Modelling Neurons as Kuramoto Oscillators

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How do neurons behave? Neurons...

1. Spike regularly
2. Spike together (or at least like to and try to)
3. Spike noisely
4. Spike responsively (to deep brain stimulation)

Neuron: A Brief Introduction

(Source: leavingbio.net)

1. Neurons spike regularly

Period = average time in between spikes (i.e. 0.3s)

Frequency = 1/Period (i.e. 1/0.3s = 3.33 Hz)

(Source: whydomath.org)

1. Neurons spike regularly

Neuron spikes can be represented as an oscillator, with each "lap" around the orbit representing a neuron spiking.

Then, the period of the accompanying sine wave of the oscillator matches the period of the neuron.

(Source: imgur.com)

2. Neurons spike together (or at least like to and try to)

Populations of neurons affect behavior. When enough neurons spike in synchrony, a strong enough signal is propogated to affect behavior (i.e. tremor in Parkinson's disease patients).

(Source: wikipedia.com)

2. Neurons spike together (or at least like to and try to)

We can represent a population of neurons as oscillators and observe their synchrony.

3. Neurons spike noisely

Many different factors (i.e. neurotransmitters, upstream neuronal signals, etc.) influence a single neuron's spike. Thus, neurons don't always consistently fire at the exact same rate (and in exact synchrony with other neurons).

(Source: wikipedia.com)

3. Neurons spike noisely

Here's how we can represent a noisy population of neurons as oscillators.

4. Neurons spike responsively (to deep brain stimulation)

Let's try to dampen PD tremors using this model!

bit.ly/kuramoto_sim