## Abstract

Spontaneous propagation of spiking within the local neocortical circuits of mature primary sensory areas is highly nonrandom, engaging specific sets of interconnected and functionally related neurons. These spontaneous activations promise insight into neocortical structure and function, but their properties in the first 2 wk of perinatal development are incompletely characterized. Previously, we have found that there is a minimal numerical sample, on the order of 400 cells, necessary to fully capture mature neocortical circuit dynamics. Therefore we maximized our numerical sample by using two-photon calcium imaging to observe spontaneous activity in populations of up to 1,062 neurons spanning multiple columns and layers in 52 acute coronal slices of mouse neocortex at each day from postnatal day (PND) 3 to PND 15. Slices contained either primary auditory cortex (A1) or somatosensory barrel field (S1BF), which allowed us to compare sensory modalities with markedly different developmental timelines. Between PND 3 and PND 8, populations in both areas exhibited activations of anatomically compact subgroups on the order of dozens of cells. Between PND 9 and PND 13, the spatiotemporal structure of the activity diversified to include spatially distributed activations encompassing hundreds of cells. Sparse activations covering the entire field of view dominated in slices taken on or after PND 14. These and other findings demonstrate that the developmental progression of spontaneous activations from active local modules in the first postnatal week to sparse, intermingled groups of neurons at the beginning of the third postnatal week generalizes across primary sensory areas, consistent with an intrinsic developmental trajectory independent of sensory input.

- spontaneous activity
- cortical waves
- calcium imaging
- postnatal development

## NEW & NOTEWORTHY

To evaluate the developmental ontogeny of spontaneous circuit activity, we compared two different areas of sensory cortex that are also differentiated by sensory inputs that follow different developmental timelines. We imaged neuronal populations in acute coronal slices of mouse neocortex taken from postnatal days 3 through 15. We observed a consistent developmental trajectory of spontaneous activity suggesting a consistent pattern for cortical microcircuit development: anatomical modules are wired together by coherent activations into functional circuits.

patterned multineuronal activity has been connected to sensory input (Luczak et al. 2007), motor output (Churchland and Shenoy 2007), and cortical computation (Harvey et al. 2012) and arises spontaneously in synaptically connected neocortical networks, including in acute slices of neocortex, where it corresponds to UP state generation in individual neurons (Cossart et al. 2003; MacLean et al. 2005; Neske et al. 2015; Shu et al. 2003). These spontaneous activations are blocked by inhibitors of excitatory neurotransmitters (Cossart et al. 2005; Runfeldt et al. 2014) and are not recapitulated by a rate-matched null model of independent Poisson neurons (Chambers and MacLean 2015).

Emergent multineuronal activity patterns reflect mono- and multisynaptic connectivity patterns (Gerstein et al. 1978) and so are of interest in the study of neocortical synaptic structure and circuit dynamics. Furthermore, these reliable spontaneous patterns have functional relevance, for example, as the instantiation of the prior distribution for Bayesian perceptual inference (Fiser et al. 2010). These multineuronal activity patterns can be succinctly summarized via functional connectivity graphs (Chambers and MacLean 2015; Feldt et al. 2011), which provide insight into the dynamical and functional properties of networks composed of hundreds of neurons (Cossart 2014; Sadovsky and MacLean 2013, 2014).

The developmental trajectory of these patterns and their graphs at the scale of neocortical columns and layers have not been determined. Previous work in vivo has shown that within layer 2/3 neurons synchronous activity transitions to sparse activity around the time of eye opening at the beginning of the third postnatal week in primary visual cortex (Siegel et al. 2012). The timing of this change suggests that sensory input is necessary. However, studies of dark-reared mice show the same sparsification process, delayed by a few days (Rochefort et al. 2009). Furthermore, the same time course was seen in somatosensory barrel field (S1BF) and was unaffected by sensory deprivation (Golshani et al. 2009). The developmental trajectory in auditory cortex is unknown. Moreover, the spatial extent of both synchronous and asynchronous activity has not been determined. We have shown previously (Gururangan et al. 2014) that dense samples of at least 400 cells across nearly a millimeter are needed to guarantee the recovery of the topological statistical structure of functional networks in adolescent neocortex.

Here we used two-photon calcium imaging to observe the spontaneous activity of up to 1,062 neurons simultaneously in 52 coronal slices taken at each postnatal day (PND) between PND 3 and the beginning of the third postnatal week (PND 15) in primary auditory cortex (A1) and in S1BF. These two areas were selected because they have markedly different developmental timelines: auditory cortex does not receive peripheral input until the cochlea becomes spontaneously active after PND 7 (Sadanaga and Morimitsu 1995), and auditory brain stem responses to external stimuli do not begin until PND 12 (Song et al. 2006), while even neonatal pups are capable of using whisker stimulation for a simple classical avoidance conditioning task (Sullivan et al. 2003), although active sensation does not occur until the second postnatal week (Mosconi et al. 2010). Similarities would suggest a common developmental trajectory that is independent of sensory experience, while differences could be due to outside sensory input or to intrinsic genetic factors. Recapitulation of results from in vivo experiments would further suggest that structural and/or transcriptional changes, rather than the effects of neuromodulators, underlie the transition from synchrony to sparsity, since all of our slices were kept in the same, neutral recording solution.

## MATERIALS AND METHODS

#### Preparation of calcium dye-loaded slices.

Neocortical slices were obtained from mice (JAX) of either sex on PND 3–15 (see Sadovsky and Maclean 2013 for solutions). Briefly, the brain was extracted and 450-μm coronal slices containing the sensory region of interest were cut perpendicular to the pial surface with a vibratome (VT1000S; Leica). Slices were placed in 35°C incubation fluid for 30–45 min and then bulk-loaded with fura-2 AM calcium dye in DMSO and Pluronic (Invitrogen) at 35°C for 13–25 min, with the shorter time used for the younger mice. ACSF solutions were continuously aerated with 95% O_{2}-5% CO_{2} gas. All procedures were performed in accordance with and were approved by the Institutional Animal Care and Use Committee at the University of Chicago.

#### Calcium dye imaging.

Experimentation was performed at room temperature in recording ACSF (Shu et al. 2003). Rapid whole-field imaging of neurons was achieved with the heuristically optimal path scanning technique (Sadovsky et al. 2011), which allowed us to detect activations of individual cells in large populations at high speeds (see Fig. 1).

#### Statistical analysis.

All statistical analyses were performed with MATLAB (MathWorks). Data are presented as means ± SD. The Wilcoxon rank sum test was used to nonparametrically compare pairs of single-variate distributions, while the sign test was used to compare the medians of single-variate distributions to 0. For tests of statistical significance, α = 0.05 was used.

#### Cell and circuit event detection.

Fluorescence traces of individual neurons indicated action potential generation in those neurons (Sadovsky et al. 2011). Neurons that exhibited fewer than two detectable fluorescence changes (at least 3 SDs above the mean) were not included in the analysis. We then inferred action potential generation in all neurons that exceeded this threshold (Sadovsky et al. 2011; Vogelstein et al. 2010). Putative spontaneous circuit events were identified by finding peaks in the active cell count with a minimum interpeak distance of 5 s. Once events were identified, we discarded any events for which the active population fluorescence average trace had <10 frames 3.5 SDs above the mean and within 25 frames of the putative event onset. The latter parameters were selected via receiver operating characteristic analysis on hand-labeled data from eight mice with 40 confirmed events, which resulted in a true positive rate of 97% and a false positive rate of 5%.

#### Event area and spatial scale.

Since the number of cells participating in a spontaneous event ranged over several orders of magnitude (between 10 and 885), the area of the convex hull containing all cells active in an event was insufficient for making statements about the scale of that event. Therefore, we defined a cell count-insensitive measurement of spatial scale as follows. First, for each identified event *i*, the convex hull area, Γ_{i}, was computed for 100 proxies generated by selecting the same number of cells from the whole field of view uniformly at random (Γ^{uniform}, below) and 100 proxies generated by selecting a single cell at random and then growing that seed by iteratively selecting nearest neighbors (Γ^{neighbor}). Scale was calculated according to the following equation, where angled brackets denote the average over the bootstrapped proxies:

Thus when the convex hull of an event *i* is the expected size for an event with the same number of cells drawn uniformly from across the entire field of view, the denominator and numerator are equal and the scale is 1. When an event *i* draws entirely locally, the numerator is 0, and so the scale is 0. This treatment reduced the Pearson's correlation between our measures of anatomical scale and population size substantially: from 0.497 with naive convex hull area to 0.200 with the above measure of scale.

#### Optimal-width kernel density estimation.

Rather than creating histograms with arbitrary bin size, we characterized the probability densities of the cell count and scale of events using optimal-width two-dimensional Gaussian kernel density estimation (Botev et al. 2010; code available online at the MATLAB Central File Exchange).

#### Functional connectivity and distance graphs.

Graphs reflecting the single-frame time-lagged activity correlation between cell pairs were constructed as described in Sadovsky and MacLean (2013). The element-wise inverses of the adjacency matrices of these graphs defined the functional distance matrices used to compute shortest internode path distances. Graph properties were calculated and node- in and out-degree-matched random graphs were constructed with the following MATLAB functions from the Brain Connectivity Toolbox (Rubinov and Sporns 2010) functions: modularity_dir, distance_wei, and randmio_dir. Shortest-path distances were computed with Dijkstra's algorithm (Dijkstra 1959) and graph modularities with Leicht and Newman's algorithm for community detection in directed graphs (Leicht and Newman 2008). Node- and degree-matched nulls were produced with the procedure outlined in Maslov and Sneppen (2002).

#### Logistic regression.

Sigmoid curves were used to relate the Euclidean distance between cell pairs and their shortest-path distances on the graph. We used the following form of the function:

The parameters are named as follows: *L* is the height parameter, *y*_{0} is the *y*-intercept, and *r* is the rate parameter. Fits were obtained with MATLAB's “lsqcurvefit” function with default settings. All fits converged to local minima.

## RESULTS

#### Spontaneous events were observed between PND 3 and PND 15 in two primary sensory areas.

To characterize the spontaneous activity at the level of the cortical microcircuit throughout early postnatal development in two areas of sensory cortex, we uniformly and densely sampled emergent activity spanning a field of view 1.1 mm in diameter in slices of mouse somatosensory barrel neocortex and auditory neocortex, using high-speed multiphoton calcium imaging (Sadovsky et al. 2011; Vogelstein et al. 2009; see Fig. 1).

In all cases, regardless of brain area or age, we recorded spontaneously arising circuit activity. We imaged 775 ± 144 (range 441-1,062) neurons within a single field of view at 11.3 ± 2.5 Hz (range 6.8–18.7). Our data set included *n* = 1,061 discrete spontaneous events in slices of neocortex taken from mice ranging in age from PND 3 to PND 15.

Circuit events in different developmental epochs varied in their size, i.e., the fraction of total cells in the field of view that were active in a given event, and in their scale, i.e., whether those cells were drawn from a local anatomical neighborhood or uniformly across the entire field of view (see Fig. 2). Our measure of scale assigned a value of 0 to the nearest-neighbor case and 1 to the uniform case, with intermediate cases falling within and more extreme cases falling outside that range (see materials and methods for details).

Below we describe three main classes of events: local, global, and sparse. Local events are those with a small size and small scale, while sparse events combine small or intermediate size with a large scale. Global events are large in size, comprising at least 40% of the visible cells, and their scale varies between intermediate and large. We observed very few events with a large size and small scale, e.g., the activation of every cell on one half of the field of view.

#### During the first two postnatal weeks, events in somatosensory barrel field begin local, then become heterogeneous, and then sparsify.

Between PND 3 and PND 8, we found that spontaneous circuit events in S1BF (*n* = 111 events, 7 slices) were local, that is, small in size and scale, with 6.3 ± 12% of the cells participating and a scale of 0.30 ± 0.24 (Fig. 3*A*). We observed <10 events from the sparse or global classes. Between PND 9 and PND 13, events (*n* = 644 events, 14 slices) were primarily global: they were more widely distributed (scale 0.63 ± 0.22, *P* < 0.001; all comparisons by Wilcoxon rank sum test unless otherwise noted) and involved a greater fraction of the cells (33 ± 22%, *P* < 0.001), although both sparse and local events also occurred frequently, as can be seen from the log-probability density in Fig. 3*B* (note that the mode of the distribution is at a much higher size and scale than the mean). Events (*n* = 72) were sparser in slices (*n* = 7) taken at the beginning of the second postnatal week, on PND 14 and PND 15. They were at the largest scale (0.82 ± 0.16, *P* < 0.001 for both comparisons) and were intermediate in their size (24% of cells ± 11%, *P* < 0.01 for both comparisons; Fig. 3*C*).

#### Events in auditory cortex exhibit a similar developmental trajectory: local, then mixed, then sparse.

We found that spontaneous circuit events in auditory cortex were quantitatively and qualitatively similar to those in barrel field across the age ranges examined. During PND 3–8, the fraction of cells active in a given event in A1 was the same as events at the same time in S1BF (4.9 ± 2.6% vs. 6.3 ± 12%, *P* = 0.264, *n* = 31 events, 7 slices; cf. Fig. 3, *A* and *D*). The scale of events in A1 was lower in this period than in S1BF (0.19 ± 0.17 vs. 0.30 ± 0.24, *P* = 0.030). Qualitatively, events in both areas were in the local regime, that of small groups of spatially contiguous cells.

Between PND 9 and PND 13, the scale and size of events also increased relative to the early period in A1 (scale 0.49 ± 0.26, active fraction 23 ± 20%, *P* < 0.001 for both comparisons, *n* = 171 events, 12 slices), though not to as great an extent as occurred in S1BF at the same time (see Fig. 3*E*). Qualitatively, slices from both areas in this time period showed a wide variety of activity: global events, sparse events, and local events were all observed. However, global events were unique to this time period for both brain areas. After PND 14, the average scale again increased dramatically, while the mean size increased only modestly (scale 0.84 ± 0.11, *P* < 0.001, active fraction 29 ± 10% *P* = 0.002, *n* = 32 events, 5 slices; see Fig. 3*F*), matching those measures for S1BF during the same period (*P* = 0.515).

Thus both cortical areas ended their development in the regime of sparse activations after passing through periods that exhibited all classes of events. Very large global events were more prominent in S1BF than in A1 during this intermediate period while A1 featured more sparse events, but in both cortical areas global events were unique to this time period.

#### Functional graphs show the same developmental trajectory.

Functional graphs provide a succinct, mathematically tractable summary of the correlation structure of large populations of neurons (Feldt et al. 2011), even though specific correlations do not necessarily reflect causal monosynaptic connections (Chambers and MacLean 2015). These graphs are defined by taking individual neurons, *i* and *j*, as nodes and then drawing a weighted, directed edge *ij* between them with weight equal to the proportion of times that activations of cell *j* were preceded by an activation of cell *i* (Fig. 4*A*). Therefore, the weight of a connection is proportional to the reliability with which an activation of neuron *j* followed an activation of neuron *i* in the preceding frame.

One common measure of graph structure is the modularity, which varies between 0 and 1 and quantifies the extent to which a graph can be separated into neighborhoods, or modules, while breaking as few edges as possible. In a graph representing a social network, a module would correspond to a group of people who are much more likely to be friends with each other than with others. A social network with a high degree of modularity is thus one with many “cliques” (Ercsey-Ravasz et al. 2013).

It is known that functional graphs describing the activity structure of adolescent cortex show a high degree of modularity compared with matched Erdłos-Rényi random graphs (Sadovsky and MacLean 2013). Whether this is also true prior to adolescence is unknown, as is the developmental trajectory of functional modularity. We began by examining this trajectory, and we found that in both cortical areas modularity decreased in the transition from the early to the middle period (S1BF: 0.622 ± 0.099 vs. 0.175 ± 0.118, *P* < 0.001; A1: 0.492 ± 0.214 vs. 0.235 ± 0.179, *P* = 0.045; Fig. 4*B*), which was then indistinguishable from the late period (S1BF: 0.206 ± 0.090, *P* = 0.479, A1: 0.202 ± 0.054, *P* = 0.721), indicating that the modular structure characteristic of mature neocortical functional networks is present early in development and persists during large, synchronous activations.

The high degree of modularity in the early period could simply be the result of the fact that the graph structure in that period is more sparse (Hlinka and Hartman 2012). To test this, we constructed 100 node- and edge-matched random nulls for each of our data sets with a rewiring procedure (Maslov and Sneppen 2002) and then computed the modularity of each random graph. We found that the modularity of 51 of 52 data sets was greater than all of the matched, randomly generated graphs.

The spatiotemporal correlation structure of events can also be characterized by looking at the relationship between Euclidean distance in anatomical space and functional distance on the graph. Functional distance on the graph is naturally defined as the shortest path length between nodes, where the “length” of a connection is the inverse of the connection weight defined above (Fig. 4, *C–E*). Local events should result in a sigmoidal or s-shaped relationship, with a low graph distance at low Euclidean distances that then hits a plateau above the scale from which cells are drawn during events. Global and sparse events should have a roughly flat or shallow linear relationship (see Fig. 4*F*, *inset*).

To capture both of these cases, we fit the functional distances to the Euclidean distances using the sigmoid function, which changes shape from approximately linear to approximately a step function as its rate parameter increases (see materials and methods). A high rate parameter in an epoch thus corresponds to local events and a low rate parameter to the global and sparse event cases.

We found that rate parameters were small but nonzero for PND 9–13 in both cortical areas (0.841 ± 0.841, *P* < 0.001 for S1BF, 1.43 ± 2.58, *P* < 0.001 for A1, both by the sign test) and for PND 14 and 15 in S1BF (0.414 ± 0.209, *P* = 0.0156) but not for A1 (0.249 ± 0.235, *P* = 0.0625). We found that the rate parameters for S1BF during PND 3–8 were significantly greater than those during PND 9–13 and PND 14 and 15 (13.75 ± 6.71; *P* = 0.007, *P* = 0.004, respectively; Fig. 4*F*). Similarly, the rate parameter for A1 during PND 3–8 was significantly greater than those during PND 9–13 and PND 14 and 15 (10.69 ± 3.93; *P* < 0.001, *P* = 0.003) in the same area. These findings indicate that spatial relationships have a strong influence on functional relationships during the period from PND 3 to PND 8 but only a weak or no effect after that time period, consistent with our above finding that scale rapidly increases on PND 9.

## DISCUSSION

We imaged spontaneous activations in neocortical slices taken from two primary sensory areas, S1BF and A1, in mice ranging in age from 3 to 15 days. We found a qualitatively and quantitatively similar developmental trajectory in both areas of neocortex. Spontaneous circuit events began as local recruitments of spatially contiguous neighborhoods of on the order of 5% of cells and then expanded on PND 9 to include global activations of up to 80% of the cells, spread over the whole field of view. Finally, after PND 14 events became sparse, still drawing from the whole field of view but recruiting only 25 ± 11% of the cells per event, as reported previously (Sadovsky and MacLean 2013).

The developmental trajectory from local modules, to global synchrony, and then finally to sparsity appears to generalize across primary sensory areas in vitro and in vivo and during conditions of sensory deprivation (Golshani et al. 2009; Rochefort et al. 2009; Siegel et al. 2012), with the same postnatal time course. The ubiquity and generality of this trajectory suggest a strong, internally mediated mechanism for patterning spontaneous activity during the development of primary sensory neocortical areas, regardless of the sensory experience of the cortical area during this developmental period. So while sensory input clearly refines cortical circuitry (Trachtenberg et al. 2002), the primary drivers of the changes we observed are most likely internal.

Because our recordings were performed in the absence of neuromodulators we can reject the hypothesis that the mechanism is primarily neuromodulatory, suggesting a role for changes of synaptic connectivity and neuronal integration in the progression of circuit dynamics. Those changes could include changes in intrinsic cell properties, e.g., the decrease in the excitability of A1 pyramidal cells between PND 10 and PND 15 as reported by Oswald and Reyes (2008), or to intercellular connectivity, in particular gap junctions, as suggested, in the first postnatal week, by Yuste et al. (1995). The maturation of the NMDA receptor channel during this time period changes the time constant of integration for strong excitatory inputs (Golshani et al. 1998), which in turn will likely drive changes in the propagation of circuit activity. Finally, the maturation of the GABAergic system during this period is also likely to also contribute to the developmental progression of circuit dynamics (He et al. 2014).

In the perinatal period, the gross phenomenology of our observations—tight spatial clusters with oblong anatomical distributions—is most consistent with studies describing electrically connected sister cells arising from the same radial lineage (Li et al. 2012; Yu et al. 2012; Yuste et al. 1995). Future studies would be necessary to determine whether this is indeed the case. Since sparse patterns arise on PND 14, some refinement of circuit structure at the mesoscale should then occur during the period between PND 9 and PND 13, suggesting that the synchronous activations we and others report serve a developmental purpose for cortico-cortical sensory connectivity similar to that which they serve for cortico-subcortical and subcortical connectivity (Blankenship and Feller 2010).

## GRANTS

C. G. Frye was supported by the Eric H. and Rachel K. Stern Health Sciences Graduate Student Award. This work was supported by National Science Foundation CAREER Award 095286.

## DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

## AUTHOR CONTRIBUTIONS

C.G.F. and J.N.M. conception and design of research; C.G.F. performed experiments; C.G.F. analyzed data; C.G.F. and J.N.M. interpreted results of experiments; C.G.F. prepared figures; C.G.F. and J.N.M. drafted manuscript; C.G.F. and J.N.M. edited and revised manuscript; C.G.F. and J.N.M. approved final version of manuscript.

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