KCC2 reverse mode helps to clear postsynaptically released potassium at glutamatergic synapses

Extracellular potassium [K+]o elevation during synaptic activity retrogradely modifies presynaptic release and astrocytic uptake of glutamate. Hence, local K+ clearance and replenishment mechanisms are crucial regulators of glutamatergic transmission and plasticity. Based on recordings of astrocytic inward rectifier potassium current IKir and K+-sensitive electrodes as sensors of [K+]o as well as on in silico modeling, we demonstrate that the neuronal K+-Cl- co-transporter KCC2 clears local perisynaptic [K+]o during synaptic excitation by operating in an activity-dependent reversed mode. In reverse mode, KCC2 replenishes K+ in dendritic spines and complements clearance of [K+]o, therewith attenuating presynaptic glutamate release and shortening LTP. We thus demonstrate a physiological role of KCC2 in neuron-glial interactions and regulation of synaptic signaling and plasticity through the uptake of postsynaptically released K+.

Gap junctions desynchronize a neural circuit to stabilize insect flight

Insect asynchronous flight is one of the most prevalent forms of animal locomotion used by more than 600,000 species. Despite profound insights into the motor patterns¹, biomechanics^2,3 and aerodynamics underlying asynchronous flight^4,5, the architecture and function of the central-pattern-generating (CPG) neural network remain unclear. Here, on the basis of an experiment-theory approach including electrophysiology, optophysiology, Drosophila genetics and mathematical modelling, we identify a miniaturized circuit solution with unexpected properties. The CPG network consists of motoneurons interconnected by electrical synapses that, in contrast to doctrine, produce network activity splayed out in time instead of synchronized across neurons. Experimental and mathematical evidence support a generic mechanism for network desynchronization that relies on weak electrical synapses and specific excitability dynamics of the coupled neurons. In small networks, electrical synapses can synchronize or desynchronize network activity, depending on the neuron-intrinsic dynamics and ion channel composition. In the asynchronous flight CPG, this mechanism translates unpatterned premotor input into stereotyped neuronal firing with fixed sequences of cell activation that ensure stable wingbeat power and, as we show, is conserved across multiple species. Our findings prove a wider functional versatility of electrical synapses in the dynamic control of neural circuits and highlight the relevance of detecting electrical synapses in connectomics.

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

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.

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.

Biophysical models of intrinsic homeostasis: Firing rates and beyond

In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of cell-intrinsic properties, biophysical models of neurons permit one to identify relevant physiological substrates that can serve as regulators of neuronal excitability and to test how feedback loops can stabilize crucial variables such as long-term calcium levels and firing rates. Mathematical theory has also revealed a rich set of complementary computational properties arising from distinct cellular dynamics and even shaping processing at the network level. Here, we provide an overview over recently explored homeostatic mechanisms derived from biophysical models and hypothesize how multiple dynamical characteristics of cells, including their intrinsic neuronal excitability classes, can be stably controlled.

Activity-mediated accumulation of potassium induces a switch in firing pattern and neuronal excitability type

During normal neuronal activity, ionic concentration gradients across a neuron’s membrane are often assumed to be stable. Prolonged spiking activity, however, can reduce transmembrane gradients and affect voltage dynamics. Based on mathematical modeling, we investigated the impact of neuronal activity on ionic concentrations and, consequently, the dynamics of action potential generation. We find that intense spiking activity on the order of a second suffices to induce changes in ionic reversal potentials and to consistently induce a switch from a regular to an intermittent firing mode. This transition is caused by a qualitative alteration in the system’s voltage dynamics, mathematically corresponding to a co-dimension-two bifurcation from a saddle-node on invariant cycle (SNIC) to a homoclinic orbit bifurcation (HOM). Our electrophysiological recordings in mouse cortical pyramidal neurons confirm the changes in action potential dynamics predicted by the models: (i) activity-dependent increases in intracellular sodium concentration directly reduce action potential amplitudes, an effect typically attributed solely to sodium channel inactivation; (ii) extracellular potassium accumulation switches action potential generation from tonic firing to intermittently interrupted output. Thus, individual neurons may respond very differently to the same input stimuli, depending on their recent patterns of activity and/or the current brain-state.

Ionic concentrations in the brain are not constant. We show that during intense neuronal activity, they can change on the order of seconds and even switch neuronal spiking patterns under identical stimulation from a regular firing mode to an intermittently interrupted one. Triggered by an accumulation of extracellular potassium, such a transition is caused by a specific, qualitative change in of the neuronal voltage dynamics—a so-called bifurcation—which affects crucial features of action-potential generation and bears consequences for how information is encoded and how neurons behave together in the network. Also, changes in intracellular sodium can induce measurable effects, like a reduction of spike amplitude that occurs independently of the fast amplitude effects attributed to sodium channel inactivation. Taken together, our results demonstrate that a neuron can respond very differently to the same stimulus, depending on its previous activity or the current brain state. This finding may be particularly relevant when other regulatory mechanisms of ionic homeostasis are challenged, for example, during pathological states of glial impairment or oxygen deprivation. Finally, categorization of cortical neurons as intrinsically bursting or regular spiking may be biased by the ionic concentrations at the time of the observation, highlighting the non-static nature of neuronal dynamics.

Firing statistics in the bistable regime of neurons with homoclinic spike generation

Neuronal voltage dynamics of regularly firing neurons typically has one stable attractor: either a fixed point (like in the subthreshold regime) or a limit cycle that defines the tonic firing of action potentials (in the suprathreshold regime). In two of the three spike onset bifurcation sequences that are known to give rise to all-or-none type action potentials, however, the resting-state fixed point and limit cycle spiking can coexist in an intermediate regime, resulting in bistable dynamics. Here, noise can induce switches between the attractors, i.e., between rest and spiking, and thus increase the variability of the spike train compared to neurons with only one stable attractor. Qualitative features of the resulting spike statistics depend on the spike onset bifurcations. This paper focuses on the creation of the spiking limit cycle via the saddle-homoclinic orbit (HOM) bifurcation and derives interspike interval (ISI) densities for a conductance-based neuron model in the bistable regime. The ISI densities of bistable homoclinic neurons are found to be unimodal yet distinct from the inverse Gaussian distribution associated with the saddle-node-on-invariant-cycle bifurcation. It is demonstrated that for the HOM bifurcation the transition between rest and spiking is mainly determined along the downstroke of the action potential-a dynamical feature that is not captured by the commonly used reset neuron models. The deduced spike statistics can help to identify HOM dynamics in experimental data.

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.

Clusters of cooperative ion channels enable a membrane-potential-based mechanism for short-term memory

Across biological systems, cooperativity between proteins enables fast actions, supra-linear responses, and long-lasting molecular switches. In the nervous system, however, the function of cooperative interactions between voltage-dependent ionic channels remains largely unknown. Based on mathematical modeling, we here demonstrate that clusters of strongly cooperative ion channels can plausibly form bistable conductances. Consequently, clusters are permanently switched on by neuronal spiking, switched off by strong hyperpolarization, and remain in their state for seconds after stimulation. The resulting short-term memory of the membrane potential allows to generate persistent firing when clusters of cooperative channels are present together with non-cooperative spike-generating conductances. Dynamic clamp experiments in rodent cortical neurons confirm that channel cooperativity can robustly induce graded persistent activity - a single-cell based, multistable mnemonic firing mode experimentally observed in several brain regions. We therefore propose that ion channel cooperativity constitutes an efficient cell-intrinsic implementation for short-term memories at the voltage level.

Homeostasis: How Neurons Achieve Temperature Invariance

Temperature influences physiological processes and can corrupt nervous system function. A modelling study shows how regulation of ion channel expression can establish an acute temperature invariance of neuronal responses despite temperature-dependent and variable ionic conductances.

Qualitative changes in phase-response curve and synchronization at the saddle-node-loop bifurcation

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.

A temperature rise reduces trial-to-trial variability of locust auditory neuron responses

The neurophysiology of ectothermic animals, such as insects, is affected by environmental temperature, as their body temperature fluctuates with ambient conditions. Changes in temperature alter properties of neurons and, consequently, have an impact on the processing of information. Nevertheless, nervous system function is often maintained over a broad temperature range, exhibiting a surprising robustness to variations in temperature. A special problem arises for acoustically communicating insects, as in these animals mate recognition and mate localization typically rely on the decoding of fast amplitude modulations in calling and courtship songs. In the auditory periphery, however, temporal resolution is constrained by intrinsic neuronal noise. Such noise predominantly arises from the stochasticity of ion channel gating and potentially impairs the processing of sensory signals. On the basis of intracellular recordings of locust auditory neurons, we show that intrinsic neuronal variability on the level of spikes is reduced with increasing temperature. We use a detailed mathematical model including stochastic ion channel gating to shed light on the underlying biophysical mechanisms in auditory receptor neurons: because of a redistribution of channel-induced current noise toward higher frequencies and specifics of the temperature dependence of the membrane impedance, membrane potential noise is indeed reduced at higher temperatures. This finding holds under generic conditions and physiologically plausible assumptions on the temperature dependence of the channels' kinetics and peak conductances. We demonstrate that the identified mechanism also can explain the experimentally observed reduction of spike timing variability at higher temperatures.

Cell-intrinsic mechanisms of temperature compensation in a grasshopper sensory receptor neuron

Changes in temperature affect biochemical reaction rates and, consequently, neural processing. The nervous systems of poikilothermic animals must have evolved mechanisms enabling them to retain their functionality under varying temperatures. Auditory receptor neurons of grasshoppers respond to sound in a surprisingly temperature-compensated manner: firing rates depend moderately on temperature, with average Q10 values around 1.5. Analysis of conductance-based neuron models reveals that temperature compensation of spike generation can be achieved solely relying on cell-intrinsic processes and despite a strong dependence of ion conductances on temperature. Remarkably, this type of temperature compensation need not come at an additional metabolic cost of spike generation. Firing rate-based information transfer is likely to increase with temperature and we derive predictions for an optimal temperature dependence of the tympanal transduction process fostering temperature compensation. The example of auditory receptor neurons demonstrates how neurons may exploit single-cell mechanisms to cope with multiple constraints in parallel.DOI: http://dx.doi.org/10.7554/eLife.02078.001.

Coding of information in limit cycle oscillators

Starting from a general description of noisy limit cycle oscillators, we derive from the Fokker-Planck equations the linear response of the instantaneous oscillator frequency to a time-varying external force. We consider the time series of zero crossings of the oscillator's phase and compute the mutual information between it and the driving force. A direct link is established between the phase response curve summarizing the oscillator dynamics and the ability of a limit cycle oscillator, such as a heart cell or neuron, to encode information in the timing of peaks in the oscillation.