1
Single-cell Networks Reorganise to Facilitate Whole-brain
Supercritical Dynamics During Epileptic Seizures
Burrows DRW
1
, Diana G
1
, Pimpel B
2,3
, Moeller F
2
, Richardson MP
1
,
Bassett DS
4,5,6
, Meyer MP
1
, Rosch RE
1,2,4 *
1 MRC Centre for Neurodevelopmental Disorders, King’s College London, London, UK
2 Department of Neurophysiology, Great Ormond Street Hospital NHS Foundation Trust,
London, UK
3 GOS-UCL Institute of Child Health, University College London, London, UK
4 Department of Bioengineering, University of Pennsylvania, Philadelphia PA, USA
5 Department of Electrical & Systems Engineering, Physics & Astronomy, Neurology, and
Psychiatry University of Pennsylvania, Philadelphia PA, USA
6 Santa Fe Institute, Santa Fe NM, USA
Correspondence and requests for materials should be addressed to RER
(richard.rosch@kcl.ac.uk).
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2
Summary
Excitation-inhibition (EI) balance may be required for the organisation of brain dynamics to a
phase transition, criticality, which confers computational benefits. Brain pathology associated
with EI imbalance may therefore occur due to a deviation from criticality. However, evidence
linking critical dynamics with EI imbalance-induced pathology is lacking. Here, we studied the
effect of EI imbalance-induced epileptic seizures on brain dynamics, using in vivo whole-brain 2-
photon imaging of GCaMP6s larval zebrafish at single-neuron resolution. We demonstrate the
importance of EI balance for criticality, with EI imbalance causing a loss of whole-brain critical
statistics. Using network models we show that a reorganisation of network topology drives this
loss of criticality. Seizure dynamics match theoretical predictions for networks driven away from
a phase transition into disorder, with the emergence of chaos and a loss of network-mediated
separation, dynamic range and metastability. These results demonstrate that EI imbalance
drives a pathological deviation from criticality.
Keywords
criticality - phase transitions - EI balance - whole-brain dynamics - epilepsy - seizures -
zebrafish - calcium imaging
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Introduction
A delicate balance between excitation and inhibition supports the diverse repertoire of neural
dynamics needed for behaviour. This excitation-inhibition (EI) balance is thought to be important
for healthy brain function as multiple neurodevelopmental disorders are linked to EI imbalance,
including schizophrenia, autism and epilepsy (Fritschy, 2008; Gao & Penzes, 2015; Lee et al.,
2017; Žiburkus et al., 2013). EI balance manifests synaptically as invariant ratios of excitatory-
inhibitory synapses along dendritic segments (Iascone et al., 2020). Interestingly, synaptic EI
balance can shape global dynamics, as demonstrated by the emergence of generalised
seizures in synaptopathies (Escayg & Goldin, 2010; Johannesen et al., 2016; R. Rosch et al.,
2019). At present, our understanding of the role of EI balance in shaping dynamics and
ultimately computation comes from small population recordings, suggesting roles in shaping
receptive fields (B. Liu et al., 2010), supporting coincidence detection (Wehr & Zador, 2003) and
enabling gain control (Bhatia et al., 2019). How synaptic EI balance shapes population
dynamics in whole-brain networks to facilitate computation remains an open question, due to
the technical difficulties of collecting and analysing such high dimensional datasets.
One appealing approach is to borrow concepts from statistical physics, which measures
microscopic variables probabilistically to estimate macroscale properties of complex systems.
Using such approaches, it has been claimed that neuronal populations exhibit dynamics
analogous to atomic spins in a ferromagnetic lattice organised to a phase transition between
order and chaos, known as criticality (Bak et al., 1987, 1988; Hesse & Gross, 2014; Sethna et
al., 2001). In fact, various statistical signatures of criticality have been documented empirically in
neural recordings across diverse scales (Beggs & Plenz, 2003; Kitzbichler et al., 2009; Meisel et
al., 2012; Ponce-Alvarez et al., 2018). However, such statistical indicators of criticality are purely
correlative and therefore the extent to which brain dynamics share universal properties of
idealised, physical systems operating exactly at a phase transition is unclear (Fontenele et al.,
2019; Wilting & Priesemann, 2019). Nonetheless, a system operating within a collection of near-
to-critical states offers a biologically plausible regime of brain activity which can support
computation (Gross, 2021; Kinouchi et al., 2020; Moretti & Muñoz, 2013; Priesemann et al.,
2014). Interestingly, in silico evidence suggests that only EI balanced networks support scale-
invariant avalanches (Poil et al., 2012), spatio-temporal cascades of neural activity that span the
entire scale of the system, a defining feature of criticality. Furthermore, perturbing EI balance in
vitro removes signatures of criticality (Haldeman & Beggs, 2005; Shew et al., 2011). Therefore,
the tendency of the brain to homeostatically maintain EI balance (Turrigiano & Nelson, 2004)
could serve to tune its dynamics near to a phase transition. The role of EI balance in shaping
near-critical dynamics has yet to be tested in vivo.
Systems at criticality maximise various computational capacities, such as: i) network-mediated
separation, the ability to separate similar inputs to distinguishable outputs (Bertschinger &
Natschläger, 2004; Maass et al., 2002), ii) dynamic range, the range of inputs that the network
can encode (Kinouchi & Copelli, 2006; Shew et al., 2011), and iii) metastability, the tendency of
the brain to transiently explore a diversity of semi-stable states supporting flexible dynamics
(Deco et al., 2017; Fingelkurts & Fingelkurts, 2001). Therefore, it has been theorised that EI
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4
imbalance-associated brain dysfunction may emerge as a deviation from the critical state
(Zimmern, 2020). In fact, epileptic seizures, which can emerge due to pathological EI
imbalances, are associated with a loss of critical statistics in EEG and MEG recordings (Arviv et
al., 2016; Meisel et al., 2012). This has led to the prediction that seizure initiation manifests as a
supercritical state (Beggs & Plenz, 2003), where dynamics move away from a transition point
into chaos (Haldeman & Beggs, 2005), thus causing inputs to exponentially grow in time and
saturate the system (Harris, 1963). Whilst some features of supercritical dynamics have been
reported using macroscale seizure recordings, such techniques coarse-grain the underlying
dynamics which obscures the heterogeneity of cellular activity and could alter critical statistics
(Keller et al., 2010; Meyer et al., 2018; Muldoon et al., 2013). Conversely, recording from
subregions of a full system can produce spurious critical statistics (Priesemann et al., 2009),
while distinct brain regions may reside at different near-critical states (Suryadi et al., 2018).
Therefore, to make strong claims about the critical nature of entire neuronal systems, we require
single cell recordings with whole-brain coverage. Whether single neuron dynamics collectively
engage to give rise to a supercritical state in whole-brain networks during seizures is untested.
Showing this experimentally, would demonstrate that synaptic EI imbalance can impair
computation by disrupting near-critical dynamics across the whole brain.
Here we take advantage of the transparency of the larval zebrafish to perform in vivo functional
imaging of the whole brain at single cell resolution (Ahrens et al., 2013). We test 2 key
hypotheses: i) EI balance regulates near-critical dynamics, and ii) epileptic seizures emerge as
a supercritical state which impairs brain computation. We find that perturbations to EI balance
give rise to abrupt changes in critical statistics, suggesting a role of EI balance in organising
dynamics near to a phase transition. Furthermore, epileptic seizures manifest as a chaotic state
giving rise to reduced network-mediated separation, dynamic range and metastability,
demonstrating that seizures emerge as a supercritical state.
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(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
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Results
To study critical dynamics in vivo we analysed neuronal activity of GCaMP6s-expressing larval
zebrafish captured via whole-brain 2-photon imaging at single cell resolution (See Figure S1).
To perturb EI balance we used the GABA
A
receptor antagonist pentylenetetrazole (PTZ), which
causes epileptiform discharges (Baraban et al., 2005; R. E. Rosch et al., 2018). We recorded 3
x 30 minute consecutive imaging blocks: 1) spontaneous activity representing EI balance, 2)
5mM PTZ causing EI imbalance giving rise to focal seizures, and 3) 20mM PTZ causing EI
imbalance giving rise to generalised seizures (See Figure S2) (Diaz Verdugo et al., 2019). We
segmented ~9,000 neurons per dataset, estimating their latent on/off states using a hidden
Markov model (HMM) (Diana et al., 2019) (See Figure S1D & 1B). This allowed us to measure
the propagation of neuronal avalanches and the evolution of population dynamics during EI
balance and imbalance (See Methods & Figure 1).
Spontaneous Neural Dynamics Exhibit Critical Statistics
Several statistical features have been reported as indicators of criticality, including (i) power-law
probability distributions of avalanche size and duration, (ii) scaling relationships between
avalanche power-law exponents, (iii) branching ratios close to unity and (iv) power-law scaling
of neuron correlation and distance. We evaluate each of these features to validate the presence
of near-critical dynamics in spontaneous activity.
A key feature of criticality is the presence of scale-invariant neuronal avalanches, contiguous
clusters of activity which propagate in space and time (See Figure 1D), giving rise to power-law
probability distributions. We estimated probability distributions for avalanche size and duration
from calcium imaging data, which were well fit by power-laws (See Figure 2A). Using log
likelihood ratio testing, we found that all datasets were better explained by power-law than
lognormal distributions, the most rigorous alternative heavy-tail distribution test (See Methods)
(Alstott et al., 2014). Importantly, measuring neuronal avalanches from sequences of oscillatory
peaks in human intracranial recordings also reveals power-law statistics in baseline activity (See
Figure S3B). This indicates the robustness of power-law relationships in neural activity across
brain scales.
However, power-laws can emerge in non-critical systems. A more robust marker of criticality is
exponent relation, which can distinguish between critical and non-critical regimes that produce
power-laws (Ma et al., 2019; Touboul & Destexhe, 2017). Exponent relation dictates that at
criticality the power-law exponents for avalanche size and duration can be predicted by a third
exponent β (See Figure 2A). We use the deviation from criticality coefficient (DCC, see
Methods) to assess exponent relation (Ma et al., 2019). Our datasets exhibit close to predicted
β, suggesting the presence of near-critical dynamics (DCC = 0.13 ± 0.04) (See Figure 2B). In
.CC-BY-NC-ND 4.0 International licenseavailable under a
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
The copyright holder for this preprintthis version posted October 16, 2021. ; https://doi.org/10.1101/2021.10.14.464473doi: bioRxiv preprint