# Physical Models of Living Systems, Second Edition

In a 2015 blog post, I discussed Philip Nelson’s then-new book Physical Models of Living Systems. I wrote that “It’s an excellent book, well written and beautifully illustrated.” Recently, Nelson published a second edition of Physical Models of Living Systems. All the nice things I wrote about the first edition remain true in the second, but now there are four new chapters to increase your fun. In this post, I’ll focus on the new chapters.

I like how Nelson organizes each chapter around a biological question and a physical idea.

Biological question: How can pulling two things apart strengthen their bond?

Physical idea: Bond breaking is a first passage process, controlled by the lowest activation barrier, and that barrier can increase upon moderate loading.

The chapter describes slip bonds and catch bonds. A slip bond is the normal case when the bond’s strength decreases as you pull on it, and a catch bond is the unusual case when its strength increases as you pull. Wikipedia compares a catch bond to one of those Chinese finger traps.

Nelson explains catch bonds using random walk simulations; first a free random walk, then one with an applied force, next one in a harmonic oscillator potential, and finally one with a oscillator potential plus a barrier, where if you reach the top of the barrier the bond breaks. The “strength” of the bond then becomes the walking time before reaching the barrier (a “first passage process”). By manipulating the potential shape, he finds clutch bond behavior. He then relates these simple simulations (which the reader can easily perform on their own computer) to T cell activation and leukocyte rolling. In each chapter, he sums up the analysis with a section he calls “The Big Picture.” For this chapter, he writes

Our physical model… was absurdly simple, but it nevertheless contained a lot of buried treasure: the basic facts about free Brownian motion, drift under constant force, equilibration in a trapping potential field, the Boltzmann distribution in equilibrium, the Arrhenius rule for escape in quasiequilibrium, and the entire surprising phenomenon of catch bonding. The key step was to understand bond breaking as a first passage problem.

Biological question: How can we combine many noisy images of a viral protein to get one clean image?

Physical idea: We must first align the images, but our best estimate of the required alignment is actually a probability distribution.

In this chapter, Nelson examines how to take noisy electron microscope images of an object that are each rotated or shifted relative to each other, and align them to get a clear picture. He warns us “You can’t win by averaging noisy signals unless you know the proper alignment.” What biological example does he look at? The coronavirus spike protein! Apparently the procedure described in this chapter played a big role in the development of the covid-19 vaccine. The story makes me want to seek out the scientists who developed this method and give them a big hug.

Biological question: Why do some outbreaks of a communicable illness spread explosively, whereas others, in similar communities, fizzle after the first few cases?

Physical idea: A tiny subpopulation of superspreader individuals can have a huge effect on the course of anepidemic.

This chapter starts with the SIR model of an epidemic (S = susceptible, I = infected, and R = recovered) that I’ve discussed before in this blog. Nelson tweaked it to examine what happens just as the epidemic begins if you have a handful of superspreaders. Once again, the model is applied to understanding covid. In the big picture Nelson writes

We have found that because outbreaks always begin with just one or a few infective individuals, the discrete, stochastic character of transmission has a large effect on outbreak dynamics. Thus, a community that is lucky to get only a mild outbreak in the first instance must not become complacent, imagining themselves to be somehow protected: Always some outbreaks fizzle, but any such instance is just as likely to be followed by a severe outbreak on a later introduction as in any other community.

There are many ways to improve the realism of the SIR model, but we focused on just one: the well documented fact that some illnesses have superspreader individuals. The implications are profound. Although Figure 14.5a is frightening, such time courses can be replaced by the milder ones in Figure 14.3 by promptly identifying and quarantining just a few percent of the infected population. For example, backward contact tracing seeks to identify contacts of each sick individual who may have been the source of that person’s infection. When multiple backward trails point to the same person, that person may be a superspreader.

Biological question: How can a pathogen hide from the immune system?

Physical idea: Positive feedback with small copy numbers can lead to a stochastic toggle that transiently changes state after a long, random delay.

I like this chapter because it makes good use of phase portrait plots. The pathogen behaves almost like a nerve, which can either sit at rest or fire an action potential, with the all-or-none response relying on a positive feedback loop.

What bet is being hedged? If you’re in a situation where normally one type of behavior is favored, but on rare occasions the environment changes and an unusual behavior may be needed to save the species, then sometimes organisms will keep most individuals in the normal state but will have a few random individuals in the unusual state just in case.

The second edition of Physical Models of Living Systems still has all the good stuff from the first edition: lovely color figures (including some by David Goodsell), lots of homework problems, comparisons to real data, and a winning combination of words, pictures, equations, and computer code. Add in the four new chapters — and a kindle price under ten dollars! — and you have a masterpiece.

My favorite part of the second edition: Like in the first edition, Nelson cites Intermediate Physics in Medicine and Biology. And, he remembers to update the citation to IPMB’s 5th edition!

Originally published at http://hobbieroth.blogspot.com.

Professor of Physics at Oakland University and coauthor of the textbook Intermediate Physics for Medicine and Biology.

Professor of Physics at Oakland University and coauthor of the textbook Intermediate Physics for Medicine and Biology.