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Chalkiadakis D, Hizanidis J. Dynamical properties of neuromorphic Josephson junctions. Phys Rev E 2022; 106:044206. [PMID: 36397509 DOI: 10.1103/physreve.106.044206] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Accepted: 09/14/2022] [Indexed: 06/16/2023]
Abstract
Neuromorphic computing exploits the dynamical analogy between many physical systems and neuron biophysics. Superconductor systems, in particular, are excellent candidates for neuromorphic devices due to their capacity to operate at great speeds and with low energy dissipation compared to their silicon counterparts. In this paper, we revisit a prior work on Josephson Junction-based neurons to identify the exact dynamical mechanisms underlying the system's neuronlike properties and reveal complex behaviors which are relevant for neurocomputation and the design of superconducting neuromorphic devices. Our paper lies at the intersection of superconducting physics and theoretical neuroscience, both viewed under a common framework-that of nonlinear dynamics theory.
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Affiliation(s)
- D Chalkiadakis
- Department of Physics, University of Crete, 71003 Herakleio, Greece
| | - J Hizanidis
- Department of Physics, University of Crete, 71003 Herakleio, Greece and Institute of Applied and Computational Mathematics, Foundation for Research and Technology-Hellas, 70013 Herakleio, Greece
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2
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Hesse J, Schleimer JH, Maier N, Schmitz D, Schreiber S. Temperature elevations can induce switches to homoclinic action potentials that alter neural encoding and synchronization. Nat Commun 2022; 13:3934. [PMID: 35803913 PMCID: PMC9270341 DOI: 10.1038/s41467-022-31195-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2020] [Accepted: 06/07/2022] [Indexed: 11/09/2022] Open
Abstract
Almost seventy years after the discovery of the mechanisms of action potential generation, some aspects of their computational consequences are still not fully understood. Based on mathematical modeling, we here explore a type of action potential dynamics – arising from a saddle-node homoclinic orbit bifurcation - that so far has received little attention. We show that this type of dynamics is to be expected by specific changes in common physiological parameters, like an elevation of temperature. Moreover, we demonstrate that it favours synchronization patterns in networks – a feature that becomes particularly prominent when system parameters change such that homoclinic spiking is induced. Supported by in-vitro hallmarks for homoclinic spikes in the rodent brain, we hypothesize that the prevalence of homoclinic spikes in the brain may be underestimated and provide a missing link between the impact of biophysical parameters on abrupt transitions between asynchronous and synchronous states of electrical activity in the brain. The intrinsic dynamics of neurons, in particular the generation action potentials, can impact neural network states and processes of encoding information. The authors demonstrate how the elevation of temperature induces a type of action potential dynamics that favors synchronization patterns in neural networks.
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Affiliation(s)
- Janina Hesse
- Institute for Theoretical Biology, Humboldt-Universität zu Berlin, Berlin, Germany.,Bernstein Center for Computational Neuroscience, Berlin, Germany.,Institute for Systems Medicine, Department of Human Medicine, MSH Medical School Hamburg-University of Applied Sciences and Medical University, Hamburg, 20457, Germany.,Charité-Universitätsmedizin Berlin, Corporate member of Freie Universität Berlin, Humboldt-Universität zu Berlin, and Berlin Institute of Health, Berlin, Germany
| | - Jan-Hendrik Schleimer
- Institute for Theoretical Biology, Humboldt-Universität zu Berlin, Berlin, Germany.,Bernstein Center for Computational Neuroscience, Berlin, Germany
| | - Nikolaus Maier
- Neuroscience Research Center - Charité-Universitätsmedizin Berlin, Corporate member of Freie Universität Berlin, Humboldt-Universität zu Berlin, and Berlin Institute of Health, German Center for Neurodegenerative Diseases (DZNE) Berlin, Berlin, 10117, Germany.,Max-Delbrück-Centrum (MDC) for Molecular Medicine, Berlin, 13125, Germany
| | - Dietmar Schmitz
- Bernstein Center for Computational Neuroscience, Berlin, Germany.,Neuroscience Research Center - Charité-Universitätsmedizin Berlin, Corporate member of Freie Universität Berlin, Humboldt-Universität zu Berlin, and Berlin Institute of Health, German Center for Neurodegenerative Diseases (DZNE) Berlin, Berlin, 10117, Germany.,Max-Delbrück-Centrum (MDC) for Molecular Medicine, Berlin, 13125, Germany
| | - Susanne Schreiber
- Institute for Theoretical Biology, Humboldt-Universität zu Berlin, Berlin, Germany. .,Bernstein Center for Computational Neuroscience, Berlin, Germany.
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3
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Kullmann R, Knoll G, Bernardi D, Lindner B. Critical current for giant Fano factor in neural models with bistable firing dynamics and implications for signal transmission. Phys Rev E 2022; 105:014416. [PMID: 35193262 DOI: 10.1103/physreve.105.014416] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2020] [Accepted: 01/05/2022] [Indexed: 06/14/2023]
Abstract
Bistability in the firing rate is a prominent feature in different types of neurons as well as in neural networks. We show that for a constant input below a critical value, such bistability can lead to a giant spike-count diffusion. We study the transmission of a periodic signal and demonstrate that close to the critical bias current, the signal-to-noise ratio suffers a sharp increase, an effect that can be traced back to the giant diffusion and large Fano factor.
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Affiliation(s)
- Richard Kullmann
- Bernstein Center for Computational Neuroscience Berlin, Philippstrasse 13, Haus 2, 10115 Berlin, Germany
- Physics Department of Humboldt University Berlin, Newtonstrasse 15, 12489 Berlin, Germany
| | - Gregory Knoll
- Bernstein Center for Computational Neuroscience Berlin, Philippstrasse 13, Haus 2, 10115 Berlin, Germany
- Physics Department of Humboldt University Berlin, Newtonstrasse 15, 12489 Berlin, Germany
| | - Davide Bernardi
- Center for Translational Neurophysiology of Speech and Communication, Fondazione Istituto Italiano di Tecnologia, via Fossato di Mortara 19, 44121 Ferrara, Italy
| | - Benjamin Lindner
- Bernstein Center for Computational Neuroscience Berlin, Philippstrasse 13, Haus 2, 10115 Berlin, Germany
- Physics Department of Humboldt University Berlin, Newtonstrasse 15, 12489 Berlin, Germany
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Niemeyer N, Schleimer JH, Schreiber S. Biophysical models of intrinsic homeostasis: Firing rates and beyond. Curr Opin Neurobiol 2021; 70:81-88. [PMID: 34454303 DOI: 10.1016/j.conb.2021.07.011] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/01/2021] [Revised: 06/14/2021] [Accepted: 07/14/2021] [Indexed: 12/01/2022]
Abstract
In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of cell-intrinsic properties, biophysical models of neurons permit one to identify relevant physiological substrates that can serve as regulators of neuronal excitability and to test how feedback loops can stabilize crucial variables such as long-term calcium levels and firing rates. Mathematical theory has also revealed a rich set of complementary computational properties arising from distinct cellular dynamics and even shaping processing at the network level. Here, we provide an overview over recently explored homeostatic mechanisms derived from biophysical models and hypothesize how multiple dynamical characteristics of cells, including their intrinsic neuronal excitability classes, can be stably controlled.
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Affiliation(s)
- Nelson Niemeyer
- Institute for Theoretical Biology, Humboldt-Universität zu Berlin, 10115, Berlin, Germany; Einstein Center for Neurosciences Berlin, Charitéplatz 1, 10117, Berlin, Germany; Bernstein Center for Computational Neuroscience, 10115, Berlin, Germany
| | - Jan-Hendrik Schleimer
- Institute for Theoretical Biology, Humboldt-Universität zu Berlin, 10115, Berlin, Germany; Bernstein Center for Computational Neuroscience, 10115, Berlin, Germany
| | - Susanne Schreiber
- Institute for Theoretical Biology, Humboldt-Universität zu Berlin, 10115, Berlin, Germany; Einstein Center for Neurosciences Berlin, Charitéplatz 1, 10117, Berlin, Germany; Bernstein Center for Computational Neuroscience, 10115, Berlin, Germany.
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5
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Contreras SA, Schleimer JH, Gulledge AT, Schreiber S. Activity-mediated accumulation of potassium induces a switch in firing pattern and neuronal excitability type. PLoS Comput Biol 2021; 17:e1008510. [PMID: 34043638 PMCID: PMC8205125 DOI: 10.1371/journal.pcbi.1008510] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Revised: 06/15/2021] [Accepted: 04/16/2021] [Indexed: 01/30/2023] Open
Abstract
During normal neuronal activity, ionic concentration gradients across a neuron’s membrane are often assumed to be stable. Prolonged spiking activity, however, can reduce transmembrane gradients and affect voltage dynamics. Based on mathematical modeling, we investigated the impact of neuronal activity on ionic concentrations and, consequently, the dynamics of action potential generation. We find that intense spiking activity on the order of a second suffices to induce changes in ionic reversal potentials and to consistently induce a switch from a regular to an intermittent firing mode. This transition is caused by a qualitative alteration in the system’s voltage dynamics, mathematically corresponding to a co-dimension-two bifurcation from a saddle-node on invariant cycle (SNIC) to a homoclinic orbit bifurcation (HOM). Our electrophysiological recordings in mouse cortical pyramidal neurons confirm the changes in action potential dynamics predicted by the models: (i) activity-dependent increases in intracellular sodium concentration directly reduce action potential amplitudes, an effect typically attributed solely to sodium channel inactivation; (ii) extracellular potassium accumulation switches action potential generation from tonic firing to intermittently interrupted output. Thus, individual neurons may respond very differently to the same input stimuli, depending on their recent patterns of activity and/or the current brain-state. Ionic concentrations in the brain are not constant. We show that during intense neuronal activity, they can change on the order of seconds and even switch neuronal spiking patterns under identical stimulation from a regular firing mode to an intermittently interrupted one. Triggered by an accumulation of extracellular potassium, such a transition is caused by a specific, qualitative change in of the neuronal voltage dynamics—a so-called bifurcation—which affects crucial features of action-potential generation and bears consequences for how information is encoded and how neurons behave together in the network. Also, changes in intracellular sodium can induce measurable effects, like a reduction of spike amplitude that occurs independently of the fast amplitude effects attributed to sodium channel inactivation. Taken together, our results demonstrate that a neuron can respond very differently to the same stimulus, depending on its previous activity or the current brain state. This finding may be particularly relevant when other regulatory mechanisms of ionic homeostasis are challenged, for example, during pathological states of glial impairment or oxygen deprivation. Finally, categorization of cortical neurons as intrinsically bursting or regular spiking may be biased by the ionic concentrations at the time of the observation, highlighting the non-static nature of neuronal dynamics.
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Affiliation(s)
- Susana Andrea Contreras
- Institute for Theoretical Biology, Humboldt-University of Berlin, Berlin, Germany
- Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany
| | - Jan-Hendrik Schleimer
- Institute for Theoretical Biology, Humboldt-University of Berlin, Berlin, Germany
- Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany
| | - Allan T. Gulledge
- Molecular and Systems Biology, Geisel School of Medicine at Dartmouth College, Hanover, New Hampshire, United States of America
| | - Susanne Schreiber
- Institute for Theoretical Biology, Humboldt-University of Berlin, Berlin, Germany
- Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany
- * E-mail:
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