I am a PhD student in the field of neuroscience. My primary interest is brain oscillations. Neurons in the brain engage in the coherent activity from time to time. We may see this non-invasively when we record electroencephalography (EEG). This activity looks like regular periodic waves, and it represents the changing electrical and magnetic fields which in turn reflect currents inside neurons. In my studies, I want to know how structural characteristics of neurons and brain tissue in general determine the way oscillations look and function. The book that I’m reviewing today related to my field of study somewhat tangentially, but I was curious to learn more about oscillations in general. The book is “Biological clocks, rhythms, and oscillations” by Daniel B. Forger.

Besides brain oscillations, there are many other periodic processes in nature and in living organisms. One widely researched example would be circadian rhythms. Many living creatures sleep. Though we still don’t know for sure the purpose of sleep, it’s logical to assume that it is an evolutionary advantage for living on the kind of planet we live on. The sun rises and sets periodically, and our organisms have the capacity to mirror to a certain precision the periodicity of the sun in the sky. Circadian rhythms are natural, internal processes that regulate the sleep-wake cycle. The book describes mathematical methods to study periodic processes, like circadian rhythms.

The first approach to studying biological rhythms is to observe them, measure them, and try to extract any statistical and mathematical characteristics. Rhythm will always have a frequency (how many cycles per unit of time occur) and a period (an inverse from frequency; how long does it take to conclude a cycle). At each point in time, we can measure an amplitude (how strong are fluctuations in whatever units oscillations are measured) and the phase (a current position in the cycle) of the rhythm. 

Additionally, we may measure the relation of rhythms to behavior. For example, are there times in the breathing cycle when a person would be more likely to move? Or whether heartbeat cycles influence perception or decision-making? To test that, one should measure the phase of breathing each time a person moves and then check if the phases are distributed non-uniformly (which means that one phase occurs more often than others). The observation approach thus may answer some questions, but it cannot address the question of how rhythmic activity occurs.

The second approach to studying biological rhythms is to model them. Scientists came up with the variety of models throughout the years, but usually one could start from a simpler one or from the one that worked before for the phenomenon in question. Modelling can bring great insights into the nature of phenomena; it can also lead us astray. Every model has underlying assumptions, and it is crucial to evaluate them for the system under investigation. Moreover, the system is modeled in isolation, but in reality, this is never fulfilled. Cells are the part of an organism; an organism is a part of an ecosystem. The modeling approach thus has intrinsic limits. 

The third approach to studying biological rhythms is to disturb them. For example, to study if circadian rhythms are in sync with the sun cycle, one can put people in the experimental conditions without natural light cues and check if their circadian rhythms would change. In fact, this experiment has been done. It turned out that the body still followed a natural rhythm, but it was off from the outside world; the sleep-wake cycles were longer than 24 hours. In some systems, perturbation is easy, while in others it is challenging. However, this approach can provide convincing evidence about functional aspects of certain parts of the system with respect to the generation of periodic activity.

The book is quite technical, with a lot of formulas. However, I discovered some interesting bits of information that I can implement in my research. Three claims I found particularly fascinating.
1. If the amplitude of an oscillator increases, its synchrony to other oscillators decreases. As if with higher amplitude, the oscillator begins minding its own business.
2. Oscillators can synchronize to a noisy input. In other words, noise can synchronize the system.
3. When the oscillator is less “rigid”, it can adapt to a much larger range of periods from other oscillators. This is also true for human negotiations, isn't it?

I think the book would be suitable for those who want to dive into details of mathematical approaches to studying rhythms.

Useful knowledge: there are apps that may help to avoid jet lag by gently shifting sleep-wave cycles. They are based on the modeling study by Serkh & Forger (2014).

February, 2025