An open question in biological neural networks is whether changes in firing modalities are mainly an individual network property or whether networks follow a joint pathway. For the early developmental period, our study focusing on a simple network class of excitatory and inhibitory neurons suggests the following answer: Networks with considerable variation of topology and dynamical parameters follow a universal firing paradigm that evolves as the overall connectivity strength and firing level increase, as seen in the process of network maturation. A simple macroscopic model reproduces the main features of the paradigm as a result of the competition between the fundamental dynamical system notions of synchronization vs chaos and explains why in simulations the paradigm is robust regarding differences in network topology and largely independent from the neuron model used. The presented findings reflect the first dozen days of dissociated neuronal in vitro cultures (upon following the developmental period bears similarly universal features but is characterized by the processes of neuronal facilitation and depression that do not require to be considered for the first developmental period).
REFERENCES
1
M.
Barahona
and L. M.
Pecora
, “Synchronization in small-world systems
,” Phys. Rev. Lett.
89
(5
), 054101
(2002
). 2
E.
Niebur
, H. G
Schuster
, D. M
Kammen
, and C.
Koch
, “Oscillator-phase coupling for different two-dimensional network connectivities
,” Phys. Rev. A
44
(10
), 6895
(1991
). 3
C.
Zhou
, A. E
Motter
, and J.
Kurths
, “Universality in the synchronization of weighted random networks
,” Phys. Rev. Lett.
96
(3
), 034101
(2006
). 4
D.
Hansel
and C.
van Vreeswijk
, “The mechanism of orientation selectivity in primary visual cortex without a functional map
,” J. Neurosci.
32
(12
), 4049
(2012
). 5
R.
Stoop
, V.
Saase
, C.
Wagner
, B.
Stoop
, and R.
Stoop
, “Beyond scale-free small-world networks: Cortical columns for quick brains
,” Phys. Rev. Lett.
110
(10
), 108105
(2013
). 6
A. A
Prinz
, D.
Bucher
, and E.
Marder
, “Similar network activity from disparate circuit parameters
,” Nat. Neurosci.
7
(12
), 1345
(2004
). 7
T. P.
Vogels
, K.
Rajan
, and L. F.
Abbott
, “Neural network dynamics
,” Annu. Rev. Neurosci.
28
, 357
(2005
). 8
H.
Markram
et al., “Reconstruction and simulation of neocortical microcircuitry
,” Cell
163
(2
), 456
(2015
). 9
C. I.
Bargmann
and E.
Marder
, “From the connectome to brain function
,” Nat. Methods
10
(6
), 483
(2013
). 10
C. M.
Constantinople
and R. M.
Bruno
, “Effects and mechanisms of wakefulness on local cortical networks
,” Neuron
69
(6
), 1061
(2011
). 11
P.
Dayan
, “Twenty-five lessons from computational neuromodulation
,” Neuron
76
(1
), 240
–256
(2012
). 12
S.-H.
Lee
and Y.
Dan
, “Neuromodulation of brain states
,” Neuron
76
(1
), 209
–222
(2012
). 13
K.
Kanders
, T.
Lorimer
, and R.
Stoop
, “Avalanche and edge-of-chaos criticality do not necessarily co-occur in neural networks
,” Chaos
27
(4
), 047408
(2017
). 14
Z.
Molnár
, “Cortical columns,” in Neural Circuit Development and Function in the Brain (Elsevier, 2013), pp. 109–129.15
B.
Roerig
and B.
Chen
, “Relationships of local inhibitory and excitatory circuits to orientation preference maps in ferret visual cortex
,” Cerebr. Cortex
12
, 187198
(2002
). 16
S.
Song
, P. J.
Sjöström
, M.
Reigl
, S.
Nelson
, and D. B.
Chklovskii
, “Highly nonrandom features of synaptic connectivity in local cortical circuits
,” PLoS Biol.
3
(3
), e68
(2005
). 17
S. H.
Hendry
, H. D.
Schwark
, E. G.
Jones
, and J.
Yan
, “Numbers and proportions of GABA-immunoreactive neurons in different areas of monkey cerebral cortex
,” J. Neurosci.
7
(5
), 1503
–1519
(1987
). 18
N. F.
Rulkov
, “Modeling of spiking-bursting neural behavior using two-dimensional map
,” Phys. Rev. E
65
(4
), 041922
(2002
). 19
N. F.
Rulkov
, I.
Timofeev
, and M.
Bazhenov
, “Oscillations in large-scale cortical networks: Map-based model
,” J. Comput. Neurosci.
17
(2
), 203
–223
(2004
). 20
K.
Kanders
and R.
Stoop
, “Phase response properties of Rulkov model neurons,” in Emergent Complexity from Nonlinearity, in Physics, Engineering and the Life Sciences, Springer Proceedings in Physics (Springer, 2017), pp. 21–35.21
P.
Fatt
and B.
Katz
, “Some observations on biological noise
,” Nature
166
(4223
), 597
(1950
). 22
S. A.
Prescott
, Y.
De Koninck
, and T. J.
Sejnowski
, “Biophysical basis for three distinct dynamical mechanisms of action potential initiation
,” PLoS Comput. Biol.
4
(10
), e1000198
(2008
). 23
A. V.
Egorov
, B. N.
Hamam
, E.
Fransén
, M. E.
Hasselmo
, and A. A.
Alonso
, “Graded persistent activity in entorhinal cortex neurons
,” Nature
420
(6912
), 173
(2002
). 24
J.-P.
Eckmann
, S.
Jacobi
, S.
Marom
, E.
Moses
, and C.
Zbinden
, “Leader neurons in population bursts of 2D living neural networks
,” New J. Phys.
10
(1
), 015011
(2008
). 25
J. G.
Orlandi
, J.
Soriano
, E.
Alvarez-Lacalle
, S.
Teller
, and J.
Casademunt
, “Noise focusing and the emergence of coherent activity in neuronal cultures
,” Nat. Phys.
9
(9
), 582
(2013
). 26
D.
Golomb
and J.
Rinzel
, “Clustering in globally coupled inhibitory neurons
,” Physica D
72
(3
), 259
–282
(1994
). 27
J. M.
Beggs
and D.
Plenz
, “Neuronal avalanches in neocortical circuits
,” J. Neurosci.
23
(35
), 11167
–11177
(2003
). 28
J.
Peinke
, J.
Parisi
, O. E.
Rössler
, and R.
Stoop
, Encounter with Chaos: Self-Organized Hierarchical Complexity in Semiconductor Experiments
(Springer Science & Business Media
, 2012
).29
J.
Hofbauer
and K.
Sigmund
, The Theory of Evolution and Dynamical Systems: Mathematical Aspects of Selection
(Cambridge University Press
, 1988
).30
M.
Ichikawa
, K.
Muramoto
, K.
Kobayashi
, M.
Kawahara
, and Y.
Kuroda
, “Formation and maturation of synapses in primary cultures of rat cerebral cortical cells: An electron microscopic study
,” Neurosci. Res.
16
(2
), 95
–103
(1993
). 31
D.
Berger
, S.
Joo
, T.
Lorimer
, Y.
Nam
, and R.
Stoop
, “Power laws in neuronal culture activity from limited availability of a shared resource,” in Emergent Complexity from Nonlinearity, in Physics, Engineering and the Life Sciences (Springer, 2017), pp. 209–220.32
R.
Baddeley
, L. F.
Abbott
, M. C. A.
Booth
, F.
Sengpiel
, T.
Freeman
, E. A.
Wakeman
, and E. T.
Rolls
, “Responses of neurons in primary and inferior temporal visual cortices to natural scenes
,” Proc. Biol. Sci.
264
(1389
), 1775
–1783
(1997
). 33
K.
Kanders
, “How topology and dynamics shape the function of neural systems,” Ph.D. thesis (ETH Zürich, 2019).34
D. R.
Chialvo
, “Emergent complex neural dynamics
,” Nat. Phys.
6
(10
), 744
(2010
). 35
M.
Bartos
, I.
Vida
, and P.
Jonas
, “Synaptic mechanisms of synchronized gamma oscillations in inhibitory interneuron networks
,” Nat. Rev. Neurosci.
8
(1
), 45
–56
(2007
). 36
E. D.
Herzog
, T.
Hermanstyne
, N. J.
Smyllie
, and M. H.
Hastings
, “Regulating the suprachiasmatic nucleus (SCN) circadian clockwork: Interplay between cell-autonomous and circuit-level mechanisms
,” Cold Spring Harb. Perspect. Biol.
9
(1
), a027706
(2017
). 37
G. M.
Freeman, Jr.
, R. M.
Krock
, S. J.
Aton
, P.
Thaben
, and E. D.
Herzog
, “GABA networks destabilize genetic oscillations in the circadian pacemaker
,” Neuron
78
(5
), 799
–806
(2013
). 38
S.
An
, R.
Harang
, K.
Meeker
, D.
Granados-Fuentes
, C. A.
Tsai
, C.
Mazuski
, J.
Kim
, F. J.
Doyle III
, L. R.
Petzold
, and E. D.
Herzog
, “A neuropeptide speeds circadian entrainment by reducing intercellular synchrony
,” Proc. Natl. Acad. Sci. U.S.A.
110
, E4355
–E4361
(2013
). 39
C.
Haldeman
and J. M.
Beggs
, “Critical branching captures activity in living neural networks and maximizes the number of metastable states
,” Phys. Rev. Lett.
94
(5
), 058101
(2005
). 40
M. O.
Magnasco
, O.
Piro
, and G. A.
Cecchi
, “Self-tuned critical anti-Hebbian networks
,” Phys. Rev. Lett.
102
(25
), 258102
(2009
). 41
A.
Pikovsky
and M.
Rosenblum
, “Dynamics of globally coupled oscillators: Progress and perspectives
,” Chaos
25
(9
), 097616
(2015
). 42
M.
Rosenblum
and R.
Cestnik
, “Reconstructing networks of pulse-coupled oscillators from spike trains
,” Phys. Rev. E
96
(1
), 012209
(2017
). © 2019 Author(s).
2019
Author(s)
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