To a retired professor of physical chemistry, the proposals outlined in “Teaching Biological Physics” (Physics Today, March 2005, page 46) concerning the inadequate course content for biophysics majors and possible remedies are rational and merit implementation to various degrees. I followed the proposals of authors Ray Goldstein, Phil Nelson, and Tom Powers up to the paragraph that refers to the “feeling for entropy.” I drew back at the totally misleading analogy in their Figure 2.
Molecules, large or small, do not hop over barriers like buffalo in a stampede. Saying, as many instructors do, that a particular chemical conversion occurs because the system is “seeking the lowest chemical potential” and in so doing “it must surmount a free energy barrier” gives students no conceptual content, only words to repeat on an examination.
Furthermore, although the entropy function developed in a course on conventional thermodynamics is fundamental, it resides in a special mental compartment. It remains unconnected to molecular and statistical concepts that provide students with the basis for constructing models of the complex processes they will encounter in biophysical studies. Why not present the molecular and statistical models early in the program?
Second-year physics and biophysics majors have learned the fundamentals of quantum mechanics, and will not reject the assertion that for each species of molecule, small or large, there is a distinctive, huge sequence of discrete energy states in the form of translations, rotations, vibrations, electronic excitations, and so forth.
Ludwig Boltzmann demonstrated that in any macroscopic sample of matter at equilibrium, the population of accessible states follows a specific temperature-dependent distribution function.
It is useful to consider a feature of the distribution, the density of accessible states, which depends on the total energy and increases rapidly with increasing energy. For the conversion of A to B, there, must be a sequence of structures that are intermediate between the original and new species. For the intermediates there exist corresponding distribution functions characterized by their distinctive densities of states. Generally, the intermediate structures have higher electronic energies than either A or B, so only the higher-energy states of A or B are close to those of the intermediates and thus have a high probability of making transitions. Clearly, only if B has a higher density of states at that level does the conversion succeed, since the higher density of accessible states accumulates the largest fraction of molecules.
The terms “enthalpy,” “entropy,” and “free energy” do not appear in the preceding outline, but they are present as weighted summations over the distribution functions.
Whether we use the language of thermodynamics or of statistical mechanics, we are concerned with huge assemblies of atoms and molecules. It is highly misleading to discuss the properties of a single molecule, large or small, in terms of changes in its free energy or chemical potential. Analysis of what happens to a long protein molecule under stress is properly treated in terms suitable for a mechanical model.
With that criticism aired, I applaud the authors for an otherwise fine article.
