Jan-Hendrik Schleimer

Source Separation and Clustering of Phase-Locked Subspaces

It has been proven that there are synchrony (or phase-locking) phenomena present in multiple oscillating systems such as electrical circuits, lasers, chemical reactions, and human neurons. If the measurements of these systems cannot detect the individual oscillators but rather a superposition of them, as in brain electrophysiological signals (electo- and magneoencephalogram), spurious phase locking will be detected. Current source-extraction techniques attempt to undo this superposition by assuming properties on the data, which are not valid when underlying sources are phase-locked. Statistical independence of the sources is one such invalid assumption, as phase-locked sources are dependent. In this paper, we introduce methods for source separation and clustering which make adequate assumptions for data where synchrony is present, and show with simulated data that they perform well even in cases where independent component analysis and other well-known source-separation methods fail. The results in this paper provide a proof of concept that synchrony-based techniques are useful for low-noise applications.

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

Spike‐timing dependent inhibitory plasticity to learn a selective gating of backpropagating action potentials

Inhibition is known to influence the forward‐directed flow of information within neurons. However, also regulation of backward‐directed signals, such as backpropagating action potentials (bAPs), can enrich the functional repertoire of local circuits. Inhibitory control of bAP spread, for example, can provide a switch for the plasticity of excitatory synapses. Although such a mechanism is possible, it requires a precise timing of inhibition to annihilate bAPs without impairment of forward‐directed excitatory information flow. Here, we propose a specific learning rule for inhibitory synapses to automatically generate the correct timing to gate bAPs in pyramidal cells when embedded in a local circuit of feedforward inhibition. Based on computational modeling of multi‐compartmental neurons with physiological properties, we demonstrate that a learning rule with anti‐Hebbian shape can establish the required temporal precision. In contrast to classical spike‐timing dependent plasticity of excitatory synapses, the proposed inhibitory learning mechanism does not necessarily require the definition of an upper bound of synaptic weights because of its tendency to self‐terminate once annihilation of bAPs has been reached. Our study provides a functional context in which one of the many time‐dependent learning rules that have been observed experimentally – specifically, a learning rule with anti‐Hebbian shape – is assigned a relevant role for inhibitory synapses. Moreover, the described mechanism is compatible with an upregulation of excitatory plasticity by disinhibition.

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 systems 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.Information processing in the brain crucially depends on coding properties of single neurons shaped by their intrinsic dynamics. Our theoretical study shows that neuronal excitability, spike-based coding, and synchronization change drastically around a special dynamical regime: the codimension-two saddle-node loop bifurcation. This bifurcation maximizes the entrainment range and turns out to be more relevant for spike-based processing than the typically considered Bogdanov-Takens point. We show that the saddle-node loop bifurcation occurs ubiquitously in a generic class of neuron models (planar type-I). Our theory, applied to optical stimulation techniques, reveals that they could manipulate a variety of information processing characteristics in nerve cells beyond pure stimulation.

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.

Cellular temperature compensation of sensory receptor neuron responses

Temperature is known to modulate ion channel kinetics and hence also action-potential generation. This poses a challenge for neural systems that need to retain their functionality also under conditions of varying temperature. Multiple strategies to counterbalance the effects of environmental temperature changes exist: mammals keep their body temperature approximately constant, while poikilothermic species need to implement temperature-compensation at the behavioral, systems, or cellular level. While mechanisms of behavioral and systems level have been identified [1], cellular mechanisms of temperature-compensation as well as their associated metabolic cost remain largely unknown. We investigated the effect of temperature on auditory processing in the grasshopper. We recorded intracellular responses of auditory receptor neurons to auditory broad-band noise stimuli at different intensities at two distinct behaviorally relevant temperatures. Interestingly, we found that changes in temperature did not have large effects on sound-intensity coding in receptor neurons. These neurons constitute the input layer of a feedforward network and hence do not receive network input. We concluded that the observed temperature robustness of receptor-neuron responses must arise from intrinsic, network unrelated effects. In general, the receptor-neuron response is shaped by two processing steps: mechanosensory transduction and spike generation. Both can contribute to temperature compensation. Either both transduction and spike generation are compensated (hypothesis I), or alternatively, their temperature dependencies can cancel each other (hypothesis II). To test hypothesis I we assumed a temperature-invariant transduction and asked, first, whether temperature-compensation could be achieved for a spike-generating mechanism with realistic temperature dependencies of the ionic conductances. The latter refers, in particular, to increases of gating kinetics by a factor of 2-4 with temperature increments of 10°C (defining a Q10 value of 2-4) as well as modest increases of peak conductances. Second, we explored whether temperature compensation, if achieved cell-intrinsically, compromises the neuronal energy budget. In other words, is temperature robustness metabolically expensive? To address these questions, we varied the temperature dependence of ionic conductances in a conductance-based neuron model. Based on the spike frequency vs. input current (f-I) relation, we estimated the ability of the model neurons to keep a robust firing rate despite changing temperature. Moreover, we computed the average energetic cost per action potential [2]. Using a database modeling approach [3], we performed a systematic sensitivity analysis for firing-rate changes and energetic cost as a function of the temperature dependence of conductance parameters (i.e. Q10 values of transition rates and peak conductances). Our analysis shows that the key parameters determining the robustness of spike generation relate to the temperature-dependence of the models potassium conductances. In contrast, energy consumption is governed by the temperature dependence of the sodium conductance. Consequently, a neuron can achieve temperature-compensation of its firing rate without compromising the energy budget. To constrain hypothesis II, we used the experimentally observed f-I curves in an objective function and inferred the corresponding transduction process for each spike generation in our sensitivity analysis. Our results predict that thermosensitive Transient Receptor Potential (TRP) channels have a role in mechanosensory transduction at the grasshopper tympanum, and therefore motivate further experiments.

Influence of biophysical properties on temporal filters in a sensory neuron.

Sensory pathways implement filters that extract relevant information from the environment [1]. These filtering properties depend in intricate ways on the biophysical parameters of the underlying neuronal architecture. Understanding the link between computational aspects, such as response properties or spike statistics, and the underlying biophysics is a question that can be addressed with theoretical methods. Many primary sensory neurons operate in a mean-driven regime, where mean intensity is represented by the average firing rate, while the temporal structure of the stimulus around its mean is encoded into the particular structure of the spike train in analogy to an irregular sampler [2]. Examples of neurons applying this strategy include the paddlefishs electrosensory system [3], grasshopper auditory receptors [4], or the vestibular system of the turtle [5]. Spikes are generated from the dynamics of voltage-dependent ion channels. Different sensory neurons, however, may use different compositions of spike-generating channel types. These do not only render the cell excitable in the first place, they also have a large influence on a neurons transfer function. In addition, some ion channels shape the subthreshold dynamics of neurons, but it is less clear, how they affect the temporal structure of spike trains when the neurons are driven tonically. Several channel types, including HCN channels, are known to cause subthreshold resonance. This property results in largest subthreshold response amplitudes of a neuron at a particular frequency, hence termed the resonance frequency. The resulting band-pass like filter properties have a strong effect on fluctuation-driven neurons. Their influence on tonic spiking, however, has been less explored. Accordingly, the influence of channels that cause subthreshold resonance, such as HCN, on sensory systems like the hair cells of the mouse inner ear is still under debate [6]. Here, we use phase-response-curve-based methods within the framework of numerical continuation to resolve whether and how the effects of these channels carry over into the suprathreshold, mean-driven dynamics. To this end, we use computational models of hair-cell mechanoreceptors [7]. Our approach is to, first, derive the phase oscillator that is input-output equivalent to the full biophysical model. Then, applying linear response theory, the transfer function can be estimated in the regime of weak-amplitude stimulation [8]. This transfer function maps time-dependent stimuli to the instantaneous firing rate. We show that the poles and zeros of the transfer spectrum are related to the Fourier components of the systems phase response curve (PRC) as well as the average intrinsic noise level, which is due to a finite ensemble of stochastic ion channels. We find that both properties (1) the PRC - a consequence of the deterministic part of the dynamical system - and (2) the intrinsic stochasticity, are affected by the presence of HCN channels. Further, we use an overall measure of information transmission, the stimulus-response information, to approximate the contribution of HCN channels to information transfer in given frequency bands.