And Multipolar Neurons7 2.1
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Implications of neuronal excitability and morphology for spike-based information transmission DISSERTATION zur Erlangung des akademischen Grades doctor rerum naturalium (Dr. rer. nat.) im Fach Biologie (Theoretische Biologie) eingereicht an der Lebenswissenschaftlichen Fakultät Humboldt-Universität zu Berlin von Janina Hesse M.Sc. Präsidentin der Humboldt-Universität zu Berlin: Prof. Dr.-Ing. Dr. Sabine Kunst Dekan der Lebenswissenschaftlichen Fakultät: Prof. Dr. Bernhard Grimm Gutachter/innen: 1. Prof. Dr. Susanne Schreiber 2. Prof. Dr. Fred Wolf 3. Prof. Dr. Jan Benda Eingereicht am 11. Mai 2017 Tag der mündlichen Prüfung: 12. Juli 2017 In Erinnerung an Magdalena Heislitz. Abstract Signal processing in nervous systems is shaped by the connectome as well as the cellular properties of nerve cells. In this thesis, two cellular properties are investigated with respect to the functional adaptations they provide: It is shown that neuronal morphology can improve signal transmission under energetic constraints, and that even small changes in biophysical parameters can switch spike generation, and thus information encoding. In the first project of the thesis, mathematical modeling and data are deployed to suggest energy-efficient signaling as a major evolutionary pressure behind morphological adaptations of cell body location: In order to save energy, the electrical signal transmission from dendrite to axon can be enhanced if a relatively small cell body is located between dendrite and axon, while a relatively large cell body should be externalized. In the second project, it is shown that biophysical parameters, such as temperature, membrane leak or capacitance, can transform neuronal excitability (i.e., the spike onset bifurcation) and, with that, spike-based information processing. This thesis identifies the so-called saddle-node-loop bifurcation as the transition with particularly drastic functional implications. Besides altering neuronal filters and stimulus locking, the saddle-node-loop bifurcation leads to an increase in network synchronization, which may potentially be relevant for the initiation of seizures in response to increased temperature, such as during fever cramps. v Zusammenfassung Signalverarbeitung im Nervensystem hängt sowohl von der Netzwerkstruktur, als auch den zellulären Eigenschaften der Nervenzellen ab. In dieser Abhandlung werden zwei zelluläre Eigenschaften im Hinblick auf ihre funktionellen Anpas- sungsmöglichkeiten untersucht: Es wird gezeigt, dass neuronale Morphologie die Signalweiterleitung unter Berücksichtigung energetischer Beschränkungen verstärken kann, und dass selbst kleine Änderungen in biophysikalischen Para- metern die Aktivierungsbifurkation in Nervenzellen, und damit deren Informa- tionskodierung, wechseln können. Im ersten Teil dieser Abhandlung wird, unter Verwendung von mathematischen Modellen und Daten, die Hypothese aufge- stellt, dass Energie-effiziente Signalweiterleitung als starker Evolutionsdruck für unterschiedliche Zellkörperlagen bei Nervenzellen wirkt. Um Energie zu sparen, kann die Signalweiterleitung vom Dendrit zum Axon verstärkt werden, indem relativ kleine Zellkörper zwischen Dendrit und Axon eingebaut werden, wäh- rend relativ große Zellkörper besser ausgelagert werden. Im zweiten Teil wird gezeigt, dass biophysikalische Parameter, wie Temperatur, Membranwiderstand oder Kapazität, den Feuermechanismus des Neurons ändern, und damit gleich- falls Aktionspotential-basierte Informationsverarbeitung. Diese Arbeit identifiziert die sogenannte “saddle-node-loop” (Sattel-Knoten-Schlaufe) Bifurkation als den Übergang, der besonders drastische funktionale Auswirkungen hat. Neben der Än- derung neuronaler Filtereigenschaften sowie der Ankopplung an Stimuli, führt die “saddle-node-loop” Bifurkation zu einer Erhöhung der Netzwerk-Synchronisation, was möglicherweise für das Auslösen von Anfällen durch Temperatur, wie bei Fieberkrämpfen, interessant sein könnte. vii Contents I. Introduction1 1. Overview3 1.1. Information processing in the nervous system...............3 1.2. Signaling in different morphologies.....................4 1.3. Spike generation and spike-based coding..................4 1.4. Energetic costs of signal processing......................5 2. Signal transmission in uni- and multipolar neurons7 2.1. The soma location................................7 2.2. Evolutionary account of the soma location..................8 2.2.1. Evolutionary origin...........................9 2.2.2. Complex signal processing......................9 2.2.3. Centralization of the nervous system................ 10 2.2.4. Cellular similarities between unipolar and multipolar neurons.. 12 2.3. Soma location under spatial constraints................... 12 2.3.1. Volume minimization......................... 12 2.3.2. Supply of nutrition to the soma.................... 13 2.4. Energy-efficient signal transmission..................... 14 2.5. Recapitulation.................................. 15 3. Signal processing in mean-driven neurons 17 3.1. Spike onset dynamics.............................. 17 3.2. Conductance-based neuron model...................... 19 3.3. Neuronal dynamics.............................. 20 3.3.1. Fixed points............................... 20 3.3.2. Limit cycles............................... 22 3.4. Phase dynamics................................. 25 3.4.1. Synchronization inferred from individual cells........... 27 3.5. Capacitance and temperature as bifurcation parameters for the saddle- node-loop bifurcation.............................. 28 3.5.1. Relative relaxation time constant as bifurcation parameter.... 29 3.5.2. Temperature affects the relative time constant........... 29 3.6. Temperature variation in animals....................... 31 3.6.1. Medical conditions with temperature dependence......... 31 3.7. Recapitulation.................................. 32 ix Contents II. Publications 33 4. Externalization of neuronal somata as an evolutionary strategy for energy economization 35 5. Qualitative changes in phase-response curve and synchronization at the saddle- node-loop bifurcation 49 III. Discussion 63 6. Outline 65 7. Evolution and functional consequences of the soma location 67 7.1. Functional polarization............................. 68 7.1.1. Neuronal polarity of unipolar cells.................. 68 7.1.2. Spike initiation zone.......................... 68 7.2. Output control.................................. 69 7.2.1. Signal regulation in central somata.................. 69 7.2.2. Signal regulation in externalized somata.............. 70 7.3. Spatial proximity................................ 72 7.3.1. Support of axon initial segment by a central soma......... 72 7.3.2. Hormonal communication....................... 72 7.3.3. Support of somatic synapses..................... 73 7.4. Organelle exclusion hypothesis........................ 73 7.4.1. Increased soma size through evolution............... 73 7.4.2. Externalized somata support large cells............... 74 7.4.3. Why large somata?........................... 75 7.4.4. Divergent evolution of unipolar and multipolar neurons..... 76 7.5. Predictions of the organelle exclusion hypothesis.............. 78 7.5.1. Relative nucleus volume........................ 78 7.5.2. Mitochondria distribution....................... 78 7.5.3. Axial resistance in organelle-dense neurites............. 79 7.6. Wiring optimization in ganglionic structures................ 79 7.6.1. Spatial ordering in the ganglionic soma layer............ 80 7.6.2. Upper bound on ganglion size.................... 80 7.7. Recapitulation.................................. 83 8. The saddle-node-loop bifurcation 85 8.1. The membrane capacitance as biological parameter............ 85 8.2. Quadratic integrate-and-fire neurons as model of the small saddle-node- loop bifurcation................................. 86 8.3. Coding properties at the saddle-node-loop bifurcation........... 88 8.3.1. Locking to external inputs....................... 88 8.3.2. Information transmission....................... 89 8.4. Energy-efficient information processing................... 90 x Contents 8.5. Phase response beyond spike onset...................... 92 8.5.1. Spiking from onset to excitation block................ 92 8.5.2. Spike onset at subcritical Hopf bifurcations............. 92 9. Temperature as a control parameter in biological systems 95 9.1. Regulation of temperature-dependence................... 95 9.2. Temperature-induced bifurcations...................... 96 9.3. Experimental evidence for a saddle-node-loop bifurcation in hippocam- pal cells...................................... 96 9.3.1. Methods................................. 97 9.3.2. Preliminary results........................... 97 10. The saddle-node-loop bifurcation as seizure onset 99 10.1. Temperature-induced seizures and saddle-node-loop bifurcations.... 99 10.2. Experimental observations........................... 100 10.3. Shift in seizure temperature in response to pH or genetic ion channel mutations.................................... 101 10.3.1. Increased pH shifts the saddle-node-loop bifurcation with respect to temperature............................. 101 10.3.2. Febrile seizure mutations shift the saddle-node-loop bifurcation with respect to temperature...................... 102 10.4. Medical applications.............................. 103 10.4.1. Seizure induction by absolute temperature or temperature increase?103 10.4.2. Brain heating.............................. 104 10.4.3. Distance