  The hippocampal system contains neural populations that encode an animal's
position and velocity as it navigates through space. Here, we show that such
populations 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 conjugates
of one another, obeying an analog of the uncertainty principle from physics:
information conveyed in R comes at the expense of information in R', and vice
versa. An exception to this trade-off occurs when spike trains encode a pair of
conjugate variables, such as position and velocity, which do not compete for
capacity across R and R'. To illustrate this, we describe two biologically
inspired methods for decoding R and R', referred to as sigma and sigma-chi
decoding, respectively. Simulations of head direction (HD) and grid cells show
that if firing rates are tuned for position (but not velocity), then position
is recovered by sigma decoding, whereas velocity is recovered by sigma-chi
decoding. Conversely, simulations of oscillatory interference among
theta-modulated "speed cells" show that if co-firing rates are tuned for
position (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, and
partially recovered by both decoders. These results suggest that neurons with
different spatial and temporal tuning properties-such as speed versus grid
cells-might not encode different information, but rather, distribute similar
information about position and velocity in different ways across R and R'.
