# Linearization of excitatory synaptic integration at no extra cost

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## Abstract

In many theories of neural computation, linearly summed synaptic activation is a pervasive assumption for the computations performed by individual neurons. Indeed, for certain nominally optimal models, linear summation is required. However, the biophysical mechanisms needed to produce linear summation may add to the energy-cost of neural processing. Thus, the benefits provided by linear summation may be outweighed by the energy-costs. Using voltage-gated conductances in a relatively simple neuron model, this paper quantifies the cost of linearizing dendritically localized synaptic activation. Different combinations of voltage-gated conductances were examined, and many are found to produce linearization; here, four of these models are presented. Comparing the energy-costs to a purely passive model, reveals minimal or even no additional costs in some cases.

## Keywords

Voltage-gated conductances Metabolic cost Sodium channel Mixed-cation channel Biophysical model## Notes

### Acknowledgements

The authors thank the University of Virginia Department of Neurosurgery for their support.

### Compliance with Ethical Standards

### Conflict of interests

The authors declare that they have no conflict of interest.

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