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Temporal correlations in neuronal avalanche occurrence.

Lombardi F, Herrmann HJ, Plenz D, de Arcangelis L - Sci Rep (2016)

Bottom Line: Moreover we evidence that sizes of consecutive avalanches are correlated.In particular, we show that an avalanche tends to be larger or smaller than the following one for short or long time separation, respectively.Our analysis represents the first attempt to provide a quantitative estimate of correlations between activity and quiescence in the framework of neuronal avalanches and will help to enlighten the mechanisms underlying spontaneous activity.

View Article: PubMed Central - PubMed

Affiliation: Institute of Computational Physics for Engineering Materials, ETH, Zurich, Switzerland.

ABSTRACT
Ongoing cortical activity consists of sequences of synchronized bursts, named neuronal avalanches, whose size and duration are power law distributed. These features have been observed in a variety of systems and conditions, at all spatial scales, supporting scale invariance, universality and therefore criticality. However, the mechanisms leading to burst triggering, as well as the relationship between bursts and quiescence, are still unclear. The analysis of temporal correlations constitutes a major step towards a deeper understanding of burst dynamics. Here, we investigate the relation between avalanche sizes and quiet times, as well as between sizes of consecutive avalanches recorded in cortex slice cultures. We show that quiet times depend on the size of preceding avalanches and, at the same time, influence the size of the following one. Moreover we evidence that sizes of consecutive avalanches are correlated. In particular, we show that an avalanche tends to be larger or smaller than the following one for short or long time separation, respectively. Our analysis represents the first attempt to provide a quantitative estimate of correlations between activity and quiescence in the framework of neuronal avalanches and will help to enlighten the mechanisms underlying spontaneous activity.

No MeSH data available.


Related in: MedlinePlus

Sizes of consecutive avalanches are correlated.The quantity δP(si+1 > λsi, Δti < t0) as a function of λ for different values of t0 and different conditions, non-driven, driven and disinhibited (PTX). The bar on each data point is 2σ(si+1 > λsi, Δti < t0). Each curve represents an average over all experimental samples in a given condition. (a) Non-driven; (b) Driven; (c) Disinhibited (PTX). Insets: The ratio δP(si+1 > λsi, Δti < t0)/σ as a function of s0 for different values of t0; dashed lines delimit the interval (−2, 2). In most cases δP(si+1 > λsi, Δti < t0)/σ is much larger than 2. Therefore results are significant at a level generally lower than 0.05 and give solid evidences of correlations between consecutive avalanches.
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f6: Sizes of consecutive avalanches are correlated.The quantity δP(si+1 > λsi, Δti < t0) as a function of λ for different values of t0 and different conditions, non-driven, driven and disinhibited (PTX). The bar on each data point is 2σ(si+1 > λsi, Δti < t0). Each curve represents an average over all experimental samples in a given condition. (a) Non-driven; (b) Driven; (c) Disinhibited (PTX). Insets: The ratio δP(si+1 > λsi, Δti < t0)/σ as a function of s0 for different values of t0; dashed lines delimit the interval (−2, 2). In most cases δP(si+1 > λsi, Δti < t0)/σ is much larger than 2. Therefore results are significant at a level generally lower than 0.05 and give solid evidences of correlations between consecutive avalanches.

Mentions: In previous sections we have shown that the size of an avalanche is significantly correlated with both the previous and the following quiet time. Here we investigate the relationship between successive synchronous firing events, namely between sizes of consecutive neuronal avalanches. In particular, we ask what is the probability of finding an avalanche whose size si+1 is larger than λ times the size si of the previous one after a quiet time shorter than t0 and consider the quantity δP(si+1 > λsi, Δt < t0). In Fig. 6 we plot this quantity as a function of λ for different values of t0. We first discuss the non-driven case (Fig. 6a). We observe that δP(si+1 > λsi, Δt < t0), and in particular its maximum, decreases by increasing t0, meaning that, correlations in size depend on the time interval separating two avalanches. At short time scales, namely for t0 < 100 ms, δP(si+1 > λsi, Δt < t0) is always positive or zero: Its maximum is located around , suggesting that, for close-in-time consecutive avalanches, the second one tends to be smaller than the first one. Conversely, for t0 > 200, δP(si+1 > λsi, Δt < t0) is negative for λ < 1 and reaches its maximum at λ > 1. Therefore for larger temporal separation, the second avalanche can be substantially larger than the previous one (Fig. 6a).


Temporal correlations in neuronal avalanche occurrence.

Lombardi F, Herrmann HJ, Plenz D, de Arcangelis L - Sci Rep (2016)

Sizes of consecutive avalanches are correlated.The quantity δP(si+1 > λsi, Δti < t0) as a function of λ for different values of t0 and different conditions, non-driven, driven and disinhibited (PTX). The bar on each data point is 2σ(si+1 > λsi, Δti < t0). Each curve represents an average over all experimental samples in a given condition. (a) Non-driven; (b) Driven; (c) Disinhibited (PTX). Insets: The ratio δP(si+1 > λsi, Δti < t0)/σ as a function of s0 for different values of t0; dashed lines delimit the interval (−2, 2). In most cases δP(si+1 > λsi, Δti < t0)/σ is much larger than 2. Therefore results are significant at a level generally lower than 0.05 and give solid evidences of correlations between consecutive avalanches.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4837393&req=5

f6: Sizes of consecutive avalanches are correlated.The quantity δP(si+1 > λsi, Δti < t0) as a function of λ for different values of t0 and different conditions, non-driven, driven and disinhibited (PTX). The bar on each data point is 2σ(si+1 > λsi, Δti < t0). Each curve represents an average over all experimental samples in a given condition. (a) Non-driven; (b) Driven; (c) Disinhibited (PTX). Insets: The ratio δP(si+1 > λsi, Δti < t0)/σ as a function of s0 for different values of t0; dashed lines delimit the interval (−2, 2). In most cases δP(si+1 > λsi, Δti < t0)/σ is much larger than 2. Therefore results are significant at a level generally lower than 0.05 and give solid evidences of correlations between consecutive avalanches.
Mentions: In previous sections we have shown that the size of an avalanche is significantly correlated with both the previous and the following quiet time. Here we investigate the relationship between successive synchronous firing events, namely between sizes of consecutive neuronal avalanches. In particular, we ask what is the probability of finding an avalanche whose size si+1 is larger than λ times the size si of the previous one after a quiet time shorter than t0 and consider the quantity δP(si+1 > λsi, Δt < t0). In Fig. 6 we plot this quantity as a function of λ for different values of t0. We first discuss the non-driven case (Fig. 6a). We observe that δP(si+1 > λsi, Δt < t0), and in particular its maximum, decreases by increasing t0, meaning that, correlations in size depend on the time interval separating two avalanches. At short time scales, namely for t0 < 100 ms, δP(si+1 > λsi, Δt < t0) is always positive or zero: Its maximum is located around , suggesting that, for close-in-time consecutive avalanches, the second one tends to be smaller than the first one. Conversely, for t0 > 200, δP(si+1 > λsi, Δt < t0) is negative for λ < 1 and reaches its maximum at λ > 1. Therefore for larger temporal separation, the second avalanche can be substantially larger than the previous one (Fig. 6a).

Bottom Line: Moreover we evidence that sizes of consecutive avalanches are correlated.In particular, we show that an avalanche tends to be larger or smaller than the following one for short or long time separation, respectively.Our analysis represents the first attempt to provide a quantitative estimate of correlations between activity and quiescence in the framework of neuronal avalanches and will help to enlighten the mechanisms underlying spontaneous activity.

View Article: PubMed Central - PubMed

Affiliation: Institute of Computational Physics for Engineering Materials, ETH, Zurich, Switzerland.

ABSTRACT
Ongoing cortical activity consists of sequences of synchronized bursts, named neuronal avalanches, whose size and duration are power law distributed. These features have been observed in a variety of systems and conditions, at all spatial scales, supporting scale invariance, universality and therefore criticality. However, the mechanisms leading to burst triggering, as well as the relationship between bursts and quiescence, are still unclear. The analysis of temporal correlations constitutes a major step towards a deeper understanding of burst dynamics. Here, we investigate the relation between avalanche sizes and quiet times, as well as between sizes of consecutive avalanches recorded in cortex slice cultures. We show that quiet times depend on the size of preceding avalanches and, at the same time, influence the size of the following one. Moreover we evidence that sizes of consecutive avalanches are correlated. In particular, we show that an avalanche tends to be larger or smaller than the following one for short or long time separation, respectively. Our analysis represents the first attempt to provide a quantitative estimate of correlations between activity and quiescence in the framework of neuronal avalanches and will help to enlighten the mechanisms underlying spontaneous activity.

No MeSH data available.


Related in: MedlinePlus