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The hippocampal system contains neural populations that encode an animal'sposition and velocity as it navigates through space. Here, we show that suchpopulations can embed two codes within their spike trains: a firing rate code(R) conveyed by within-cell spike intervals, and a co-firing rate code (R')conveyed by between-cell spike intervals. These two codes behave as conjugatesof one another, obeying an analog of the uncertainty principle from physics:information conveyed in R comes at the expense of information in R', and viceversa. An exception to this trade-off occurs when spike trains encode a pair ofconjugate variables, such as position and velocity, which do not compete forcapacity across R and R'. To illustrate this, we describe two biologicallyinspired methods for decoding R and R', referred to as sigma and sigma-chidecoding, respectively. Simulations of head direction (HD) and grid cells showthat if firing rates are tuned for position (but not velocity), then positionis recovered by sigma decoding, whereas velocity is recovered by sigma-chidecoding. Conversely, simulations of oscillatory interference amongtheta-modulated "speed cells" show that if co-firing rates are tuned forposition (but not velocity), then position is recovered by sigma-chi decoding,whereas velocity is recovered by sigma decoding. Between these two extremes,information about both variables can be distributed across both channels, andpartially recovered by both decoders. These results suggest that neurons withdifferent spatial and temporal tuning properties-such as speed versus gridcells-might not encode different information, but rather, distribute similarinformation about position and velocity in different ways across R and R'.

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