Spare the (Elastic) Rod

Physicists love emergence. From a welter of complex details about a system's constituents, simple and universal rules sometimes emerge that adequately describe the collective behavior of the components. Even if these rules are not completely universal, they often have only a few relevant parameters, a vast simplification compared to the many that describe the constituents individually. But as Vafabakhsh and Ha remind us on page 1097 of this issue (1), emergent behavior can conceal important aspects of a system. Using a beautiful application of fluorescence microscopy, the authors provide the clearest evidence to date that the elastic-rod model for DNA mechanics, an emergent description that works well on long length scales, breaks down on shorter length scales relevant to cell biology. Disciplines Physical Sciences and Mathematics | Physics This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/510 Spare the (Elastic) Rod Physicists love emergence. Out of a welter of complex details about a system’s constituents, sometimes simple and universal rules adequately describe their collective behavior. Or if the rules are not completely universal, often they have only a few relevant parameters, a vast simplification compared to the many that describe the constituents individually. But emergence can be a two-edged sword, as Vafabakhsh and Ha remind us this week [1]. Emergence is frequently observed as a function of increasing length scale. Thus the complex intermolecular dynamics of individual water molecules can all be forgotten when we design plumbing; for this purpose it suffices to know just two parameters (mass density and viscosity). However, the very forgetfulness of Nature that simplifies its long-scale character can also conceal from us the details that we need to know if we are to understand shorter-scale regimes. A case in point concerns the mechanical properties of DNA. It is tempting to regard this famous molecule as just a database containing the algorithm for constructing an organism—pure information. But DNA is also a thing, a physical object; its everyday transactions involve constantly bending, releasing, twisting, and so on. Particularly important, DNA is often observed to be tightly bent, in contexts such as gene regulation and packaging (Fig. 1). Polymer physicists have long known that a stiff polymer like DNA will display emergence: For phenomena on long length scales, such a molecule may be adequately described as an elastic rod, that is, a rod that resists bending with a linear (Hooke-law) relation. The mathematics of elastic rods was well developed in the 19 century; all that is needed in the polymer context is to ≈ 10 nm ≈ 50 nm ≈ 8.5 nm a b c Figure 1: Biological examples of tightly bent DNA. (a) DNA winds around a protein core (lavender) to form the nucleosome; (b) A transcription factor (green) forces DNA into a tight loop; (c) A bacterial virus packs over 10 000 basepairs of DNA into a small capsid. (Illustration courtesy of David S. Goodsell and the RCSB Protein Data Bank.)