the body to undergo a given acceleration. The ratio of the typical inertial force to the typical viscous force is called the Reynolds number. For a bacterium about 1 micrometer in diameter swimming in water at a speed of 10 micrometers per second, the Reynolds number is 10–5.
All other things being equal, as the size of a body decreases, the viscous forces per unit volume increase more rapidly than do the inertial forces per unit volume. A microorganism thus encounters viscous forces that are huge compared with the inertial forces it experiences. Inertia is therefore irrelevant at the micro scale. To get a sense of what swimming is like for a bacterium, imagine swimming in tar. The bacterium has to use drag to swim. In contrast, efficient human swimming relies on coasting, which is only possible when viscous forces are small compared with inertial forces. A person 2 meters tall swimming at 1 meter per second has a Reynolds number of 2 × 106.
The fact that we don’t experience the dramatically small Reynolds numbers with which bacteria have to contend helps explain why we find the micro world so strange. Dusenbery also gives other examples of surprising phenomena related to viscosity. For instance, in a highly viscous environment, the drag on a thin filament is roughly the same as the drag on a sphere with a diameter equal to the length of the filament. He also points out that waving a rigid oar back and forth in highly viscous fluid doesn’t get you anywhere. Dusenbery ties the physics of these things nicely to biological observations, presenting physical arguments to explain why the swimming appendages of microorganisms tend to be filaments rather than paddles, and why motile bacteria tend to be larger than those that just float about.
A second major theme of Dusenbery’s book is that diffusion transports and reorients molecules more rapidly than do the typical flows found at the micro scale. Again, this physical fact leads to unexpected consequences. For example, the rate at which randomly diffusing molecules bump into the surface of a cell is proportional to the diameter of that cell, and not its surface area. Also, because microorganisms tend to drag a halo of fluid with them as they move, bacteria cannot increase the collision rate of molecules at their cell surfaces by swimming.
The physics of diffusion and viscous flow leads to size limits for biological processes such as gravity sensing, pheromone detection and guidance by heat or chemicals. These limits are summarized in the figure on this page. Note that many of the critical values are close to one micrometer, which (as Dusenbery explains) is because these limits depend on just a few parameters: temperature, viscosity and the energy density of organisms. The author’s account of how these size limits are calculated and how the behavior of real organisms conforms to them is one of the most fascinating parts of the book.
Dusenbery sketches the history of the development of scientific techniques and ideas such as microscopy, molecular theory and information theory. These passages remind the reader that powerful ideas can drive scientific progress in disparate fields. For example, he describes how the 19th-century botanist Robert Brown showed that any type of particle that is sufficiently small exhibits constant random motion when suspended in water, and that this is a physical rather than a biological phenomenon. Subsequent work by Einstein and others on this Brownian motion made the existence of molecules undeniable and set the stage for the study of macromolecules. Likewise, the same statistical ideas that were important for describing Brownian motion proved useful for Claude Shannon’s formulation of information theory. And Shannon’s ideas have in turn proved useful in understanding the limitations on what microorganisms can find out about their environments.
Dusenbery also recounts some of his own scientific discoveries. These passages show the many connections between different areas of science and illustrate its human elements.
Dusenbery has supplied everything a reader might need to understand the ideas he presents in the book, including 12 appendices, which explain such topics as sedimentation equilibrium, the chemical potential and the mathematics of ellipsoids. Two of these appendices even review calculus and simple approximation rules. The mathematical nature of physics is hard to avoid, and it is hard to imagine that a reader who needs such a review will be able to follow some of the more complex mathematical arguments in the book. Nevertheless, the author obviously has put a lot of work into finding simple, intuitive explanations for many of the physical and mathematical concepts he describes. As a result, the book will be accessible and useful to a wide audience of people interested in biology, physics or engineering. And the provocative questions presented are sure to be the subject of intense activity in the research community for years to come.
Thomas R. Powers is associate professor of engineering at Brown University. His research interests include locomotion at low Reynolds numbers and the physics of soft matter, such as polymers, membranes and liquid crystals.