Benedek and Villars, Volume 2

Physics With Illustrative Examples
From Medicine and Biology, Volume 2,
by Benedek and Villars.

Last week I discussed volume 1 of Benedek and Villars’ three-volume textbook Physics With Illustrative Examples From Medicine and Biology, which dealt with mechanics. The second volume discusses statistical physics. The preface to their first edition of Volume 2 states

In the present volume we develop and present the ideas of statistical physics, of which statistical mechanics and thermodynamics are but one part. We seek to demonstrate to students, early in their career, the power, the broad range, and the astonishing usefulness of a probabilistic, non-deterministic view of the origin of a wide range of physical phenomena. By applying this approach analytically and quantitatively to problems such as: the size of random coil polymers; the diffusive flow of solutes across permeable membranes; the survival of bacteria after viral attack; the attachment of oxygen to the binding sites on the hemoglobin molecule; and the effect of solutes on the boiling point and vapor pressure of volatile solvents; we demonstrate that the probabilistic analysis of statistical physics provides a satisfying understanding of important phenomena in fields as diverse as physics, biology, medicine, physiology, and physical chemistry.

Many of the topics in Volume 2 of Benedek and Villars are similar to Chapters 3–5 in the 4th edition of Intermediate Physics for Medicine and Biology: the Boltzmann factor, diffusion, and osmotic pressure. As I said last week, I’m most interested in those topics Benedek and Villars discuss that are not covered in Intermediate Physics for Medicine and Biology, such as their fascinating description of the use of Poisson statistics by Luria and Delbruck.

If a bacterial culture is brought into contact with bacteriophage virus particles, the viruses will attack the bacteria and kill them in a matter of hours. However, a small number of bacteria do survive the attack. These survivors will reproduce and pass on to their descendants their resistance to the virus. The form of resistance of the offspring of the surviving bacteria is that their surface does not adsorb the attacking virus. Bacterial strains can also be resistant to metabolic inhibitors, such as streptomycin, penicillin, and sulphonamide. If a bacterial culture is subjected to attack by these antibiotics, the resistant strain will emerge just as in the case of the phage resistant bacteria.

In the early 1940s, Luria and Delbruck were working on ‘mixed infection’ experiments in which the bacteriophage resistant strain of E. coli bacteria were used as indicators in studies they were making on T1 and T2 virus particles. Starting in the Fall of 1942, they began to put aside the mixed infection experiment and asked themselves: What is the origin of those resistant bacterial strains that they were using as indicators?

They go on to give a detailed description of how Poisson statistics were used by Luria and Delbruck to study mutations.

Russ Hobbie and I discuss the Poisson distribution in our Appendix J. The Poisson distribution is an approximation of the more familiar binomial distribution, applicable for large numbers and small probabilities. One can see how this distribution would be appropriate for Luria and Delbruick, who had large numbers of viruses and a small probability of a mutation.

Russ and I cite Volume 1 of Benedek and Villars’ text in our Chapter 1 on biomechanics. We draw the data for our Fig. 4.12 from Benedek and Villars’ Volume 2. We never cite their Volume 3, about electricity and magnetism, which I’ll discuss next week.