Bistable dynamics underlying excitability of ion homeostasis in neuron models

When neurons fire action potentials, dissipation of free energy is usually not directly considered, because the change in free energy is often negligible compared to the immense reservoir stored in neural transmembrane ion gradients and the long-term energy requirements are met through chemical energy, i.e., metabolism. However, these gradients can temporarily nearly vanish in neurological diseases, such as migraine and stroke, and in traumatic brain injury from concussions to severe injuries. We study biophysical neuron models based on the Hodgkin-Huxley (HH) formalism extended to include time-dependent ion concentrations inside and outside the cell and metabolic energy-driven pumps. We reveal the basic mechanism of a state of free energy-starvation (FES) with bifurcation analyses showing that ion dynamics is for a large range of pump rates bistable without contact to an ion bath. This is interpreted as a threshold reduction of a new fundamental mechanism of 'ionic excitability' that causes a long-lasting but transient FES as observed in pathological states. We can in particular conclude that a coupling of extracellular ion concentrations to a large glial-vascular bath can take a role as an inhibitory mechanism crucial in ion homeostasis, while the Na$^+$/K$^+$ pumps alone are insufficient to recover from FES. Our results provide the missing link between the HH formalism and activator-inhibitor models that have been successfully used for modeling migraine phenotypes, and therefore will allow us to validate the hypothesis that migraine symptoms are explained by disturbed function in ion channel subunits, Na$^+$/K$^+$ pumps, and other proteins that regulate ion homeostasis.Comment: 14 pages, 8 figures, 4 table

Dynamics from seconds to hours in Hodgkin-Huxley model with time-dependent ion concentrations and buffer reservoirs

The classical Hodgkin--Huxley (HH) model neglects the time-dependence of ion concentrations in spiking dynamics. The dynamics is therefore limited to a time scale of milliseconds, which is determined by the membrane capacitance multiplied by the resistance of the ion channels, and by the gating time constants. We study slow dynamics in an extended HH framework that includes time-dependent ion concentrations, pumps, and buffers. Fluxes across the neuronal membrane change intra- and extracellular ion concentrations, whereby the latter can also change through contact to reservoirs in the surroundings. Ion gain and loss of the system is identified as a bifurcation parameter whose essential importance was not realized in earlier studies. Our systematic study of the bifurcation structure and thus the phase space structure helps to understand activation and inhibition of a new excitability in ion homeostasis which emerges in such extended models. Also modulatory mechanisms that regulate the spiking rate can be explained by bifurcations. The dynamics on three distinct slow times scales is determined by the cell volume-to-surface-area ratio and the membrane permeability (seconds), the buffer time constants (tens of seconds), and the slower backward buffering (minutes to hours). The modulatory dynamics and the newly emerging excitable dynamics corresponds to pathological conditions observed in epileptiform burst activity, and spreading depression in migraine aura and stroke, respectively.Comment: 18 pages, 11 figure

when channels cooperate or capacitance varies

Die elektrische Signalverarbeitung in Nervenzellen basiert auf deren erregbarer Zellmembran. Üblicherweise wird angenommen, dass die in der Membran eingebetteten leitfähigen Ionenkanäle nicht auf direkte Art gekoppelt sind und dass die Kapazität des von der Membran gebildeten Kondensators konstant ist. Allerdings scheinen diese Annahmen nicht für alle Nervenzellen zu gelten. Im Gegenteil, verschiedene Ionenkanäle “kooperieren” und auch die Vorstellung von einer konstanten spezifischen Membrankapazität wurde kürzlich in Frage gestellt. Die Auswirkungen dieser Abweichungen auf die elektrischen Eigenschaften von Nervenzellen ist das Thema der folgenden kumulativen Dissertationsschrift. Im ersten Projekt wird gezeigt, auf welche Weise stark kooperative spannungsabhängige Ionenkanäle eine Form von zellulärem Kurzzeitspeicher für elektrische Aktivität bilden könnten. Solche kooperativen Kanäle treten in der Membran häufig in kleinen räumlich getrennte Clustern auf. Basierend auf einem mathematischen Modell wird nachgewiesen, dass solche Kanalcluster als eine bistabile Leitfähigkeit agieren. Die dadurch entstehende große Speicherkapazität eines Ensembles dieser Kanalcluster könnte von Nervenzellen für stufenloses persistentes Feuern genutzt werden -- ein Feuerverhalten von Nutzen für das Kurzzeichgedächtnis. Im zweiten Projekt wird ein neues Dynamic Clamp Protokoll entwickelt, der Capacitance Clamp, das erlaubt, Änderungen der Membrankapazität in biologischen Nervenzellen zu emulieren. Eine solche experimentelle Möglichkeit, um systematisch die Rolle der Kapazität zu untersuchen, gab es bisher nicht. Nach einer Reihe von Tests in Simulationen und Experimenten wurde die Technik mit Körnerzellen des *Gyrus dentatus* genutzt, um den Einfluss von Kapazität auf deren Feuerverhalten zu studieren. Die Kombination beider Projekte zeigt die Relevanz dieser oft vernachlässigten Facetten von neuronalen Membranen für die Signalverarbeitung in Nervenzellen.Electrical signaling in neurons is shaped by their specialized excitable cell membranes. Commonly, it is assumed that the ion channels embedded in the membrane gate independently and that the electrical capacitance of neurons is constant. However, not all excitable membranes appear to adhere to these assumptions. On the contrary, ion channels are observed to gate cooperatively in several circumstances and also the notion of one fixed value for the specific membrane capacitance (per unit area) across neuronal membranes has been challenged recently. How these deviations from the original form of conductance-based neuron models affect their electrical properties has not been extensively explored and is the focus of this cumulative thesis. In the first project, strongly cooperative voltage-gated ion channels are proposed to provide a membrane potential-based mechanism for cellular short-term memory. Based on a mathematical model of cooperative gating, it is shown that coupled channels assembled into small clusters act as an ensemble of bistable conductances. The correspondingly large memory capacity of such an ensemble yields an alternative explanation for graded forms of cell-autonomous persistent firing – an observed firing mode implicated in working memory. In the second project, a novel dynamic clamp protocol -- the capacitance clamp -- is developed to artificially modify capacitance in biological neurons. Experimental means to systematically investigate capacitance, a basic parameter shared by all excitable cells, had previously been missing. The technique, thoroughly tested in simulations and experiments, is used to monitor how capacitance affects temporal integration and energetic costs of spiking in dentate gyrus granule cells. Combined, the projects identify computationally relevant consequences of these often neglected facets of neuronal membranes and extend the modeling and experimental techniques to further study them

Synthesis of neuromorphic circuits with neuromodulatory properties

The field of neuromorphic engineering shows great promise in delivering novel devices inspired by biological principles that would undertake sensory and processing tasks with an unprecedented level of efficiency. In order to achieve that, engineers are required to understand and implement the many complex biological regulatory mechanisms that allow the nervous system to robustly operate and adapt over scales covering many orders of magnitude, while at the same time using unreliable and noisy components. As a step towards that, this thesis aims at discussing and implementing the principles of neuromodulation in neuromorphic hardware, mechanisms which allow neurons to change and regulate their behaviour through the continuous control of their internal currents. We discuss how neural dynamics and its modulation can be broken down into four essential feedback loops, and we introduce a simplified model of the neural membrane respecting this fundamental structure. We present a novel methodology for controlling the neuron's behaviour through the shaping of its I-V curves in distinct timescales, thus characterising the behaviour of the neural circuit through its input-output properties. We show how modulation of the feedback loops affects the behaviour, and importantly, captures the transition between spiking and bursting oscillatory regimes, two major signalling modes of neurons. We then show how the architecture can be easily implemented using well-known neuromorphic building blocks based on subthreshold MOSFET circuits. Finally, we discuss how the excitability switch captured by the model can be exploited in simple network settings, thus opening up the possibility for future research into novel architectures where the control of cellular properties is utilised to shape the global behaviour of the network

Effects of ionic concentration dynamics on neuronal activity

Neuronen sind bei der Informationsübertragung des zentralen Nervensystems von entscheidender Bedeutung. Ihre Aktivität liegt der Signalverarbeitung und höheren kognitiven Prozessen zugrunde. Neuronen sind in den extrazellulären Raum eingebettet, der mehrere Teilchen, darunter auch Ionen, enthält. Ionenkonzentrationen sind nicht statisch. Intensive neuronale Aktivität kann intrazelluläre und extrazelluläre Ionenkonzentrationen verändern. In dieser Arbeit untersuche ich das Wechselspiel zwischen neuronaler Aktivität und der Dynamik der Ionenkonzentrationen. Dabei konzentriere ich mich hauptsächlich auf extrazelluläre Kalium- und intrazelluläre Natriumkonzentrationen. Mit Hilfe der Theorie dynamischer Systeme zeige ich, wie moderate Änderungen dieser Ionenkonzentrationen die neuronale Aktivität qualitativ verändern können, wodurch sich möglicherweise die Signalverarbeitung verändert. Dann modelliere ich ein leitfähigkeitsbasiertes neuronales Netzwerk mit Spikes. Das Modell sagt voraus, dass eine moderate Änderung der Konzentrationen, die einen Mikroschaltkreis von Neuronen umgeben, die Leistungsspektraldichte der Populationsaktivität verändern könnte. Insgesamt unterstreicht diese Arbeit die Bedeutung der Dynamik der Ionenkonzentrationen für das Verständnis neuronaler Aktivität auf langen Zeitskalen und liefert technische Erkenntnisse darüber, wie das Zusammenspiel zwischen ihnen modelliert und analysiert werden kann.Neurons are essential in the information transfer mechanisms of the central nervous system. Their activity underlies both basic signal processing, and higher cognitive processes. Neurons are embedded in the extracellular space, which contains multiple particles, including ions which are vital to their functioning. Ionic concentrations are not static, intense neuronal activity alters the intracellular and extracellular ionic concentrations which in turn affect neuronal functioning. In this thesis, I study the interplay between neuronal activity and ionic concentration dynamics. I focus specifically on the extracellular potassium and intracellular sodium concentrations. Using dynamical systems theory, I illustrate how moderate changes in these ionic concentrations can qualitatively change neuronal activity, potentially altering signal processing. I then model a conductance-based spiking neural network. The model predicts that a moderate change in the concentrations surrounding a microcircuit of neurons could modify the power spectral density of the population activity. Altogether, this work highlights the need to consider ionic concentration dynamics to understand neuronal activity on long time scales and provides technical insights on how to model and analyze the interplay between them

Neuromodulation of Neuromorphic Circuits

We present a novel methodology to enable control of a neuromorphic circuit in close analogy with the physiological neuromodulation of a single neuron. The methodology is general in that it only relies on a parallel interconnection of elementary voltage-controlled current sources. In contrast to controlling a nonlinear circuit through the parameter tuning of a state-space model, our approach is purely input-output. The circuit elements are controlled and interconnected to shape the current-voltage characteristics (I-V curves) of the circuit in prescribed timescales. In turn, shaping those I-V curves determines the excitability properties of the circuit. We show that this methodology enables both robust and accurate control of the circuit behavior and resembles the biophysical mechanisms of neuromodulation. As a proof of concept, we simulate a SPICE model composed of MOSFET transconductance amplifiers operating in the weak inversion regime.The research leading to these results has received funding from the European Research Council under the Advanced ERC Grant Agreement Switchlet n.67064

A biophysical model explains the spontaneous bursting behavior in the developing retina

During early development, waves of activity propagate across the retina and play a key role in the proper wiring of the early visual system. During the stage II these waves are triggered by a transient network of neurons, called Starburst Amacrine Cells (SACs), showing a bursting activity which disappears upon further maturation. While several models have attempted to reproduce retinal waves, none of them is able to mimic the rhythmic autonomous bursting of individual SACs and reveal how these cells change their intrinsic properties during development. Here, we introduce a mathematical model, grounded on biophysics, which enables us to reproduce the bursting activity of SACs and to propose a plausible, generic and robust, mechanism that generates it. The core parameters controlling repetitive firing are fast depolarizing $V$-gated calcium channels and hyperpolarizing $V$-gated potassium channels. The quiescent phase of bursting is controlled by a slow after hyperpolarization (sAHP), mediated by calcium-dependent potassium channels. Based on a bifurcation analysis we show how biophysical parameters, regulating calcium and potassium activity, control the spontaneously occurring fast oscillatory activity followed by long refractory periods in individual SACs. We make a testable experimental prediction on the role of voltage-dependent potassium channels on the excitability properties of SACs and on the evolution of this excitability along development. We also propose an explanation on how SACs can exhibit a large variability in their bursting periods, as observed experimentally within a SACs network as well as across different species, yet based on a simple, unique, mechanism. As we discuss, these observations at the cellular level have a deep impact on the retinal waves description.Comment: 25 pages, 13 figures, submitte