Intermediate Physics for Medicine and Biology: Good Vibrations

In Chapter 10 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss negative feedback loops. Feedback is often used to maintain an important variable nearly constant. This idea underlies homeostasis and is fundamental to physiology.

"Are Physiological Oscillations Physiological?"
by Ivy Xiong and Alan Garfinkel.

So imagine my surprise when I read Ivy Xiong and Alan Garfinkel’s topical review in The Journal of Physiology titled “Are Physiological Oscillations Physiological?” (In Press), which changed the way I look at homeostasis and feedback. Its abstract states

Despite widespread and striking examples of physiological oscillations, their functional role is often unclear. Even glycolysis, the paradigm example of oscillatory biochemistry, has seen questions about its oscillatory function. Here, we take a systems approach to argue that oscillations play critical physiological roles, such as enabling systems to avoid desensitization, to avoid chronically high and therefore toxic levels of chemicals, and to become more resistant to noise. Oscillation also enables complex physiological systems to reconcile incompatible conditions such as oxidation and reduction, by cycling between them, and to synchronize the oscillations of many small units into one large effect. In pancreatic β-cells, glycolytic oscillations synchronize with calcium and mitochondrial oscillations to drive pulsatile insulin release, critical for liver regulation of glucose. In addition, oscillation can keep biological time, essential for embryonic development in promoting cell diversity and pattern formation. The functional importance of oscillatory processes requires a re-thinking of the traditional doctrine of homeostasis, holding that physiological quantities are maintained at constant equilibrium values, a view that has largely failed in the clinic. A more dynamic approach will initiate a paradigm shift in our view of health and disease. A deeper look into the mechanisms that create, sustain and abolish oscillatory processes requires the language of nonlinear dynamics, well beyond the linearization techniques of equilibrium control theory. Nonlinear dynamics enables us to identify oscillatory (‘pacemaking’) mechanisms at the cellular, tissue and system levels.

In their introduction, Xiong and Garfinkel get straight to the point. Homeostasis examines an equilibrium stabilized by negative feedback loops. Such systems are studied by linearizing the system around the equilibrium point. Oscillatory systems, on the other hand, correspond to limit cycle attractors in a nonlinear system. The regulatory mechanism must both create the oscillation and stabilize it.

In Russ’s and my defense, we do talk about oscillations in our chapter on feedback. One source of oscillations is when a feedback loop has two time constants (Section 10.6), but these aren’t what Xiong and Garfinkel are talking about because those oscillations are transient and only affect the approach to equilibrium. A true oscillation is more like the case of negative feedback plus a time delay (Sec. 10.10 of IPMB). Russ and I mention that such a model can lead to sustained oscillations, but in light of Xiong and Garfinkel’s review I wish now we had stressed that observation more. We analyzed the specific case but missed the big picture; the paradigm shift.

Another mechanism Xiong and Garfinkel highlight is what they call “negative resistance.” They use the FitzHugh-Nagumo model (analyzed in Problem 35 of Chapter 10 in IPMB) as an example of “short-range destabilizing positive feedback, making the equilibrium point inherently unstable.” Although they don’t mention it, I think another example is the Hodgkin and Huxley model of the squid axon with an added constant leakage current destabilizing the resting potential (Section 6.18 of IPMB). Xiong and Garfinkel do discuss oscillations in the heart’s sinoatrial node, which operate by a mechanism similar to the Hodgkin-Huxley model with that extra current.

A third mechanism generating oscillations is illustrated by premature ventricular contractions in the heart caused by “the repolarization gradient that manifests as the T wave.” As a cardiac modeling guy, I am embarrassed that I’m not more aware of this fascinating idea. To learn about it, I recommend you (and I) start with Xiong and Garfinkel’s review (we have no excuse; it’s open access) and then examine some of their references.

Even more interesting is Xiong and Garfinkel’s contention that “oscillations are not an unwanted product of negative feedback regulation. Rather, they represent an essential design feature of nearly all physiological systems.” They’re a feature, not a bug. Presumably evolution has selected for oscillating systems. I wonder how. (Xiong already has a background in molecular biology, bioinformatics, and mathematical modeling; perhaps while she’s at it she should add evolutionary biology.) Let me stress that Xiong and Garfinkel are not merely speculating; they provide many examples and cite many publications supporting this hypothesis.

A key paragraph in their paper introduces a new term: “homeodynamics.”

“If oscillatory processes are central to physiology, then we will need to take a fresh look at the doctrine of homeostasis. We suggest that the concept of homeostasis needs to be parsed into two separate components. The first component is the idea that physiological processes are regulated and must respond to environmental changes. This is obviously critical and true. The second component is that this physiological regulation takes the form of control to a static equilibrium point, a view which we believe is largely mistaken. ‘Homeodynamics’ is a term that has been used in the past to try to combine regulation with the idea that physiological processes are oscillatory... It may be time to revive this terminology.”

This topical review reminds me of Leon Glass and Michael Mackey’s wonderful book From Clocks to Chaos (cited in IPMB), which introduced the idea of a “dynamical disease.” Like Glass and Mackey, Xiong and Garfinkel present a convincing argument in support of a new paradigm in biology, rooted in the mathematics of nonlinear dynamics.

In their cleverly titled section on “Bad Vibrations,” Xiong and Garfinkel note that “not all oscillations serve a positive physiological function. Oscillations in physiology can also be pathological and dysfunctional.” I suspect their section title is a sly reference to the Beach Boys hit “Good Vibrations.” After all, Xiong and Garfinkel are both from California and their review can be summed up as the mathematical modeling of good vibrations.

From Clocks to Chaos,
by Glass and Mackey.

You know what: I think the upcoming 6^th edition of Intermediate Physics for Medicine and Biology needs more emphasis on nonlinear dynamics. I’m lucky Xiong and Garfinkel’s article came out just as Gene Surdutovich and I were revising and updating the 5^th edition of IPMB. God Only Knows that as I sit here In My Room working on the revision I’ll have Fun, Fun, Fun. Don’t Worry Baby, now that it’s spring and we have The Warmth of the Sun, Gene and I should make good progress. Unfortunately, because we’re working here in Michigan, we can’t occasionally take a break to Catch A Wave. Wouldn’t It be Nice if we could go on a Surfin’ Safari? (Sorry, I got a little carried away.)

So the answer to the question in the title—are physiological oscillations physiological?—is a resounding “Yes!” I’ll conclude with Xiong and Garfinkel’s final sentence, which I wholeheartedly agree with (except for the annoying British spelling of “center”):