Altered patterning of neural activity in a tauopathy mouse model

Abstract

Alzheimer’s disease (AD) is a complex neurodegenerative condition that manifests at multiple levels and involves a spectrum of abnormalities ranging from the cellular to cognitive. Here, we investigate the impact of AD-related tau-pathology on hippocampal circuits in mice engaged in spatial navigation, and study changes of neuronal firing and dynamics of extracellular fields. While most studies are based on analyzing instantaneous or time-averaged characteristics of neuronal activity, we focus on intermediate timescales—spike trains and waveforms of oscillatory potentials, which we consider as single entities. We find that, in healthy mice, spike arrangements and wave patterns (series of crests or troughs) are coupled to the animal’s location, speed, and acceleration. In contrast, in tau-mice, neural activity is structurally disarrayed: brainwave cadence is detached from locomotion, spatial selectivity is lost, the spike flow is scrambled. Importantly, these alterations start early and accumulate with age, which exposes progressive disinvolvement the hippocampus circuit in spatial navigation. These features highlight qualitatively different neurodynamics than the ones provided by conventional analyses, and are more salient, thus revealing a new level of the hippocampal circuit disruptions.

I. INTRODUCTION

Alzheimer’s Disease (AD) is a devastating neurodegenerative condition that is extensively studied at multiple levels, from molecular, to cellular, to organismal [1–3]. It is particularly challenging to understand how all these levels connect and to identify which functional intermediaries link neural pathologies to cognitive deterioration. For instance, it is believed that $A\beta$-plaques and neurofibrillary tangles disrupt the synergistic coordination of circuit dynamics [4, 5]. However, their subsequent contribution to the observed behavioral symptoms of AD remain unclear [6–9]. Many studies of AD-related changes of spiking activity and synchronized extracellular field dynamics reveal disturbances, including alteration of neuronal firing rates [10, 11], slowing of brainwave rhythms [12, 13], reductions in signal complicacy [14], and increased epileptiform activity [15–20]. Despite these efforts, systemic insight into the circuit-level impact of AD pathologies is still lacking due to the prohibitive complexity of the network dynamics, sheer amount of interconnected elements, and intricacy of interactions which render detailed data analyses and realistic modeling nearly intractable.

On the other hand, this very intricateness begets simplification by bringing forth statistical aspects of circuit activity. As it turns out, large pools of spike trains and waveforms exhibit universal statistical properties that have generic, mathematical origins, independent from the underlying physiological mechanisms. The ways in which these statistics unfold in time open a new venue for examining circuit dynamics differences between normal and pathological brains.

In this study, we consider neuronal spike trains and waveforms of locally recorded extracellular field potentials (LFP) as basic observables characterizing circuit dynamics. We analyze these temporally extended entities without averaging, evaluating their instantaneous behavior, or decomposing into simpler constituents. Instead, we use certain morphological properties of data segments to obtain their integral descriptions at structural level, which opens a new narrative and creates new perspectives on the underlying physiological phenomena. As an illustration of our approach, consider the brainwaves illustrated on Fig. 1A, which are scaled to same mean amplitude and frequency range. Yet, they are visibly different: one could argue, e.g., that top waves are more regular, with stereotypical undulatory shapes, or perhaps more ordered. Similarly, the spike trains shown on the top of Fig. 1B are less cluttered, less haphazard and more uniform than their bottom counterparts. Surprisingly, these intuitive distinctions can be captured formally and used for quantifying neurodynamics [21]. In the following, we apply these methods to study hippocampal activity in a mouse model of tau pathology and extracted a number of constitutive, pathological deviations of their circuit activity.

FIG. 1. Patterns of neural activity in wild type (WT) and and mice affected by brain tauopathy.

A. LFP waves recorded in WT (gray trace) and tau (purple trace) mice, with their significant peaks and troughs marked by dots, boxed. Differences between the resulting patterns are apparent, although the waves are scaled to the same frequencies and amplitudes. The shapes of the waves are easily recognizable, e.g., the ones on the left, marked “$\theta$,” correspond to the $\theta$-waves (4 – 12 Hz). Would it be surprising if they were marked as “$\gamma$” (30 – 80 Hz) or “ripples” (150 – 250 Hz)? How surprising? Also note that tauopathic $\theta$-waveforms are somewhat less regular than the WT $\theta$-waveforms, whereas WTs’ $\gamma$- and ripple waveforms appear more cluttered than in tau-mice. Could these differences be attributed to random fluctuations of the waves’ shapes or should they be taken as signatures of qualitative changes? How to capture the morphological differences mathematically? B. Spike trains recorded from WT (gray) and tau (purple) interneurons also demonstrate different patterns, suggesting that tau-pathologies alter the flow of information exchange.

II. METHODS

Experimental procedures.

Spike and LFP data were recorded from the hippocampal CA1 area of healthy wild type (WT) and transgenic mouse models of tau pathology (rTg4510). rTg4510 mice which develop tau neurofibrillary tangles and neuronal loss similar to those observed in human tauopathies [22, 23]. The animals were trained in a familiar room to run back and forth on about 2 m long rectangular track for food reward. The daily recording procedure consisted of two 15-minute-long running sessions, followed by 15-minute sleep breaks. The LFP data was sampled at 2 kHz rate and the animals’ positions were sampled at 33 Hz with a resolution of approximately ±0.2 cm, by tracking two head-mounted color diodes. Further details on the surgery, tetrode recordings and other procedures can be found in [24, 25].

Computational procedures

Computational procedures are based on applying two complementary measures.

$\mathit{\lambda }$-score

$\lambda$-score, introduced by A. Kolmogorov, quantifies the “randomness” or “haphazardness” of patterns through their deviation from an expected mean trend (Fig. 2A). Remarkably, these deviations exhibit regular statistical behaviors, described by a universal probability distribution, $P\left(\lambda \right)$ (Fig. 2B, [26–29]). According to its structure, most patterns produce $\lambda$-scores confined between certain limits, e.g., about 99.7% of patterns have $\lambda$-scores between ${\lambda }^{-}=0.4$ and ${\lambda }^{+}=1.8$, and only 0.3% fall outside of these bounds. Thus, the patterns with $\lambda$-scores within that range can be qualified as “stochastically typical,” whereas those that fall outside of it are “atypical.”

FIG. 2. Pattern statistics.

A. Given a series of values, $X=\left\{x_1,x_2,\dots ,x_n\right\}$, e.g., a series of $n=19$ wave crests shown at the bottom, we build its empirical distribution—a staircase that makes a unit step up at each consecutive $x_i$. The slope of the staircase is defined by the mean trend (blue line), e.g. about eight $\theta$-peaks are expected every second. The $\lambda$-score of $X$ is the greatest deviation of its points from this trend, normalized by the sample size. B. The distribution of $\lambda$-scores, $P\left(\lambda \right)$, is universal and defines the impartial probability of a given pattern’s appearance. On average, $\lambda$-scores are close to ${\lambda }^{*}\approx 0.87$; patterns that closely follow the prescribed behavior produce small $\lambda \text{s}$, and those that deviate significantly from the mean trend have large $\lambda$-scores. About 99.7% of patterns score between ${\lambda }^{-}=0.4$ and ${\lambda }^{+}=1.8$ (pink stripe) and are hence “typical”, whereas patterns with small $(\lambda <0.4)$ or large $(\lambda >1.8)$ $\lambda$-scores are “atypical”. The selection of bounds is motivated by analogy with the Gaussian distribution (top panel), in which typical values are those that fall closer than $3\sigma$ from the mean (gray stripe, 99.7% of cases) and the atypical ones lay farther out (0.3%). C. Placing $n$ elements of $X$ around a circle, summing the squared arc lengths, and normalizing the result by the circumference yields $\beta \left(X\right)$. For periodic arrangements (red points) $\beta$ is small, $\beta \approx 1$, for “clustered” patterns (blue points) $\beta$ is large (up to $\beta \approx n$), and for generic layouts (green points) $\beta \approx 2—\text{a}$ surprising statistical universality. D. The distribution of $\beta$-values for a pattern, $X$, of length $n=30$: similar to $\lambda$-scores, typical $\beta$ values fall between specific bounds ${\beta }_{n=30}^{-}=1.4$ and ${\beta }_{n=30}^{+}=3.6$. The general form of $\beta$-distributions depends on the pattern’s size, as illustrated on Fig. M1D. E. Shown are $\lambda$ (top) and $\beta$ (bottom) dynamics, evaluated by “sliding” a 25-peak window along a $\gamma$-wave. The pink stripe represents the typical range of $\lambda \text{s}$ as on panel B (laid horizontally), and the blue stripe is the same as on panel D. F. An example of a “statistically mundane” pattern (green point on panel E, $\lambda =0.9$ and $\beta =1.9$) and patterns with small or large values of $\lambda$ and $\beta$ (red and blue points on $\text{E}$, respectively).

In practice, the mean trend of recurring neurophysiological activity is often easy to estimate, e.g., one can evaluate the mean rate of LFP oscillations by averaging the number of crests or troughs over sufficiently long periods—such as a running session. However, these trends are known to change with the animal’s physiological state. For instance, the LFP’s overall cadence alters between active movement and quiescence [30–32] (Fig. S1). Correspondingly, the “reference point” for computing the patterns’ statistics also changes. Taking these alterations into account allows for contextual $\lambda$-scores that produce more nuanced descriptions of circuit dynamics, discussed below.

$\mathit{\beta }$-score

$\beta$-score provides an alternative measure of stochasticity that emphasizes patterns’ orderliness (Fig. 2C). As shown in [27–29], nearly periodic, ordered patterns of $n$ elements produce smaller $\beta$-values (the minimal value, $\beta =1$, is produced by a strictly regular, periodic pattern). Clustering patterns yield larger $\beta$-values: the maximum, $\beta =n$, is reached when all elements lump together. As it turns out, impartially scattered patterns produce $\beta$-scores close to 2—as a matter of another surprising universality [21, 27].

Curiously, the shapes of the $\beta$-distributions, $P_n\left(\beta \right)$, albeit $n$-dependent, are similar to the shape of Kolmogorov distribution, $P\left(\lambda \right)$, in one important aspect: they all have a dominant “hump” and rapidly decaying tails (Fig. 2D). Moreover, all $\beta$-distributions have similar modes and means, that converge to ${\beta }^{*}\approx 2$ as the sample size increases (Fig. M1). One can therefore specify limits, ${\beta }_n^{-}$ and ${\beta }_n^{+}$, that confine the “typical” $\beta$-scores and exclude the “atypical” ones. For instance, ${\beta }_{30}^{-}\approx 1.4$ and ${\beta }_{30}^{+}\approx 3.6$, confines 99.7% of patterns containing $n=30$ elements (Fig. 2D).

Dynamics of stochasticity

Dynamics of stochasticity can be computed by evaluating the $\lambda$ - and $\beta$-scores for local data segments, e.g., for waveforms or spike trains contained in a time window of width $L$, centered at time $t$. As the window shifts forward in time, this “snapshot” of the data evolves, yielding time-dependent haphazardness, $\lambda \left(t\right)$, and orderliness, $\beta \left(t\right)$, that describe pattern changes. We emphasize here that circuit dynamics can drive the brain waves into assuming highly improbable waveforms, characterized by very low probabilities of accidental appearance. For example, periodic patterns are too orderly to happen by chance, but they can be enforced by limit cycles in the network’s phase space. In the following, we detect qualitative changes in the hippocampal dynamics by identifying atypical network patterns.

In order to construct $\lambda \left(t\right)$ and $\beta \left(t\right)$ dynamics empirically, one can either use a time window of fixed width, shifting it by a pre-specified time step, or adapt the width at each step, so that each window contains a pre-specified number of spikes or LFP peaks (Fig. S2). Numerically, these algorithms differ only marginally, but they catch different aspects of the patterns’ statistics. Intuitively, the first method captures changes in discretized “physical” time, and the second method follows the alterations relative to the network’s own tempo of activity. In the following, we analyze the dynamics of LFP patterns using the latter approach, to highlight pattern changes with respect to the hippocampal network’s own ebb and flow.

III. RESULTS

We used two groups of mice: “young” $\left(Y\right)$ and “old” $\left(O\right)$ animals, 2.4 – 3.8 and 7 – 9 months of age respectively, and studied the patterns of their neuronal spiking and principal brain waves. There was significant histpathological difference between old WT and tau hippocampi, but not in young mice, including cortical thinning in old tau mice despite immunohistological confirmation of abundant abnormal tau protein in both young and old tau brains (for details see [25]). On average, it took the mice 15 seconds to traverse the track (Fig. 3A), which included lapsing over the straight segments, turning around the junctions, and pausing at the food wells (Fig. 3B). To capture the dynamics of circuit activity in the context of ongoing behavioral and physiological states, we studied patterns that lasted about $L\approx 2\text{ sec}$ (thrice shorter than in [21] for improved temporal resolution), which are long enough to produce stable scoring of waveforms and spike trains.

FIG. 3. Locomotion.

A. No significant difference in the times of lapping from one food well to the other, for all age groups and phenotypes $(p=0.42)$. A typical lap takes young WT males $\left(Y_{♂}^w\right)$ 10 sec, young tau-males $\left(Y_{♂}^{\tau }\right)$ 17 sec, old WT males $\left(O_{♂}^w\right)$ 19 sec, old tau-males $\left(O_{♂}^{\tau }\right)$ 15 sec, old WT females $\left(O_{♀}^w\right)$ 10 sec, and old tau-females $\left(O_{♀}^{\tau }\right)$ 18 sec. B. The gray lines trace the mouse’s runs between top and bottom food wells, $F_b$ and $F_t$ (red dots), during one recording session. Behaviorally, inbound trajectories (horizontally aligned quadrilateral) and outbound trajectories (skewed quadrilateral) are different, e.g., the animals tend to turn slowly around the top right corner and dash to $F_t$, while $F_b$ is approached more leisurely.

$\theta$-rhythm

$\theta$-rhythm (4 – 12 Hz) plays major roles in spatial memory, cognition, movement and other phenomena [33–39]. AD-induced alterations of $\theta$-rhythmicity were reported in many studies, based on analyzing instantaneous and averaged parameters of neural activity [40, 41]. We hence inquired whether tau-pathologies also affect the patterning of $\theta$-waveforms, to which end we evaluated their haphazardness $\left({\lambda }_{\theta }\right)$ and orderliness $\left({\beta }_{\theta }\right)$ scores in both phenotypes, and followed their dynamics.

We noticed two immediate properties in the WT-patterns that are absent in the tau-mice, despite the apparent similarity of their $\theta$-rhythms: 1) coupling between haphazardness of ${\theta }^w$-waveforms and the animals’ speed, and 2) changes of ${\theta }^w$-patterns between activity and quiescence (Fig. 4A,B). During rapid moves, the stochasticity scores are low, ${\lambda }_{\theta }^w=0.232\pm 0.001,{\lambda }_{\theta }^{\tau }=0.238\pm 0.001,p<0.001$, much lower than the Kolmogorov mean $\left({\lambda }^{*}\approx 0.87\right)$, and ${\beta }_{\theta }^w=1.204\pm 0.001,{\beta }_{\theta }^{\tau }=1.198\pm 0.001,p<0.001$, which barely exceeds the minimal value (Fig. 4E). The tiny probabilities of such values (e.g., $\Phi (\lambda \le 0.23)\approx 8.11\times {10}^{-10},{\Psi }_{16}(\beta \le 1.2)\approx 6.74\times {10}^{-4}$, Fig. M1C) show just how rare nearly-periodic patterns are among all possible waveforms. During slowdowns and quiescence, patterns randomize (stochasticity scores grow), as reported in [21].

FIG. 4. Haphazardness of $\theta$-waveforms referenced to different physiological contexts.

The dark red $\left(\lambda \right)$ and the dark blue $\left(\beta \right)$ points in all panels represent stochasticity scores evaluated during fast-running periods. One such period is highlighted by the vertical black box for each phenotype. The yellow $\left(\lambda \right)$ and the light blue $\left(\beta \right)$ points correspond to slow motions and quiescence. Prolonged quiescence is emphasized by gray-shaded backgrounds. A. The $\lambda$-score computed relative to the $\theta$-rate averaged over the entire running session, closely follows the animal’s speed (gray trace) during runs and dissociates from it during quiescence in WT mice (left). In tau-mice (right), coupling with speed is weaker. During prolonged quiescence, the $\theta$-patterns randomize: $\lambda$-values fall into the generic range, $0.4<\lambda <1.8$ (pink stripe same as on Fig.2B). B. ${\lambda }_{\theta }^w$-score assessed relative to the ${\theta }^w$-rate during active runs shows strict adherence with expected trend during speed ups and increases during slowdowns. In contrast, ${\lambda }_{\theta }^{\tau }$-score for tau-mice appear unaffected by the change in reference. C. Relative to quiescence, the adherence of ${\lambda }_{\theta }^w\left(t\right)$-dynamics to speed is even tighter than relative to global mean (panel A), while ${\lambda }_{\theta }^{\tau }$-score remains unchanged in both frames of reference. D. If $\theta$-rate is assessed relative to movement during movement and relative to quiescence during quiescence, then ${\theta }^w$-patterns get atypically regular during runs but remain as randomized during quiescence as before, which suggests an unbiased, context-free stochasticity of the latter. Haphazardness of ${\theta }^{\tau }$-patterns once again remains indifferent to behavior—note the similarity across the right A-D panels. E. The ${\beta }^{\theta }$-scores do not depend on the choice of reference behavior.

The $\theta$-patterns’ haphazardness scores discussed above were evaluated relative to the mean oscillatory rates observed over the entire running session, ${\bar{n}}_{\theta }^w\approx 8.3,{\bar{n}}_{\theta }^{\tau }\approx 8.1$ peaks per second. On the other hand, it is also well-known that not only the amplitude, but also the mean rate of $\theta$-rhythmicity changes noticeably between activity and quiescence. Hence, we inquired how would $\theta$-stochasticity be affected by taking the trending changes into account, and computed two $\lambda$-scores: one referenced to the mean rhythm exhibited during active explorations (${\bar{n}}_{\theta }^w\approx 8.6,{\bar{n}}_{\theta }^{\tau }\approx 8.5$ peaks per second, Fig. 4B), and the other referenced to the mean oscillatory rate over the quiescent periods (${\bar{n}}_{\theta }^w\approx 7.9,{\bar{n}}_{\theta }^{\tau }\approx 8.2$ peaks per second, Fig. 4C), for each phenotype. The results demonstrate that the correspondence between a pattern’s “ongoing haphazardness” and the animals’ speed, reported in [21], is manifested most clearly relative to quiescence. In the “moving frame of reference,” i.e., relative to the rate produced during active moves, $\lambda$-scores are low during runs (foreseeably, since now these patterns are expected by design), with the mean value ${\bar{\lambda }}_{\theta }^w\approx 0.125$, and grow more than twice, to ${\bar{\lambda }}_{\theta }^w\approx 0.28$, during slowdowns. In other words, relative to quiescence, the faster the animal moves, the less anticipated, more haphazard $\theta$-waveforms s/he generates, whereas relative to activity, such waveforms are stipulated—the chance of cycling squarely at the expected mean rate is vanishing $\Phi (\lambda \le 0.125)=2.5\times {10}^{-33}$. Note here that $\beta$-scores do not depend on the “reference frame,” i.e., orderliness is always impartial.

In contrast, the hippocampi of tau-mice produce much less structured patterns in both reference frames. Despite some difference in the mean oscillatory rates during active movement and quiescence (8.2 vs. 8.5 peaks per second respectively, Fig. S1), the tau-associated $\theta$-rhythm produces same ${\lambda }^{\tau }$-dynamics, whether it is referenced to quiescence or to movement. Unlike the speed-coordinated ${\theta }^w$-patterns, ${\theta }^{\tau }$-patterns largely ignore the speed dynamics, regardless of reference trend. Even referencing to the ongoing, instantaneous rate reveals no behavioral dependence of the ${\theta }^{\tau }$-stochasticity, which only increase disorder (${\beta }^w\approx 1.17\text{ vs}.\left.{\beta }^{\tau }\approx 1.20,p<0.001\right)$.

This stark contrast with the behaviorally contingent $\lambda$-scores of WT mice exposes a curious dissociation of tauopathic network activity from behavior (Fig. 4B–D, right panels). These effects are particularly salient in old animals, which may be due to the net burden on the animal’s physical abilities, as evidenced by lower speed, frequent pausing, etc. (Fig. 5D, [43–45]). However, weakened coupling of $\theta$-waveforms to speed and acceleration are also present in young tau-mice, who do not exhibit locomotive idiosyncrasies (Fig. 5C,D). In fact, there is a highly significant drop of the mean stochasticity scores in all tau-mice’s (except for the haphazardnesses in $O_{♂}$ mice)—a feature that clearly separates the two phenotypes (Fig 5E).

FIG. 5. -patterning and AD progression.

$\theta$ A. During lap running, the haphazardness of ${\theta }^{\omega }$-waveforms in young mice shows coupling to speed (gray line). Prolonged quiescence (gray bands) diversifies ${\theta }^w$-patterns. The horizontal pink band shows the range of “typical” ${\lambda }_{\theta }^w$-scores, same as on Fig. 2B. The middle panel shows the dynamics of orderliness of ${\theta }^w$-patterns. Blue stripe outlines the domain of generic ${\beta }_{\theta }^w$-values. During fast moves, $\theta$-waves are close to periodic (${\beta }_{\theta }^w\approx 1.1$) and slightly more disordered during protracted rest. B. In the 9-month old WT mice, ${\theta }^w$-waveforms are similar to those in young mice: quasiperiodic (low ${\beta }_{\theta }^w$), adherent to the mean (low ${\lambda }_{\theta }^w$), coupled to speed during lap running, randomizing during quiescence, and disordering during slowdowns. C. In young tau-mice, ${\theta }^{\tau }$-patterns are more haphazard (higher ${\lambda }_{\theta }^{\tau }$), but strangely, less disordered (${\beta }_{\theta }^{\tau }$ bottom panels) and do not discriminate between the running and the resting states. D. Old tau-mice exhibit stronger discordance between ${\theta }^{\tau }$-patterning and locomotion. E. There is a significant difference between the mean $\lambda$s in $Y_{♂}(n^w=5,n^{\tau }=4\text{ mice})$ and $O_{♀}(n^w=4,n^{\tau }=5\text{ mice})$ cohorts. Orderliness of $\theta$-patterns differs significantly between all animal groups. F. LCSS distance between ${\lambda }_{\theta }$ and speed, as well as between ${\beta }_{\theta }$ and acceleration, is significantly larger in tau-mice. G. Healthy mice demonstrate spatial specificity of $\theta$-patterns, consist between laps. In contrast, unsystematic layout of ${\theta }^{\tau }$-waveforms begins prior to locomotive dysfunction in $Y^{\tau }♂$ mice and grows with age (data shown for $n^w=5,n^{\tau }=6O_{♂}^{\tau }$ animals).

Similarity between stochasticity dynamics, speed and acceleration

Similarity between stochasticity dynamics, speed and acceleration can be quantified using the Longest Common Sub-Sequence (LCSS) technique, which allows aligning two profiles through a series of local stretches [46–48]. This measure is robust, as it avoids excessively irregular portions of the data series, is defined in relative terms (percentage difference between the compared functions) and is intuitive. For example, there is no LCSS difference between properly aligned sinusoids, e.g., for $f_1=\text{sin}\left(x\right),f_2=2\text{sin}\left(x\right)$ and $f_3=\text{sin}\left(2x\right)$, one gets $D\left(f_1,f_2\right)=0$ and $D\left(f_1,f_3\right)=0$, even with some noise added (Fig. M3A), while combinations of distinct sinusoids exhibit differences (Fig. 6). In other words, LCSS accounts for qualitative, essential mismatches between profiles, ignoring trivial shifts, stretches, and jitters (Fig. M3B).

FIG. 6. Locomotion.

A. LCSS distance between $f_1=\text{sin}\left(x\right)$ and $f_2=\text{cos}\left(x\right)$ is $D\left(f_1,f_2\right)=1.4\%$, which reflects the horizontal adjustments required to match the two sequences. B. LCSS distance between $f_1=\text{sin}\left(x\right)$ and $f_4=\text{sin}\left(x\right)+\text{sin}\left(2x\right)$ is more than six times higher, $D\left(f_1,f_4\right)=9.5\%$, due to the increased mismatch in the functions’ shapes. Shown is the best match achieved after optimal horizontal and vertical scalings and alignments.

With this in mind, the mean LCSS separation between the $\theta$-haphazardness and speed, $s\left(t\right)$, is twice as large in tau-mice than in WT mice (Fig. 5F). Likewise, the dissimilarity between $\theta$-orderliness, ${\beta }_{\theta }^w\left(t\right)$, and acceleration, $a\left(t\right)$, is about twice larger in tau-mice. In comparison, the Fourier power of the $\theta$-band and its frequency drop by ~27% and ~5% respectively ($P^w=0.92\text{ vs} P^{\tau }=0.67,p=0.362$, and $f^w=8.9\text{ vs }{f}^{\tau }=8.5\text{ Hz},p=0.041$, Fig. S5). In other words, changes in $\theta$-patterning are much more expressive than the changes captured by spectral analyses.

Spatial maps of stochasticity

Spatial maps of stochasticity are produced by associating the $\lambda \left(t\right)$ and $\beta \left(t\right)$ scores with the mouse’s ongoing position [21]. As shown on Fig. 5G, healthy mice, both young and old, show location-specific $\theta$-patterning, reproduced consistently between laps. Close to the food wells, ${\beta }_{\theta }^w$ grows, marking a disordering of the ${\theta }^w$-waveforms, whereas the quiescence-referenced ${\lambda }_{\theta }^w$ decreases, indicating that ${\theta }^w$-wave recovers its expected behavior as the mouse slows down and pauses to eat. Higher $\lambda$-values at the corner nearest to the top food well occur as the mouse arrives to $F_t$, as opposed to when it departs from it, which marks qualitative changes produced at the inactivity onset. Likewise, ${\beta }_{\theta }^w$ maps also show higher values as the mouse transitions from movement to quiescence (Fig. 5G). From the quiescence-referenced perspective, patterns randomize further away from the food wells, in the outer expanses of the track, where ${\lambda }_{\theta }^w$ increases and ${\beta }_{\theta }^w$ drops, indicating the appearance of orderly, but offbeat (relative to reposing expectations) trains of $\theta$-peaks. In either case, the stochasticity maps of WT mice consistently highlight behaviorally significant locations along the animal’s trajectory.

In contrast, old tau-mice lose these properties altogether: both ${\lambda }_{\theta }^{\tau }$ and ${\beta }_{\theta }^{\tau }$ become unanchored to the location and scatter arbitrarily along the animal’s path (Fig. 5H). Even the three-month-old tau-mice, who do not exhibit perceptible changes in lap running behavior, already have blurred maps of $\theta$-waveforms, which suggests that tau-disturbance of circuits begins before discernible locomotive abnormalities. These phenomena are even more apparent on the linearized spatial maps (Fig. S6), highlighting the failure of tau-mice to follow the spatial context, which may contribute to spatial cognition and memory dysfunction in the brains of tau mice. In particular, the coupling between ${\lambda }^w$-stochasticity and the speed exhibited by WT mice as they approach the food wells is absent in the tau-mice, which may indicate that the former anticipate forthcoming quiescence and food more than the latter (Fig. S4).

Place cell activity.

The space-specific LFP waveforms in WT mice cannot be explained naively via location-specific firing of the hippocampal principal neurons [49, 50]. First, the layout of place cells in the hippocampus is not topographic, i.e., close principal neurons may respond to far-apart place fields, and vice versa, cells with proximate place fields may lie far from each other in the network, and therefore rarely co-contribute to the field detected at a given electrode’s tip [51–54]. Second, although the fields’ layout—the place field map—controls the order of firing, it does not define how the spike trains intersperse, i.e., the overall patterning of spikes arriving from different cells. Furthermore, since place cells’ firing is modulated by the mouse’s location and speed, i.e., is spatially and temporally nonuniform, it is unclear which aspect of a given cell’s spiking should be attributed to its own operational stochasticity, and which part is due to the animal’s behavioral variability. On the other hand, an ensemble of cells, whose fields jointly cover the track, provide a roughly continual spiking flow that allows, e.g., tracking the animal’s position in real time [55–58]. Correspondingly, spike patterning in such a flow can be investigated in the same vein as the series of peaks in waveforms.

We studied ensembles of place cells recorded during a single running session, with place field maps shown on Fig. 7A, and obtained the spike trains’ stochasticity dynamics illustrated on Fig. 7B. Despite the limited number of simultaneously recorded cells, the scores ${\lambda }_P^w$ and ${\beta }_P^w\left(t\right)$ recovered in WT mice trace out a tight motif, pointing at a well-defined, dynamic coupling between spiking and locomotion. In other words, spike trains spanning two-second windows (2 – 3 place fields) yield stochastically consistent spike flow, within the limits of generic haphazardness and the orderliness.

FIG. 7. Spike stochasticity.

A. Place fields of simultaneously recorded 9-month WT (left) and 9-month tau-mice (right) place cell ensemble jointly cover the track. Each dot represents a spike, color corresponds to a particular place cell, clusters of similarly colored dots represent place fields. The WT-fields are clearly defined, the tau-fields are smeared. B. In WT, the combined spike flow produced by the ensemble of all recorded place cells forms a tight motif. The values are stochastically generic at the lower food well, $F_b$, and along the track itself. At the other food well, the spike trains become deviant and exhibit high clustering $\left({\beta }_P^w\approx 15\right)$, indicating that, at $F_t$, place cells are engaged in offline, bristle, autonomous activity. These dependencies are not observed in tau-mice, implying that their rapid spiking activity is subdued. Note the greatest upswings of $\beta$ are dark blue, i.e., occur as the mouse is actively running. Below spike times are marked by by vertical streaks, colored as dots on panel A. C. The maps of haphazardness (${\lambda }_P$, left pair of maps) and orderliness (${\beta }_P$, right pair) for WT and tau-mice reveal a structural deterioration of place cell activity—segments of generic and atypical spike patterns intersperse throughout the trajectory. D. Haphazardness of interneuronal spike trains in fast running $Y_{♂}^w$ mice is coupled with speed during runs, and rises conspicuously during quiescence (${\lambda }_I^w\approx 10$), thus indicating either an implausible-by-chance deviation of firing from the ongoing trend or a trend change. The spike trains (bottom panels) become sparser and cluster more during the rest periods $\left({\beta }_I^w\approx 4\right)$, but then replete and regularize $\left({\beta }_I^w\approx 1\right)$ during active laps. Older WT mice show similar spike patterns, but on a larger scale, from ${\lambda }_I^w\approx 1.5$ and ${\beta }_I^w\approx 1$ during running, to ${\lambda }_I^w\approx 10$ and ${\beta }_I^w\approx 5$ during quiescence, which suggests that the increase of spiking stochasticity range is likely to be cause by de-tuning. E. In tau-mice, interneurons produce generic spike trains at all times—both ${\lambda }_I^{\tau }$ and ${\beta }_I^{\tau }$ are in their respective “typicality bands,” i.e., the ordinance of tau-spiking is akin to random re-shuffling. F. Interneuron spike trains differ significantly between WT and tau-mice, in all demographic groups. G. Regardless of age or sex, the haphazardness and orderliness of WT interneurons responded to behavioral context more than tau-interneurons. H. The spatial patterning of interneuron spike trains in WT mice is modulated by its position. I. Tau-interneurons demonstrate a loss of spatially localized spike patterning

When the animal leaves the top food well (note the rapid approaches to $F_t$ along the vertical protrusion), ${\lambda }_P^w$-stochasticity increases to very large values, ${\lambda }_P^w\approx 10$, which cannot occur by chance $\left(\Phi \right(\lambda \ge 10)\approx 0$, Fig. 7B,C). This implies that the spiking trend changes qualitatively, as expected: during runs, place cell firing is triggered by the animal’s physical traversal through the place fields, whereas in quiescence spiking is produced by “offline,” endogenous network activity [59–63]. The latter firings include replays or preplays of spiking sequences at a rapid timescale, repeated spiking of individual cells, or a combination these activities, which impact the stochasticity scores [69–76]. Indeed, a replay may last between a couple of dozens to a couple of hundreds of milliseconds, which is comparable to the characteristic interval between spikes triggered by the animal’s physical passing through place fields [60, 64–68]. These brisk, endogenous network activities clutter the overall spike patterns and drive the ${\beta }_P$ and ${\lambda }_P$ scores up (Figs. 8 and M2). During active movements, the spike disorderliness may also get high, e.g., in the case illustrated on Fig. 7B, ${\beta }_P^w\approx 5$ as the mouse approaches food at the top arm, which also indicates heightened endogenous network activity.

FIG. 8. Clustering boosts both $\mathit{\beta }\mathbf{ }\mathbf{a}\mathbf{n}\mathbf{d}\mathbf{ }\mathit{\lambda }$.

A. To achieve high values of $\beta$, the sequence must cluster. As an example, a unit circle divided into 4 segments covering $Q_i=1\%,80\%,1\%,18\%$ of the circle, and containing, respectively, $n_i=\mathrm{2,2},\mathrm{4,7}$ uniformly spaced points that jointly produce $\beta =4.9$. B. By moving a single point from in the sequence from $Q_2$ to $Q_4$ (black dot with red outline), $\beta$ increases to 9.7.

Tauopathic place cell spiking also changes between generic and cluttering, but it lacks the behavioral specificity of WT place cells. In particular, the occurrences of patterns with atypically high ${\lambda }_P^{\tau }$ and ${\beta }_P^{\tau }$ are not tuned to specific physiological states (Fig. 7B), pointing at circuit-level disassociation of collective place cell spiking, both during active behavior and offline [77–79]. Thus, not only the individual tau-cells’ spatial spiking (Fig. 7A), but also the temporal pattern of the ensemble place cell activity is disrupted (Fig. 7B).

The spiking stochasticity maps also illustrate the disruption of place cell ensemble activity in tauopathy (Fig. 7C). In WTs, the distribution of ${\lambda }_P^w$-values is place-specific, with and lows occurring in the same positions along the mouse’s trajectory. Curiously, the WT spike patterns also discriminate between the two food wells, exhibiting higher atypicality at one of them. On the other hand, the place cells of tau-mice produce sporadic, stochastically generic patterns anywhere on the animal’s path, and react to both food wells similarly.

Interneurons

Interneurons regulate the hippocampal circuit through inhibition, shaping $\theta$-rhythmicity and other brain waves, in synchrony with the excitatory outputs of principal cells [80–86]. Although the interneurons spike perpetually and at higher frequencies than the $\theta$-waves oscillate (~20 Hz vs. ~8 Hz, we found their pattern dynamics to be qualitatively similar. First, the haphazardness of interneuronal spike trains, ${\lambda }_I^w$, is clearly coupled to speed, and their orderliness, ${\beta }_I^w$, follows the acceleration (Fig. 7E). Curiously, spike trains visibly sparse out during prolonged rest periods, at which times their scores, ${\lambda }_I^w$ and ${\beta }_I^w$, attain very high, improbable values, indicating trend changes relative to active running (Fig. 7D).

Also, the pattern range is wider: during active explorations, spike trains are stochastically generic, unlike the nearly-periodic $\theta$-waves. This suggests that, during lapping, generic interneurons’ spiking contributes to the nearly periodic patterning of ${\theta }^w$, and during quiescence, clustered spike trains drive spasmodic ${\theta }^w$-patterns. Note that, since neuronal spiking is coupled to $\theta$-phase, $\theta$-disturbances may in turn randomize spiking.

In contrast, neural stochasticity in tau-mice lingers within typical range, both in activity and in quiescence (Fig. 7E). During the former, the stochasticity dynamics alienates from locomotion $\left(D\left({\lambda }_I^{\tau },s\right)\approx 2D\left({\lambda }_I^w,s\right);D\left({\beta }_I^{\tau },-a\right)\approx 4D\left({\beta }_I^w,-a\right)\right.$, Fig. 7G). While the WT mice reproduce interneuronal spiking patterns lap after lap, tau-spikes are largely emancipated from the mice’s position, which by itself may be a source of behaviorally incongruent ${\theta }^{\tau }$-patterning (Fig. 7H). In summary, WT and tau-associated neuronal spikings are manifestly different: the former are location-specific and well-tuned to speed, while the latter are scattered all over the track and generic.

$\gamma$-rhythm

$\gamma$-rhythm (30–80 Hz) is the second key LFP component that directs information flow in the hippocampal network, controls coupling to sensory inputs, synaptic plasticity, mediates attention, and is involved in a score of other phenomena [87–91]. Previous studies have reported spectral alterations of the $\gamma$-rhythms in animal models of AD even before plaque formation [92, 93], and linked aberrant $\gamma$-activity to cognitive dysfunction [94]. Indeed, our wavelet scalograms show stronger $\gamma$-power (40–80 Hz) in WT mice, particularly during periods of active track running between the food wells, while tau-mice do not produce salient $\gamma$ oscillations (Fig. S5). Pattern analyses allow detailing these differences in much more detail.

To compare $\gamma$-waveforms in WT and tau-mice, we extracted patterns of $\gamma$-troughs that fit into our selected temporal window, comprised of about ${\bar{n}}_{\gamma }^w\approx 59$ and ${\bar{n}}_{\gamma }^{\tau }\approx 57$ elements. The first observation, compliant with [21], is that $\gamma$-waveforms in WT animals are much more variegated than $\theta$-waveforms, as indicated by a wider range of the stochasticity scores (Fig. 9). Relative to quiescence, the ${\gamma }^w$-haphazardness (${\lambda }_{\gamma }^w$-score) consistently co-varies with the speed, while the orderliness, ${\beta }_{\gamma }^w$, drops to low values during the fast moves. Thus, as with the $\theta$-waves, $\gamma$-rhythmicity in WT mice has distinct running and quiescent dynamics, with different appearances in the two frames of reference (Fig. S7).

FIG. 9. -waveform dynamics.

A. In WT mice, ${\gamma }^w$-waveforms are, for the most part, stochastically generic, constrained within the typicality zones, but more diverse than the $\theta$-waveforms (wider ${\lambda }_{\gamma }$- and ${\beta }_{\gamma }$-ranges). During active explorations, ${\gamma }^w$-patterns in $Y_{♂}^w$ mice show coupling to speed (gray trace) and complex dynamics during quiescence (gray bands). ${\beta }_{\gamma }^w\left(t\right)$-scores show that ${\gamma }^w$-waves are close to periodic during activity and disorganize during quiescence, especially at the food wells. B. Surprisingly, in tau-mice, the dynamics of $\gamma$-stochasticity is similar: haphazardness of ${\gamma }^{\tau }$-troughs is also coupled with speed and elevated during quiescence. The orderliness, ${\beta }_{\gamma }^{\tau }\left(t\right)$, likewise, drops during runs and rises to generic levels, ${\beta }^{\tau }\approx 2$, when s/he stalls. C. Mean ${\lambda }_{\gamma }$ and ${\beta }_{\gamma }$ are significantly lower in tau-mice, in all groups-once again, subdued stochasticity is a signature of tauopathy. D. The LCSS difference between haphazardness and speed (left) and between orderliness, ${\beta }_{\gamma }^w$, and acceleration (right) in WT mice, is more than twice smaller than in tau-mice. E. Spatial maps show similar lap-consistent patterning of WT (left panels) and tauopathic (right panels) $\gamma$-rhythms.

Unexpectedly, $\gamma$-waveforms in tau-mice show similar behavior: the ${\lambda }_{\gamma }^{\tau }$-scores also reliably rise and fall with speed, covering about the same range of values, including the periods of prolonged quiescence (Fig. 9A,B). However, tau-haphazardness slightly distances from speed, $D\left({\lambda }_{\gamma }^{\tau },s^{\tau }\right)\approx 3D\left({\lambda }_{\gamma }^w,s^w\right)$, and the orderliness moves farther from the acceleration, $D\left({\beta }_{\gamma }^{\tau },-a^{\tau }\right)\approx 3D\left({\beta }_{\gamma }^w,-a^w\right)$ (Fig. 9D), which may reflect weaker hippocampal coordination of motor effort.

The spatial maps of $\gamma$-stochasticity also maintain consistency between laps, in all mice (Fig. 9E). Near the food wells, $\gamma$-waveforms in both WT and tau-mice assume shapes typical for quiescence, despite heightened disorder in this area (smaller ${\lambda }_{\gamma }^x$, bigger ${\beta }_{\gamma }^x$ values). Conversely, series of $\gamma$-troughs consistently become more haphazard and yet more orderly (take nearly-sinusoidal forms), as the mouse rounds the track’s corner furthest from the food.

Relative to the fast-moving mean, the story can be retold as follows: during runs, $\gamma$-waveforms tightly match with the pseudoperiodic moving trend (${\lambda }_{\gamma }^x$ drop), and during extended rest they scramble (${\lambda }_{\gamma }^x$ rises, Fig. S7B). In tau-mice, $\gamma$-waveforms show similar behavior-specific alterations, albeit more subdued than their WT littermates. The $\lambda$-maps further emphasize the dichotomy of $\gamma$-patterns between movement and quiescence.

The fact that $\theta$-waveforms in tau-mice are affected more than $\gamma$-waveforms also implies that neuropathology weakens coherence of $\theta$- and $\gamma$-patternings. A number of studies based on correlative analyses of $\theta$- and $\gamma$-waves’ instantaneous amplitudes, frequencies and phases [95–97], show that physiologically functional $\theta /\gamma$-comodulation in WT animals [98, 99] gets disrupted at early stages of AD [92, 100, 101]. Our results show similar effects at the level of patterns: the LCSS distance between $\theta$- and $\gamma$-haphazardness, $D\left({\lambda }_{\theta },{\lambda }_{\gamma }\right)$, are significantly larger in tauopathic than in WT mice (Fig. S8A). Curiously, the differences between and speed and $\theta$- and $\gamma$-haphazardness are comparable in WT mice of all ages and sexes, whereas in the older tau-mice, speed is weaker coupled to ${\theta }^{\tau }$- than to ${\gamma }^{\tau }$-waveforms, suggesting that ${\theta }^{\tau }/{\gamma }^{\tau }$ decoupling is due to deterioration of the former.

Ripple events

Ripple events $\left(R\right)$ are perturbations of the high-frequency (150 – 250 Hz) extracellular field oscillations, which reflect the dynamics of autonomous activity in the hippocampal network [102–105]. For example, $R$ are known to co-occur with replays and preplays, which indicates a connection with memory processing and offline cognitive activity [62, 63, 106–111]. Several mouse models of AD show disruptions of hippocampal rippling, including increases and decreases of ripple frequency, amplitude, phase alterations, as well as disrupted temporal profile, and even disappearance of the Sharp Wave Ripple (SWR) events [66, 17, 112, 113]. Yet, the overall structure of the LFP’s high frequency domain, as captured by wavelet and Fourier transforms, are fairly comparable between both phenotypes (Fig. S9), whereas pattern-level differences are distinct.

To evaluate these differences, we identified “splashes” of the ripple waves’ (amplitudes that exceeded two standard deviations from the mean) and selected series of these events that fall within our selected time window¹. The resulting $R$ patterns contained, on average, a similar number of items in WT and tau-mice (${\bar{n}}_R^w\approx 14$ and ${\bar{n}}_R^{\tau }\approx 16$ respectively², Fig. S3).

In accordance with [21], the range of WT stochasticity scores referenced to quiescence is wide, encompassing both strongly deviating and overly compliant patterns (Fig. 10A). The haphazardness of rippling in healthy mice, ${\lambda }_R^w$, exhibits clear coupling with speed (Fig 10 A,D), and counter-phase coupling with acceleration. At high speeds, $R^w$ series are nearly periodic, ${\beta }_R^w\approx 1$, and range from nearly-periodic to clustering (${\beta }_R^w\gtrsim 4$) during quiescence. In contrast, tau-mice exhibit a smaller assortment of rippling for all age and sex groups ((narrower range of ${\beta }_R^{\tau }$ and ${\lambda }_R^{\tau }$, opposite to spikes, Fig. 10B,C), and more than twice weaker coupling between orderliness and acceleration (Fig. 10D). Additionally, ${\lambda }_R^w$ is sensitive to changes of reference trend, while the tauopathic rippling patterns are indifferent to cross-referencing (Fig. S10). This loss of coherence between $R^{\tau }$-patterning and physiological state, speed or acceleration, suggests that functionality of rapid network dynamics is also compromised or lost in tauopathy: tau-rippling is akin to sluggish responding to random disturbances (generic-lowish ${\lambda }_R^{\tau }$, whereas WT ripples are driven by targeted activity (Fig. 8).

FIG. 10. Ripple event stochasticity.

A. The haphazardness of $R$-patterns in young WT mice (top panel) and old WT mice (bottom panel), is trending during inactivity and scrambles during runs, in a speed-coupled manner. The disorder is also high during quiescence (${\beta }_R^w\ge 2$), and nearly periodic during movement (${\beta }_R^w\approx 1$ at maximal speed). (continued) B. In tau-mice, $R$-patterns do not distinguish between moving and quiescent states, and are uncoupled from speed. Additionally, both orderliness and haphazardness remain much lower than in WTs and do not get atypical, indicating that tau-rippling is stochastically uneventful and unresponsive to moves or quiescence. C. WT $R^w$-patterns produce significantly higher $\lambda$- and $\beta$-scores, indicating a much wider range of patterns compared to tau-mice. D. On average, speed is twice closer to ${\lambda }_R^w$ than to ${\lambda }_R^{\tau }$, and acceleration is twice closed to ${\beta }_R^w$ that to ${\beta }_R^{\tau }$. E. Spatial maps of ${\lambda }_R^w$ and ${\beta }_R^w$ for both young and old mice reveal spatially specific patterning of $R$. In contrast, spatially scattered ${\lambda }_R^{\tau }$- and ${\beta }_R^{\tau }$-values indicate disorder and varied patterns throughout and between laps.

In terms of spatial maps, both young and old WT mice show clear lap-dependent $R$-patterning as well as a higher diversity of patterns at the food wells, while tau-mice ripple impartially, with scores deviating sporadically from the background (Fig. 10E,F, S10).

IV. DISCUSSION

Most studies focus on cellular AD pathologies or the associated cognitive changes, whereas circuit-level mechanisms of neurodegeneration receive less attention [1–3]. This is partly explained by the immense complexity of the hippocampo-cortical network, intricacy of its dynamics, and multitude of external inputs, which render detailed, deterministic, causal connections nearly intractable. Furthermore, understanding the mechanisms by which the individual neurons and synapses contribute to large-scale phenomena, such as the rhythmicity of extracellular fields, is complicated due to the preponderance of collective, emergent effects, such as spontaneous synchronization [114–118]. Additionally, concurring neuronal dynamics have different origins and functions. For instance, $\theta$-rhythms are generated by medial septal inputs and local interactions between interneurons and principal cells [42, 119], whereas $\gamma$-rhythms are produced via local ensemble activity and perisomatic inhibition [103, 120].

Remarkably, despite the differences in spatiotemporal scales, mechanisms and implementations, patterns of neural activity follow the same universal statistics described by Kolmogorov and Arnold distributions. In other words, the mathematical laws governing the probability of patterns’ appearance overrides the exhaustive physiological details, much like the sampling distribution of the means is always Gaussian, irrespective of the mechanisms that contribute individual inputs (Fig. 11). Consequently, time-variations of stochasticity scores, $\lambda \left(t\right)$ and $\beta \left(t\right)$, evaluated for continuously evolving waveforms and spike trains provide an impartial description of the circuit dynamics, emancipated from the minutiae.

FIG. 11. Statistical universality of patterns.

Normalized histograms of haphazardness ($\lambda$, pink) and orderliness ($\beta$, blue), evaluated for 1,000,000 of 25-point sequences of: A. $\theta$-peak fluctuations; B. $\gamma$-peaks; C. ripple events; D. interneuronal spikes. Dashed lines show the shapes of the theoretical Kolmogorov and Arnold distributions, scaled to the histograms’ heights. These results demonstrate, first, that the varieties of waveforms are broad enough to capture the distribution’s ranges and shapes in both WT and tau-mice. Moreover, these distributions hold true regardless of data source (i.e. phenotype, age, LFP, single neuron, etc.). In the case of $\gamma$-patterns and ripples, ${\beta }_{\gamma }$ and ${\beta }_R$ histograms deviate from the impartial $\beta$-statistics, due to larger proportions of cluttering waveforms. Data collected from 14 WT and 16 tau-mice, the spikes are recorded from 12 WT and 5 tau-interneurons.

An important advantage of the $\lambda /\beta$ stochasticity scoring is its intuitive transparency, that enables reasoning about neural activity in colloquial terms, focusing on structural regularities or peculiarities, e.g., atypical periodicity, excessive clustering, etc. Due to their universality, these quantities may potentially be actualized, i.e., represented explicitly in the brain, and used to guide system-level information exchange, movement coordination, memory encoding, retrieval and other phenomena.

Returning to the phenotype comparisons, generic differences between tau pathology and WT cases can be summarized as follows. While healthy mice exhibit well-tuned, purposeful, behavior-modulated LFP rhythmicity and spiking patterns, tau-mice show dissociation of neural activity from physiological and behavioral states. The way in which the hippocampal spiking is produced, modulated by the brain waves and imparted onto downstream networks is qualitatively altered by tau-pathology.

These observations are in line with previous studies demonstrating that compromised coupling between LFP rhythms and locomotion, loss of spatial and temporal fidelity of hippocampal neurons are key contributors to learning and memory impairments [100, 101, 121, 122]. We demonstrate that not only do tau-pathologies disturb individual neurons and rhythms, but they also scramble the overall spatiotemporal architecture of the hippocampal activity, which is saliently manifested. The morphological alterations illustrated on Fig. 1 may indeed be indicative of systemic alterations in circuit activity and can hence serve as signatures of neurodegeneration.

Significance.

We expose differences in WT and tau brains, emerging at the circuit level, using a novel, morphological perspective on neural activity. This approach allows identifying qualitative changes in spiking patterns and in extracellular field oscillations, that are not discernible through traditional time-localized or time-averaged analyses. In particular, analyses of activity patterns facilitates detection of neurodegenerative deviations, conspicuously linking their effects to behavior and locomotion, thus opening a new venue for understanding how the architecture of neural activity shifts from normal to pathological.