PT  - JOURNAL ARTICLE
AU  - Ryan Grgurich
AU  - Hugh T. Blair
TI  - An uncertainty principle for neural coding: Conjugate representations of position and velocity are mapped onto firing rates and co-firing rates of neural spike trains
AID  - 10.1101/743310
DP  - 2019 Jan 01
TA  - bioRxiv
PG  - 743310
4099  - http://biorxiv.org/content/early/2019/08/22/743310.short
4100  - http://biorxiv.org/content/early/2019/08/22/743310.full
AB  - The hippocampal system contains neural populations that encode an animal’s position and velocity as it navigates through space. Here, we show that a population of spiking neurons can map information about position and velocity onto two orthogonal codes—a firing rate code (R) and a co-firing rate code (Ṙ)—which behave as conjugates of one another: if one code conveys information about position, then the other conveys information about velocity. We describe two biologically inspired methods for decoding R and Ṙ, referred to as sigma and sigma-chi decoding, respectively. Simulations of head direction (HD) and grid cell spike trains show that if neural firing rates are tuned for position (but not velocity), then position is recovered from R via sigma decoding, whereas velocity is recovered from Ṙ via sigma-chi decoding. Conversely, simulations of an oscillatory interference code implemented by theta cell spike trains show that if co-firing rates are tuned for position (but not velocity), then position is recovered from Ṙ via sigma-chi decoding, whereas velocity is recovered from R via sigma decoding. This conjugate relationship between R and Ṙ mirrors the “uncertainty principle” from physics, in that the more information one code conveys about position, the more the other conveys about velocity, and vice versa. Theoretical models of hippocampal networks are often simulated using linear units that derive their outputs only from R, and not from Ṙ. The conjugate coding principle implies that these models may be limited in their ability generate accurate predictions about connectivity within biological networks composed from nonlinear neurons that are capable of deriving their outputs from both and R and Ṙ.