Physics for Biologists — Beyond Biophysics

Steven Vogel, Duke University

One might expect that a perusal of either literature or programs listed under the heading “biophysics” might offer just what we need, a guide to the bits of biology to which physics bears immediate relevance. But, perhaps purely by historical accident, the term has unfortunately come to describe a far more limited domain and thus as guidance proves more likely to mislead than to guide a physicist attempting to devise a course.

“Biophysics” as a term traces to Karl Pearson, now best remembered as a pioneering statistician, who, in 1892, defined it in sweeping terms, “This branch of science which endeavours to show that the facts of Biology constitute particular cases of general physical laws” [1].

But a look at the faculty, their research areas, or the courses in any contemporary biophysics program, undergraduate or graduate, reveals something closer to molecular and a little cellular biology, with both merely viewed from a physical perspective. Scarcely a trace can be found of macroscopic physics. Even where one encounters “structural biology” no euphemistic neologism for anatomy is intended; “structure” here means macromolecular structure. The tacit definitional narrowing appears to have taken hold when the earliest specifically biophysics programs appeared during the 1950s in non-clinical medical science departments. It seems to have been echoed a little later as specializations within physics departments — although I cannot claim to have done a full historical trace.

The peculiarity was brought home to me when I found no reference to the Biophysical Journal among the over 800 sources cited in the 2013 revision of my textbook, Comparative Biomechanics. By design the book takes a macroscopic, organismal approach, and no paper apparently proved directly relevant. Similarly, I now find that no journal whose title includes the word “biophysics” or “biophysical” makes my list of the 90 for which over the past 50 years I have reviewed contributions.

So what items of physics ought a biologist be familiar? Without attempting any logical presentation, I offer two entry points. The first is a set of everyday examples of an essentially macroscopic, organismic character, ones that happen to be of little interest to biophysicists — examples admittedly reflecting my own interests.

Example 1. Feel your pulse at your wrist and you will experience the short systolic pulses of your left ventricle as expansions of the artery beneath the skin — blood flow has speeded up and the artery swells. But wait — Bernoulli’s equation says that faster flow should come with lower pressure and thus shrinkage of a compliant vessel. Why is its prediction exactly opposite reality? The usual physics course takes little note of viscosity, the no-slip condition, Reynolds number, or, of most immediate relevance, the Hagen-Poiseuille equation.

Example 2. Hand-held infrared thermometers are now everyday items, most often used for checking heat leakage from homes. They provide a wonderfully enriched view of our thermal environment. I pointed one at a waist-high, sun-lit oak leaf on a still, hot (36º C) day; the middle of the leaf ran around 51º, fully 15º hotter. It occasionally dipped a degree as the leaf twitched in an air current too gentle for me to feel. A paper cut-out of a leaf became still warmer than a detached real leaf. A few months later I pointed the tool at a sky-exposed magnolia leaf on a cold (-8º), clear dawn; I got readings around -20º. Why doesn’t leaf temperature match air temperature, and why don’t leaves, when grasped, feel all that hot or cold? Does the physics course consider radiant heat exchange, with the Stefan-Boltzmann equation (and perhaps Wien’s displacement law), as well as free and forced convection, thermal capacity, and thermal conductivity?

Example 3. Ordinary trees grow to 30 or 40 meters in height and in a few places giants approach 100 meters. Evaporation from the leaves extracts liquid water from the interstices of the soil and raises it from the roots against both gravity and viscous pressure losses. By the time it reaches the leaves, hydrostatic pressure has dropped well below zero, often reaching negative tens of atmospheres by highly reliable direct and indirect measurements. No, capillary rise does not contribute significantly. For that to work, assuming perfect wetting, a 50-meter tree could have vessels no wider than 0.6 micrometers, vastly smaller than the typical value of 100 micrometers. The mechanism brings front and center the difference between gaseous and liquid states of matter, the near-incompressibility of water, the speed of sound in water and other media, as well as some highly instructive historical physical measurements. Not to mention the reason delicate marine organisms easily withstand the pressures at great oceanic depths, even if most fishes require quite special equipment to manage them.

Example 4. The same trees can profitably be viewed as mechanical devices. Spectacular failure of the simplest model can be used either as an introduction to specific treatment of real-world mechanics or as an open-ended assignment that will force students to discover for themselves the options missed by excessive idealization. How high might a cylindrical column of living oak extend upward before the wood on the bottom suffers compressive failure? Living oak has a density of about 600 kilograms per cubic meter, or a downward force of 6000 newtons per cubic meter [2]. It has a crushing strength of about 30 meganewtons per square meter [3]. Dividing the latter by the former gives a maximum height of no less than 5000 meters, fifty times the height of any tree. Examining what has been missed brings up other modes of compressive failure, in particular Euler buckling, plus Young’s modulus, flexural stiffness, and second moment of area. Further probing suggests that wind loading matters more, introducing drag and drag coefficients plus moment arms for both the load and the resistance to turning of the base plate and soil. Loading of bones follows the same logic if providing less tidy examples.

Example 5. Wet a piece of absorbent cotton and let it dry completely. Fluff has become dense mat as the receding air-water interfaces drew the hydrophilic fibers together. The relevance of surface tension, the culprit, goes far beyond determining just who can walk on water (although students might calculate the maximum weight of a water-walking human). Those same trees, again, could not manage without it. Only the surface tension of the sub-micrometer interfaces in the fibrous walls of cells within the leaves keeps air from being drawn into the open tops of the columns of water by the enormously low pressures within. The other critical variable, the size of the interfaces, operates via the Young-Laplace relationship, a recurring determinant in biology. Our own lungs need a special mechanism (a particular surfactant) to ensure that all alveoli will inflate simultaneously instead of, as would happen with simple elasticity, all the air going into whichever went first. And function in a diversity of systems commonly ties to the degree of hydrophobicity of surfaces, including some that have exceeded old textbook values, so-called superhydrophobic ones.

Table 1. A listing of bioportentous physical variables

The second viewpoint consists of a list of what one might call bioportentous physical variables. The list given in Table 1 is a heterogeneous one, with some items representing lumpings of what are multidimensional factors; it mainly gives a sense of the scope of the relevant. I assert merely that for each variable I can cite at least one biological situation for which it matters — with no claim of completeness. (Obvious universals such as force, temperature, and length have been omitted, and I have not fully plumbed the range of thermodynamic properties.)

Now one should not contrive a course based too heavily on external desiderata — pedagogical effectiveness requires some logical development, a “story-line” if you will. And packing in too much material, especially diverse material, assures ineffectiveness. But I do feel that two of these external considerations ought to be borne in mind. First, the physics that matters in the life sciences not only does not coincide with biophysics, it extends beyond the traditional purview of departments of physics. Electrical phenomena depend on conduction in aqueous solutions, not copper wires. Solids approach rigidity only where special conditions require it; otherwise, meaning normally, a whole complex of material properties comes into play. And so on. But the life science students you teach will rarely be exposed to much physical chemistry and even less often to mechanical engineering — so you are their last chance. Second, traditional courses emphasize the simple, regular, and law-abiding, in the process transmitting the misleading view that our science deals with an extremely orderly world. In biology we pick trivial characters that happen to be the rare observable features that follow the Mendelian laws; in physics you avoid the untidiness of fluids and real materials as part of an apparently analogous imperative.

Steven Vogel is an emeritus professor of Biology at Duke University. He is the author of Comparative Biomechanics: Life’s Physical World, among other books. His research focus is on how the structural arrangements of organisms reflect adaptation to the mechanics of moving fluids. He presented his views on Biophysics and Bio-engineering at the March IPLS conference and the June Gordon Conference.

1. Pearson, K. 1892. The Grammar of Science. London, UK: Walter Scott (also Dover Publications, 2004).
2. Vogel, S. 2013. Comparative Biomechanics, 2nd ed. Princeton, NJ: Princeton University Press.
3. Niklas, K. J. and H.-C. Spatz 2012. Plant Physics. Chicago, IL: University of Chicago Press.

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