244 research outputs found

    Bistable dynamics underlying excitability of ion homeostasis in neuron models

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    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

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    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

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    Die elektrische Signalverarbeitung in Nervenzellen basiert auf deren erregbarer Zellmembran. Üblicherweise wird angenommen, dass die in der Membran eingebetteten leitfĂ€higen IonenkanĂ€le nicht auf direkte Art gekoppelt sind und dass die KapazitĂ€t des von der Membran gebildeten Kondensators konstant ist. Allerdings scheinen diese Annahmen nicht fĂŒr alle Nervenzellen zu gelten. Im Gegenteil, verschiedene IonenkanĂ€le “kooperieren” und auch die Vorstellung von einer konstanten spezifischen MembrankapazitĂ€t wurde kĂŒrzlich 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 spannungsabhĂ€ngige IonenkanĂ€le eine Form von zellulĂ€rem Kurzzeitspeicher fĂŒr elektrische AktivitĂ€t bilden könnten. Solche kooperativen KanĂ€le treten in der Membran hĂ€ufig in kleinen rĂ€umlich getrennte Clustern auf. Basierend auf einem mathematischen Modell wird nachgewiesen, dass solche Kanalcluster als eine bistabile LeitfĂ€higkeit agieren. Die dadurch entstehende große SpeicherkapazitĂ€t eines Ensembles dieser Kanalcluster könnte von Nervenzellen fĂŒr stufenloses persistentes Feuern genutzt werden -- ein Feuerverhalten von Nutzen fĂŒr das KurzzeichgedĂ€chtnis. Im zweiten Projekt wird ein neues Dynamic Clamp Protokoll entwickelt, der Capacitance Clamp, das erlaubt, Änderungen der MembrankapazitĂ€t in biologischen Nervenzellen zu emulieren. Eine solche experimentelle Möglichkeit, um systematisch die Rolle der KapazitĂ€t 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 KapazitĂ€t auf deren Feuerverhalten zu studieren. Die Kombination beider Projekte zeigt die Relevanz dieser oft vernachlĂ€ssigten Facetten von neuronalen Membranen fĂŒr 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

    Effects of ionic concentration dynamics on neuronal activity

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    Neuronen sind bei der InformationsĂŒbertragung des zentralen Nervensystems von entscheidender Bedeutung. Ihre AktivitĂ€t liegt der Signalverarbeitung und höheren kognitiven Prozessen zugrunde. Neuronen sind in den extrazellulĂ€ren Raum eingebettet, der mehrere Teilchen, darunter auch Ionen, enthĂ€lt. Ionenkonzentrationen sind nicht statisch. Intensive neuronale AktivitĂ€t kann intrazellulĂ€re und extrazellulĂ€re Ionenkonzentrationen verĂ€ndern. In dieser Arbeit untersuche ich das Wechselspiel zwischen neuronaler AktivitĂ€t und der Dynamik der Ionenkonzentrationen. Dabei konzentriere ich mich hauptsĂ€chlich auf extrazellulĂ€re Kalium- und intrazellulĂ€re Natriumkonzentrationen. Mit Hilfe der Theorie dynamischer Systeme zeige ich, wie moderate Änderungen dieser Ionenkonzentrationen die neuronale AktivitĂ€t qualitativ verĂ€ndern können, wodurch sich möglicherweise die Signalverarbeitung verĂ€ndert. Dann modelliere ich ein leitfĂ€higkeitsbasiertes neuronales Netzwerk mit Spikes. Das Modell sagt voraus, dass eine moderate Änderung der Konzentrationen, die einen Mikroschaltkreis von Neuronen umgeben, die Leistungsspektraldichte der PopulationsaktivitĂ€t verĂ€ndern könnte. Insgesamt unterstreicht diese Arbeit die Bedeutung der Dynamik der Ionenkonzentrationen fĂŒr das VerstĂ€ndnis neuronaler AktivitĂ€t auf langen Zeitskalen und liefert technische Erkenntnisse darĂŒber, 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

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    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

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    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 VV-gated calcium channels and hyperpolarizing VV-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
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