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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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Hesse J, Schleimer JH, Schreiber S. Qualitative changes in phase-response curve and synchronization at the saddle-node-loop bifurcation. Phys Rev E 2017; 95:052203. [PMID: 28618541 DOI: 10.1103/physreve.95.052203] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2016] [Indexed: 06/07/2023]
Abstract
Prominent changes in neuronal dynamics have previously been attributed to a specific switch in onset bifurcation, the Bogdanov-Takens (BT) point. This study unveils another, relevant and so far underestimated transition point: the saddle-node-loop bifurcation, which can be reached by several parameters, including capacitance, leak conductance, and temperature. This bifurcation turns out to induce even more drastic changes in synchronization than the BT transition. This result arises from a direct effect of the saddle-node-loop bifurcation on the limit cycle and hence spike dynamics. In contrast, the BT bifurcation exerts its immediate influence upon the subthreshold dynamics and hence only indirectly relates to spiking. We specifically demonstrate that the saddle-node-loop bifurcation (i) ubiquitously occurs in planar neuron models with a saddle node on invariant cycle onset bifurcation, and (ii) results in a symmetry breaking of the system's phase-response curve. The latter entails an increase in synchronization range in pulse-coupled oscillators, such as neurons. The derived bifurcation structure is of interest in any system for which a relaxation limit is admissible, such as Josephson junctions and chemical oscillators.
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Affiliation(s)
- Janina Hesse
- Institute for Theoretical Biology, Department of Biology, Humboldt-Universität zu Berlin, Philippstrasse 13, Haus 4, 10115 Berlin, Germany and Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany
| | - Jan-Hendrik Schleimer
- Institute for Theoretical Biology, Department of Biology, Humboldt-Universität zu Berlin, Philippstrasse 13, Haus 4, 10115 Berlin, Germany and Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany
| | - Susanne Schreiber
- Institute for Theoretical Biology, Department of Biology, Humboldt-Universität zu Berlin, Philippstrasse 13, Haus 4, 10115 Berlin, Germany and Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany
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