# One oscillation plus one oscillation equals how many?

I’m back from a fairly brief trip to Sydney, where I spent almost equal amounts of time talking to a collaborator in the School of Physics (Peter Robinson and his colleagues) at the University of Sydney and sat in traffic jams on buses / taxis (and waiting for delayed trains). Anyone who thinks Hamilton traffic is bad doesn’t know what they’re missing…

Anyway, we talked a bit about one of our projects. I shan’t of course describe it to you in full detail, because most of you won’t be interested (it concerns computer modelling of groups of neurons in the cerebral cortex), but I will describe a little bit of the flavour of this work (N.B. actually, what I describe is closer to the work that has been done in Sydney than to that done in Hamilton, but it’s pretty similar)

A neuron (brain cell) will ‘fire’ signals to other neurons, at a rate that depends on the signals it receives. If the neuron receives more signal, it fires more quickly. So, assuming a constant signal in, it will fire at a constant rate. That is one oscillation. (An oscillation being something that is repetitive.) But a group of neurons can also have other oscillation frequencies. This is the group behaviour – e.g. the group as a whole might fire a little quicker, then a little slower, then a little quicker, etc. That is another oscillation.

So we have individual neurons, that have their own firing frequency, that are driven by an oscillating input at another frequency. What happens?

We do a little bit of this in our undergraduate teaching, but for simpler systems. For example, a car driving over bumps in the road. The suspension system of a car has its own resonance frequency (push down on the bonnet and time how long it takes for the bonnet to rise), and the bumps on the road occur at another frequency. In this case, if you drive over the series of bumps, you’ll find that the response of the car ‘slaves’ to the frequency of the input – i.e. the bumps. The frequency at which you go up and down is the frequency at which the bumps occur, not the natural frequency of the suspension. It’s a forced oscillator, which we can solve neatly mathematically.

So what about the neurons? These are more complicated. The answer depends on the difference between the two oscillation frequencies. If the two are very different, each neuron will ‘ignore’ the underlying oscillation in the input, and just fire at its own natural frequency (unlike the car driving over the bumps). But if the two are similar, the neuron will abandon its own preferred natural frequency, and instead take up (nearly) the frequency of the input. In fact, we can get sudden jumps in behaviour…start with the two frequencies similar and slowly increase the input frequency. The neuron starts by following the input and slowly increases its frequency, but then suddenly jumps out of this pattern and then reverts to its natural frequency. So it fires at one frequency, or the other, depending on how similar they are.

This complicated behaviour (non-linear) makes it quite a tricky system to study, but a very interesting one. Worth a trip to Sydney for.

My travels continue next week.