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Irregular spiking of pyramidal neurons organizes as scale-invariant neuronal avalanches in the awake state.

Bellay T, Klaus A, Seshadri S, Plenz D - Elife (2015)

Bottom Line: As the animal transitions from the anesthetized to awake state, spontaneous single neuron firing increases in irregularity and assembles into scale-invariant avalanches at the group level.In vitro spike avalanches emerged naturally yet required balanced excitation and inhibition.This demonstrates that neuronal avalanches are linked to the global physiological state of wakefulness and that cortical resting activity organizes as avalanches from firing of local PN groups to global population activity.

View Article: PubMed Central - PubMed

Affiliation: Section on Critical Brain Dynamics, National Institute of Mental Health, Bethesda, United States.

ABSTRACT
Spontaneous fluctuations in neuronal activity emerge at many spatial and temporal scales in cortex. Population measures found these fluctuations to organize as scale-invariant neuronal avalanches, suggesting cortical dynamics to be critical. Macroscopic dynamics, though, depend on physiological states and are ambiguous as to their cellular composition, spatiotemporal origin, and contributions from synaptic input or action potential (AP) output. Here, we study spontaneous firing in pyramidal neurons (PNs) from rat superficial cortical layers in vivo and in vitro using 2-photon imaging. As the animal transitions from the anesthetized to awake state, spontaneous single neuron firing increases in irregularity and assembles into scale-invariant avalanches at the group level. In vitro spike avalanches emerged naturally yet required balanced excitation and inhibition. This demonstrates that neuronal avalanches are linked to the global physiological state of wakefulness and that cortical resting activity organizes as avalanches from firing of local PN groups to global population activity.

No MeSH data available.


Related in: MedlinePlus

Ongoing spiking in local PNs organizes as neuronal avalanches in vivo.(A) Sketch of cluster formation at given Δt and chosen λthr = 1. Gray boxes delineate clusters of activity (i.e., consecutive time bins with λ > λthr). (B) Maximal cluster rate at intermediate λthr for different Δt in the AW condition. Vertical arrows indicate the respective  at which cluster rate is maximal. (C) Individual distributions of normalized cluster sizes, s, in AW (top; Δt = 88 ms, n = 10 recordings, threshold at ). Dotted line, predicted cut-off at s = 1; dashed line, power law with α = −1.5. (D) Corresponding distributions after shuffling λ. Shuffling destroys spatiotemporal correlations in activity and abolishes the power law in cluster sizes. (E) Relationship between α and branching ratio σ for all three temporal resolutions, Δt. Note the systematic change for increasing Δt as shown previously for avalanche dynamics based on the LFP. (F) Distribution of cluster lifetimes, T, for different Δt. Dashed line, slope = −2.DOI:http://dx.doi.org/10.7554/eLife.07224.008
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fig3: Ongoing spiking in local PNs organizes as neuronal avalanches in vivo.(A) Sketch of cluster formation at given Δt and chosen λthr = 1. Gray boxes delineate clusters of activity (i.e., consecutive time bins with λ > λthr). (B) Maximal cluster rate at intermediate λthr for different Δt in the AW condition. Vertical arrows indicate the respective at which cluster rate is maximal. (C) Individual distributions of normalized cluster sizes, s, in AW (top; Δt = 88 ms, n = 10 recordings, threshold at ). Dotted line, predicted cut-off at s = 1; dashed line, power law with α = −1.5. (D) Corresponding distributions after shuffling λ. Shuffling destroys spatiotemporal correlations in activity and abolishes the power law in cluster sizes. (E) Relationship between α and branching ratio σ for all three temporal resolutions, Δt. Note the systematic change for increasing Δt as shown previously for avalanche dynamics based on the LFP. (F) Distribution of cluster lifetimes, T, for different Δt. Dashed line, slope = −2.DOI:http://dx.doi.org/10.7554/eLife.07224.008

Mentions: In the preceding section, we quantified how irregular spontaneous firing in individual PNs and their pairwise correlations change as the animal transitions from the AN to the AW state. None of these measures, though, allows us to identify neuronal avalanches, which reflect a scale-invariant relationship of neuronal group activities. In fact, we recently demonstrated that event rate and pairwise correlation R are insufficient to predict neuronal avalanches in cortical activity (Yu et al., 2011). In a first approach, we therefore identified spatiotemporal activity clusters in the neuronal population. This was done by concatenating firing events of neurons that co-occurred either within Δt or within consecutive periods of Δt (Figure 3A; gray areas) and separating clusters by quiescent periods of at least Δt, the original approach to identify avalanche dynamics (Beggs and Plenz, 2003). For a given neuronal population and 2-PI, this process has two free parameters: (1) the temporal resolution Δt, which is fixed by the scanning frame rate of 2-PI and (2) the activity threshold, λthr, of a firing event. In general, if λthr is low, most firing events will be concatenated into few large clusters. Similarly, if λthr is high, the few remaining firing events will group into few clusters. Thus, a maximal number of clusters is expected at an intermediate threshold . We first studied this relationship in the AW state. Indeed, for a given recording at Δt, the cluster rate increased with λthr and was maximal at an intermediate threshold (Figure 3B, arrows). As expected, shifted towards smaller λthr values at higher temporal resolutions due to the improved resolution of fast λ fluctuations. Next, we studied the cluster size s, that is, the sum of all firing events within a cluster normalized by the predicted cluster size limit Λ, which is determined by the number of ROIs and their respective average firing rate (see ‘Materials and methods’). If the activity of neurons was rather independent from each other, as one might assume from the low average pairwise correlation in λ (Figure 1), the distribution in cluster size should be close to an exponential function. On the other hand, if interactions between neurons contribute significantly to spontaneous firing, then the cluster size distribution deviates from an exponential function, and, in the case of avalanche dynamics, should follow a power law (Plenz and Thiagarajan, 2007). Importantly, we found that cluster sizes distributed according to a power law over approximately two orders of magnitude (Figure 3C: α = 1.63 ± 0.13, LLR = 25.7–201.4 favors power law over exponential, p < 0.003 for all n = 10 experiments, Δt = 88 ms at individual ). To determine whether the AP activities in PN groups that resulted in power-law distributed cluster sizes were indeed a result of spatiotemporal correlations, we performed, as a control, time-shuffling of the corresponding λ events. As shown in Figure 3D, time-shuffled λ events did not yield power-law size distributions, and instead, cluster size distributions were better fit by an exponential (LLR = −66.6 to −6.9, favors exponential over power law, p < 0.05 for 7/10 experiments, Δt = 88 ms; thresholded at obtained for each distribution individually).10.7554/eLife.07224.008Figure 3.Ongoing spiking in local PNs organizes as neuronal avalanches in vivo.


Irregular spiking of pyramidal neurons organizes as scale-invariant neuronal avalanches in the awake state.

Bellay T, Klaus A, Seshadri S, Plenz D - Elife (2015)

Ongoing spiking in local PNs organizes as neuronal avalanches in vivo.(A) Sketch of cluster formation at given Δt and chosen λthr = 1. Gray boxes delineate clusters of activity (i.e., consecutive time bins with λ > λthr). (B) Maximal cluster rate at intermediate λthr for different Δt in the AW condition. Vertical arrows indicate the respective  at which cluster rate is maximal. (C) Individual distributions of normalized cluster sizes, s, in AW (top; Δt = 88 ms, n = 10 recordings, threshold at ). Dotted line, predicted cut-off at s = 1; dashed line, power law with α = −1.5. (D) Corresponding distributions after shuffling λ. Shuffling destroys spatiotemporal correlations in activity and abolishes the power law in cluster sizes. (E) Relationship between α and branching ratio σ for all three temporal resolutions, Δt. Note the systematic change for increasing Δt as shown previously for avalanche dynamics based on the LFP. (F) Distribution of cluster lifetimes, T, for different Δt. Dashed line, slope = −2.DOI:http://dx.doi.org/10.7554/eLife.07224.008
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fig3: Ongoing spiking in local PNs organizes as neuronal avalanches in vivo.(A) Sketch of cluster formation at given Δt and chosen λthr = 1. Gray boxes delineate clusters of activity (i.e., consecutive time bins with λ > λthr). (B) Maximal cluster rate at intermediate λthr for different Δt in the AW condition. Vertical arrows indicate the respective at which cluster rate is maximal. (C) Individual distributions of normalized cluster sizes, s, in AW (top; Δt = 88 ms, n = 10 recordings, threshold at ). Dotted line, predicted cut-off at s = 1; dashed line, power law with α = −1.5. (D) Corresponding distributions after shuffling λ. Shuffling destroys spatiotemporal correlations in activity and abolishes the power law in cluster sizes. (E) Relationship between α and branching ratio σ for all three temporal resolutions, Δt. Note the systematic change for increasing Δt as shown previously for avalanche dynamics based on the LFP. (F) Distribution of cluster lifetimes, T, for different Δt. Dashed line, slope = −2.DOI:http://dx.doi.org/10.7554/eLife.07224.008
Mentions: In the preceding section, we quantified how irregular spontaneous firing in individual PNs and their pairwise correlations change as the animal transitions from the AN to the AW state. None of these measures, though, allows us to identify neuronal avalanches, which reflect a scale-invariant relationship of neuronal group activities. In fact, we recently demonstrated that event rate and pairwise correlation R are insufficient to predict neuronal avalanches in cortical activity (Yu et al., 2011). In a first approach, we therefore identified spatiotemporal activity clusters in the neuronal population. This was done by concatenating firing events of neurons that co-occurred either within Δt or within consecutive periods of Δt (Figure 3A; gray areas) and separating clusters by quiescent periods of at least Δt, the original approach to identify avalanche dynamics (Beggs and Plenz, 2003). For a given neuronal population and 2-PI, this process has two free parameters: (1) the temporal resolution Δt, which is fixed by the scanning frame rate of 2-PI and (2) the activity threshold, λthr, of a firing event. In general, if λthr is low, most firing events will be concatenated into few large clusters. Similarly, if λthr is high, the few remaining firing events will group into few clusters. Thus, a maximal number of clusters is expected at an intermediate threshold . We first studied this relationship in the AW state. Indeed, for a given recording at Δt, the cluster rate increased with λthr and was maximal at an intermediate threshold (Figure 3B, arrows). As expected, shifted towards smaller λthr values at higher temporal resolutions due to the improved resolution of fast λ fluctuations. Next, we studied the cluster size s, that is, the sum of all firing events within a cluster normalized by the predicted cluster size limit Λ, which is determined by the number of ROIs and their respective average firing rate (see ‘Materials and methods’). If the activity of neurons was rather independent from each other, as one might assume from the low average pairwise correlation in λ (Figure 1), the distribution in cluster size should be close to an exponential function. On the other hand, if interactions between neurons contribute significantly to spontaneous firing, then the cluster size distribution deviates from an exponential function, and, in the case of avalanche dynamics, should follow a power law (Plenz and Thiagarajan, 2007). Importantly, we found that cluster sizes distributed according to a power law over approximately two orders of magnitude (Figure 3C: α = 1.63 ± 0.13, LLR = 25.7–201.4 favors power law over exponential, p < 0.003 for all n = 10 experiments, Δt = 88 ms at individual ). To determine whether the AP activities in PN groups that resulted in power-law distributed cluster sizes were indeed a result of spatiotemporal correlations, we performed, as a control, time-shuffling of the corresponding λ events. As shown in Figure 3D, time-shuffled λ events did not yield power-law size distributions, and instead, cluster size distributions were better fit by an exponential (LLR = −66.6 to −6.9, favors exponential over power law, p < 0.05 for 7/10 experiments, Δt = 88 ms; thresholded at obtained for each distribution individually).10.7554/eLife.07224.008Figure 3.Ongoing spiking in local PNs organizes as neuronal avalanches in vivo.

Bottom Line: As the animal transitions from the anesthetized to awake state, spontaneous single neuron firing increases in irregularity and assembles into scale-invariant avalanches at the group level.In vitro spike avalanches emerged naturally yet required balanced excitation and inhibition.This demonstrates that neuronal avalanches are linked to the global physiological state of wakefulness and that cortical resting activity organizes as avalanches from firing of local PN groups to global population activity.

View Article: PubMed Central - PubMed

Affiliation: Section on Critical Brain Dynamics, National Institute of Mental Health, Bethesda, United States.

ABSTRACT
Spontaneous fluctuations in neuronal activity emerge at many spatial and temporal scales in cortex. Population measures found these fluctuations to organize as scale-invariant neuronal avalanches, suggesting cortical dynamics to be critical. Macroscopic dynamics, though, depend on physiological states and are ambiguous as to their cellular composition, spatiotemporal origin, and contributions from synaptic input or action potential (AP) output. Here, we study spontaneous firing in pyramidal neurons (PNs) from rat superficial cortical layers in vivo and in vitro using 2-photon imaging. As the animal transitions from the anesthetized to awake state, spontaneous single neuron firing increases in irregularity and assembles into scale-invariant avalanches at the group level. In vitro spike avalanches emerged naturally yet required balanced excitation and inhibition. This demonstrates that neuronal avalanches are linked to the global physiological state of wakefulness and that cortical resting activity organizes as avalanches from firing of local PN groups to global population activity.

No MeSH data available.


Related in: MedlinePlus