Applied Mathematics Colloquium

The typical neuron integrates tens of thousands of synaptic inputs distributed in space and time over its dendritic tree en route to firing an action potential from its spike initiation zone. This multi-input, single-output scenario lends itself well to radical dimension reduction techniques that reproduce the cell's original input-output map, retain the model's RLC-circuit description, while replacing the original 10,000 ordinary differential equations with 10. We argue that this compact description yields functional insight into synaptic programs implemented by single cells and we demonstrate that networks of reduced cells reduce simulation times by a factor of 10.