Abstract
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 () 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 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 and R˙. To illustrate this, we describe two biologically inspired methods for decoding and R˙, referred to as sigma and sigma‐chi decoding, respectively. Simulations of head direction 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 populations 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 and R˙. Such conjugate coding of position and velocity may influence how hippocampal populations are interconnected to form functional circuits, and how biological neurons integrate their inputs to decode information from firing rates and spike correlations.
Highlights
The rodent hippocampal system contains populations of neurons that encode an animal’s position and velocity as it navigates through space. These populations are named for variables that modulate their firing rates: “head-direction” (HD) cell firing rates are tuned for the angular position of the head (Taube et al, 1990), “grid” cell firing rates are periodically tuned for the animal’s spatial position (Hafting et al, 2005), “place” cell firing rates are non-periodically tuned for the animal’s spatial position (O’Keefe & Dostrovsky, 1971), “border” cell firing rates increase near environmental boundaries (Solstad et al, 2008; Savelli et al, 2008; Lever et al, 2009), “speed” cell firing rates increase in proportion with the animal’s running speed (Kropf et al, 2015; Hinman et al, 2016; Gois & Tort, 2018), and “theta” cell firing rates are temporally modulated by 4-12 Hz theta oscillations
Over 10 independent simulations with different behavior data, we found that decoding qqfrom theta cell firing rates and co-firing rates together was not more accurate than decoding from firing rates alone (Fig. 10C)
We showed that a population of spiking neurons can simultaneously convey information via two coding channels: a firing rate code (RR) conveyed by within-cell spike intervals, and a co-firing rate code (RṘ ) conveyed by between-cell spike intervals
Summary
The rodent hippocampal system contains populations of neurons that encode an animal’s position and velocity as it navigates through space In the literature, these populations are named for variables that modulate their firing rates: “head-direction” (HD) cell firing rates are tuned for the angular position of the head (Taube et al, 1990), “grid” cell firing rates are periodically tuned for the animal’s spatial position (Hafting et al, 2005), “place” cell firing rates are non-periodically tuned for the animal’s spatial position (O’Keefe & Dostrovsky, 1971), “border” (or “boundary”) cell firing rates increase (or decrease) near environmental boundaries (Solstad et al, 2008; Savelli et al, 2008; Lever et al, 2009), “speed” cell firing rates increase (or decrease) in proportion with the animal’s running speed (Kropf et al, 2015; Hinman et al, 2016; Gois & Tort, 2018), and “theta” cell firing rates are temporally modulated by 4-12 Hz theta oscillations. If neural populations can simultaneously encode information in different ways, how should information about the world be distributed among different coding channels?
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