Preconfigured neuronal firing sequences in human brain organoids

Abstract

Neuronal firing sequences are thought to be the building blocks of information and broadcasting within the brain. Yet, when these sequences emerge during neurodevelopment remains unclear. Here, we demonstrate that structured firing sequences appear in spontaneous activity of human and murine brain organoids, both unguided and forebrain identity directed, as well as ex vivo neonatal murine cortical slices. We observed temporally rigid and flexible firing patterns in human and murine brain organoids and early postnatal murine somatosensory cortex, but not in dissociated primary cortical cultures. These results suggest that temporal sequences do not arise in an experience-dependent manner, but are rather constrained by a preconfigured architecture established during neurodevelopment. By demonstrating the developmental recapitulation of neural firing patterns, these findings highlight the potential of brain organoids as a model for neuronal circuit assembly.

Introduction

A growing body of experimental evidence supports the notion that intrinsic activity plays a central role in brain function, challenging the traditional Jamesian view that higher order function is an emergent product of sensory input¹. The mesoscale wiring of the cortex is dominated by recurrent, lognormally distributed networks², where only a small fraction of connections directly relay sensory input³. This skewed organization is thought to support the ability of neuronal assemblies to generate temporally structured spiking sequences^4–6. Sequential activity patterns represent discrete and temporally consolidated packets of neuronal activity, thought of being the basic building blocks of neural coding and information broadcasting within the brain⁷. In mature brain circuits, spiking sequences predict spatial navigation and memory in the murine hippocampus⁸, where ‘preplay’ encodes novel experiences from pre-existing sequence motifs^9,10 that arise before experience dependent representations form (e.g. before exploration beyond the nest)¹¹. In the murine visual cortex, evoked responses closely mirror spontaneous sequential patterns¹². Similar phenomena have also been reported in the human cortex, where the replay of sequences underlies episodic memory formation and retrieval¹³. Moreover, spiking sequences in the human cortex organize into a temporal backbone of rigid and flexible sequence elements that are stable over time and cognitive states¹⁴, support visual categorization tasks, and encode non-redundant information beyond latency and rate encoding¹⁵.

However, the emergence of spiking sequences during development is not yet well understood. During the third postnatal week, the murine hippocampus generates spiking sequences that resemble those that will later be produced during navigation in a linear environment¹¹. Importantly, these sequences emerge in an experience-independent manner and do not improve upon additional experience in the same postnatal week. Whether similar spiking sequences, potentially representing other forms of experience, exist in other brain areas or at earlier developmental stages remains an open question. The existence of such sequences would provide strong evidence in support of the notion that spiking sequences are not experience-dependent but are instead constrained by an innate architecture that is established during neurodevelopment¹⁶.

Brain organoids, three-dimensional stem cell derived models of the mammalian brain that recapitulate key facets of the anatomical organization and cellular composition found in the developing brain^17–19, represent an ideal system in which to examine intrinsic (i.e., sensory-independent) aspects of neurophysiological development. Neurons within brain organoids form functional synapses¹⁹ and establish spontaneous network activity^20,21. These self-organized neuronal systems contain cellular diversity and cytoarchitecture necessary to sustain complex network dynamics²² as evidenced by the expression of layer specific excitatory pyramidal neurons and inhibitory GABAergic interneurons^23,24. Brain organoids also generate local field potential oscillations (LFP) that mirror preterm EEG patterns²⁵, and have been used to model network dynamics associated with rare genetic disorders²⁶.

Here, we analyzed single-unit activity from four models of brain development: (1) human iPSC-derived brain organoids from two independent laboratories^22,27, (2) murine ESC-derived cortical organoids of dorsal forebrain identity, (3) ex vivo neonatal murine somatosensory cortex slices, and (4) dissociated two-dimensional primary cortical cultures^28,29. Across all models, we observed bursting dynamics on the order of 10² milliseconds, consistent with biophysical integration time constants that extend beyond single-neuron refractoriness^30,31. Within organoids and neonatal slices, a subpopulation of neurons generated non-random sequential firing patterns, referred to as backbone sequences¹⁴, which were absent in two-dimensional cultures. Backbone sequence-generating neurons occupied the tails of right-skewed lognormal firing rate and connectivity distributions. At the population level, activity partitioned into low-dimensional subspaces delineated by temporally rigid sequences, and higher-dimensional subspaces containing more flexible units. Finally, for stable and flexible computation, theory suggests that neural systems must exist near a regime called criticality, characterized by scale-invariant dynamics across timescales³². Using temporal renormalization group theory³³, we found organoids, slices, and two-dimensional cultures operate near criticality, with subsets exhibiting correlations spanning multiple timescales. These results indicate that brain organoids recapitulate preconfigured, experience-independent sequence dynamics while maintaining near-critical states, providing insight into organizational principles that underlie the neural code³⁴.

Results

Temporal dynamics of neuronal firing sequences in brain organoids

Using high-density CMOS-based microelectrode arrays²², we investigated the temporal dynamics of spontaneous neuronal activity across guided and unguided human and mouse brain organoids. Single-unit spike events revealed population bursts lasting several hundred milliseconds, followed by quiescent periods up to several seconds (Fig. 1A). Moreover, we observed that the distribution of firing rates follows a heavy-tailed, right-skewed lognormal distribution (n = 8, R² = 0.97 ± 0.04, Extended Data Fig. 1A–C). This represents one facet of functional activity conserved across brain regions and states in vivo³.

Figure 1. Temporal structure of spontaneous single-unit neuronal firing patterns during population bursts in human brain organoids.

(A) Raster plot of single-unit spiking (black dots) measured across the surface of a 500 μm thick human brain organoid slice, positioned on top of a microelectrode array. The population firing rate is shown by the red solid line. Population bursts are marked by sharp increases in the population rate. Burst peak events are denoted by local maxima that exceed 4x-RMS fluctuations in the population rate. The shaded gray regions denote the burst duration window as defined by the time interval in which the population rate remains above 10% of its peak value in the burst. (B) Top, the instantaneous firing rate of single-unit activity from panel A. Bottom, zoomed in view of the neuronal firing during population bursts reveals temporal segregation and contiguous tiling of the peak firing rate of single-unit activity. Here the subset of units that fire at least two times during the burst are shown, re-ordered for each burst individually based on the time at which the unit has its maximum firing rate during the burst period. (C) The population firing rate (gray lines) is plotted relative to the burst peak for 46 burst events measured across a three-minute interval for the same organoid. The mean value is shown by the solid line and the dotted lines represent 1 STD. (D) Burst durations are plotted from four different organoids. (E) The distribution of single-unit firing rate peak times relative to population burst peaks for the same organoids as in D. Box plots (panels D–E): boxes span the 25th–75th percentiles; the center line marks the median (50th). Whiskers extend to the most extreme values within 1.5× the interquartile range from quartile 1 and quartile 3. In violin plots, minima and maxima equal the lowest and highest observations; the shaded area shows the variable’s probability density.

Reordering single-units by the timing of their peak firing rate revealed sequential activation patterns during bursts (Fig. 1B). Bursts exhibited consistent rate profiles within organoids (Fig. 1C), with durations spanning timescales on the order of ≈ 10² milliseconds (Fig. 1D, Supplementary Fig. 1 C). A majority of units firing rates peaked in close proximity to the population burst maxima (Fig. 1E). These timescales align with spontaneous and evoked sequences in the murine⁴ and reptile cortex⁵, as well as during memory retrieval in the human cortex^13,14. Moreover, the dominant neuronal response time of sensory cortices peaks with similar constants across regions and species^30,35,36, suggesting a conserved temporal motif in cortical computation.

To assess stereotypy, we separated units into two classes. Backbone units were defined as those spiking in every burst (Fig. 2A, above dashed line), all other units were defined as non-rigid (below dashed line). Backbone units, residing in the high-firing tail of the lognormal distribution (Extended Data Fig. 1D), displayed stable temporal delays across bursts (Fig. 2B-C, Extended Data Fig. 2). Clustering bursts by their pairwise correlation matrix confirmed that backbone patterns were preserved across clusters, whereas non-rigid units varied substantially (P < 10⁻²⁰, linear mixed-effects model; Extended Data Fig. 3). Longitudinal recordings showed that the relative fraction of backbone units declined over development (Supplementary Fig. 2). This transition parallels the in vivo incorporation of inhibitory interneurons into maturing excitatory networks³⁷, also observed histologically in our human (Supplementary Figs. 3-4) and murine organoids (Supplementary Figs. 5-7).

Figure 2. Sequential activation patterns in human brain organoids generate a stereotyped temporal backbone.

(A) Single-units were divided into backbone and non-rigid units. Backbone units, defined as spiking at least twice in every burst, are plotted above the dashed line; non-rigid units are below. Within each group, units are ordered by their median firing peak time relative to the burst peak across all bursts. (B) Zoomed view of the backbone units across four bursts with the same unit order. (C) Average burst peak–centered firing rates from 46 burst events. Units maintain the same order A,B. Note the progressive shift in firing peak times relative to the burst peak and an increased spread of activity for units peaking later. (D) Spiking activity of three units is plotted over a fixed time window relative to burst event peaks. Rows represent spikes from a single burst. Two backbone units are shown with strong temporal alignment to the burst peak and one non-rigid unit with poor alignment. Heatmaps of burst-to-burst cross-correlations coefficients of the burst-centered firing rates from the units. (E) Backbone neurons consistently exhibited higher burst-to-burst correlation coefficients compared to non-rigid units (P < 10⁻¹⁶, two-sided linear mixed-effects model, n = 4 organoids and 507 single-units). Box plots: boxes span the 25th–75th percentiles; the center line marks the median (50th). Whiskers extend to the most extreme values within 1.5× the interquartile range from quartile 1 and quartile 3. In violin plots, minima and maxima equal the lowest and highest observations; the shaded area shows the variable’s probability density. (F) Firing rate peak times relative to burst peaks for backbone units. Black dots mark individual bursts, and red shading indicates the probability distribution. (G) Variance of relative firing peak times for backbone units across four organoids. Units are ordered by median peak time, showing significantly greater variability in later-firing neurons (P = 1 × 10⁻⁶, two-sided linear mixed-effects model for relation between relative firing rate peak and peak time variance). The line represents the mean, and shaded area the 95% confidence interval.

To further test the impact of inhibitory tone on backbone neurons, we administered gabazine (10 μM) via bath application to block GABA_A receptors in murine cortical organoids. Gabazine increased burst frequency, backbone participation and their rank-order statistics relative to control conditions. In contrast, blocking AMPA (10 μM NBQX) and NMDA (20 μM R-CPP) receptors, inhibiting excitatory synaptic transmission, abolished bursts, consistent with prior work²² and eliminated sequences (Extended Data Fig. 4). These findings highlight the dual role of excitation and inhibition in shaping spike timing and sequence rigidity.

To quantify firing consistency during spontaneous bursts, we analyzed single-unit activity relative to the burst peak, following methods used in vivo⁴. Some units displayed sharp peaks with narrow jitter (Fig. 2D, left), others showed delayed but consistent responses (middle), while many lacked preference and fired irregularly (right). Backbone units, comprising 28% ± 14% (mean ± STD) of total neurons (n = 8 organoids, Supplementary Fig. 1), displayed significantly higher burst-to-burst correlations (Fig. 2E). Their firing patterns remained stable across hours (Supplementary Fig. 8) and persisted over months, with correlations increasing during development in both human and murine organoids (Supplementary Fig. 2C, P < 10⁻⁵, two-way ANOVA). Randomized spike trains that preserved mean and single-unit firing rates abolished sequences and significantly reduced burst-to-bust correlations (Extended Data Fig. 5, Supplementary Figs. 9-10). This resembled two-dimensional primary cultures with randomized architectures that also lacked sequential firing (Extended Data Fig. 6). Finally, the variability of firing peak times increased with their average latency (Fig. 2F), a relationship consistently observed across organoids (Fig. 2G, P < 10⁻⁵, linear mixed-effects model). These results indicate that brain organoids can support stereotypical sequential activation with variable dynamics that mirror the propagation of spontaneous activity within the cortical mantle in vivo^4,5,13.

Backbone units are a highly correlated ensemble

To quantify firing patterns during spontaneous bursts, we examined pairwise correlations of single-unit firing rates. Backbone units generated stereotyped activation sequences that were preserved across bursts (Fig. 3A). Our analysis of sequential co-activation showed consistent firing onsets and peak times with average phase lags of ≈ 10 milliseconds (Fig. 3B, example units a to b = 5 ms, example units b to c = 7 ms), as well as longer lags spanning hundreds of milliseconds between backbone pairs due to recurring sequential activity (Supplementary Fig. 11). Cross-correlation analysis revealed that backbone units formed a highly correlated ensemble with non-zero phase lags (Fig. 3C-D). Correlation coefficients were significantly higher in backbone compared to non-rigid units (Fig. 3E) and occupied the tail of lognormal distribution (Fig. 3F, Supplementary Fig. 12C–E). Together, these results suggest that a minority population of high firing rate neurons are strongly tuned to population dynamics and function as a stop-watch in the backbone among the more rigid units of the population.

Figure 3. Firing patterns between single backbone units within bursts are nonrandom.

(A) Spike times and computed firing rates for three representative units are shown for the first and last burst event of the recording, respectively. (B) Burst peak centered average firing rates for the three units shown in A are calculated over all burst events. The narrow lines indicate the firing rates for each individual burst event. The thick lines (dotted black lines in inset) indicate the average over all bursts. (C) Pairwise cross correlation coefficients computed between the instantaneous firing rates of all pairs of units with at least 30 spikes counted over all burst events. A maximum lag time of 350 ms was used. The solid red lines separate the backbone units and the non-rigid units. (D) lag times leading to the maximum cross correlation values presented in C. Values are clipped at ±150ms. (E) Pairwise cross-correlation scores are plotted between unit types. Correlations between backbone units (blue) are significantly higher (P < 10⁻²⁰, 2-sided linear mixed effects model, n = 4 organoids and 34,056 single unit pairs) than the cross-correlations between pairs of backbone and non-rigid units (gray) and pairs of non-rigid units (yellow). Box plots: boxes span the 25th–75th percentiles; the center line marks the median (50th). Whiskers extend to the most extreme values within 1.5× the interquartile range from quartile 1 and quartile 3. In violin plots, minima and maxima equal the lowest and highest observations; the shaded area shows the variable’s probability density. (F) The histogram of all pairwise cross-correlations follows a skewed, lognormal distribution (x-axis is log scale). The pairwise connections between pairs of backbone units populate the tail of this distribution for all organoids as can be seen from the distribution means of the backbone-to-backbone distributions in E and marked on each histogram (circles on line).

Population firing rate timing across burst epochs

In previous sections, we analyzed pairwise single-unit relationships. We next asked whether firing rates were temporally structured at the population level during bursts. By calculating cosine similarity of instantaneous firing rates across bursts, we observed a sharp similarity peak coinciding with backbone activation, followed by a plateau and decay after burst termination (Fig. 4A-B). Variance in similarity showed the opposite trend: it was high during non-bursting periods, rapidly declining at burst onset, and remaining low until bursts ended (Fig. 4C).

Figure 4. Backbone units provide a stable, low-dimensional reference frame for the population bursts.

(A) Population firing rates from 46 burst events from a single human brain organoid are shown relative to burst peaks (gray traces). The mean firing rate is shown by the solid black line, and the dashed black lines denote the standard deviation. The red trace shows the average burst similarity score, plotted on the right axis. The blue box highlights the period from the earliest to latest average firing rate peak times across all backbone units. (B) Burst similarity between each pair of bursts is plotted at two reference points: 50 ms before the burst peak (left) and 100 ms after the burst peak (right), corresponding to the vertical dashed lines in A. (C) Burst similarity across all pairs of bursts is plotted relative to the burst peak. Each gray line reflects a burst pair, and the red trace represents the standard deviation per recording frame. The blue box marks the backbone window described in A. (D) Average similarity computed separately for backbone units, non-rigid units, and shuffled data. Backbone units consistently display significantly higher similarity throughout the backbone window compared with non-rigid or shuffled controls (P < 10⁻²⁰, paired two-sided t-test). (E) The average burst similarity increased consistently across organoids following the onset of the backbone period. (F) Plot of the first two principal components of the single-unit firing rates for all units (left), backbone units (middle) and non-rigid units (right). Each dot represents a recording frame and is colored by the time point relative to the closest burst peak. Note that backbone units reproduce the circular manifold of all units. Non-rigid units lack this trajectory, and variance explained by the first two components is reduced. The inset shows the burst-aligned population rate, color-coded by time relative to the burst peak, illustrating the correspondence between activity and manifold trajectory. (G) Cumulative variance explained by PCA for backbone (blue) and non-rigid (yellow) subsets relative to all units. Across organoids, the first principal components of backbone activity account for more variance than the full population, while non-rigid units account for less.

Separating units revealed that backbone ensembles displayed significantly higher similarity than non-rigid units or shuffled data (Fig. 4D). Notably, the top 20th percentile of highly correlated units (from Fig. 3C) generated significantly higher burst similarity than the full population, with the effect diminishing as larger percentiles were included (Supplementary Fig. 13A,C). Conversely, the lowest 20th percentile reduced similarity, with differences shrinking as more weakly correlated units were added (Supplementary Fig. 13B,C). Across organoids, burst similarity increased at backbone onset and plateaued during their activation (Fig. 4E, Supplementary Fig. 13D, n = 8 organoids), underscoring the temporal stability backbone ensembles provide across bursts.

We next examined firing trajectories with principal component analysis (PCA). Burst-related trajectories occupied conserved paths in PC-space aligned to burst timing (Fig. 4F, left). When populations were divided, backbone units captured far more variance (73%) in the first two PCs compared to non-rigid units (25%) (Fig. 4F middle/right, Fig. 4G, Supplementary Figs. 14-15). Thus, backbone ensembles define a low-dimensional subspace, while non-rigid units exhibit irregular, higher-dimensional dynamics requiring more PCs. Importantly, randomization preserving both population and single-unit mean rates abolished these trajectories (Extended Data Fig. 5), demonstrating that structured temporal correlations are not explained by mean firing rates alone.

Revealing temporal structure with a hidden Markov model

We previously demonstrated that functional connectivity in human brain organoids follows a heavy-tailed distribution²², consistent with scaling rules observed in cortical circuits². These motifs are thought to underlie spontaneous activity that propagates broadly across the cortical mantle, mirroring sensory-evoked responses in vivo^4,7. To further probe this repertoire of dynamics, we applied a hidden Markov model (HMM).

Single-unit activity was binned into 30 ms intervals, capturing fast electrophysiological timescales typical of cortical circuits (~10–50 ms)³⁰, and the HMM was stable over this variable time window (Supplementary Fig. 16). The HMM clustered the data into discrete states, each representing a linear combination of single-unit firing patterns occurring together within bursts. The state transitions are visualized as shaded raster plots aligned closely with burst trajectories (Fig. 5A). Heatmaps of unit firing and histograms of average rates revealed distinct manifolds of activity delineated by differential gain and attenuation across units associated for each state (Fig. 5B). While a 20-state model was used for visualization, similar results were obtained across a range of hidden state counts (Supplementary Fig. 17). Importantly, randomized data preserving mean unit and population rates³⁸ yielded lower log-likelihoods (Supplementary Fig. 18), confirming that the transitions in real data reflected meaningful structure rather than trivial differences explained by the mean rate. Analysis of transitions showed that firing states represent both increases and decreases in relative unit activity (Fig. 5B). Low-probability states appeared before the burst peak, rapidly converged into high-probability transitions at and immediately after the peak, and then relaxed back to low probabilities per unit time (Fig. 5C). This narrowing effect in state space may establish a sequential arrow of time, where initial states preserve more precise timing relative to following states (Supplementary Fig. 19). As bursts attenuated, the number of states broadened again. The number of realized states during bursts remained similar over a variable range of hidden states, an effect consistent across different hidden state counts (Supplementary Fig. 20), highlighting the robustness of the model.

Figure 5. Hidden Markov Models (HMMs) explore stable trajectories and population motifs.

(A) Repeated sequences of discrete hidden states are shown during three example bursts. The HMM assigns each 30 ms bin of spiking activity a hidden state, represented by background colors. The stereotyped trajectory of these states is visible both in the sequence of state transitions and in the population firing rate (red trace). Spiking events are shown as a raster, with 27 backbone units displayed above and 104 non-rigid units below a dividing line. (B) Each hidden state represents a stochastic but repeated activity pattern across units. Example realizations of three states are displayed as heatmaps, along with subpanels showing the average firing rate (FR) of each unit and their difference between adjacent states (ΔFR, red). (C) The sequence of hidden states follows a stereotyped path across bursts. Heatmap of state probabilities relative to the burst peak shows low variability during the first 0.3 s, corresponding to the structured backbone sequence, with substantially higher variability before the burst begins and later in the burst. (D) The probability of unit activity across hidden states is displayed as a heatmap for an example HMM. Backbone units (left) remain consistently active across multiple states, including those outside the burst peak states 11 and 12. Non-rigid units (right) are active in various states. (E) Backbone and non-rigid units are nearly linearly separable when classified by their consistency across states. First two principal components of vectors representing each unit as the sequence of its consistency across states. Backbone and non-rigid units are indicated with color. (F) Firing rate alone is insufficient to classify units. Violin plots show linear separability scores across fitted HMMs from eight organoids. State-based classification significantly outperforms firing rate–based classification (diamond marker) in all cases (two-sided Student’s t-test, P = 0.00021, n = 8 organoids). Box plots (F): boxes span the 25th–75th percentiles; the center line marks the median (50th). Whiskers extend to the most extreme values within 1.5× the interquartile range from quartile 1 and quartile 3. In violin plots, minima and maxima equal the lowest and highest observations; the shaded area shows the variable’s probability density.

We next asked how these states mapped onto backbone versus non-rigid units. Backbone ensembles spanned a larger pool of HMM states than non-rigid units (Fig. 5D, Supplementary Fig. 21). PCA of state vs. unit realizations revealed separability between these groups by hidden state structure (Fig. 5E). Linear support vector machine classifiers trained on hidden state features distinguished backbone from non-rigid units with 83.9% ± 12.0% accuracy, significantly exceeding the 63.2% ± 10.4% achieved when using firing rate alone (Fig. 5F). Together, these findings highlight that spontaneous bursts in brain organoids are composed of ensembles, linked together in time to establish neuronal manifolds with temporal structure not observed in randomized data (Supplementary Fig. 22). These manifolds represent a latent multidimensional space of temporally rigid and flexible neuronal subpopulations whose probabilistic trajectories are Markovian in time; namely future states depend on the system’s current state. Such dynamics align with recent experimental and computational models proposing that local pairwise correlations drive irreversibility in noisy logical computations, that contribute to a local arrow of time, and generate an irreversible Markovian process independent of sensory input³⁹.

Endogenous sequences in early developing neonatal cortex

We next asked if spiking sequences also emerge in early developing cortical circuits. Sequential activity patterns are crucial components of mature brain function⁷ and support early navigational tasks¹¹, yet it is not known whether such patterns are present before eye opening and exploration occur. To address this question, we performed acute extracellular recordings from coronal slices of neonatal murine somatosensory cortex. We observed alternating periods of quiescence and abrupt, synchronized burst events resembling those described in vivo (Fig. 6A, n = 6 slices, Extended Data Fig. 7). At this stage, cortical activity is discontinuous, alternating between bursts and quiescent periods, and spike trains are highly correlated³⁷. With the exception of olfaction, which controls cognitive maturation⁴⁰, most sensory systems remain underdeveloped.

Figure 6. Recurring sequential activation patterns in murine neonatal cortical slices generate a stereotyped temporal backbone.

(A) Raster plot of single-unit spiking recorded from the somatosensory cortex of a P13 murine neonatal brain slice placed on a microelectrode array. The red trace shows the population firing rate, with bursts marked by sharp increases. Burst peaks are denoted by local maximas that exceed 4x-RMS fluctuations in the population rate. Shaded gray regions denote burst durations, defined as intervals where the population rate remains above 10% of its peak. (B) Instantaneous firing rates of units from A after reordering. Backbone units are plotted above the dotted line, non-rigid units below. Units are ordered by their median firing rate peak time relative to the burst peak. For slices, backbone units were defined as spiking at least twice in ≥70% of bursts. (C) Average burst peak–centered firing rates across all bursts. Units maintain the same order as in B. A progressive delay in peak times relative to the burst peak is observed, with later-firing units showing broader activity windows. (D) Example spike trains for two backbone units across bursts, one aligned near the peak and one delayed, along with corresponding average burst-centered firing rates (red). Heatmaps of burst-to-burst correlation coefficients are shown below for the same units. (E) Pairwise cross-correlations of instantaneous firing rates from all units with ≥30 spikes. Backbone and non-rigid groups are separated by red lines. (F) Average burst-to-burst correlations for backbone and non-rigid units for all neonatal cortical slices. Backbone units consistently exhibited higher correlations than non-rigid units (P < 10⁻²⁰, two-sided linear mixed-effects model, n = 6 mice and 959 single units). (G) Pairwise correlations from all unit pairs grouped as backbone–backbone, backbone–non-rigid, or non-rigid–non-rigid. Backbone–backbone correlations were significantly stronger than mixed or non-rigid pairs (P < 10⁻²⁰, two-sided linear mixed-effects model, n = 6 mice and 125607 single unit pairs). Box plots (panels F–G): boxes span the 25th–75th percentiles; the center line marks the median (50th). Whiskers extend to the most extreme values within 1.5× the interquartile range from quartile 1 and quartile 3. In violin plots, minima and maxima equal the lowest and highest observations; the shaded area shows the variable’s probability density.

We next quantified the consistency of firing patterns. Single units were divided into backbone and non-rigid groups based on recruitment within bursts, following the approach used in organoids (Fig. 6B, Supplementary Fig. 1, Extended Data Fig. 7). Averaging each unit’s firing relative to burst peaks revealed sequential activity among backbone units consistently recruited during bursts (Fig. 6C). Analysis of spike times confirmed preserved temporal offsets between unit peaks with consistent shifts between their peak firing rates (Fig. 6D). As in organoids, backbone units formed a strongly correlated core compared to non-rigid units (Fig. 6E–G, Supplementary Figs. 9,12), with that activity generating temporal sequences that spanned ≈ 10² millisecond timescales. Together, these results demonstrate that slices of the developing murine somatosensory cortex generate both rigid and flexible firing patterns that establish sequential activation patterns commonly observed in mature cortical circuits across a range of species and brain regions⁷.

Comparing sequences across neurodevelopmental models

To understand the role of three-dimensionality in neurodevelopment, we compared neuronal firing patterns generated by two-dimensional murine primary cortical cultures to that observed in human and murine brain organoids and acute murine neonatal slices. All four systems displayed population bursts with consistent firing units recruited during burst epochs (Supplementary Fig. 1). Backbone neurons had significantly higher firing rates than non-rigid counterparts (Fig. 7A, P < 10⁻⁶, linear mixed-effects model, Supplementary Fig. 23). However, primary cultures exhibited overall higher firing rates across both populations (P < 10⁻¹⁰ for organoids and neonatal slices). In contrast, backbone units in organoids and neonatal slices showed significantly stronger normalized burst-to-burst single-unit firing correlations compared to primary cultures (Fig. 7B, Supplementary Fig. 9). After normalization relative to randomized data, backbone units remained significantly more correlated than non-rigid units in organoids and slices (P < 10⁻¹⁰ and P = 7×10⁻⁴, linear mixed-effects model), whereas no significant difference was observed in primary cultures (P = 0.06). Despite variability between batches, these differences were consistent across human and murine organoids, across whole and sliced preparations measured in different laboratories (Extended Data Figs. 2,8 and Supplementary Fig. 9).

Figure 7. Backbone units provide a stable reference frame in brain organoids and murine neonatal cortical slices but not in murine primary cultures.

(A) Average firing rate for backbone and non-rigid groups from human brain organoids (n = 8, 1048 units), murine cortical organoids (n = 9, 1179 units), murine neonatal cortical slices (n = 6, 786 units), and murine primary cultures (n = 8, 1048 units). Each model type differed significantly from the others, and within each model backbone and non-rigid units were significantly different (P < 10⁻²⁰). (B) Normalized average burst-to-burst correlations grouped as in A. Significant differences were observed between model types and between backbone and non-rigid units for organoids and slices (human organoids: P < 10⁻²⁰; murine organoids: P = 0.0011; murine slices: P = 0.0066; murine primaries: P = 0.93). (C) Normalized pairwise cross-correlations grouped into backbone–backbone and non-rigid–non-rigid pairs. Backbone pairs showed significantly higher correlations in organoids (human: P = 9 × 10⁻⁷; murine: P = 1 × 10⁻⁸), but not in slices (P = 0.10) or primaries (P = 0.16). (D) Correlation Lag-times between backbone units were larger for organoids compared to primary cultures (human organoid vs primary: P = 1 × 10⁻⁸; murine organoids vs primary: P = 0.011), with human organoid differing from murine organoids (P = 0.0096) and slices (P = 0.0002). Murine organoids vs slices (P = 0.47) and primary cultures were not significant (P = 0.53). (E) Normalized variance explained by the first-three principal components for all units, backbone, and non-rigid groups. Differences were significant for organoids (human: P = 2 × 10⁻⁷; murine: P = 0.036), but not slices (P = 0.29) or primaries (P = 0.21). (F) Hidden Markov models revealed higher-dimensional state-spaces in organoids compared with primary cultures. Dimensionality was defined as the number of components explaining 75% of variance. Organoids required more dimensions than primaries (human: P = 1.2 × 10⁻⁶; murine: P = 0.0026), but not compared with slices (human vs slices: P = 0.036; murine vs slices: P = 0.51). A two-sided linear mixed-effects model with interactions for unit type and model type was used for A–F (sample sizes in A). Box plots (panels A–D): boxes span the 25th–75th percentiles; the center line marks the median (50th). Whiskers extend to the most extreme values within 1.5× the interquartile range from quartile 1 and quartile 3. In violin plots, minima and maxima equal the lowest and highest observations; the shaded area shows the variable’s probability density.

Pairwise cross-correlations further underscored the differences between single-unit firing rates among backbone and non-rigid units (Fig. 7C, Supplementary Fig. 12). Backbone-to-backbone pairs in organoids and slices exhibited significantly higher correlations compared to randomized controls (P < 10⁻¹⁰, linear mixed-effects model), an effect not observed in primary cultures (P > 0.99). These differences were observed in organoids across developmental time points (Supplementary Fig. 2B–D), across different cell lines and human organoid protocols and laboratories^22,27 (Extended Data Fig. 2F), and in murine forebrain organoids (Supplementary Figs. 5, 12). In contrast, two-dimensional primary cultures exhibited synchronous, burst-centered activity that lacked sequential structure (Extended Data Fig. 6C), identical to randomized organoid data (Extended Data Fig. 5C). Consequently, human and murine organoids showed significantly larger cross-correlation lag times among backbone pairs compared to primary cultures (Fig. 7D, P < 10⁻⁷ and P = 0.011), highlighting their ability to sustain correlated activity on ~10² millisecond timescales typical of cortical and subcortical circuits with the capacity to support sequential firing patterns^7,30,34,36.

We next applied principal component analysis (PCA) to quantify variance explained by backbone and non-rigid units. In organoids, backbone units explained a significantly larger fraction of variance than other model types (Fig. 7E, Supplementary Fig. 15, P < 0.001, linear mixed-effects model). These findings highlight that organoids generate sequential patterns residing in a lower-dimensional subspace (explained by fewer PCs) embedded within a higher-dimensional background of irregular activity. Neonatal slices also contained backbone units capable of generating sequences that span ~10² milliseconds timescales, but with less stereotypy than organoids. By contrast, recurring sequential activation was not sustained in two-dimensional primary cultures.

We next asked if our analysis using Hidden Markov models (HMMs) would provide further insight. Across models, non-rigid units were predominantly Poisson, while backbone units were non-Poisson (Supplementary Fig. 24). In the in vivo cortex, Poisson randomness is not universal³¹, where architectonically defined regions generate homologous firing patterns that differ systematically across brain regions but remain conserved across species⁴¹. To compare complexity across models, we defined dimensionality as the number of PCs required to explain a fraction θ of HMM variance. With θ = 0.75, human organoids were separable from slice data (P = 0.04, linear mixed-effects model with Poisson observations), while primary cultures had significantly lower dimensionality than both human (P < 0.0001) and murine organoids (P = 0.003) (Fig. 7F), with similar trends existing for a range of values of θ (Supplementary Fig. 25). Within organoids, hidden states captured multidimensional clusters of activity, whereas randomization collapsed them to a one-dimensional space which scales with the population rate (Supplementary Fig. 22). Although the number of realized states was relatively insensitive to the number of hidden states (Supplementary Fig. 20), traversal rates differed: three-dimensional models exhibited lower rates than two-dimensional primary cultures (Supplementary Fig. 26).

Firing pattern stability

Despite similarities in firing patterns and stable sequences observed in organoids and neonatal slices, two-dimensional counterparts are dominated by Poisson-like irregularity, which precludes the generation of sustained temporal patterns and confines state transitions, as defined by HMM, to a lower-dimensional space (Fig. 7F). However, all models are capable of generating complex firing patterns with structured population dynamics across multiple timescales. Across phylogeny, brains and other complex systems exhibit signs of criticality⁴². Criticality is a dynamical state of multi-scale, marginally stable dynamics that simultaneously optimizes information transmission, storage, dynamic range, susceptibility, and robustness. Criticality is widely considered a homeostatic endpoint in the brain³², that is, in the intact brain, maintained by sleep⁴³. While measurements of criticality traditionally require extended sampling of a system’s activity, recent progress solves this problem by applying renormalization group theory³³. We used this framework to quantify how close neural dynamics are to temporal scale-invariance. At criticality, temporal correlations span many timescales without a characteristic scale, captured by the distance metric d₂. Values between 0.0–0.1 indicate near-critical dynamics that span many timescales without a characteristic scale, while larger values reflect deviation. A subset of all preparations produced activity consistent with autoregressive models and exhibited near-critical dynamics (Supplementary Fig. 27). Spike-time shuffling consistently abolished temporal criticality across preparations, producing significantly larger d₂ values (P < 10⁻¹⁰ compared to intact data, two-sided Welch t-test). Murine organoids showed particularly strong agreement between empirical data and model predictions. This indicates that the capacity for scale-invariant dynamics may be a fundamental property of neural circuits that emerges during development, independent of precise circuit architecture or environmental context.

Discussion

Neuronal sequences are believed to form the basis for information broadcasting and computation in the brain^4,6,8–11. Whether such sequences are emergent features of early brain development, a stage dominated by spontaneous activity with the potential to encode information, remains unclear³⁴. We report that temporally structured neuronal sequences emerge in human and murine brain organoids that assemble in the absence of sensory experience. We identify a sub-population of temporally-rigid, sequence generating ‘backbone’ neurons that reside in a low-dimensional subspace. In contract, we found a larger population with more irregular activity, residing in higher-dimensional space. Sequence generating backbone neurons were also observed in neonatal murine cortical slices that developed under minimal sensory input, but were absent in two-dimensional murine cortical cultures where intrinsic anatomical organization is disrupted. Our results support the hypothesis that neuronal sequences are ‘preconfigured’ as an innate three-dimensional architecture established during neurodevelopment, arising independent of experience.

To address the open questions above, we leveraged state-of-the-art high density extracellular recordings from three-dimensional stem cell derived models of the human and murine brain, known as brain organoids, which represent an intrinsically self-organized neuronal system that recapitulates key facets of early brain development^17–20 and the establishment of functional circuits^21,22,26. Our results demonstrate that temporally rigid sequences represent a subpopulation that projects back onto a minority of strong functional connections with a lognormal distribution (Fig. 3). In a seminal paper, Hopfield demonstrated that emergent computational properties from simple properties of many cells, rather than complex circuits, are capable of generalization and time sequence retention⁴⁴. Therefore, it’s not surprising that the temporal structure of spontaneous and evoked patterns of cortical circuits are similar^45,46, since such representations are drawn from a functionally connected neuronal pool with right-skewed, lognormal scaling rules².

Units that fire within neuronal sequences exhibit varying temporal precision. Neurons firing at the beginning of population bursts are most constrained, whereas later-firing units are more flexible (Fig. 2F,G). An analogous organization is present in rat somatosensory and auditory cortex⁴ and the three-layered turtle cortex⁵. In the hippocampus, experience-dependent replay emerges from spontaneous, experience-independent preconfigured sequences¹¹. The balance between temporally correlated and irregular spiking populations is essential for information processing. For example, large-scale recordings from mouse visual cortex and monkey brain reveal a low-dimensional subspace of neurons entrained to population dynamics, insensitive to external stimuli³⁸. Similarly, in organoids we observe a backbone subspace embedded within higher-dimensional irregular activity (Fig. 4). Stochastic firing in randomized organoid data closely mirrors two-dimensional dissociated cortical cultures, which show culture-wide synchronization that cannot sustain sequential patterns (Extended Data Fig. 5-6), likely reflecting highly redundant two-dimensional network configurations. These findings highlight that neurogenesis and synaptogenesis in organoids generate structured networks rather than random assemblies. Our results support the hypothesis that construction of complex networks capable of recapitulating in vivo neural dynamics requires morphogenesis in three-dimensions. Indeed, recent work has demonstrated that human brain organoid circuits, when combined with a machine-interface, can act as reservoirs for computing, including speech recognition and nonlinear equation prediction⁴⁷.

In vivo, a minority pool of strongly correlated neurons has been proposed to form a fast-acting system embedded within a more weakly coupled background, functioning as a preconfigured brain state³. The balance between rigid and flexible spiking and the emergence of sequential patterns are features of three-dimensional cytoarchitecture, supported by our analysis of spontaneous activity in the neonatal mouse somatosensory cortex (Fig. 6). A neurophysiological backbone is likely organized during neurogenesis, as pyramidal progenitors establish high-firing subnetworks that remain functionally connected across brain states¹⁶. In human and murine organoids, highly correlated backbone units increase in burst-to-burst correlation over development (Supplementary Fig. 2). This transition coincides with the incorporation of inhibitory interneurons^22,48 and reflects an excitatory–inhibitory balance shifting toward inhibition observed in vivo³⁷, while preserving right-skewed functional rules⁴⁹. Temporal rigidity of sequences is strongly modulated by GABAergic inhibition (Extended Data Fig. 4), where blockade induces heightened burst synchronization, consistent with GABA’s inhibitory role. These results underscore interneuron signaling as critical for network homeostasis and for shaping early dynamics prior to sensory input³⁷. Although GABA was once thought excitatory during early development⁵⁰, growing evidence indicates inhibitory effects occur much earlier^51,37,52. Our findings align with this perspective, highlighting interneurons as key contributors to the temporal structure of early neuronal sequences. Brain organoids thus provide a powerful platform to study how specific cell types and regional interactions assemble functional microcircuits⁵³.

Brain organoids represent a self-organized neurodevelopmental system that operates as a closed system devoid of external input, yet capable of generating activity patterns resembling early brain dynamics. Within these firing patterns we observed overlap between non-Poisson-like activity in organoids and neonatal slices. By contrast, primary cortical cultures with randomized cytoarchitecture showed lower-dimensional state transitions in a hidden Markov model (Fig. 7F). In vivo, brain regions balance firing patterns ranging from irregular Poisson to clock-like regularity, depending on local architectures, and these are thought critical for higher-order function³¹. In fact, a minority “backbone” of consistently firing neurons can predict motor control with high accuracy in humans⁵⁴ and have been proposed as an ‘ansatz’, or initial estimate for aligning behavior to environmental input³. We posit that highly correlated, non-Poisson components may provide the basis for temporal sequence emergence in development. Early sequences may function as an internal reference for larger-scale dynamics in mature circuits⁷, later calibrated by sensory–motor interactions³⁴. Indeed, in postnatal murine brain, preconfigured motifs arise spontaneously in rest and are not improved by sequential experience during the third week¹¹. We further show that firing in organoids and neonatal slices generates strong non-random correlations with temporal jitter and non-zero phase lags. These ensembles form manifolds of trajectories identifiable by a hidden Markov model, with a core of strongly interacting units (Fig. 5C-D). Such subsets may act as ‘irreversible’ noisy logic elements that establish a local arrow of time, similar to recent findings in retinal circuits, neuronal activity remains irreversible even when their inputs are not³⁹.

In summary, our analysis of spontaneous activity generated by stem cell derived human and murine brain organoids, demonstrates that structured spiking sequences can emerge without sensory experience and motor output, supporting the pre-configured brain hypothesis. These results are in line with recent work showing how pharmacologically abolishing all central nervous system activity during the development of the larval zebrafish did not alter an oculomotor behavior⁵⁵, suggesting that complex sensory-motor systems are hard-wired by activity-independent mechanisms. Our findings recall the philosophy of Immanuel Kant in Critique of Pure Reason⁵⁶, who posited an a priori construction of a space-time map that in modern terms, could serve as a ‘scaffold’ to enable the brain to interact with and make sense of the world. In conclusion, brain organoids provide a heuristic platform for exploring how exogenous inputs refine self-organized neuronal circuits imbued with the innate capacity to process information and compute⁴⁷, while also facilitating new studies into the genetic mechanisms governing the assembly of functional circuitry during early human brain development^57–61.

Methods

Human brain organoid slice recordings and pre-processing

The human brain organoids extracellular field recordings presented in Fig. 1–4 were sourced from Sharf et al.²². Organoids with less than 20 active units were not considered as significant to reliably separate a backbone and non-rigid population. Briefly, brain organoids were grown based on methods developed by Lancaster et al.¹⁸ and were of predominant forebrain identity based on single cell RNA sequencing analysis²². The recordings were made using complementary metal-oxide-semiconductor (CMOS) micro-electrode array (MEA) technology (MaxOne, MaxWell Biosystems, Zurich, Switzerland) using MaxLab Live version 19.2.19. The electrode selection was made based on automatic activity scans (tiled blocks of 1,020 electrodes) to identify the spatial distribution of electrical activity across the surface of the organoid. The 1,020 most active electrodes were chosen with a minimum spacing distance of at least two electrodes (2 × 17.5 μm), providing sufficient electrode redundancy per neuron to enable accurate identification of single units by spike sorting⁶², while simultaneously sampling network activity across the whole organoid surface interfacing the MEA. Measurements were made in a culture incubator (5% CO₂ at 37 °C) with a sampling rate of 20 kHz for all recordings and saved in HDF5 file format. The raw extracellular recordings were band-pass filtered between 300–6000 Hz and subsequently spike sorted using the Kilosort2 algorithm⁶³ through a custom Python pipeline. The spike sorting output was then further curated by removing units with an ISI violation threshold⁶⁴ above 0.3, an average firing rate below 0.05 Hz and/or a signal to noise ratio (SNR) below 5.

Whole human brain organoid recordings

Additional electrophysiology data from whole human brain organoids (Fig. 7) was sourced from Alam El Din et al.²⁷ which made use of high-density MEAs integrated into 6-well configuration (MaxTwo, MaxWell Biosystems, Zurich, Switzerland). Whole organoids were attached to MEAs at 9.5 weeks old and grown for 32 days. Recordings were performed using the same methods in the previous section using MaxLab Live version 22.2.6. The organoids were grown from human iPSCs (NIBSC8 iPSC line) and cultured in mTESR Plus medium on vitronectin and differentiated into organoids based on a previously established protocol⁶⁵. Neural differentiation was induced with Neural Induction medium via SMAD inhibition (Gibco) and organoids were differentiated under gyratory shaking (88 rpm, 50 mm orbit) for up to 8 weeks in Neurobasal Plus medium supplemented with 1× B27-Plus, 10 ng/ml human recombinant GDNF (GeminiBio^™), 10 ng/ml human recombinant BDNF (GeminiBio^™), 1% Pen/Strep/Glutamine (Gibco, Thermo Fisher Scientific). Half changes of medium were performed 3-times a week. See Supplementary Methods for additional details regarding ESC maintenance, organoid generation, single cell RNA sequencing and immunohistochemistry characterization.

Mouse embryonic stem cell derived cortical organoids

Organoids were generated from three distinct mouse embryonic stem cell lines: C57BL/6, E14TG2a (129/Ola), and KH2 (129/SvJ × C57BL/6 hybrid). Embryonic stem cells (ESCs) were dissociated into single cells using TrypLE Express Enzyme (Thermo Fisher Scientific, #12604021) for 5 minutes at 37°C. After dissociation, the cells were re-aggregated in lipidure-coated 96-well V-bottom plates at a density of 3,000 cells per well in 150 μL of mESC maintenance medium, supplemented with 10 μM Rho Kinase Inhibitor (Y-27632, Tocris #1254) and 1,000 units/mL Recombinant Mouse Leukemia Inhibitory Factor (Millipore Sigma, #ESG1107). Following 24 hours of re-aggregation, the medium was replaced with cortical differentiation medium (Supplementary Methods).

Daily medium changes were performed, with N-2 and B-27 supplements added post-filtration to preserve their hydrophobic components. On Day 5, organoids were transferred to ultra-low adhesion plates (Millipore Sigma, #CLS3471), where the medium was replaced with fresh neuronal differentiation medium. The plates were then placed on an orbital shaker set to 68 rpm to prevent organoid fusion. To ensure optimal growth conditions, 16 organoids per well were consistently maintained. Organoids were plated whole at an age of around 30 days and recordings started when consistent population bursts were observed, in a similar manner as the human brain organoid slices described previously. Recordings were performed using MaxLab Live version 25.1.6 (MaxWell Biosystems).

Neonatal murine brain-slice preparation

All experiments involving murine neonatal acute slice recordings were approved by the Basel-Stadt veterinary office according to Swiss federal laws on animal welfare. Animal housing was equipped with an artificial light source providing a daylight-like spectrum. The light phase of the dark/light cycle lasted from 6:30 am to 6:30 pm GMT, with a 30-minute twilight period during both dark-to-light and light-to-dark transitions. Ambient temperature was maintained at 20–24 °C, and relative humidity at 45–65%. Briefly, mouse pups (P12–14; both sexes; C57BL/6JRj from Janvier Labs) were decapitated under isoflurane anesthesia, followed by brain dissection in ice-cold artificial CSF (aCSF) bubbled with carbogen gas (95% O₂, 5% CO₂). To promote self-sustained cortical activity⁶⁶, the following aCSF recipe was used (in mM): 126 NaCl, 3.5 KCl, 1.25 NaH₂PO₄, 1 MgSO₄, 2 CaCl₂, 26 NaHCO₃, and 10 glucose, at approximately pH 7.3 when bubbled with carbogen. Coronal brain slices (370 μm) were prepared using a vibratome (VT1200S, Leica, Wetzlar, Germany). Slices were subsequently transferred to a chamber submerged in carbogenated aCSF and stored at room temperature until use.

Acute recordings from neonatal murine brain slices

For recordings, a brain slice containing somatosensory cortex was transferred from the storage chamber onto the sensing area of the CMOS MEA and fixated with a customized MaxOne Tissue Holder (MaxWell Biosystems, Zurich, Switzerland). The slice was perfused with heated aCSF (32–34 °C). Recordings were performed using MaxLab Live version 22.2.8 (MaxWell Biosystems). Sparse, rectangular electrode configurations were selected to find active regions of the somatosensory cortex, with a sparsity of two or three to allow for a good spike-sorting performance.

Primary planar culture preparation

The presented primary neuronal recordings (Pr) were sourced from Yuan et al.²⁸ for Pr1–4 and from Bartram et al.²⁹ for Pr5– 8. Briefly, neuronal cultures according to Yuan et al. were prepared from embryonic day 18 Wistar rat cortices and plated at a density of 3,000 cells/mm² onto high-density CMOS MEAs (MaxOne, MaxWell Biosystems) and maintained in a cell culture incubator (5% CO₂ at 37 °C). The recordings were made at 20 days in vitro. The recordings can be obtained here: https://www.research-collection.ethz.ch/handle/20.500.11850/431730.

Comparing data from different sources

No statistical methods were used to pre-determine sample sizes but our sample sizes are similar to those reported in previous publications^{22,27–29,66}. The recording durations of all recordings coming from the same source were kept consistent. The recording durations per data source were selected so that each recording contained around 40 bursts (38 ± 4 bursts, mean ± SE), using the first x minutes of the recording to get to this value.

Data distributions were assumed to be normal but this was not formally tested. Where distributions visually deviated from a normal distribution, a log-transformation was performed or the distribution was modeled with a generalized linear model. Where data distributions contained a number of samples that was too large to be plotted individually, violin plots were used to report the shape of the distribution. Data analyses were performed blind to the conditions of the experiments.

Single-unit firing rate and CV2 calculations scores

All of the following analyses were performed using custom MATLAB scripts. MATLAB version R2018b was used. The firing rate of each individual spike-sorted unit with at least 30 detected spikes in the recording was computed by obtaining the inter spike interval between each spike event and applying a Gaussian smoothing with a 50 ms kernel to its inverse. A lognormal distribution was fitted to the distribution of firing rates averaged over the whole recording period for each unit. The goodness of the fit was assessed using the R² metric. In addition, for the same selection of units, the CV2 score of the spiking activity was computed per unit as described by Holt et al.⁶⁷ as a measure of spiking variability. The same CV2 computations were performed on 100 different shuffled spike matrices and the results from the original spike matrices were z-score normalized using the mean and standard deviation over all shuffled datasets.

Population rate calculations

The population firing rate was computed by summing spikes over all units per frame followed by smoothing with a 20 ms sliding square window and a subsequent 100 ms sliding Gaussian kernel. For the detection of the burst start, end and peak, population activity bursts were defined when the population-averaged spike rate exceeded 4x its RMS value (using the built in MATLAB function findpeaks with min_dist = 700 ms. For recordings with long duration bursts, min_dist was increased up to 2000 ms in order to prevent peaks in the tail of the burst from being detected as separate burst instances). The burst start and end times were determined to be the first time points where the multi-unit activity fell below 10% of the detected peak value, before and after the burst peaks respectively. The actual burst peak time was then obtained by recomputing the population firing rate using a 5 ms square window and a 5 ms Gaussian kernel and finding the frame with the highest value between the burst start and end time. For murine primary planar cultures, a 20 ms square window, a 50 ms Gaussian kernel and a 3 × RMS threshold were used for population peak detection and a 20% threshold for the burst start and end time detection. These values were chosen to account for stronger jitteriness of the population activity and more abundant inter-burst activity.

Firing rate sequences and burst backbones

For each individual unit, the firing rate centered by the burst peak was averaged from −250 ms to 500 ms relative to the burst peak. In addition, the time relative to the population burst peak at which this unit had a peak in its firing rate within the burst start and end window was selected. The median and variance of the firing rate peak times was computed per unit over all bursts in which this unit fired at least two action potentials. The median values were used for reordering the units for different plotting purposes and the variance was used to fit a linear mixed-effects model to study the relationship between the effect of the relative position of the peak (from 0 to 1) on the variance of the peak.

Units that fired at least two action potentials in all the bursts in a recording were defined as backbone units. For murine organoids and cortical slices, a threshold of 80% and 90% of bursts was used respectively since only a small fraction of units had at least two action potentials in all bursts (Supplementary Fig. 2A). A Backbone unit sequence was defined by ordering all backbone units based on their median firing rate peak time. For each sample, the burst backbone period was defined as the average firing rate peak time of the earliest backbone unit until the average firing rate peak time of the latest backbone unit in the sequence. For different plotting purposes, the backbone period was rescaled from 0 to 1 and data per organoid were overlaid and averaged over the rescaled backbone period for comparison.

Burst-to-burst firing rate correlations

For each unit, the firing rate was recomputed after removing all spikes that fell outside of the burst windows. Next, this firing rate was selected from −250 ms to 500 ms relative to each individual burst peak and a cross correlation was computed for the unit firing rate between each pair of bursts for each individual unit (using the built in MATLAB function xcorr with maxlag = 10ms and normalization = “coeff”). Only bursts with at least 2 detected action potentials and units with at least 2 spikes in at least 30% of all bursts were considered for this analysis. Afterwards the average over the maximum correlations for all the burst pairs with at least 2 detected action potentials was computed per unit, yielding the burst-to-burst correlation. The same computations were performed on 100 different shuffled spike matrices and the results from the original spike matrices were normalized using the (A−B)/(A+B) strategy, where A is the measured value and B is the averaged value computed over the 100 shuffled datasets.

In a separate analysis, burst-to-burst correlations were computed between bursts from two recordings from the same organoid slice at four-hour intervals. Average burst-to-burst correlations were computed for pairs of bursts within each of the two same recordings, as well as for pairs of bursts where one burst came from the recording at zero hours and the other burst from the recording at four hours.

Pairwise firing rate correlations

Using the same firing rates computed after removing spikes outside burst windows, cross-correlations were computed between each pair of units (using the built in MATLAB function xcorr with maxlag = 350 ms and normalization = “coeff”, a maxlag of 350 ms was chosen since the median backbone period over all samples except the murine primary cultures was 348 ms). The rate for the whole recording was used. The maximum correlation values for each unit pair were compared between pairs of backbone units, pairs of one backbone and one non-rigid unit and pairs of non-rigid units. The same computations were performed on 100 different shuffled spike matrices and the results from the original spike matrices were normalized using the (A−B)/(A+B) strategy, where A is the measured value and B is the averaged value computed over the 100 shuffled datasets. In addition, for all pairs of backbone units, the lag time corresponding to the maximum correlation value was compared to the average absolute lag time over all shuffled datasets for the same unit pair.

Burst similarity score

At every frame relative to the burst peak, a vector containing the firing rates for each unit was obtained. For every pair of bursts, the cosine similarity was computed between the vectors from the two different bursts. This yielded a matrix with pairwise burst similarity values at every frame relative to the burst peak. The average of this matrix was defined to be the burst similarity score for that relative frame. This score was computed for every frame in the period from the earliest burst start time - relative to the burst peak over all bursts - until the latest burst end time - relative to the burst peak over all bursts. The same computations were performed on the spike matrices after shuffling.

Besides computing the burst similarity score over all units, burst similarity scores were also computed for only a subset of units. In the first case, these subsets consisted of all backbone units and all non-rigid units respectively. Subsequently, at each frame the burst similarity score distribution for all burst pairs was compared using a paired sample, two-sided t-test (using the built in MATLAB function t-test). In the second case, these subsets consisted of units with an average correlation value (Methods: Pairwise firing rate correlations) in the top/bottom i^th percentile where i ranged from 20 to 95. Subsequently, the difference between the top and bottom i^th percentile was quantified for this range as the sum of the burst similarity score over all frames in the backbone period. This was done to assess the burst similarity based only on highly/lowly correlated units. Similarly, the burst similarity score distribution for all burst pairs was compared between the top/bottom 20 percent of units and all units using a paired sample, two-sided t-test.

PCA manifold analysis

The spike rate matrix of an organoid with n units can be interpreted as a set of points in n dimensional space, where each axis holds the spike-rate trajectory of a specific unit. The principal components (PC) of this system are the directions in this space that capture the majority of the dataset’s variance. A dimensionality reduction is achieved by linearly projecting the dataset onto these PCs. This transformation collapses the n dimensional system to p dimensions where p < n, while preserving the dominant patterns exhibited by the system. For this analysis, the PCs are computed by the Eigen-decomposition of the covariance matrix computed as follows:

Prior to the dimensionality reduction step, the firing rate data was normalized for each unit individually using the z-score method, which centers the data around zero mean and unit standard deviation. The dimensionality reduction was performed on three separate selections of units: all units, backbone units only and non-rigid units only.

The cumulative sum of the variance explained per PC was computed for the PCs ordered from high variance to low. For each recording, the results for all units were subtracted from the results for backbone units only and non-rigid units only. Negative values mean that the cumulative sum of the variance explained by all units is larger than for the subset of units and positive values mean that the cumulative sum of the variance explained by all units is smaller.

Furthermore, the sum of the variance explained by the first three PCs was computed and divided by the summed explained variance of the first X principal components, where X is the lowest number of total PCs from the three selections, all units, backbone and non-rigid. This was done to account for differences in the total number of PCs per selection. This value was computed for the original data and for 100 different shuffled spike matrices and the results from the original spike matrices were normalized using the (A−B)/(A+B) strategy, where A is the measured value and B is the averaged value computed over the 100 shuffled datasets. These scores were compared between the three selections and between the different model types as described in Methods: statistical analyses for model comparisons.

Randomized recording

Randomization of single-unit spike times were performed based on the methods of Okun et al.^38,68 to preserve each neuron’s mean firing rate as well as the population averaged firing rate distribution. This is necessary to avoid trivial differences that would arise simply by changes in the mean firing rate of a neuron. Briefly, whenever analyses were performed on a randomized recording, the randomization was done as follows (unless stated otherwise): Two separate units, A and B, were selected and two separate frames, 1 and 2, were selected where A but not B fired in frame 1 and B but not A fires in frame 2. Next, the spikes from unit A and B were switched between frames 1 and 2. The resulting spike matrix still has an equal number of spikes per unit (same average firing rate) and an equal number of spikes per frame (same population rate). This shuffling procedure was performed 5x as many times as there were spikes in the spike matrix, resulting in each spike getting shuffled 10x on average. This method was applied to produce 100 different shuffled spike matrices per original recording.

Statistical analyses for model comparisons

Statistical modeling was carried out in the R environment (version 4.2.1). Nested data were analyzed with linear mixed-effects models (lmer function of the lme4 R package⁶⁹) with “organoid” or “unit ID” as random effect. Non-nested data were analyzed with linear models (lm function). Right-skewed and heavy-tailed data were log-transformed and analyzed with a linear model. Statistical significance for linear mixed-effects models was computed with the lmerTest R package⁷⁰ and the summary (type III sums of squares) R function. Statistical significance for linear models was computed with the summary R function. When possible, model selection was performed according to experimental design. When this was not possible, models were compared using the compare_performance function of the performance R package⁷¹, and model choice was based on a holistic comparison of AIC, BIC, RMSE and R2. Model output was plotted with the plot_model (type=‘pred’) function of the sjPlot R package⁷². 95% confidence intervals were computed using the confint R function. Post hoc analysis was carried out using the emmeans and emtrends functions of the emmeans R package.

Extended Data

Extended Data Figure 1. Backbone units occupy the tail of skewed firing rate distributions.

(A) A histogram of the distribution of average firing rates for all units in organoid 1. The majority of units have low average firing rates while a long tail in the distribution contains a small subset of units with high average firing rates. A lognormal distribution is fitted to the histogram. The inset shows the histogram for the logarithm of the average firing rates of the same organoid. A normal distribution is fitted to the histogram. (B) Normal distributions fit to the logarithm of the average firing rate per unit for the 8 different organoids. (C) The R-squared values for the fitted normal distributions shown in B. R² = 0.97 ± 0.04 (mean±STD) across the 8 human brain organoids. Backbone neurons alone are not well described by a lognormal distribution. R² values are 0.45±0.30 across the 8 human brain organoids. (D) The distribution of average firing rates per organoid for backbone and non-rigid units separated. Red bars mark the distribution medians. The backbone units populate the tail of the skewed average firing rate distributions in all organoids. See Fig. 7A for statistical comparisons.

Extended Data Figure 2. Reproducible firing patterns in human brain organoids.

(A) Raster plot visualization of single-unit spiking (blue dots) measured across the surface of a human brain organoid slice from Alam El Din et al. (HO5), positioned on top of the same Maxwell Biosystems microelectrode array as used for the organoid recordings included in the main figures. The population firing rate is shown by the red solid line. Population bursts are marked by sharp increases in the population rate. Burst peak events are denoted by local maxima (black dots) that exceed 4x-RMS fluctuations in the population rate. The shaded gray regions denote the burst duration window as defined by the time interval in which the population rate remains above 10% of its peak value in the burst. (B) The instantaneous firing rate of single-unit activity from panel A after reordering. The backbone units are plotted above the dashed line while non-rigid units are plotted below the dashed line. In each category, units are ordered based on their median firing rate peak time relative to the burst peak, considered over all bursts in the recording. (C) The average burst peak centered firing rate measured across all burst events for the example recording of which part is shown in A. The burst peak is indicated by the dotted line. The unit order is the same as B. Note the progressive increase in the firing rate peak time relative to the burst peak, as well as a spread in the active duration for units having their peak activity later in the burst. The average firing rate is normalized per unit to aid in visual clarity. (D) The distributions of the log of the average firing rate per unit, separated for backbone and non-rigid units. All units from the 4 Sharf recordings are pooled together and all units from the 4 Alam El Din recordings are pooled together. (Sharf et al. P < 10⁻²⁰, Alam El Din et al. P = 0.40, two-sided linear mixed-effect model, n = 4 organoids each) (E) The distributions of the average burst to burst correlations per unit after average rate normalization, separated for backbone and non-rigid units. All units from the 4 Sharf recordings are pooled together and all units from the 4 Alam El Din recordings are pooled together. Note the significant difference between backbone and non-rigid units present for both sets of recordings (Sharf et al. P = 1×10⁻¹⁰, Alam El Din et al. P = 0.0092, two-sided linear mixed-effect model, n = 4 organoids each). (F) The distributions of the pairwise correlations per unit pair after average rate normalization, separated for backbone pairs, backbone and non-rigid combinations and non-rigid pairs. All unit pairs from the 4 Sharf recordings are pooled together and all unit pairs from the 4 Alam El Din recordings are pooled together. Note that only the normalized correlation for backbone pairs are significantly larger than 0 for both sets of recordings (Sharf et al. P = 0.0001, 0.145 and 1 respectively, Alam El Din et al. P = 7×10⁻¹¹, 1 and 1 respectively, one-sided linear mixed-effect model, n = 4 organoids each).

Extended Data Figure 3. Burst clustering distinguishes non-rigid from backbone unit variability.

(A) Pairwise firing rate correlations per burst (computed over a window ranging from −250 ms until 500 ms relative to the burst peak) projected onto the first two principal components, labeled by the identified clusters, show a clear separation between different burst clusters. The results for example recording Or5 are shown. (B) The population rate for a snippet of the recording for Or5 covering several bursts labeled by their cluster. (C) Firing rates per unit for 8 different example bursts per cluster. (D) The average firing rate per unit for the different detected burst clusters. (E) A selection of non-rigid units is most variable in their activity between the different burst clusters as reflected by a higher CV score for their firing rate in the different burst clusters (CV score are computed per row for the 4 columns shown in D. (F) The CV scores for the firing rate over the different burst clusters is significantly higher for non-rigid units compared to backbone units. (P ≤ 10⁻²⁰ for difference between backbone and non-rigid, two-sided linear mixed-effect model).

Extended Data Figure 4. Pharmacological modulation of excitatory and inhibitory signaling impacts bursts and sequences.

(A) Raster plot visualization of single-unit spiking (blue dots) measured across the surface of a murine organoid (MO10), positioned on top of the same type of microelectrode array as used for the recordings included in the main figures. The population firing rate is shown by the red solid line. Population bursts are marked by sharp increases in the population rate. The shaded gray regions denote the burst duration window as defined by the time interval in which the population rate remains above 10% of its peak value in the burst. Top: baseline recording. Middle: recording of the same organoid using the same electrode configuration, after treatment with 10 μM gabazine to inhibit inhibitory signaling by blocking GABA_A receptors. Bottom: recording of the same organoid slice using the same electrode configuration, after blocking AMPA and NMDA receptors with bath application of NBQX (10 μM) and R-CPP (20 μM) to inhibit components of excitatory synaptic transmission. (B) Number of detected population bursts for 5 different murine organoids (MO10–14) under baseline conditions, after treatment with gabazine and after treatment with NBQX and R-CPP. Note that bursting disappears after NBQX and R-CPP treatment reflected as a significant decrease in bursting compared to baseline conditions (P < 0.001, two-sided linear mixed-effect model). Meanwhile, the number of bursts increase after gabazine treatment (P < 0.05, two-sided linear mixed-effect model). (C) Fraction of bursts in which a unit fires at least 2 spikes for the 5 different murine organoids under baseline conditions compared to the gabazine treatment. The fraction of bursts in which units are active increases significantly after gabazine treatment (P < 10⁻⁷, two-sided linear mixed-effect model). (D) Normalized Spearman rank order correlations comparing the sequential order of backbone sequences for all burst pairs of 5 different murine organoids (MO10–14) under baseline conditions and after treatment with gabazine. Correlation scores are z-scored relative to shuffled spike matrices such that values above 0 indicate a more consistent backbone sequence than the shuffled data. There is a significant increase in backbone sequence order similarity after treatment with gabazine (P < 10⁻²⁰, two-sided linear mixed-effect model).

Extended Data Figure 5. Sequential activations and burst-to-burst similarity are not present after shuffling.

(A) Same raster plot visualization as Fig. 1A after shuffling. The population firing rate remains the same after shuffling and is shown by the red solid line. Population bursts exist in the same frames after shuffling and are denoted by local maxima (black dots) that exceed 4x-RMS fluctuations in the population rate. The burst duration windows remain the same after shuffling and are marked by the shaded gray regions, which denote the interval in which the population rate remains above 10% of its peak value in the burst. The average firing rate per unit remains the same after shuffling. (B) Same instantaneous firing rate visualization as Fig. 2B. The same ordering is used as in Fig. 2B. (C) Same average burst peak centered firing rate visualization as Fig. 2C after shuffling. The burst peak is indicated by the dotted line. The unit order is the same as Fig. 2C. Note that the progressive increase in the firing rate peak time relative to the burst peak, as well as a spread in the active duration for units having their peak activity later in the burst are not present anymore after shuffling. The average firing rate is normalized per unit to aid in visual clarity. (D) Same burst-peak-centered spike times and pairwise burst-to-burst correlations as in Fig. 2D after shuffling. For (i) and (ii), the consistent firing patterns relative to the burst peak as exemplified in Fig. 2D are not present anymore and the average burst-to-burst correlation scores have decreased from 0.96 to 0.69 and from 0.82 to 0.53 respectively. Meanwhile, the average burst to burst correlation for the non-rigid unit exemplified in (iii) decreased from 0.51 to 0.49.

Extended Data Figure 6. Intrinsic activity in murine primary cultures resembles organoids after shuffling.

(A) Raster plot visualization of single-unit spiking (blue dots) measured across a 2D murine primary culture from Yuan et al. (Pr1) recorded on a high-density microelectrode array. The population firing rate is shown by the red solid line. Population bursts are marked by sharp increases in the population rate. Burst peak events are denoted by local maxima (black dots) that exceed 4x-RMS fluctuations in the population rate. The shaded gray regions denote the burst duration window as defined by the time interval in which the population rate remains above 10% of its peak value in the burst. (B) The instantaneous firing rate of single-unit activity from panel A after reordering. The backbone units are plotted above the dashed line while non-rigid units are plotted below the dashed line. In each category, units are ordered based on their median firing rate peak time relative to the burst peak, considered over all bursts in the recording. (C) The average burst peak centered firing rate measured across all burst events for the example recording of which part is shown in A. The burst peak is indicated by the dotted line. The unit order is the same as B. Note that the progressive increase in the firing rate peak time relative to the burst peak, as well as a spread in the active duration for units having their peak activity later in the burst are not present in the murine primary recording, similar to the organoid data after shuffling as shown in Extended Data Fig. 5. The average firing rate is normalized per unit to aid in visual clarity.

Extended Data Figure 7. Consistent results in brain slices from different animals.

(A) Raster plot visualization of single-unit spiking (blue dots) measured across the surface of a murine neonatal cortical slice from a different animal (M3S1) dissected at P13, positioned on top of the same type of microelectrode array as used for the recordings included in the main figures. The population firing rate is shown by the red solid line. Population bursts are marked by sharp increases in the population rate. Burst peak events are denoted by local maxima (black dots) that exceed 4x-RMS fluctuations in the population rate. The shaded gray regions denote the burst duration window as defined by the time interval in which the population rate remains above 10% of its peak value in the burst. (B) The instantaneous firing rate of single-unit activity from panel A after reordering. The backbone units are plotted above the dashed line while non-rigid units are plotted below the dashed line. In each category, units are ordered based on their median firing rate peak time relative to the burst peak, considered over all bursts in the recording. (C) The average burst peak centered firing rate measured across all burst events for the example recording of which part is shown in A. The burst peak is indicated by the dotted line. The unit order is the same as B. Note the progressive increase in the firing rate peak time relative to the burst peak, as well as a spread in the active duration for units having their peak activity later in the burst. The average firing rate is normalized per unit to aid in visual clarity.

Extended Data Figure 8. Backbone sequences observed during spontaneous population bursts in murine cortical organoids.

(A) Raster plot visualization of single-unit spiking (blue dots) measured across the surface of a murine organoid (MO1) recorded at 42 DIV, positioned on top of the same type of microelectrode array as used for the recordings included in the main figures. The population firing rate is shown by the red solid line. Population bursts are marked by sharp increases in the population rate. Burst peak events are denoted by local maxima (black dots) that exceed 4x-RMS fluctuations in the population rate. The shaded gray regions denote the burst duration window as defined by the time interval in which the population rate remains above 10% of its peak value in the burst. (B) The instantaneous firing rate of single-unit activity from panel A after reordering. The backbone units are plotted above the dashed line while non-rigid units are plotted below the dashed line. In each category, units are ordered based on their median firing rate peak time relative to the burst peak, considered over all bursts in the recording. (C) The average burst peak centered firing rate measured across all burst events for the example recording of which part is shown in A. The burst peak is indicated by the dotted line. The unit order is the same as B. Note the progressive increase in the firing rate peak time relative to the burst peak, as well as a spread in the active duration for units having their peak activity later in the burst. The average firing rate is normalized per unit to aid in visual clarity.

Data Availability:

The data supporting the findings of this study are available within the article and its supplementary information. Raw and curated electrophysiology recordings can be found here https://dandiarchive.org/dandiset/001603. scRNA-seq data have been deposited and are publicly available in the NCBI Gene Expression Omnibus (GEO; http://www.ncbi.nlm.nih.gov/geo) under accession GSE290330.

Code Availability:

Spike sorting was performed in Python 3.6 using SpikeInterface 0.13.0 and previously published⁶², which can be found at https://github.com/SpikeInterface/spikeinterface. Custom code for electrophysiology analysis is available at https://github.com/braingeneers/Protosequences