Irreversible behavior drives neural flows in the hippocampus

TL;DR

The paper addresses how irreversibility in neural activity relates to irreversibility in behavior by examining hippocampal place-cell dynamics as a mouse moves through a virtual environment. It quantifies neural irreversibility with time-delayed cross-correlations $C_{ij}(tau)$ and the aggregate flow $Sigma(tau)$, showing that place cells drive strong, nonreversible neural flows that mirror physical movement. A minimal three-parameter model with velocity $v$, diffusion $D$, and place-field width $sigma$ reproduces the key features, including a peak in irreversibility at $tau^*$ and diffusion-driven decay, with $tau^* \approx 2.7$ s and $sigma \approx 7$ cm in the data. These results provide a mechanistic link between symmetry breaking in the brain and behavior, offering a compact framework with testable predictions for how external variables shape neural irreversibility.

Abstract

In the brain, neural activity undergoes directed flows between states, thus breaking time-reversal symmetry. At the same time, animals also exhibit irreversible flows between behavioral states. Yet it remains unclear whether -- and how -- irreversibility in the brain relates to irreversibility in behavior. Here, we explore this connection in the hippocampus, where neural activity encodes physical location. We show that hippocampal irreversibility can be quantified using the time-delayed cross-correlations between neurons. As a mouse moves along a virtual track, we find that physical flows through the animal's environment generate neural flows through its cognitive map. Strikingly, this neural irreversibility is explained by a minimal model with only three parameters: the average velocity of the mouse, the variance in this velocity, and the resolution of the neural encoding. Together, these results provide a mechanistic understanding of irreversibility in the hippocampus and shed light on the links between symmetry breaking in the brain and behavior.

Figures (8)

• Figure 1: Fig. 1 $|$ Flows between neural states in the hippocampus.a, Place fields for four hypothetical place cells spaced evenly around a circular track as a mouse runs with constant velocity and period $T$. b-d, Flows between neural states $C_{ij}(\tau)$ for different timescales $\tau$, with grey arrows indicating negligible flows. As the mouse advances along the track, flows progress from clockwise (b) to directly across the track (c) to counterclockwise (d). e, Firing probabilities for the hypothetical cells in a-d, defined by Gaussians (with uniform variance) spaced evenly along a four-meter track. f, Net flows $C_{ij}(\tau) - C_{ji}(\tau)$ from cell 1 to cells 2, 3, and 4 as functions of the normalized time delay $\tau/T$. g, Place fields for four neurons recorded experimentally from the hippocampus of a mouse as it runs along virtual track of length $L = 4$ m. h, Net flows $C_{ij}(\tau) - C_{ji}(\tau)$ from cell 1 to cells 2, 3, and 4 in g as functions of the time delay $\tau$.
• Figure 1: Fig. S\ref{['SIfig:1']}$|$ Neural flow with heterogeneous place fields and constant velocity.a, Synthetic place cells are defined by noisy place fields with random centers, widths, and overall firing rates. Example conditional firing probabilities for 40 such cells (left) and total neural flow $\Sigma(\tau)$ for $400$ cells (right). b, Synthetic place cells are defined by noisy place fields with constant widths, random firing rates, and centers concentrated near the midpoint of the track. Example conditional firing probabilities for 40 such cells (left) and total neural flow $\Sigma(\tau)$ for $400$ cells (right). In both panels, the firing rates for each neuron are normalized such that the sum across bins equals one. Total neural flows are computed using simulations with a mouse running at constant velocity $v = 10.2\,\text{cm/s}$.
• Figure 2: Fig. 2 $|$ Neural flow in the hippocampus across timescales.a, Total neural flow $\Sigma(\tau)$ across a population of $1485$ neurons in the hippocampus of a mouse running along a circular track (Methods).Gauthier-01Meshulam-01 Null values are computed for the same population, but with the activity time-series of each neuron shifted by a random length of time (Methods). b, Total neural flow $\Sigma(\tau)$ among the subpopulation of $462$ place cells and among the remaining $1023$ non-place cells.
• Figure 2: Fig. S\ref{['SIfig:2']}$|$ Total flow in simulated neural population. Total neural flow $\Sigma(\tau)$ computed by simulating $462$ place cells and $1023$ non-place cells. Mouse trajectory is generated by a biased random walk. Simulations use experimental parameter values $v=10.2\,$cm/s, $D=58\,\text{cm}^2$/s, and $\sigma=7\,$cm.
• Figure 3: Fig. 3 $|$ Mouse velocity determines period of oscillations in neural flow.a, Example of four place cells in our model, each with a place field defined by a Gaussian centered at a random location along a track of length $L = 4\,\text{m}$ with a common standard deviation $\sigma = 20\,\text{cm}$. b, Net flows $C_{ij}(\tau) - C_{ji}(\tau)$ from cell 1 to the other three cells for a mouse moving at a constant velocity $v = 10\,\text{cm/s}$, yielding a period $T = 40\,\text{s}$. The net flows between all cells vanish for multiples of $\tau=\frac{T}{2}$, the half-period of the mouse's movement. c-e, Total neural flow $\Sigma(\tau)$ between $462$ synthetic place cells for mice running at different velocities $v$. For $v=10.2\,\text{cm/s}$ (d), the period of oscillations matches that measured in experiments (Fig. \ref{['fig:2']}).