Neuroscientist’s create mathematical model for how the brain keeps a beat

For the musically fortunate, keeping a beat is as natural as breathing. But for those without the talent, the notion of producing and keeping a beat may seem an impossibility.

On Thursday this week, researchers announced a mathematical model that describes a potential mechanism by which the brain may keep a musical beat. The paper, published in PLOS Computational Biology, is a joint effort between Amitabha Bose of New Jersey Institute of Technology; as well as Aine Byrne and John Rinzel of New York University.

The team of mathematicians and neuroscientists developed a neuromechanistic framework featuring computational version of a neuron that is capable of learning and reproducing a beat. The beat generator neuron — or BGN, as the scientists call it — learns a beat from a stimulus frequency and then oscillates at that frequency without the presence of the stimulus frequency.
The BGN does this by learning about the period of the stimulus sound wave — the length of time required before the sound wave repeats itself — and then modifies its own oscillations to match that of the stimulus frequency.

This model relies on the idea of a gamma counter. Gamma rhythms are those in the frequency range of 30 to 90 Hz. The scientists here utilized waves at 40 Hz to count two different events important to their model: the gamma cycles between the onset of the stimulus sound and between the oscillation spikes of the BGN. Using an error-correction algorithm, the BGN is able to use the difference between how often it spikes, compared to the stimulus spikes, to reproduce the beat of the stimulus.

Using this approach, the BGN was able to learn isochronous beats in the frequency range of .5 Hz to 8 Hz, which the researchers say is “relevant for beat generation and perception.”

Beat perception and beat generation are related but different ideas; the BGN is an example of the latter.

“Beat perception involves listening to an external sound source as a precursor to trying to discern and synchronize with the beat,” the researches describe in the paper. “Alternatively, we might ask how do we (humans) learn and then later reproduce a beat in the absence of any external cues.”

This model is simple in that it describes only one aspect of beat generation — at the level of a single computational unit, a model of a neuron. However, the usefulness of understanding beat generation within the brain shouldn’t be underestimated.

Beat generation is an example of the brain’s more general ability to learn and reproduce periodic rhythms without synchronizing to a present stimulus. Someday, perhaps, such a model may prove useful in understanding neurological disorders characterized by abnormalities of neural networks to reproduce the necessary oscillations for healthy brain function.

Further, this model has the potential to broadly influence the field of artificial intelligence as well. There are a number of problems in the field that can be reduced to learning and repeating a frequency-based stimulus, for which this model may prove beneficial.

This was originally published on Medium.

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