The hippocampal theta oscillation may be generated by chimera dynamics

The 8-12 Hz theta rhythm observed in hippocampal local field potentials of animals can be regarded as a “clock” that regulates the timing of spikes. While different interneuron sub-types synchronously phase lock to different phases for every theta cycle, the phase of pyramidal neurons’ spikes asynchronously vary in each theta cycle, depending on the animal’s position. On the other hand, pyramidal neurons tend to fire slightly faster than the theta oscillation in what is termed hippocampal phase precession. Chimera states are specific solutions to dynamical systems where synchrony and asynchrony coexist, similar to the hippocampal theta oscillation. Here, we test the hypothesis that the hippocampal theta oscillation emerges from chimera dynamics with computational modelling. We utilized multiple network topologies and sizes of Kuramoto oscillator networks that are known to collectively display chimera dynamics. We found that by changing the oscillators’ intrinsic frequency, the frequency ratio between the synchronized and unsynchronized oscillators can match the frequency ratio between the hippocampal theta oscillation (≈8 Hz) and phase precessing pyramidal neurons (≈9 Hz). The faster firing population of oscillators also displays theta-sequence-like behaviour and phase precession. Finally, we trained networks of spiking integrate-and-fire neurons to output a chimera state by using the Kuramoto-chimera system as a dynamical supervisor. We found that the firing times of subsets of individual neurons display phase precession. These results imply that the hippocampal theta oscillation may be a chimera state, further suggesting the importance of chimera states in neuroscience.

[1]  C. Simon,et al.  Chimera patterns in conservative Hamiltonian systems and Bose–Einstein condensates of ultracold atoms , 2023, Scientific reports.

[2]  J. Davidsen,et al.  Embedded chimera states in recurrent neural networks , 2022, Communications Physics.

[3]  György Buzsáki,et al.  Cooling of Medial Septum Reveals Theta Phase Lag Coordination of Hippocampal Cell Assemblies , 2019, Neuron.

[4]  T. Sejnowski,et al.  Cortical chimera states predict epileptic seizures. , 2019, Chaos.

[5]  Wilten Nicola,et al.  A diversity of interneurons and Hebbian plasticity facilitate rapid compressible learning in the hippocampus , 2019, Nature Neuroscience.

[6]  Soumen Majhi,et al.  Chimera states in neuronal networks: A review. , 2019, Physics of life reviews.

[7]  Jean M Vettel,et al.  Cognitive chimera states in human brain networks , 2018, Science Advances.

[8]  Mark P. Brandon,et al.  Hippocampal Neural Circuits Respond to Optogenetic Pacing of Theta Frequencies by Generating Accelerated Oscillation Frequencies , 2018, Current Biology.

[9]  J. Hizanidis,et al.  Three-dimensional chimera patterns in networks of spiking neuron oscillators. , 2018, Physical review. E.

[10]  Frances K. Skinner,et al.  Deciphering the Contribution of Oriens-Lacunosum/Moleculare (OLM) Cells to Intrinsic θ Rhythms Using Biophysical Local Field Potential (LFP) Models , 2018, eNeuro.

[11]  Jörn Davidsen,et al.  Symmetry-breaking spirals , 2017 .

[12]  Eckehard Schöll,et al.  Chimera states in brain networks: Empirical neural vs. modular fractal connectivity. , 2017, Chaos.

[13]  Frances K Skinner,et al.  Combining Theory, Model, and Experiment to Explain How Intrinsic Theta Rhythms Are Generated in an In Vitro Whole Hippocampus Preparation without Oscillatory Inputs , 2017, eNeuro.

[14]  Carlo R. Laing,et al.  Chimeras in Two-Dimensional Domains: Heterogeneity and the Continuum Limit , 2017, SIAM J. Appl. Dyn. Syst..

[15]  Eckehard Schöll,et al.  Chimera states in complex networks: interplay of fractal topology and delay , 2017, The European Physical Journal Special Topics.

[16]  Angus Chadwick,et al.  Flexible theta sequence compression mediated via phase precessing interneurons , 2016, eLife.

[17]  Wilten Nicola,et al.  Supervised learning in spiking neural networks with FORCE training , 2016, Nature Communications.

[18]  Andrew C. Heusser,et al.  Episodic sequence memory is supported by a theta-gamma phase code , 2016, Nature Neuroscience.

[19]  Marc W Howard,et al.  Time Cells in Hippocampal Area CA3 , 2016, The Journal of Neuroscience.

[20]  Antoine Adamantidis,et al.  Causal evidence for the role of REM sleep theta rhythm in contextual memory consolidation , 2016, Science.

[21]  Katharina Krischer,et al.  A classification scheme for chimera states. , 2016, Chaos.

[22]  Xiaojie Gao,et al.  Theta oscillations regulate the speed of locomotion via a hippocampus to lateral septum pathway , 2015, Nature Communications.

[23]  Hon Wai Lau,et al.  Linked and knotted chimera filaments in oscillatory systems. , 2015, Physical review. E.

[24]  Carlo R Laing,et al.  Chimera states in networks of phase oscillators: The case of two small populations. , 2015, Physical review. E.

[25]  Carey Y. L. Huh,et al.  Network models provide insights into how oriens–lacunosum-moleculare and bistratified cell interactions influence the power of local hippocampal CA1 theta oscillations , 2015, Front. Syst. Neurosci..

[26]  Yuri Maistrenko,et al.  Chimera states in three dimensions , 2015 .

[27]  Richard B. Reilly,et al.  Medial septum regulates the hippocampal spatial representation , 2015, Front. Behav. Neurosci..

[28]  Antoine Adamantidis,et al.  Parvalbumin Interneurons of Hippocampus Tune Population Activity at Theta Frequency , 2015, Neuron.

[29]  David Hansel,et al.  Asynchronous Rate Chaos in Spiking Neuronal Circuits , 2015, bioRxiv.

[30]  S. Romani,et al.  Theta sequences are essential for internally generated hippocampal firing fields , 2014, Nature Neuroscience.

[31]  Matthew A Wilson,et al.  Enhancement of encoding and retrieval functions through theta phase-specific manipulation of hippocampus , 2014, eLife.

[32]  Richard Kempter,et al.  Modeling Inheritance of Phase Precession in the Hippocampal Formation , 2014, The Journal of Neuroscience.

[33]  Mark J Panaggio,et al.  Chimera states on the surface of a sphere. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Michaël Zugaro,et al.  Reversed theta sequences of hippocampal cell assemblies during backward travel , 2014, Nature Neuroscience.

[35]  Srdjan Ostojic,et al.  Two types of asynchronous activity in networks of excitatory and inhibitory spiking neurons , 2014, Nature Neuroscience.

[36]  Chantal E. Stern,et al.  Theta rhythm and the encoding and retrieval of space and time , 2014, NeuroImage.

[37]  Ghislain St-Yves,et al.  Spiral wave chimeras in complex oscillatory and chaotic systems. , 2013, Physical review letters.

[38]  Philipp Hövel,et al.  When nonlocal coupling between oscillators becomes stronger: patched synchrony or multichimera states. , 2012, Physical review letters.

[39]  Mark J Panaggio,et al.  Chimera states on a flat torus. , 2012, Physical review letters.

[40]  Michael Lagler,et al.  Behavior-dependent specialization of identified hippocampal interneurons , 2012, Nature Neuroscience.

[41]  Jesse Jackson,et al.  Self-generated theta oscillations in the hippocampus , 2009, Nature Neuroscience.

[42]  L. F. Abbott,et al.  Generating Coherent Patterns of Activity from Chaotic Neural Networks , 2009, Neuron.

[43]  Matthew A. Wilson,et al.  Hippocampal Replay of Extended Experience , 2009, Neuron.

[44]  Carlo R. Laing,et al.  The dynamics of chimera states in heterogeneous Kuramoto networks , 2009 .

[45]  Evgueniy V. Lubenov,et al.  Hippocampal theta oscillations are travelling waves , 2009, Nature.

[46]  H. Eichenbaum.  Faculty Opinions recommendation of Internally generated cell assembly sequences in the rat hippocampus. , 2008 .

[47]  P. Somogyi,et al.  Neuronal Diversity and Temporal Dynamics: The Unity of Hippocampal Circuit Operations , 2008, Science.

[48]  Richard Kempter,et al.  Phase Precession Through Synaptic Facilitation , 2008, Neural Computation.

[49]  G. Buzsáki,et al.  Forward and reverse hippocampal place-cell sequences during ripples , 2007, Nature Neuroscience.

[50]  M. Wilson,et al.  Spatial selectivity and theta phase precession in CA1 interneurons , 2007, Hippocampus.

[51]  Eric A. Zilli,et al.  Hippocampal CA1 spiking during encoding and retrieval: Relation to theta phase , 2007, Neurobiology of Learning and Memory.

[52]  M. Hasselmo,et al.  Encoding and retrieval in the CA3 region of the hippocampus: a model of theta-phase separation. , 2005, Journal of neurophysiology.

[53]  S. Strogatz,et al.  c ○ World Scientific Publishing Company CHIMERA STATES IN A RING OF NONLOCALLY COUPLED OSCILLATORS , 2005 .

[54]  S. Strogatz,et al.  Chimera states for coupled oscillators. , 2004, Physical review letters.

[55]  Eugene M. Izhikevich,et al.  Simple model of spiking neurons , 2003, IEEE Trans. Neural Networks.

[56]  P. Somogyi,et al.  Brain-state- and cell-type-specific firing of hippocampal interneurons in vivo , 2003, Nature.

[57]  Albert K. Lee,et al.  Memory of Sequential Experience in the Hippocampus during Slow Wave Sleep , 2002, Neuron.

[58]  Y. Kuramoto,et al.  Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators , 2002, cond-mat/0210694.

[59]  Michael E. Hasselmo,et al.  A Proposed Function for Hippocampal Theta Rhythm: Separate Phases of Encoding and Retrieval Enhance Reversal of Prior Learning , 2002, Neural Computation.

[60]  G. Buzsáki.  Theta Oscillations in the Hippocampus , 2002, Neuron.

[61]  Michael Recce,et al.  A Temporal Mechanism for Generating the Phase Precession of Hippocampal Place Cells , 2000, Journal of Computational Neuroscience.

[62]  G Buzsáki,et al.  Interactions between Hippocampus and Medial Septum during Sharp Waves and Theta Oscillation in the Behaving Rat , 1999, The Journal of Neuroscience.

[63]  M. Hasselmo,et al.  Encoding and retrieval of episodic memories: Role of cholinergic and GABAergic modulation in the hippocampus , 1998, Hippocampus.

[64]  B. McNaughton,et al.  Population dynamics and theta rhythm phase precession of hippocampal place cell firing: A spiking neuron model , 1998, Hippocampus.

[65]  J. O’Keefe,et al.  The rhythmicity of cells of the medial septum/diagonal band of Broca in the awake freely moving rat: relationships with behaviour and hippocampal theta , 1998, The European journal of neuroscience.

[66]  G. Buzsáki,et al.  Hippocampal theta activity following selective lesion of the septal cholinergic systeM , 1994, Neuroscience.

[67]  J. O’Keefe,et al.  Phase relationship between hippocampal place units and the EEG theta rhythm , 1993, Hippocampus.

[68]  G. Buzsáki.  Two-stage model of memory trace formation: A role for “noisy” brain states , 1989, Neuroscience.

[69]  J. O'Keefe,et al.  The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely-moving rat. , 1971, Brain research.

[70]  M. Hasselmo.  What is the function of hippocampal theta rhythm?—Linking behavioral data to phasic properties of field potential and unit recording data , 2005, Hippocampus.

[71]  P. Somogyi,et al.  Defined types of cortical interneurone structure space and spike timing in the hippocampus , 2005, The Journal of physiology.

[72]  J. O’Keefe,et al.  Dual phase and rate coding in hippocampal place cells: Theoretical significance and relationship to entorhinal grid cells , 2005, Hippocampus.

[73]  P. Somogyi,et al.  Spike timing of dendrite-targeting bistratified cells during hippocampal network oscillations in vivo , 2004, Nature Neuroscience.

[74]  B. McNaughton,et al.  Theta phase precession in hippocampal neuronal populations and the compression of temporal sequences , 1996, Hippocampus.