Linear versus nonlinear signal transmission in neuron models with adaptation currents or dynamic thresholds

Electrical Signaling Beyond Neurons

Neural action potentials (APs) are difficult to interpret as signal encoders and/or computational primitives. Their relationships with stimuli and behaviors are obscured by the staggering complexity of nervous systems themselves. We can reduce this complexity by observing that "simpler" neuron-less organisms also transduce stimuli into transient electrical pulses that affect their behaviors. Without a complicated nervous system, APs are often easier to understand as signal/response mechanisms. We review examples of nonneural stimulus transductions in domains of life largely neglected by theoretical neuroscience: bacteria, protozoans, plants, fungi, and neuron-less animals. We report properties of those electrical signals-for example, amplitudes, durations, ionic bases, refractory periods, and particularly their ecological purposes. We compare those properties with those of neurons to infer the tasks and selection pressures that neurons satisfy. Throughout the tree of life, nonneural stimulus transductions time behavioral responses to environmental changes. Nonneural organisms represent the presence or absence of a stimulus with the presence or absence of an electrical signal. Their transductions usually exhibit high sensitivity and specificity to a stimulus, but are often slow compared to neurons. Neurons appear to be sacrificing the specificity of their stimulus transductions for sensitivity and speed. We interpret cellular stimulus transductions as a cell's assertion that it detected something important at that moment in time. In particular, we consider neural APs as fast but noisy detection assertions. We infer that a principal goal of nervous systems is to detect extremely weak signals from noisy sensory spikes under enormous time pressure. We discuss neural computation proposals that address this goal by casting neurons as devices that implement online, analog, probabilistic computations with their membrane potentials. Those proposals imply a measurable relationship between afferent neural spiking statistics and efferent neural membrane electrophysiology.

The vitals for steady nucleation maps of spontaneous spiking coherence in autonomous two-dimensional neuronal networks

Thin pancake-like neuronal networks cultured on top of a planar microelectrode array have been extensively tried out in neuroengineering, as a substrate for the mobile robot's control unit, i.e., as a cyborg's brain. Most of these attempts failed due to intricate self-organizing dynamics in the neuronal systems. In particular, the networks may exhibit an emergent spatial map of steady nucleation sites ("n-sites") of spontaneous population spikes. Being unpredictable and independent of the surface electrode locations, the n-sites drastically change local ability of the network to generate spikes. Here, using a spiking neuronal network model with generative spatially-embedded connectome, we systematically show in simulations that the number, location, and relative activity of spontaneously formed n-sites ("the vitals") crucially depend on the samplings of three distributions: (1) the network distribution of neuronal excitability, (2) the distribution of connections between neurons of the network, and (3) the distribution of maximal amplitudes of a single synaptic current pulse. Moreover, blocking the dynamics of a small fraction (about 4%) of non-pacemaker neurons having the highest excitability was enough to completely suppress the occurrence of population spikes and their n-sites. This key result is explained theoretically. Remarkably, the n-sites occur taking into account only short-term synaptic plasticity, i.e., without a Hebbian-type plasticity. As the spiking network model used in this study is strictly deterministic, all simulation results can be accurately reproduced. The model, which has already demonstrated a very high richness-to-complexity ratio, can also be directly extended into the three-dimensional case, e.g., for targeting peculiarities of spiking dynamics in cerebral (or brain) organoids. We recommend the model as an excellent illustrative tool for teaching network-level computational neuroscience, complementing a few benchmark models.

Adaptive spike threshold dynamics associated with sparse spiking of hilar mossy cells are captured by a simple model

Hilar mossy cells (hMCs) in the dentate gyrus (DG) receive inputs from DG granule cells (GCs), CA3 pyramidal cells and inhibitory interneurons, and provide feedback input to GCs. Behavioural and in vivo recording experiments implicate hMCs in pattern separation, navigation and spatial learning. Our experiments link hMC intrinsic excitability to their synaptically evoked in vivo spiking outputs. We performed electrophysiological recordings from DG neurons and found that hMCs displayed an adaptative spike threshold that increased both in proportion to the intensity of injected currents, and in response to spiking itself, returning to baseline over a long time scale, thereby instantaneously limiting their firing rate responses. The hMC activity is additionally limited by a prominent medium after-hyperpolarizing potential (AHP) generated by small conductance K+ channels. We hypothesize that these intrinsic hMC properties are responsible for their low in vivo firing rates. Our findings extend previous studies that compare hMCs, CA3 pyramidal cells and hilar inhibitory cells and provide novel quantitative data that contrast the intrinsic properties of these cell types. We developed a phenomenological exponential integrate-and-fire model that closely reproduces the hMC adaptive threshold nonlinearities with respect to their threshold dependence on input current intensity, evoked spike latency and long-lasting spike-induced increase in spike threshold. Our robust and computationally efficient model is amenable to incorporation into large network models of the DG that will deepen our understanding of the neural bases of pattern separation, spatial navigation and learning. KEY POINTS: Previous studies have shown that hilar mossy cells (hMCs) are implicated in pattern separation and the formation of spatial memory, but how their intrinsic properties relate to their in vivo spiking patterns is still unknown. Here we show that the hMCs display electrophysiological properties that distinguish them from the other hilar cell types including a highly adaptive spike threshold that decays slowly. The spike-dependent increase in threshold combined with an after-hyperpolarizing potential mediated by a slow K+ conductance is hypothesized to be responsible for the low-firing rate of the hMC observed in vivo. The hMC's features are well captured by a modified stochastic exponential integrate-and-fire model that has the unique feature of a threshold intrinsically dependant on both the stimulus intensity and the spiking history. This computational model will allow future work to study how the hMCs can contribute to spatial memory formation and navigation.

Short-term neuronal and synaptic plasticity act in synergy for deviance detection in spiking networks

Sensory areas of cortex respond more strongly to infrequent stimuli when these violate previously established regularities, a phenomenon known as deviance detection (DD). Previous modeling work has mainly attempted to explain DD on the basis of synaptic plasticity. However, a large fraction of cortical neurons also exhibit firing rate adaptation, an underexplored potential mechanism. Here, we investigate DD in a spiking neuronal network model with two types of short-term plasticity, fast synaptic short-term depression (STD) and slower threshold adaptation (TA). We probe the model with an oddball stimulation paradigm and assess DD by evaluating the network responses. We find that TA is sufficient to elicit DD. It achieves this by habituating neurons near the stimulation site that respond earliest to the frequently presented standard stimulus (local fatigue), which diminishes the response and promotes the recovery (global fatigue) of the wider network. Further, we find a synergy effect between STD and TA, where they interact with each other to achieve greater DD than the sum of their individual effects. We show that this synergy is caused by the local fatigue added by STD, which inhibits the global response to the frequently presented stimulus, allowing greater recovery of TA-mediated global fatigue and making the network more responsive to the deviant stimulus. Finally, we show that the magnitude of DD strongly depends on the timescale of stimulation. We conclude that highly predictable information can be encoded in strong local fatigue, which allows greater global recovery and subsequent heightened sensitivity for DD.

Beat encoding at mistuned octaves within single electrosensory neurons

Beats are slow periodic amplitude modulations resulting from the superposition of two spectrally close periodic signals. The difference frequency between the signals sets the frequency of the beat. A field study in the electric fish Apteronotus rostratus showed the behavioral relevance of very high difference frequencies. Contrary to expectations from previous studies, our electrophysiological data show strong responses of p-type electroreceptor afferents whenever the difference frequency approaches integer multiples (mistuned octaves) of the fish's own electric field frequency (carrier). Mathematical reasoning and simulations show that common approaches to extract amplitude modulations, such as Hilbert transform or half-wave rectification, are not sufficient to explain the responses at carrier octaves. Instead, half-wave rectification needs to be smoothed out, for example by a cubic function. Because electroreceptive afferents share many properties with auditory nerve fibers, these mechanisms may underly the human perception of beats at mistuned octaves as described by Ohm and Helmholtz.

Spike-frequency adaptation inhibits the pairwise spike correlation

Introduction

The spike train output correlation with pairwise neurons determines the neural population coding, which depends on the average firing rate of individual neurons. Spike frequency adaptation (SFA), which serves as an essential cellular encoding strategy, modulates the firing rates of individual neurons. However, the mechanism by which the SFA modulates the output correlation of the spike trains remains unclear.

Methods

We introduce a pairwise neuron model that receives correlated inputs to generate spike trains, and the output correlation is qualified using Pearson correlation coefficient. The SFA is modeled using adaptation currents to examine its effect on the output correlation. Moreover, we use dynamic thresholds to explore the effect of SFA on output correlation. Furthermore, a simple phenomenological neuron model with a threshold-linear transfer function is utilized to confirm the effect of SFA on decreasing the output correlation.

Results

The results show that the adaptation currents decreased the output correlation by reducing the firing rate of a single neuron. At the onset of a correlated input, a transient process shows a decrease in interspike intervals (ISIs), resulting in a temporary increase in the correlation. When the adaptation current is sufficiently activated, the correlation reached a steady state, and the ISIs are maintained at higher values. The enhanced adaptation current achieved by increasing the adaptation conductance further reduces the pairwise correlation. While the time and slide windows influence the correlation, they make no difference in the effect of SFA on decreasing the output correlation. Moreover, SFA simulated by dynamic thresholds also decreases the output correlation. Furthermore, the simple phenomenological neuron model with a threshold-linear transfer function confirms the effect of SFA on decreasing the output correlation. The strength of the signal input and the slope of the linear component of the transfer function, the latter of which can be decreased by SFA, could together modulate the strength of the output correlation. Stronger SFA will decrease the slope and hence decrease the output correlation.

Conclusions

The results reveal that the SFA reduces the output correlation with pairwise neurons in the network by reducing the firing rate of individual neurons. This study provides a link between cellular non-linear mechanisms and network coding strategies.

A dynamic spike threshold with correlated noise predicts observed patterns of negative interval correlations in neuronal spike trains

Negative correlations in the sequential evolution of interspike intervals (ISIs) are a signature of memory in neuronal spike-trains. They provide coding benefits including firing-rate stabilization, improved detectability of weak sensory signals, and enhanced transmission of information by improving signal-to-noise ratio. Primary electrosensory afferent spike-trains in weakly electric fish fall into two categories based on the pattern of ISI correlations: non-bursting units have negative correlations which remain negative but decay to zero with increasing lags (Type I ISI correlations), and bursting units have oscillatory (alternating sign) correlation which damp to zero with increasing lags (Type II ISI correlations). Here, we predict and match observed ISI correlations in these afferents using a stochastic dynamic threshold model. We determine the ISI correlation function as a function of an arbitrary discrete noise correlation function [Formula: see text], where k is a multiple of the mean ISI. The function permits forward and inverse calculations of the correlation function. Both types of correlation functions can be generated by adding colored noise to the spike threshold with Type I correlations generated with slow noise and Type II correlations generated with fast noise. A first-order autoregressive (AR) process with a single parameter is sufficient to predict and accurately match both types of afferent ISI correlation functions, with the type being determined by the sign of the AR parameter. The predicted and experimentally observed correlations are in geometric progression. The theory predicts that the limiting sum of ISI correlations is [Formula: see text] yielding a perfect DC-block in the power spectrum of the spike train. Observed ISI correlations from afferents have a limiting sum that is slightly larger at [Formula: see text] ([Formula: see text]). We conclude that the underlying process for generating ISIs may be a simple combination of low-order AR and moving average processes and discuss the results from the perspective of optimal coding.

Theoretical analysis of effects of transcranial magneto-acoustical stimulation on neuronal spike-frequency adaptation

BACKGROUND

Transcranial magneto-acoustical stimulation (TMAS) is a noninvasive technique that has advantages in spatial resolution and penetration depth. It changes the firing properties of neurons through the current generated by focused ultrasound and a static magnetic field. Spike-frequency adaptation is an important dynamic characteristic of neural information processing.

METHODS

To address the effects of TMAS on neural spike-frequency adaptation, this study employs some ultrasound and magnetic field parameters, such as magnetic flux density, ultrasonic intensity, fundamental ultrasonic frequency, modulation frequency, and duty cycle. Using these different ultrasound and magnetic field parameters, membrane potential curves, spike-frequency curves, and adapted onset spike-frequency curves are exhibited and analyzed.

RESULTS

The results show that spike-frequency adaptation is strongly dependent on ultrasonic intensity and magnetic flux density and is rarely affected by other parameters. However, modulation frequency and duty cycle influence membrane potentials and spike frequencies to some degree.

CONCLUSIONS

This study reveals the mechanism of the effects of TMAS on neural spike-frequency adaptation and serves as theoretical guidance for TMAS experiments.

Interspike interval correlations in neuron models with adaptation and correlated noise

The generation of neural action potentials (spikes) is random but nevertheless may result in a rich statistical structure of the spike sequence. In particular, contrary to the popular renewal assumption of theoreticians, the intervals between adjacent spikes are often correlated. Experimentally, different patterns of interspike-interval correlations have been observed and computational studies have identified spike-frequency adaptation and correlated noise as the two main mechanisms that can lead to such correlations. Analytical studies have focused on the single cases of either correlated (colored) noise or adaptation currents in combination with uncorrelated (white) noise. For low-pass filtered noise or adaptation, the serial correlation coefficient can be approximated as a single geometric sequence of the lag between the intervals, providing an explanation for some of the experimentally observed patterns. Here we address the problem of interval correlations for a widely used class of models, multidimensional integrate-and-fire neurons subject to a combination of colored and white noise sources and a spike-triggered adaptation current. Assuming weak noise, we derive a simple formula for the serial correlation coefficient, a sum of two geometric sequences, which accounts for a large class of correlation patterns. The theory is confirmed by means of numerical simulations in a number of special cases including the leaky, quadratic, and generalized integrate-and-fire models with colored noise and spike-frequency adaptation. Furthermore we study the case in which the adaptation current and the colored noise share the same time scale, corresponding to a slow stochastic population of adaptation channels; we demonstrate that our theory can account for a nonmonotonic dependence of the correlation coefficient on the channel's time scale. Another application of the theory is a neuron driven by network-noise-like fluctuations (green noise). We also discuss the range of validity of our weak-noise theory and show that by changing the relative strength of white and colored noise sources, we can change the sign of the correlation coefficient. Finally, we apply our theory to a conductance-based model which demonstrates its broad applicability.

Spike frequency adaptation supports network computations on temporally dispersed information

For solving tasks such as recognizing a song, answering a question, or inverting a sequence of symbols, cortical microcircuits need to integrate and manipulate information that was dispersed over time during the preceding seconds. Creating biologically realistic models for the underlying computations, especially with spiking neurons and for behaviorally relevant integration time spans, is notoriously difficult. We examine the role of spike frequency adaptation in such computations and find that it has a surprisingly large impact. The inclusion of this well-known property of a substantial fraction of neurons in the neocortex - especially in higher areas of the human neocortex - moves the performance of spiking neural network models for computations on network inputs that are temporally dispersed from a fairly low level up to the performance level of the human brain.

Regular spiking in high-conductance states: The essential role of inhibition

Strong inhibitory input to neurons, which occurs in balanced states of neural networks, increases synaptic current fluctuations. This has led to the assumption that inhibition contributes to the high spike-firing irregularity observed in vivo. We used single compartment neuronal models with time-correlated (due to synaptic filtering) and state-dependent (due to reversal potentials) input to demonstrate that inhibitory input acts to decrease membrane potential fluctuations, a result that cannot be achieved with simplified neural input models. To clarify the effects on spike-firing regularity, we used models with different spike-firing adaptation mechanisms, and we observed that the addition of inhibition increased firing regularity in models with dynamic firing thresholds and decreased firing regularity if spike-firing adaptation was implemented through ionic currents or not at all. This fluctuation-stabilization mechanism provides an alternative perspective on the importance of strong inhibitory inputs observed in balanced states of neural networks, and it highlights the key roles of biologically plausible inputs and specific adaptation mechanisms in neuronal modeling.

Neural adaptation

The term 'neural adaptation' refers to the common phenomenon of decaying neuronal activities in response to repeated or prolonged stimulation. Many different roles of adaptation in neural computations have been discussed. On a single-cell level adaptation introduces a high-pass filter operation as a basic element for predictive coding. Interactions of adaptation processes with nonlinearities are key to many more computations including generation of invariances, stimulus selectivity, denoising, and sparsening. Neural adaptation is observed all the way along neuronal pathways from the sensory periphery to the motor output and adaptation usually gets stronger at higher levels. Non-adapting neurons or neurons that increase their sensitivity are rare exceptions. What computations arise by repeated adaptation mechanisms along a processing pathway? After giving some background on neural adaptation, underlying mechanisms, dynamics, and resulting filter properties, I will discuss computational properties of four examples of serial and parallel adaptation processes, demonstrating that adaptation acts together with other mechanisms, in particular threshold nonlinearities, to eventually compute meaningful perceptions. Python code and further details of the simulations illustrating this primer are available at https://github.com/janscience/adaptationprimer.

A spiking and adapting tactile sensor for neuromorphic applications

The ongoing research on and development of increasingly intelligent artificial systems propels the need for bio inspired pressure sensitive spiking circuits. Here we present an adapting and spiking tactile sensor, based on a neuronal model and a piezoelectric field-effect transistor (PiezoFET). The piezoelectric sensor device consists of a metal-oxide semiconductor field-effect transistor comprising a piezoelectric aluminium-scandium-nitride (AlxSc1-xN) layer inside of the gate stack. The so augmented device is sensitive to mechanical stress. In combination with an analogue circuit, this sensor unit is capable of encoding the mechanical quantity into a series of spikes with an ongoing adaptation of the output frequency. This allows for a broad application in the context of robotic and neuromorphic systems, since it enables said systems to receive information from the surrounding environment and provide encoded spike trains for neuromorphic hardware. We present numerical and experimental results on this spiking and adapting tactile sensor.

A Discrete Time Framework for Spike Transfer Process in a Cortical Neuron With Asynchronous EPSP, IPSP, and Variable Threshold

Interpretation of high level cognitive behavior of human brain requires comprehensive understanding of spike transfer process at neuronal level. Synapses play major role in spike transfer process from one neuron to another. An expanded leaky integrate and fire model of a neuron in multiple input and single output configuration with threshold variability for spike transfer process is proposed in this paper. Asynchronous generation of post synaptic potential is considered. Multiple types of excitatory and inhibitory post-synaptic potentials are also included in the model. An analytical expression of membrane potential including threshold variability and activity dependant noise process has been developed. The model captures several important features of a spiking neuron through a set of well defined parameters. Simulation results are provided to explain various aspects of the proposed model. A functionally scaled version of the model has also been compared with limited experimental data, available from the Allen Institute of Brain Science.

DNA breathing dynamics under periodic forcing: Study of several distribution functions of relevant Brownian functionals

In this paper, we study DNA breathing dynamics in the presence of an external periodic force by proposing and inspecting several probability distribution functions (PDFs) of relevant Brownian functionals which specify the bubble lifetime, reactivity, and average size. We model the bubble dynamics process by an overdamped Langevin equation of broken base pairs on the Poland-Scheraga free energy landscape. Introducing an effective time-independent description for timescales larger than T[over ̃]=2π/ω (where ω is the frequency of external periodic force) and using an elegant backward Fokker-Planck method we derive closed form expressions of several PDFs associated with such stochastic processes. For instance, with an initial bubble size of x_{0}, we derive the following analytical expressions: (i) the PDF P(t_{f}|x_{0}) of the first passage time t_{f} which specifies the lifetime of the DNA breathing process, (ii) the PDF P(A|x_{0}) of the area A until the first passage time, and it provides much valuable information about the average bubble size and reactivity of the process, and (iii) the PDF P(M) associated with the maximum bubble size M of the breathing process before complete denaturation. Our analysis is limited to two limits: (a) large bubble size and (b) small bubble size. We further confirm our analytical predictions by computing the same PDFs with direct numerical simulations of the corresponding Langevin equations. We obtain very good agreement of our theoretical predictions with the numerically simulated results. Finally, several nontrivial scaling behaviors in the asymptotic limits for the above-mentioned PDFs are predicted, which can be verified further from experimental observation. Our main conclusion is that the large bubble dynamics is unaffected by the rapidly oscillating force, but the small bubble dynamics is significantly affected by the same periodic force.

Spike threshold adaptation diversifies neuronal operating modes in the auditory brain stem

Single neurons function along a spectrum of neuronal operating modes whose properties determine how the output firing activity is generated from synaptic input. The auditory brain stem contains a diversity of neurons, from pure coincidence detectors to pure integrators and those with intermediate properties. We investigated how intrinsic spike initiation mechanisms regulate neuronal operating mode in the avian cochlear nucleus. Although the neurons in one division of the avian cochlear nucleus, nucleus magnocellularis, have been studied in depth, the spike threshold dynamics of the tonically firing neurons of a second division of cochlear nucleus, nucleus angularis (NA), remained unexplained. The input-output functions of tonically firing NA neurons were interrogated with directly injected in vivo-like current stimuli during whole cell patch-clamp recordings in vitro. Increasing the amplitude of the noise fluctuations in the current stimulus enhanced the firing rates in one subset of tonically firing neurons ("differentiators") but not another ("integrators"). We found that spike thresholds showed significantly greater adaptation and variability in the differentiator neurons. A leaky integrate-and-fire neuronal model with an adaptive spike initiation process derived from sodium channel dynamics was fit to the firing responses and could recapitulate >80% of the precise temporal firing across a range of fluctuation and mean current levels. Greater threshold adaptation explained the frequency-current curve changes due to a hyperpolarized shift in the effective adaptation voltage range and longer-lasting threshold adaptation in differentiators. The fine-tuning of the intrinsic properties of different NA neurons suggests they may have specialized roles in spectrotemporal processing.NEW & NOTEWORTHY Avian cochlear nucleus angularis (NA) neurons are responsible for encoding sound intensity for sound localization and spectrotemporal processing. An adaptive spike threshold mechanism fine-tunes a subset of repetitive-spiking neurons in NA to confer coincidence detector-like properties. A model based on sodium channel inactivation properties reproduced the activity via a hyperpolarized shift in adaptation conferring fluctuation sensitivity.

Cellular and Network Mechanisms May Generate Sparse Coding of Sequential Object Encounters in Hippocampal-Like Circuits

The localization of distinct landmarks plays a crucial role in encoding new spatial memories. In mammals, this function is performed by hippocampal neurons that sparsely encode an animal’s location relative to surrounding objects. Similarly, the dorsolateral pallium (DL) is essential for spatial learning in teleost fish. The DL of weakly electric gymnotiform fish receives both electrosensory and visual input from the preglomerular nucleus (PG), which has been hypothesized to encode the temporal sequence of electrosensory or visual landmark/food encounters. Here, we show that DL neurons in the Apteronotid fish and in the Carassius auratus (goldfish) have a hyperpolarized resting membrane potential (RMP) combined with a high and dynamic spike threshold that increases following each spike. Current-evoked spikes in DL cells are followed by a strong small-conductance calcium-activated potassium channel (SK)-mediated after-hyperpolarizing potential (AHP). Together, these properties prevent high frequency and continuous spiking. The resulting sparseness of discharge and dynamic threshold suggest that DL neurons meet theoretical requirements for generating spatial memory engrams by decoding the landmark/food encounter sequences encoded by PG neurons. Thus, DL neurons in teleost fish may provide a promising, simple system to study the core cell and network mechanisms underlying spatial memory.

Interspike interval correlations in networks of inhibitory integrate-and-fire neurons

We study temporal correlations of interspike intervals, quantified by the network-averaged serial correlation coefficient (SCC), in networks of both current- and conductance-based purely inhibitory integrate-and-fire neurons. Numerical simulations reveal transitions to negative SCCs at intermediate values of bias current drive and network size. As bias drive and network size are increased past these values, the SCC returns to zero. The SCC is maximally negative at an intermediate value of the network oscillation strength. The dependence of the SCC on two canonical schemes for synaptic connectivity is studied, and it is shown that the results occur robustly in both schemes. For conductance-based synapses, the SCC becomes negative at the onset of both a fast and slow coherent network oscillation. We then show by means of offline simulations using prerecorded network activity that a neuron's SCC is highly sensitive to its number of presynaptic inputs. Finally, we devise a noise-reduced diffusion approximation for current-based networks that accounts for the observed temporal correlation transitions.

Complex Dynamics in Simplified Neuronal Models: Reproducing Golgi Cell Electroresponsiveness

Brain neurons exhibit complex electroresponsive properties – including intrinsic subthreshold oscillations and pacemaking, resonance and phase-reset – which are thought to play a critical role in controlling neural network dynamics. Although these properties emerge from detailed representations of molecular-level mechanisms in “realistic” models, they cannot usually be generated by simplified neuronal models (although these may show spike-frequency adaptation and bursting). We report here that this whole set of properties can be generated by the extended generalized leaky integrate-and-fire (E-GLIF) neuron model. E-GLIF derives from the GLIF model family and is therefore mono-compartmental, keeps the limited computational load typical of a linear low-dimensional system, admits analytical solutions and can be tuned through gradient-descent algorithms. Importantly, E-GLIF is designed to maintain a correspondence between model parameters and neuronal membrane mechanisms through a minimum set of equations. In order to test its potential, E-GLIF was used to model a specific neuron showing rich and complex electroresponsiveness, the cerebellar Golgi cell, and was validated against experimental electrophysiological data recorded from Golgi cells in acute cerebellar slices. During simulations, E-GLIF was activated by stimulus patterns, including current steps and synaptic inputs, identical to those used for the experiments. The results demonstrate that E-GLIF can reproduce the whole set of complex neuronal dynamics typical of these neurons – including intensity-frequency curves, spike-frequency adaptation, post-inhibitory rebound bursting, spontaneous subthreshold oscillations, resonance, and phase-reset – providing a new effective tool to investigate brain dynamics in large-scale simulations.

The impact of spike-frequency adaptation on balanced network dynamics

A dynamic balance between strong excitatory and inhibitory neuronal inputs is hypothesized to play a pivotal role in information processing in the brain. While there is evidence of the existence of a balanced operating regime in several cortical areas and idealized neuronal network models, it is important for the theory of balanced networks to be reconciled with more physiological neuronal modeling assumptions. In this work, we examine the impact of spike-frequency adaptation, observed widely across neurons in the brain, on balanced dynamics. We incorporate adaptation into binary and integrate-and-fire neuronal network models, analyzing the theoretical effect of adaptation in the large network limit and performing an extensive numerical investigation of the model adaptation parameter space. Our analysis demonstrates that balance is well preserved for moderate adaptation strength even if the entire network exhibits adaptation. In the common physiological case in which only excitatory neurons undergo adaptation, we show that the balanced operating regime in fact widens relative to the non-adaptive case. We hypothesize that spike-frequency adaptation may have been selected through evolution to robustly facilitate balanced dynamics across diverse cognitive operating states.

Dendritic Properties Control Energy Efficiency of Action Potentials in Cortical Pyramidal Cells

Neural computation is performed by transforming input signals into sequences of action potentials (APs), which is metabolically expensive and limited by the energy available to the brain. The metabolic efficiency of single AP has important consequences for the computational power of the cell, which is determined by its biophysical properties and morphologies. Here we adopt biophysically-based two-compartment models to investigate how dendrites affect energy efficiency of APs in cortical pyramidal neurons. We measure the Na⁺ entry during the spike and examine how it is efficiently used for generating AP depolarization. We show that increasing the proportion of dendritic area or coupling conductance between two chambers decreases Na⁺ entry efficiency of somatic AP. Activating inward Ca²⁺ current in dendrites results in dendritic spike, which increases AP efficiency. Activating Ca²⁺-activated outward K⁺ current in dendrites, however, decreases Na⁺ entry efficiency. We demonstrate that the active and passive dendrites take effects by altering the overlap between Na⁺ influx and internal current flowing from soma to dendrite. We explain a fundamental link between dendritic properties and AP efficiency, which is essential to interpret how neural computation consumes metabolic energy and how biophysics and morphologies contribute to such consumption.

Combining Theory, Model, and Experiment to Explain How Intrinsic Theta Rhythms Are Generated in an In Vitro Whole Hippocampus Preparation without Oscillatory Inputs

Scientists have observed local field potential theta rhythms (3-12 Hz) in the hippocampus for decades, but understanding the mechanisms underlying their generation is complicated by their diversity in pharmacological and frequency profiles. In addition, interactions with other brain structures and oscillatory drives to the hippocampus during distinct brain states has made it difficult to identify hippocampus-specific properties directly involved in theta generation. To overcome this, we develop cellular-based network models using a whole hippocampus in vitro preparation that spontaneously generates theta rhythms. Building on theoretical and computational analyses, we find that spike frequency adaptation and postinhibitory rebound constitute a basis for theta generation in large, minimally connected CA1 pyramidal (PYR) cell network models with fast-firing parvalbumin-positive (PV⁺) inhibitory cells. Sparse firing of PYR cells and large excitatory currents onto PV⁺ cells are present as in experiments. The particular theta frequency is more controlled by PYR-to-PV⁺ cell interactions rather than PV⁺-to-PYR cell interactions. We identify two scenarios by which theta rhythms can emerge, and they can be differentiated by the ratio of excitatory to inhibitory currents to PV⁺ cells, but not to PYR cells. Only one of the scenarios is consistent with data from the whole hippocampus preparation, which leads to the prediction that the connection probability from PV⁺ to PYR cells needs to be larger than from PYR to PV⁺ cells. Our models can serve as a platform on which to build and develop an understanding of in vivo theta generation.

Tonotopic Optimization for Temporal Processing in the Cochlear Nucleus

In the auditory system, sounds are processed in parallel frequency-tuned circuits, beginning in the cochlea. Auditory nerve fibers reflect this tonotopy and encode temporal properties of acoustic stimuli by "locking" discharges to a particular stimulus phase. However, physiological constraints on phase-locking depend on stimulus frequency. Interestingly, low characteristic frequency (LCF) neurons in the cochlear nucleus improve phase-locking precision relative to their auditory nerve inputs. This is proposed to arise through synaptic integration, but the postsynaptic membrane's selectivity for varying levels of synaptic convergence is poorly understood. The chick cochlear nucleus, nucleus magnocellularis (NM), exhibits tonotopic distribution of both input and membrane properties. LCF neurons receive many small inputs and have low input thresholds, whereas high characteristic frequency (HCF) neurons receive few, large synapses and require larger currents to spike. NM therefore presents an opportunity to study how small membrane variations interact with a systematic topographic gradient of synaptic inputs. We investigated membrane input selectivity and observed that HCF neurons preferentially select faster input than their LCF counterparts, and that this preference is tolerant of changes to membrane voltage. We then used computational models to probe which properties are crucial to phase-locking. The model predicted that the optimal arrangement of synaptic and membrane properties for phase-locking is specific to stimulus frequency and that the tonotopic distribution of input number and membrane excitability in NM closely tracks a stimulus-defined optimum. These findings were then confirmed physiologically with dynamic-clamp simulations of inputs to NM neurons.

SIGNIFICANCE STATEMENT

One way that neurons represent temporal information is by phase-locking, which is discharging in response to a particular phase of the stimulus waveform. In the auditory system, central neurons are optimized to retain or improve phase-locking precision compared with input from the auditory nerve. However, the difficulty of this computation varies systematically with stimulus frequency. We examined properties that contribute to temporal processing both physiologically and in a computational model. Neurons processing low-frequency input benefit from integration of many weak inputs, whereas those processing higher frequencies progressively lose precision by integration of multiple inputs. Here, we reveal general features of input-output optimization that apply to all neurons that process time varying input.

Noise-enhanced coding in phasic neuron spike trains

The stochastic nature of neuronal response has lead to conjectures about the impact of input fluctuations on the neural coding. For the most part, low pass membrane integration and spike threshold dynamics have been the primary features assumed in the transfer from synaptic input to output spiking. Phasic neurons are a common, but understudied, neuron class that are characterized by a subthreshold negative feedback that suppresses spike train responses to low frequency signals. Past work has shown that when a low frequency signal is accompanied by moderate intensity broadband noise, phasic neurons spike trains are well locked to the signal. We extend these results with a simple, reduced model of phasic activity that demonstrates that a non-Markovian spike train structure caused by the negative feedback produces a noise-enhanced coding. Further, this enhancement is sensitive to the timescales, as opposed to the intensity, of a driving signal. Reduced hazard function models show that noise-enhanced phasic codes are both novel and separate from classical stochastic resonance reported in non-phasic neurons. The general features of our theory suggest that noise-enhanced codes in excitable systems with subthreshold negative feedback are a particularly rich framework to study.

Relationship in Pacemaker Neurons Between the Long-Term Correlations of Membrane Voltage Fluctuations and the Corresponding Duration of the Inter-Spike Interval

Several studies of the behavior in the voltage and frequency fluctuations of the neural electrical activity have been performed. Here, we explored the particular association between behavior of the voltage fluctuations in the inter-spike segment (VFIS) and the inter-spike intervals (ISI) of F1 pacemaker neurons from H. aspersa, by disturbing the intracellular calcium handling with cadmium and caffeine. The scaling exponent α of the VFIS, as provided by detrended fluctuations analysis, in conjunction with the corresponding duration of ISI to estimate the determination coefficient R ² (48-50 intervals per neuron, N = 5) were all evaluated. The time-varying scaling exponent α(t) of VFIS was also studied (20 segments per neuron, N = 11). The R ² obtained in control conditions was 0.683 ([0.647 0.776] lower and upper quartiles), 0.405 [0.381 0.495] by using cadmium, and 0.151 [0.118 0.222] with caffeine (P < 0.05). A non-uniform scaling exponent α(t) showing a profile throughout the duration of the VFIS was further identified. A significant reduction of long-term correlations by cadmium was confirmed in the first part of this profile (P = 0.0001), but no significant reductions were detected by using caffeine. Our findings endorse that the behavior of the VFIS appears associated to the activation of different populations of ionic channels, which establish the neural membrane potential and are mediated by the intracellular calcium handling. Thus, we provide evidence to consider that the behavior of the VFIS, as determined by the scaling exponent α, conveys insights into mechanisms regulating the excitability of pacemaker neurons.

Adaptive responses of peripheral lateral line nerve fibres to sinusoidal wave stimuli

Sensory adaptation is characterized by a reduction in the firing frequency of neurons to prolonged stimulation, also called spike frequency adaptation. This has been documented for sensory neurons of the visual, olfactory, electrosensory, and auditory system both in response to constant-amplitude and to sinusoidal stimuli, but has thus far not been described systematically for the lateral line system. We recorded neuronal activity from primary afferent nerve fibres in the lateral line in goldfish in response to sinusoidal wave stimuli. Depending on stimulus characteristics, afferent fibre responses exhibited a distinct onset followed by a decline in firing rate to an apparent steady-state level, i.e., they exhibited adaptation. The degree of adaptation, measured as the percent decrease in firing rate between onset and steady-state, increased with stimulus amplitude and frequency and with increasing steepness of the rising flank of the stimulus. This may in part be due to the velocity and/or acceleration sensitivity of the lateral line receptors. The time course of the response decline, i.e., the time course of adaptation was best-fit by a power function. This is consistent with the previous studies on spike frequency adaptation in sensory afferents of weakly electric fish.

Metabolic Energy of Action Potentials Modulated by Spike Frequency Adaptation

Spike frequency adaptation (SFA) exists in many types of neurons, which has been demonstrated to improve their abilities to process incoming information by synapses. The major carrier used by a neuron to convey synaptic signals is the sequences of action potentials (APs), which have to consume substantial metabolic energies to initiate and propagate. Here we use conductance-based models to investigate how SFA modulates the AP-related energy of neurons. The SFA is attributed to either calcium-activated K⁺ (I_AHP) or voltage-activated K⁺ (I_M) current. We observe that the activation of I_AHP or I_M increases the Na⁺ load used for depolarizing membrane, while produces few effects on the falling phase of AP. Then, the metabolic energy involved in Na⁺ current significantly increases from one AP to the next, while for K⁺ current it is less affected. As a consequence, the total energy cost by each AP gets larger as firing rate decays down. It is also shown that the minimum Na⁺ charge needed for the depolarization of each AP is unaffected during the course of SFA. This indicates that the activation of either adaptation current makes APs become less efficient to use Na⁺ influx for their depolarization. Further, our simulations demonstrate that the different biophysical properties of I_M and I_AHP result in distinct modulations of metabolic energy usage for APs. These investigations provide a fundamental link between adaptation currents and neuronal energetics, which could facilitate to interpret how SFA participates in neuronal information processing.

The influence of increased membrane conductance on response properties of spinal motoneurons

During functional spinal neural network activity motoneurons receive massive synaptic excitation and inhibition, and their membrane conductance increases considerably - they are switched to a high-conductance state. High-conductance states can substantially alter response properties of motoneurons. In the present study we investigated how an increase in membrane conductance affects spike frequency adaptation, the gain (i.e., the slope of the frequency-current relationship) and the threshold for action potential generation. We used intracellular recordings from adult turtle motoneurons in spinal cord slices. Membrane conductance was increased pharmacologically by extracellular application of the GABAA receptor agonist muscimol. Our findings suggest that an increase in membrane conductance of about 40-50% increases the magnitude of spike frequency adaptation, but does not change the threshold for action potential generation. Increased conductance causes a subtractive rather than a divisive effect on the initial and the early frequency-current relationships and may have not only a subtractive but also a divisive effect on the steady-state frequency-current relationship.

Burst Firing in the Electrosensory System of Gymnotiform Weakly Electric Fish: Mechanisms and Functional Roles

Neurons across sensory systems and organisms often display complex patterns of action potentials in response to sensory input. One example of such a pattern is the tendency of neurons to fire packets of action potentials (i.e., a burst) followed by quiescence. While it is well known that multiple mechanisms can generate bursts of action potentials at both the single-neuron and the network level, the functional role of burst firing in sensory processing is not so well understood to date. Here we provide a comprehensive review of the known mechanisms and functions of burst firing in processing of electrosensory stimuli in gymnotiform weakly electric fish. We also present new evidence from existing data showing that bursts and isolated spikes provide distinct information about stimulus variance. It is likely that these functional roles will be generally applicable to other systems and species.

Adaptive Spike Threshold Enables Robust and Temporally Precise Neuronal Encoding

Neural processing rests on the intracellular transformation of information as synaptic inputs are translated into action potentials. This transformation is governed by the spike threshold, which depends on the history of the membrane potential on many temporal scales. While the adaptation of the threshold after spiking activity has been addressed before both theoretically and experimentally, it has only recently been demonstrated that the subthreshold membrane state also influences the effective spike threshold. The consequences for neural computation are not well understood yet. We address this question here using neural simulations and whole cell intracellular recordings in combination with information theoretic analysis. We show that an adaptive spike threshold leads to better stimulus discrimination for tight input correlations than would be achieved otherwise, independent from whether the stimulus is encoded in the rate or pattern of action potentials. The time scales of input selectivity are jointly governed by membrane and threshold dynamics. Encoding information using adaptive thresholds further ensures robust information transmission across cortical states i.e. decoding from different states is less state dependent in the adaptive threshold case, if the decoding is performed in reference to the timing of the population response. Results from in vitro neural recordings were consistent with simulations from adaptive threshold neurons. In summary, the adaptive spike threshold reduces information loss during intracellular information transfer, improves stimulus discriminability and ensures robust decoding across membrane states in a regime of highly correlated inputs, similar to those seen in sensory nuclei during the encoding of sensory information.

A neuron is a tiny computer that transforms electrical inputs into electrical outputs. While neurons have been investigated and modeled for many decades, some aspects remain elusive. Recently, it was demonstrated that the membrane (voltage) state of a neuron determines its threshold to spiking. In the present study we asked, what are the consequences of this dependence for the computation the neuron performs. We find that this so called adaptive threshold allows neurons to be more focused on inputs which arrive close in time with other inputs. Also, it allows neurons to represent their information more robustly, such that a readout of their activity is less influenced by the state the brain is in. The present use of information theory provides a solid foundation for these results. We obtained the results primarily in detailed simulations, but performed neural recordings to verify these properties in real neurons. In summary, an adaptive spiking threshold allows neurons to specifically compute robustly with a focus on tight temporal correlations in their input.

The Gamma renewal process as an output of the diffusion leaky integrate-and-fire neuronal model

Statistical properties of spike trains as well as other neurophysiological data suggest a number of mathematical models of neurons. These models range from entirely descriptive ones to those deduced from the properties of the real neurons. One of them, the diffusion leaky integrate-and-fire neuronal model, which is based on the Ornstein-Uhlenbeck (OU) stochastic process that is restricted by an absorbing barrier, can describe a wide range of neuronal activity in terms of its parameters. These parameters are readily associated with known physiological mechanisms. The other model is descriptive, Gamma renewal process, and its parameters only reflect the observed experimental data or assumed theoretical properties. Both of these commonly used models are related here. We show under which conditions the Gamma model is an output from the diffusion OU model. In some cases, we can see that the Gamma distribution is unrealistic to be achieved for the employed parameters of the OU process.

Impact of slow K(+) currents on spike generation can be described by an adaptive threshold model

A neuron that is stimulated by rectangular current injections initially responds with a high firing rate, followed by a decrease in the firing rate. This phenomenon is called spike-frequency adaptation and is usually mediated by slow K(+) currents, such as the M-type K(+) current (I M ) or the Ca(2+)-activated K(+) current (I AHP ). It is not clear how the detailed biophysical mechanisms regulate spike generation in a cortical neuron. In this study, we investigated the impact of slow K(+) currents on spike generation mechanism by reducing a detailed conductance-based neuron model. We showed that the detailed model can be reduced to a multi-timescale adaptive threshold model, and derived the formulae that describe the relationship between slow K(+) current parameters and reduced model parameters. Our analysis of the reduced model suggests that slow K(+) currents have a differential effect on the noise tolerance in neural coding.

Analytical approach to an integrate-and-fire model with spike-triggered adaptation

The calculation of the steady-state probability density for multidimensional stochastic systems that do not obey detailed balance is a difficult problem. Here we present the analytical derivation of the stationary joint and various marginal probability densities for a stochastic neuron model with adaptation current. Our approach assumes weak noise but is valid for arbitrary adaptation strength and time scale. The theory predicts several effects of adaptation on the statistics of the membrane potential of a tonically firing neuron: (i) a membrane potential distribution with a convex shape, (ii) a strongly increased probability of hyperpolarized membrane potentials induced by strong and fast adaptation, and (iii) a maximized variability associated with the adaptation current at a finite adaptation time scale.

Emergence of Diversity in a Group of Identical Bio-Robots

Learning capabilities, often guided by competition/cooperation, play a fundamental and ubiquitous role in living beings. Moreover, several behaviours, such as feeding and courtship, involve environmental exploration and exploitation, including local competition, and lead to a global benefit for the colony. This can be considered as a form of global cooperation, even if the individual agent is not aware of the overall effect. This paper aims to demonstrate that identical biorobots, endowed with simple neural controllers, can evolve diversified behaviours and roles when competing for the same resources in the same arena. These behaviours also produce a benefit in terms of time and energy spent by the whole group. The robots are tasked with a classical foraging task structured through the cyclic activation of resources. The result is that each individual robot, while competing to reach the maximum number of available targets, tends to prefer a specific sequence of subtasks. This indirectly leads to the global result of task partitioning whereby the cumulative energy spent, in terms of the overall travelled distance and the time needed to complete the task, tends to be minimized. A series of simulation experiments is conducted using different numbers of robots and scenarios: the common emergent result obtained is the role-specialization of each robot. The description of the neural controller and the specialization mechanisms are reported in detail and discussed.

Spike timing precision changes with spike rate adaptation in the owl's auditory space map

Spike rate adaptation (SRA) is a continuing change of responsiveness to ongoing stimuli, which is ubiquitous across species and levels of sensory systems. Under SRA, auditory responses to constant stimuli change over time, relaxing toward a long-term rate often over multiple timescales. With more variable stimuli, SRA causes the dependence of spike rate on sound pressure level to shift toward the mean level of recent stimulus history. A model based on subtractive adaptation (Benda J, Hennig RM. J Comput Neurosci 24: 113-136, 2008) shows that changes in spike rate and level dependence are mechanistically linked. Space-specific neurons in the barn owl's midbrain, when recorded under ketamine-diazepam anesthesia, showed these classical characteristics of SRA, while at the same time exhibiting changes in spike timing precision. Abrupt level increases of sinusoidally amplitude-modulated (SAM) noise initially led to spiking at higher rates with lower temporal precision. Spike rate and precision relaxed toward their long-term values with a time course similar to SRA, results that were also replicated by the subtractive model. Stimuli whose amplitude modulations (AMs) were not synchronous across carrier frequency evoked spikes in response to stimulus envelopes of a particular shape, characterized by the spectrotemporal receptive field (STRF). Again, abrupt stimulus level changes initially disrupted the temporal precision of spiking, which then relaxed along with SRA. We suggest that shifts in latency associated with stimulus level changes may differ between carrier frequency bands and underlie decreased spike precision. Thus SRA is manifest not simply as a change in spike rate but also as a change in the temporal precision of spiking.

Impact of sub and supra-threshold adaptation currents in networks of spiking neurons

Neuronal adaptation is the intrinsic capacity of the brain to change, by various mechanisms, its dynamical responses as a function of the context. Such a phenomena, widely observed in vivo and in vitro, is known to be crucial in homeostatic regulation of the activity and gain control. The effects of adaptation have already been studied at the single-cell level, resulting from either voltage or calcium gated channels both activated by the spiking activity and modulating the dynamical responses of the neurons. In this study, by disentangling those effects into a linear (sub-threshold) and a non-linear (supra-threshold) part, we focus on the the functional role of those two distinct components of adaptation onto the neuronal activity at various scales, starting from single-cell responses up to recurrent networks dynamics, and under stationary or non-stationary stimulations. The effects of slow currents on collective dynamics, like modulation of population oscillation and reliability of spike patterns, is quantified for various types of adaptation in sparse recurrent networks.

A stimulus-dependent spike threshold is an optimal neural coder

A neural code based on sequences of spikes can consume a significant portion of the brain's energy budget. Thus, energy considerations would dictate that spiking activity be kept as low as possible. However, a high spike-rate improves the coding and representation of signals in spike trains, particularly in sensory systems. These are competing demands, and selective pressure has presumably worked to optimize coding by apportioning a minimum number of spikes so as to maximize coding fidelity. The mechanisms by which a neuron generates spikes while maintaining a fidelity criterion are not known. Here, we show that a signal-dependent neural threshold, similar to a dynamic or adapting threshold, optimizes the trade-off between spike generation (encoding) and fidelity (decoding). The threshold mimics a post-synaptic membrane (a low-pass filter) and serves as an internal decoder. Further, it sets the average firing rate (the energy constraint). The decoding process provides an internal copy of the coding error to the spike-generator which emits a spike when the error equals or exceeds a spike threshold. When optimized, the trade-off leads to a deterministic spike firing-rule that generates optimally timed spikes so as to maximize fidelity. The optimal coder is derived in closed-form in the limit of high spike-rates, when the signal can be approximated as a piece-wise constant signal. The predicted spike-times are close to those obtained experimentally in the primary electrosensory afferent neurons of weakly electric fish (Apteronotus leptorhynchus) and pyramidal neurons from the somatosensory cortex of the rat. We suggest that KCNQ/Kv7 channels (underlying the M-current) are good candidates for the decoder. They are widely coupled to metabolic processes and do not inactivate. We conclude that the neural threshold is optimized to generate an energy-efficient and high-fidelity neural code.

Spike-frequency adaptation of a two-compartment neuron modulated by extracellular electric fields

Spike-frequency adaptation has been shown to play an important role in neural coding. Based on a reduced two-compartment model, here we investigate how two common adaptation currents, i.e., voltage-sensitive potassium current (I(M)) and calcium-sensitive potassium current (I(AHP)), modulate neuronal responses to extracellular electric fields. It is shown that two adaptation mechanisms lead to distinct effects on the dynamical behavior of the neuron to electric fields. These effects depend on a neuronal morphological parameter that characterizes the ratio of soma area to total membrane area and internal coupling conductance. In the case of I(AHP) current, changing the morphological parameter switches spike initiation dynamics between saddle-node on invariant cycle bifurcation and supercritical Hopf bifurcation, whereas it only switches between subcritical and supercritical Hopf bifurcations for I(M) current. Unlike the morphological parameter, internal coupling conductance is unable to alter the bifurcation scenario for both adaptation currents. We also find that the electric field threshold for triggering neuronal steady-state firing is determined by two parameters, especially by the morphological parameter. Furthermore, the neuron with I(AHP) current generates mixed-mode oscillations through the canard phenomenon for some small values of the morphological parameter. All these results suggest that morphological properties play a critical role in field-induced effects on neuronal dynamics, which could qualitatively alter the outcome of adaptation by modulating internal current between soma and dendrite. The findings are readily testable in experiments, which could help to reveal the mechanisms underlying how the neuron responds to electric field stimulus.

Diverse synaptic plasticity mechanisms orchestrated to form and retrieve memories in spiking neural networks

Synaptic plasticity, the putative basis of learning and memory formation, manifests in various forms and across different timescales. Here we show that the interaction of Hebbian homosynaptic plasticity with rapid non-Hebbian heterosynaptic plasticity is, when complemented with slower homeostatic changes and consolidation, sufficient for assembly formation and memory recall in a spiking recurrent network model of excitatory and inhibitory neurons. In the model, assemblies were formed during repeated sensory stimulation and characterized by strong recurrent excitatory connections. Even days after formation, and despite ongoing network activity and synaptic plasticity, memories could be recalled through selective delay activity following the brief stimulation of a subset of assembly neurons. Blocking any component of plasticity prevented stable functioning as a memory network. Our modelling results suggest that the diversity of plasticity phenomena in the brain is orchestrated towards achieving common functional goals.

Effects of spike-triggered negative feedback on receptive-field properties

Sensory neurons are often described in terms of a receptive field, that is, a linear kernel through which stimuli are filtered before they are further processed. If information transmission is assumed to proceed in a feedforward cascade, the receptive field may be interpreted as the external stimulus' profile maximizing neuronal output. The nervous system, however, contains many feedback loops, and sensory neurons filter more currents than the ones representing the transduced external stimulus. Some of the additional currents are generated by the output activity of the neuron itself, and therefore constitute feedback signals. By means of a time-frequency analysis of the input/output transformation, here we show how feedback modifies the receptive field. The model is applicable to various types of feedback processes, from spike-triggered intrinsic conductances to inhibitory synaptic inputs from nearby neurons. We distinguish between the intrinsic receptive field (filtering all input currents) and the effective receptive field (filtering only external stimuli). Whereas the intrinsic receptive field summarizes the biophysical properties of the neuron associated to subthreshold integration and spike generation, only the effective receptive field can be interpreted as the external stimulus' profile maximizing neuronal output. We demonstrate that spike-triggered feedback shifts low-pass filtering towards band-pass processing, transforming integrator neurons into resonators. For strong feedback, a sharp resonance in the spectral neuronal selectivity may appear. Our results provide a unified framework to interpret a collection of previous experimental studies where specific feedback mechanisms were shown to modify the filtering properties of neurons.

Emergence of band-pass filtering through adaptive spiking in the owl's cochlear nucleus

In the visual, auditory, and electrosensory modalities, stimuli are defined by first- and second-order attributes. The fast time-pressure signal of a sound, a first-order attribute, is important, for instance, in sound localization and pitch perception, while its slow amplitude-modulated envelope, a second-order attribute, can be used for sound recognition. Ascending the auditory pathway from ear to midbrain, neurons increasingly show a preference for the envelope and are most sensitive to particular envelope modulation frequencies, a tuning considered important for encoding sound identity. The level at which this tuning property emerges along the pathway varies across species, and the mechanism of how this occurs is a matter of debate. In this paper, we target the transition between auditory nerve fibers and the cochlear nucleus angularis (NA). While the owl's auditory nerve fibers simultaneously encode the fast and slow attributes of a sound, one synapse further, NA neurons encode the envelope more efficiently than the auditory nerve. Using in vivo and in vitro electrophysiology and computational analysis, we show that a single-cell mechanism inducing spike threshold adaptation can explain the difference in neural filtering between the two areas. We show that spike threshold adaptation can explain the increased selectivity to modulation frequency, as input level increases in NA. These results demonstrate that a spike generation nonlinearity can modulate the tuning to second-order stimulus features, without invoking network or synaptic mechanisms.

Kv7 channels regulate pairwise spiking covariability in health and disease

Low-threshold M currents are mediated by the Kv7 family of potassium channels. Kv7 channels are important regulators of spiking activity, having a direct influence on the firing rate, spike time variability, and filter properties of neurons. How Kv7 channels affect the joint spiking activity of populations of neurons is an important and open area of study. Using a combination of computational simulations and analytic calculations, we show that the activation of Kv7 conductances reduces the covariability between spike trains of pairs of neurons driven by common inputs. This reduction is beyond that explained by the lowering of firing rates and involves an active cancellation of common fluctuations in the membrane potentials of the cell pair. Our theory shows that the excess covariance reduction is due to a Kv7-induced shift from low-pass to band-pass filtering of the single neuron spike train response. Dysfunction of Kv7 conductances is related to a number of neurological diseases characterized by both elevated firing rates and increased network-wide correlations. We show how changes in the activation or strength of Kv7 conductances give rise to excess correlations that cannot be compensated for by synaptic scaling or homeostatic modulation of passive membrane properties. In contrast, modulation of Kv7 activation parameters consistent with pharmacological treatments for certain hyperactivity disorders can restore normal firing rates and spiking correlations. Our results provide key insights into how regulation of a ubiquitous potassium channel class can control the coordination of population spiking activity.

Estimating nonstationary inputs from a single spike train based on a neuron model with adaptation

Because every spike of a neuron is determined by input signals, a train of spikes may contain information about the dynamics of unobserved neurons. A state-space method based on the leaky integrate-and-fire model, describing neuronal transformation from input signals to a spike train has been proposed for tracking input parameters represented by their mean and fluctuation [11]. In the present paper, we propose to make the estimation more realistic by adopting an LIF model augmented with an adaptive moving threshold. Moreover, because the direct state-space method is computationally infeasible for a data set comprising thousands of spikes, we further develop a practical method for transforming instantaneous firing characteristics back to input parameters. The instantaneous firing characteristics, represented by the firing rate and non-Poisson irregularity, can be estimated using a computationally feasible algorithm. We applied our proposed methods to synthetic data to clarify that they perform well.

A simple Markov model of sodium channels with a dynamic threshold

Characteristics of action potential generation are important to understanding brain functioning and, thus, must be understood and modeled. It is still an open question what model can describe concurrently the phenomena of sharp spike shape, the spike threshold variability, and the divisive effect of shunting on the gain of frequency-current dependence. We reproduced these three effects experimentally by patch-clamp recordings in cortical slices, but we failed to simulate them by any of 11 known neuron models, including one- and multi-compartment, with Hodgkin-Huxley and Markov equation-based sodium channel approximations, and those taking into account sodium channel subtype heterogeneity. Basing on our voltage-clamp data characterizing the dependence of sodium channel activation threshold on history of depolarization, we propose a 3-state Markov model with a closed-to-open state transition threshold dependent on slow inactivation. This model reproduces the all three phenomena. As a reduction of this model, a leaky integrate-and-fire model with a dynamic threshold also shows the effect of gain reduction by shunt. These results argue for the mechanism of gain reduction through threshold dynamics determined by the slow inactivation of sodium channels.

Patterns of interval correlations in neural oscillators with adaptation

Neural firing is often subject to negative feedback by adaptation currents. These currents can induce strong correlations among the time intervals between spikes. Here we study analytically the interval correlations of a broad class of noisy neural oscillators with spike-triggered adaptation of arbitrary strength and time scale. Our weak-noise theory provides a general relation between the correlations and the phase-response curve (PRC) of the oscillator, proves anti-correlations between neighboring intervals for adapting neurons with type I PRC and identifies a single order parameter that determines the qualitative pattern of correlations. Monotonically decaying or oscillating correlation structures can be related to qualitatively different voltage traces after spiking, which can be explained by the phase plane geometry. At high firing rates, the long-term variability of the spike train associated with the cumulative interval correlations becomes small, independent of model details. Our results are verified by comparison with stochastic simulations of the exponential, leaky, and generalized integrate-and-fire models with adaptation.

How adaptation currents change threshold, gain, and variability of neuronal spiking

Many types of neurons exhibit spike rate adaptation, mediated by intrinsic slow K(+) currents, which effectively inhibit neuronal responses. How these adaptation currents change the relationship between in vivo like fluctuating synaptic input, spike rate output, and the spike train statistics, however, is not well understood. In this computational study we show that an adaptation current that primarily depends on the subthreshold membrane voltage changes the neuronal input-output relationship (I-O curve) subtractively, thereby increasing the response threshold, and decreases its slope (response gain) for low spike rates. A spike-dependent adaptation current alters the I-O curve divisively, thus reducing the response gain. Both types of an adaptation current naturally increase the mean interspike interval (ISI), but they can affect ISI variability in opposite ways. A subthreshold current always causes an increase of variability while a spike-triggered current decreases high variability caused by fluctuation-dominated inputs and increases low variability when the average input is large. The effects on I-O curves match those caused by synaptic inhibition in networks with asynchronous irregular activity, for which we find subtractive and divisive changes caused by external and recurrent inhibition, respectively. Synaptic inhibition, however, always increases the ISI variability. We analytically derive expressions for the I-O curve and ISI variability, which demonstrate the robustness of our results. Furthermore, we show how the biophysical parameters of slow K(+) conductances contribute to the two different types of an adaptation current and find that Ca(2+)-activated K(+) currents are effectively captured by a simple spike-dependent description, while muscarine-sensitive or Na(+)-activated K(+) currents show a dominant subthreshold component.

Cellular adaptation facilitates sparse and reliable coding in sensory pathways

Most neurons in peripheral sensory pathways initially respond vigorously when a preferred stimulus is presented, but adapt as stimulation continues. It is unclear how this phenomenon affects stimulus coding in the later stages of sensory processing. Here, we show that a temporally sparse and reliable stimulus representation develops naturally in sequential stages of a sensory network with adapting neurons. As a modeling framework we employ a mean-field approach together with an adaptive population density treatment, accompanied by numerical simulations of spiking neural networks. We find that cellular adaptation plays a critical role in the dynamic reduction of the trial-by-trial variability of cortical spike responses by transiently suppressing self-generated fast fluctuations in the cortical balanced network. This provides an explanation for a widespread cortical phenomenon by a simple mechanism. We further show that in the insect olfactory system cellular adaptation is sufficient to explain the emergence of the temporally sparse and reliable stimulus representation in the mushroom body. Our results reveal a generic, biophysically plausible mechanism that can explain the emergence of a temporally sparse and reliable stimulus representation within a sequential processing architecture.

Slack, Slick and Sodium-Activated Potassium Channels

The Slack and Slick genes encode potassium channels that are very widely expressed in the central nervous system. These channels are activated by elevations in intracellular sodium, such as those that occur during trains of one or more action potentials, or following activation of non-selective cationic neurotransmitter receptors such as AMPA receptors. This review covers the cellular and molecular properties of Slack and Slick channels and compares them with findings on the properties of sodium-activated potassium currents (termed K_Na currents) in native neurons. Human mutations in Slack channels produce extremely severe defects in learning and development, suggesting that K_Na channels play a central role in neuronal plasticity and intellectual function.