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How Does the Biological Clock Tick?

Mathematical models of human brain functioning – Interdisciplinary Research in the DFG Research Unit “Computational Modeling of Behavioral, Cognitive, and Neural Dynamics”

Pic.: Nneirda/
Photo :
Pic.: Nneirda/

Physicists and psychologists have collaborated in interdisciplinary projects in Potsdam for about 20 years. What might at first glance seem surprising makes sense upon closer examination, because many biological and neurophysiological processes can be described using mathematical and physical methods. From a physical point of view, the rhythmically pumping heart is an oscillator – and might serve as a clock for perceiving short time intervals in the brain.

We can see, hear, smell, taste, and touch, but lack a sensory organ for perceiving how time passes. Nevertheless, we are often confronted with situations where we have to estimate duration: How much time is left before I have to hand in my exam? Is the egg already hard-boiled?

In most cases this works quite well. But how? This is what the researchers want to find out in their experiments. Subjects hear two acoustic signals in different, very short intervals and can determine quite precisely the respective interval’s duration, despite having to complete tasks between the signals aimed at preventing mere counting.

Do we have something like an internal clock after all? Most likely not in the form of specific body parts or cells but perhaps indirectly: Apart from many other bodily signals, our brain’s “insular cortex” also registers and processes the rhythm of our heartbeat and respiration. Thus we can perceive the passing of time at least for intervals between 2 and 25 seconds.

This, at least, is the assumption of psychologist Olga Pollatos. She led a research project dedicated to the “search for the influence of heartbeat and respiration on the perception of time and the production of rhythms”. Pollatos was in charge of the experimental design and measurements. Arkady Pikovsky, Michael Rosenblum, and Azamat Yeldesbay, who work at the Institute of Physics and Astronomy, did the mathematical modeling.

To a layperson, this collaboration might be surprising at a first glance. What does the psychology of perception have to do with non-linear dynamic and statistical physics? This question makes Rosenblum smile. “We have always had interdisciplinary interests,” he answers. “We have the methods for data analysis and modeling. We have been dealing with oscillators and their weak interaction for 20 years.”

An oscillator, to physicists, is any system that behaves periodically, i.e. that swings rhythmically back and forth between two states. Oscillators are found in all fields. The clock pendulum is the best-known model. A violin string begins to oscillate when the bow draws against it. The metronome ticks the meter for musicians. Business cycles also follow periodic patterns.

The human body has several oscillators: Apart from heart and lungs constantly pumping blood, air, and carbon dioxide up and down, the electrical activity of the brain’s neurons mounts up to an even rhythm that appears as a wavelike pattern in an electroencephalogram (EEG). As soon as two or more independently swinging oscillators are loosely connected, their different rhythms approximate, and, after some time, they oscillate in a common mode. Physicists call this synchronization.

To explain the phenomenon, Rosenblum takes us on a journey through time back to the 17th century. Dutch mathematician and physicist Christiaan Huygens designed the first functioning and highly accurate pendulum clock. These high-tech instruments were meant to solve a difficult naval problem – establishing the exact longitude. Huygens used two instruments to make sure that at least one timing device would work if the other stopped. He fastened both to the same wooden beam with a hook – and unwittingly established a coupling. One day when the scholar was sick in bed, he observed something strange. At first the pendulums of both clocks moved independently but eventually began oscillating precisely in time. This also happened when the synchronous oscillation was disrupted by holding one of the pendulums. Huygens spoke of an “odd kind of sympathy” between the two clocks and identified imperceptible movements of the wooden beam as the cause.

Mathematicians and physicists have since developed formulas to describe and calculate not only the synchronization of two or more coupled oscillators but even of a great many and also if they behave chaotically. It was reasonable to ask whether the perception of time observed in the experiment described above might be based on the synchronization of brain waves, heartbeat, and respiration because, from a physical point of view, biological oscillators are “dissipative non-linear systems” that can be represented with the help of “autonomous differential equations”.

This is what Pikovsky and Rosenblum did with the data from Olga Pollatos' tests – in a process that is only somewhat comprehensible to non-physicists and just superficially visible. It requires coffee as fuel, chalk for the scientists to sketch symbols and figures on a big blackboard, and computers. “The biggest challenge is to identify the tiniest of synchronization properties,” says Pikovsky, “because things do not work as exactly as with Huygens.” The preliminary findings, published this spring in a scientific journal, said that the heart might serve as an ‘internal clock’, at least in the ‘feeling’ of short time intervals.

Although this specific study in this project has ended, some other examinations are ongoing, like the other six projects of the research group “Computational Modeling of Behavioral, Cognitive, and Neural Dynamics” funded by the Deutsche Forschungsgemeinschaft (DFG). The participating scientists of the University of Potsdam and Humboldt-Universität zu Berlin come from different fields of research: experimental psychology, cognitive sciences, computer science, theoretical physics and applied mathematics. The aim of this multidisciplinary collaboration is to bring together the results of psychological experiments with brain processes. This means identifying basic patterns of human behavior, perception, and information processing and expressing them in mathematical and computer models.

How we comprehend language is one of the issues being examined. For example, scientists of the research group in Potsdam-Golm record eye movements during reading to find out how we make sense of individual words, whole sentences and texts. Others deal with the influence of movements and gestures on our cognition and how, with the help of small changes in our posture, we unconsciously maintain our body’s balance. Yet others examine brain activity during certain tasks to determine brain signal transmission duration and individual response times. All of these experimental findings, time series, and recordings are traceable to mathematically delineable processes that can determine whether they follow a specific rhythm or occur by mere chance, whether in a controlled sequence or erratically.

Physicists Pikovsky and Rosenblum have already turned to project number 7 in the research group. Together with the PhD student Azamat Yeldesbay, they are working on a model that describes the mutual influence of “non-linear oscillators” in the brain and neurons and their electrical activity.

DFG Research Group “Computational Modeling of Behavioral, Cognitive, and Neural Dynamics”

The Deutsche Forschungsgemeinschaft (DFG) regards Research Units as a “medium-term collaboration, in which those involved collaborate closely on specific medium-term research projects, whose anticipated findings would not be able to be achieved within the scope of the individual grants program”. The research group 868 “Computational Modeling of Behavioral, Cognitive, and Neural Dynamics” brings together more than 20 scientists from the University of Potsdam and Humboldt-Universität zu Berlin. Prof. Ralf Engbert from the Department Psychology of the University of Potsdam is the group’s spokesperson.


One of the research interests of physicist Prof. Arkady Pikovsky is synchronization. Since 1997, Pikovsky has been head of the working group Statistical Physics and Theory of Chaos at the Institute of Physics and Astronomy of the University of Potsdam.

Apl. Prof. Michael Rosenblum, at Potsdam since 1995, focuses his research on synchronization and the analyses of time series.

Prof. Olga Pollatos was Junior Professor for Emotion and Motivation Psychology in the Department Psychology at the University of Potsdam from 2009 to 2012. Today she is teaching and researching at the University of Ulm.


Prof. Dr. Ralf Engbert, Spokesperson of the DFG Research Group 868
Department Psychologie
Karl-Liebknecht-Straße 24-25, 14476 Potsdam
Tel. 0331-977 2140/2874

Text: Sabine Sütterlin, Online-Editing: Julia Schwaibold, Translation: Susanne Voigt