Temperature elevations can induce switches to homoclinic action potentials that alter neural encoding and synchronization

The article processing charge was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 491192747 and the Open Access Publication Fund of Humboldt-Universität zu Berlin.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.Peer Reviewe

A dynamic clamp protocol to artificially modify cell capacitance

Dynamics of excitable cells and networks depend on the membrane time constant, set by membrane resistance and capacitance. Whereas pharmacological and genetic manipulations of ionic conductances of excitable membranes are routine in electrophysiology, experimental control over capacitance remains a challenge. Here, we present capacitance clamp, an approach that allows electrophysiologists to mimic a modified capacitance in biological neurons via an unconventional application of the dynamic clamp technique. We first demonstrate the feasibility to quantitatively modulate capacitance in a mathematical neuron model and then confirm the functionality of capacitance clamp in in vitro experiments in granule cells of rodent dentate gyrus with up to threefold virtual capacitance changes. Clamping of capacitance thus constitutes a novel technique to probe and decipher mechanisms of neuronal signaling in ways that were so far inaccessible to experimental electrophysiology.Peer Reviewe

A statement by Scientists for Future concerning the protests for more climate protection

In March 2019, German-speaking scientists and scholars calling themselves Scientists for Future, published a statement in support of the youth protesters in Germany, Austria, and Switzerland (Fridays for Future, Klimastreik/Climate Strike), verifying the scientific evidence that the youth protestors refer to. In this article, they provide the full text of the statement, including the list of supporting facts (in both English and German) as well as an analysis of the results and impacts of the statement. Furthermore, they reflect on the challenges for scientists and scholars who feel a dual responsibility: on the one hand, to remain independent and politically neutral, and, on the other hand, to inform and warn societies of the dangers that lie ahead

Spike statistics and coding properties of phase models

Ziel dieser Arbeit ist es eine Beziehung zwischen den biophysikalischen Eigenschaften der Nervenmembran, und den ausgeführten Berechnungen und Filtereigenschaften eines tonisch feuernden Neurons, unter Einbeziehen intrinsischer Fluktuationen, herzustellen. Zu diesem Zweck werden zu erst die mikroskopischen Fluktuationen, die durch das stochastische Öffnen und Schließen der Ionenkanäle verursacht werden, zu makroskopischer Varibilität in den Zeitpunkten des Auftretens der Aktionspotentiale übersetzt, denn es sind diese Spikezeiten die in vielen sensorischen Systemen informationstragenden sind. Die Methode erlaubt es das stochastischer Verhalten komplizierter Ionenkanalstrukturen mit einer großen Zahl an Untereinheiten, in Spikezeitenvariabilität zu übersetzen. Als weiteres werden die Filtereigenschaften der Nervenzellen in der überschwelligen Dynamik, also bei Existenz eines stabilen Grenzzyklus, aus ihren Phasenantwortkurven (PAK), einer Eigenschaft des linearisierten adjungierten Flusses auf dem Grenzzyklus, in einem stöhrungstheoretischen Ansatz berechnet. Es ergibt sich, dass Charakteristika des Filter, wie beispielsweise die DC Komponente und die Eigenschaften des Filters um die Fundamentalfrequenz und ihrer Harmonien, von den Fourierkomponenten der PAK abhängen. Unter Verwendung der hergeleiteten Filter und weiterer Annahmen ist es möglich das frequenzabhängige Signal-zu-Rauschen Verhältnis zu berechnen, und damit eine untere Schranke für die Informationstransferrate eines Leitfähigkeitsmodells zu berechnen. Unter Zuhilfenahme der numerischen Kontinuierungsmethode ist es möglich die Veränderungen in der Spikevariabilität und den Filtern für jeden biophysikalischen Parameter des System zu verfolgen. Weiterhin wurde die verwendete Phasenreduktion durch eine Korrektur ergänzt, die die Radialdynamik einbezieht. Es zeigt sich, dass die Krümmung der Isochronen einen Einfluss darauf hat ob das Rauschen einen positiven oder negativen Frequenzschift hervorruft.The goal of the thesis is to establish quantitative, analytical relations between the biophysical properties of nerve membranes and the performed neuronal computations for neurons in a tonically spiking regime and in the presence of intrinsic noise. For this purpose, two major lines of investigation are followed. Firstly, microscopic noise caused by the stochastic opening and closing of ion channels is mapped to the macroscopic spike jitter that affects neural coding. The method is generic enough to allow one to treat Markov channel models with complicated, high-dimensional state spaces and calculate from them the noise in the coding variable, i.e., the spike time. Secondly, the suprathreshold filtering properties of neurons are derived, based on the phase response curves (PRCs) by perturbing the associated Fokker-Planck equations. It turns out that key characteristics of the filter, such as the DC component of the gain and the behaviour near the fundamental frequency and its harmonics are related to the particular Fourier components of the PRC and hence the bifurcation type of the neuron. With the help of the derived filter and further approximations one is able to calculate the frequency resolved signal-to-noise ration and finally the total information transmission rate of a conductance based model. Using the method of numerical continuation it is possible to calculate the change in spike time noise level as well as the filtering properties for arbitrary changes in biophysical parameter such as varying channel densities or mean input to the cell. We extend the phase reduction to include correction terms from the amplitude dynamics that are related to the curvature of the isochrons and provide a method to identify the required amplitude sensitivities numerically. It can be shown that the curvature of the isochron has a direct consequence for the noise induced frequency shift

Phase Synchronisation in Superimposed Electrophysiological Data

There is experimental and theoretical evidence that functional units on various scales of the nervous system express properties of self-sustained oscillators. For example, this quality is present in several models for a neuron’s membrane potential dynamics. Perturbation theory then leads to a formulation of the oscillator’s dynamic interactions solely based on phase evolutions. In such models mutual synchronisation can occur. Verification that this effect takes place in the nervous system and is relevant for information integration requires calculating quantities such as a matrix of bivariate phase-locking statistics from multi-unit electrophysiological measurements. For this, data with high temporal resolution is favourable, rendering invasive recordings of local field potentials or non-invasive techniques like EEG or MEG suitable. This thesis provides interpretation for the spectral analysis of the synchronisation matrix with respect to phase reduced oscillator dynamics underlying the data. The relation of eigenvectors and order parameters as well as eigenvalues and population size are highlighted and the clustering into phase locked subpopulations is described

Modifications of sodium channel voltage dependence induce arrhythmia-favouring dynamics of cardiac action potentials

Heart arrhythmia is a pathological condition where the sequence of electrical impulses in the heart deviates from the normal rhythm. It is often associated with specific channelopathies in cardiac tissue, yet how precisely the changes in ionic channels affect the electrical activity of cardiac cells is still an open question. Even though sodium channel mutations that underlie cardiac syndromes like the Long-Q-T and the Brugada-syndrome are known to affect a number of channel parameters simultaneously, previous studies have predominantly focused on the persistent late component of the sodium current as the causal explanation for an increased risk of heart arrhythmias in these cardiac syndromes. A systematic analysis of the impact of other important sodium channel parameters is currently lacking. Here, we investigate the reduced ten-Tusscher-model for single human epicardium ventricle cells and use mathematical bifurcation analysis to predict the dependence of the cardiac action potential on sodium channel activation and inactivation time-constants and voltage dependence. We show that, specifically, shifts of the voltage dependence of activation and inactivation curve can lead to drastic changes in the action potential dynamics, inducing oscillations of the membrane potential as well as bistability. Our results not only demonstrate a new way to induce multiple co-existing states of excitability (biexcitability) but also emphasize the critical role of the voltage dependence of sodium channel activation and inactivation curves for the induction of heart-arrhythmias.Peer Reviewe