Influence of ionic conductances on spike timing reliability of cortical neurons for suprathreshold rhythmic inputs

Balanced bidirectional optogenetics reveals the causal impact of cortical temporal dynamics in sensory perception

Whether the fast temporal dynamics of neural activity in brain circuits causally drive perception and cognition remains one of most longstanding unresolved questions in neuroscience 1-6 . While some theories posit a 'timing code' in which dynamics on the millisecond timescale is central to brain function, others instead argue that mean firing rates over more extended periods (a 'rate code') carry most of the relevant information. Existing tools, such as optogenetics, can be used to alter temporal structure of neural dynamics 7 , but they invariably change mean firing rates, leaving the interpretation of such experiments ambiguous. Here we developed and validated a new approach based on balanced, bidirectional optogenetics that can alter temporal structure of neural dynamics while mitigating effects on mean activity. Using this new approach, we found that selectively altering cortical temporal dynamics substantially reduced performance in a sensory perceptual task. These results demonstrate that endogenous temporal dynamics in the cortex are causally required for perception and behavior. More generally, this new bidirectional optogenetic approach should be broadly useful for disentangling the causal impact of different timescales of neural dynamics on behavior.

Stimulus-specific plasticity of macaque V1 spike rates and gamma

When a visual stimulus is repeated, average neuronal responses typically decrease, yet they might maintain or even increase their impact through increased synchronization. Previous work has found that many repetitions of a grating lead to increasing gamma-band synchronization. Here, we show in awake macaque area V1 that both repetition-related reductions in firing rate and increases in gamma are specific to the repeated stimulus. These effects show some persistence on the timescale of minutes. Gamma increases are specific to the presented stimulus location. Further, repetition effects on gamma and on firing rates generalize to images of natural objects. These findings support the notion that gamma-band synchronization subserves the adaptive processing of repeated stimulus encounters.

Cortical gamma-band resonance preferentially transmits coherent input

Synchronization has been implicated in neuronal communication, but causal evidence remains indirect. We use optogenetics to generate depolarizing currents in pyramidal neurons of the cat visual cortex, emulating excitatory synaptic inputs under precise temporal control, while measuring spike output. The cortex transforms constant excitation into strong gamma-band synchronization, revealing the well-known cortical resonance. Increasing excitation with ramps increases the strength and frequency of synchronization. Slow, symmetric excitation profiles reveal hysteresis of power and frequency. White-noise input sequences enable causal analysis of network transmission, establishing that the cortical gamma-band resonance preferentially transmits coherent input components. Models composed of recurrently coupled excitatory and inhibitory units uncover a crucial role of feedback inhibition and suggest that hysteresis can arise through spike-frequency adaptation. The presented approach provides a powerful means to investigate the resonance properties of local circuits and probe how these properties transform input and shape transmission.

Rhythmic synchronization has been implicated in neuronal communication, yet causal evidence has remained scarce. Lewis et al. optogenetically stimulate the visual cortex to emulate synaptic input while recording spike output. Cortex resonates at the gamma band (30–90 Hz) and preferentially transmits input that is coherent to the ongoing gamma-band rhythm.

Conditioning by subthreshold synaptic input changes the intrinsic firing pattern of CA3 hippocampal neurons

Unlike synaptic strength, intrinsic excitability is assumed to be a stable property of neurons. For example, learning of somatic conductances is generally not incorporated into computational models, and the discharge pattern of neurons in response to test stimuli is frequently used as a basis for phenotypic classification. However, it is increasingly evident that signal processing properties of neurons are more generally plastic on the timescale of minutes. Here we demonstrate that the intrinsic firing patterns of CA3 neurons of the rat hippocampus in vitro undergo rapid long-term plasticity in response to a few minutes of only subthreshold synaptic conditioning. This plasticity on the spike timing could also be induced by intrasomatic injection of subthreshold depolarizing pulses and was blocked by kinase inhibitors, indicating that discharge dynamics are modulated locally. Cluster analysis of firing patterns before and after conditioning revealed systematic transitions toward adapting and intrinsic burst behaviors, irrespective of the patterns initially exhibited by the cells. We used a conductance-based model to decide appropriate pharmacological blockade and found that the observed transitions are likely due to recruitment of low-voltage calcium and Kv7 potassium conductances. We conclude that CA3 neurons adapt their conductance profile to the subthreshold activity of their input, so that their intrinsic firing pattern is not a static signature, but rather a reflection of their history of subthreshold activity. In this way, recurrent output from CA3 neurons may collectively shape the temporal dynamics of their embedding circuits.NEW & NOTEWORTHY Although firing patterns are widely conserved across the animal phyla, it is still a mystery why nerve cells present such diversity of discharge dynamics upon somatic step currents. Adding a new timing dimension to the intrinsic plasticity literature, here we show that CA3 neurons rapidly adapt through the space of known firing patterns in response to the subthreshold signals that they receive from their embedding circuit, potentially adjusting their network processing to the temporal statistics of their circuit.

Membrane potential resonance frequency directly influences network frequency through electrical coupling

Oscillatory networks often include neurons with membrane potential resonance, exhibiting a peak in the voltage amplitude as a function of current input at a nonzero (resonance) frequency (f_res). Although f_res has been correlated to the network frequency (f_net) in a variety of systems, a causal relationship between the two has not been established. We examine the hypothesis that combinations of biophysical parameters that shift f_res, without changing other attributes of the impedance profile, also shift f_net in the same direction. We test this hypothesis, computationally and experimentally, in an electrically coupled network consisting of intrinsic oscillator (O) and resonator (R) neurons. We use a two-cell model of such a network to show that increasing f_res of R directly increases f_net and that this effect becomes more prominent if the amplitude of resonance is increased. Notably, the effect of f_res on f_net is independent of the parameters that define the oscillator or the combination of parameters in R that produce the shift in f_res, as long as this combination produces the same impedance vs. frequency relationship. We use the dynamic clamp technique to experimentally verify the model predictions by connecting a model resonator to the pacemaker pyloric dilator neurons of the crab Cancer borealis pyloric network using electrical synapses and show that the pyloric network frequency can be shifted by changing f_res in the resonator. Our results provide compelling evidence that f_res and resonance amplitude strongly influence f_net, and therefore, modulators may target these attributes to modify rhythmic activity.

Pathophysiological signatures of functional connectomics in parkinsonian and dyskinetic striatal microcircuits

A challenge in neuroscience is to integrate the cellular and system levels. For instance, we still do not know how a few dozen neurons organize their activity and relations in a microcircuit or module of histological scale. By using network theory and Ca(2+) imaging with single-neuron resolution we studied the way in which striatal microcircuits of dozens of cells orchestrate their activity. In addition, control and diseased striatal tissues were compared in rats. In the control tissue, functional connectomics revealed small-world, scale-free and hierarchical network properties. These properties were lost during pathological conditions in ways that could be quantitatively analyzed. Decorticated striatal circuits disclosed that corticostriatal interactions depend on privileged connections with a set of highly connected neurons or "hubs". In the 6-OHDA model of Parkinson's disease there was a decrease in hubs number; but the ones that remained were linked to dominant network states. l-DOPA induced dyskinesia provoked a loss in the hierarchical structure of the circuit. All these conditions conferred distinct temporal sequences to circuit activity. Temporal sequences appeared as particular signatures of disease process thus bringing the possibility of a future quantitative pathophysiology at a histological scale.

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.

Dynamics and Reliability of Bistable Neurons Driven with Time-Dependent Stimuli

The reliability of a spiking neuron depends on the frequency content of the driving input signal. Previous studies have shown that well above threshold, regularly firing neurons generate reliable responses when the input signal resonates with the firing frequency of the cell. Instead, well below threshold, reliable responses are obtained when the input frequency resonates with the subthreshold oscillations of the neuron. Previous theories, however, provide no clear prediction for the input frequency giving rise to maximally reliable spiking at threshold, which is probably the most relevant firing regime in mammalian cortex under physiological conditions. In particular, when the firing onset is governed by a subcritical Hopf bifurcation, the frequency of subthreshold oscillations often differs from the firing rate at threshold. The predictions of previous studies, hence, cannot be smoothly merged at threshold. Here we explore the behavior of reliability in bistable neurons near threshold using three types of driving stimuli: constant, periodic, and stochastic. We find that the two natural frequencies of the system, associated with the two coexisting attractors, provide a rich variety of possible locking modes with the external signal. Reliability is determined by the sensitivity to noise of each locking mode and by the transition probabilities between modes. Noise increases the amount of spike time jitter, and minimal jitter is obtained for input frequencies coinciding with the suprathreshold firing rate of the cell. In addition, noise may either enhance or inhibit transitions between the two attractors, depending on the input frequency. The dual role played by noise in bistable systems implies that reliability is determined by a delicate balance between spike time jitter and the rate of transitions between attractors.

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.

Neuronal spike timing adaptation described with a fractional leaky integrate-and-fire model

The voltage trace of neuronal activities can follow multiple timescale dynamics that arise from correlated membrane conductances. Such processes can result in power-law behavior in which the membrane voltage cannot be characterized with a single time constant. The emergent effect of these membrane correlations is a non-Markovian process that can be modeled with a fractional derivative. A fractional derivative is a non-local process in which the value of the variable is determined by integrating a temporal weighted voltage trace, also called the memory trace. Here we developed and analyzed a fractional leaky integrate-and-fire model in which the exponent of the fractional derivative can vary from 0 to 1, with 1 representing the normal derivative. As the exponent of the fractional derivative decreases, the weights of the voltage trace increase. Thus, the value of the voltage is increasingly correlated with the trajectory of the voltage in the past. By varying only the fractional exponent, our model can reproduce upward and downward spike adaptations found experimentally in neocortical pyramidal cells and tectal neurons in vitro. The model also produces spikes with longer first-spike latency and high inter-spike variability with power-law distribution. We further analyze spike adaptation and the responses to noisy and oscillatory input. The fractional model generates reliable spike patterns in response to noisy input. Overall, the spiking activity of the fractional leaky integrate-and-fire model deviates from the spiking activity of the Markovian model and reflects the temporal accumulated intrinsic membrane dynamics that affect the response of the neuron to external stimulation.

Spike adaptation is a property of most neurons. When spike time adaptation occurs over multiple time scales, the dynamics can be described by a power-law. We study the computational properties of a leaky integrate-and-fire model with power-law adaptation. Instead of explicitly modeling the adaptation process by the contribution of slowly changing conductances, we use a fractional temporal derivative framework. The exponent of the fractional derivative represents the degree of adaptation of the membrane voltage, where 1 is the normal leaky integrator while values less than 1 produce increasing correlations in the voltage trace. The temporal correlation is interpreted as a memory trace that depends on the value of the fractional derivative. We identify the memory trace in the fractional model as the sum of the instantaneous differentiation weighted by a function that depends on the fractional exponent, and it provides non-local information to the incoming stimulus. The spiking dynamics of the fractional leaky integrate-and-fire model show memory dependence that can result in downward or upward spike adaptation. Our model provides a framework for understanding how long-range membrane voltage correlations affect spiking dynamics and information integration in neurons.

Impact of neuronal properties on network coding: roles of spike initiation dynamics and robust synchrony transfer

Neural networks are more than the sum of their parts, but the properties of those parts are nonetheless important. For instance, neuronal properties affect the degree to which neurons receiving common input will spike synchronously, and whether that synchrony will propagate through the network. Stimulus-evoked synchrony can help or hinder network coding depending on the type of code. In this Perspective, we describe how spike initiation dynamics influence neuronal input-output properties, how those properties affect synchronization, and how synchronization affects network coding. We propose that synchronous and asynchronous spiking can be used to multiplex temporal (synchrony) and rate coding and discuss how pyramidal neurons would be well suited for that task.

The new KCNQ2 activator 4-Chlor-N-(6-chlor-pyridin-3-yl)-benzamid displays anticonvulsant potential

BACKGROUND AND PURPOSE

KCNQ2-5 channels are voltage-gated potassium channels that regulate neuronal excitability and represent suitable targets for the treatment of hyperexcitability disorders. The effect of Chlor-N-(6-chlor-pyridin-3-yl)-benzamid was tested on KCNQ subtypes for its ability to alter neuronal excitability and for its anticonvulsant potential.

EXPERIMENTAL APPROACH

The effect of 4-Chlor-N-(6-chlor-pyridin-3-yl)-benzamid was evaluated using whole-cell voltage-clamp recordings from CHO cells and Xenopus laevis oocytes expressing different types of KCNQ channels. Epileptiform afterdischarges were recorded in fully amygdala-kindled rats in vivo. Neuronal excitability was assessed using field potential and whole cell recording in rat hippocampus in vitro.

KEY RESULTS

4-Chlor-N-(6-chlor-pyridin-3-yl)-benzamid caused a hyperpolarizing shift of the activation curve and a pronounced slowing of deactivation in KCNQ2-mediated currents, whereas KCNQ3/5 heteromers remained unaffected. The effect was also apparent in the Retigabine-insensitive mutant KCNQ2-W236L. In fully amygdala-kindled rats, it elevated the threshold for induction of afterdischarges and reduced seizure severity and duration. In hippocampal CA1 cells, 4-Chlor-N-(6-chlor-pyridin-3-yl)-benzamid strongly damped neuronal excitability caused by a membrane hyperpolarization and a decrease in membrane resistance and induced an increase of the somatic resonance frequency on the single cell level, whereas synaptic transmission was unaffected. On the network level, 4-Chlor-N-(6-chlor-pyridin-3-yl)-benzamid caused a significant reduction of γ and θ oscillation peak power, with no significant change in oscillation frequency.

CONCLUSION AND IMPLICATIONS

Our data indicate that 4-Chlor-N-(6-chlor-pyridin-3-yl)-benzamid is a potent KCNQ activator with a selectivity for KCNQ2 containing channels. It strongly reduces neuronal excitability and displays anticonvulsant activity in vivo.

Dopamine, cognitive function, and gamma oscillations: role of D4 receptors

Cognitive deficits in individuals with schizophrenia (SCZ) are considered core symptoms of this disorder, and can manifest at the prodromal stage. Antipsychotics ameliorate positive symptoms but only modestly improve cognitive symptoms. The lack of treatments that improve cognitive abilities currently represents a major obstacle in developing more effective therapeutic strategies for this debilitating disorder. While D4 receptor (D4R)-specific antagonists are ineffective in the treatment of positive symptoms, animal studies suggest that D4R drugs can improve cognitive deficits. Moreover, recent work from our group suggests that D4Rs synergize with the neuregulin/ErbB4 signaling pathway, genetically identified as risk factors for SCZ, in parvalbumin (PV)-expressing interneurons to modulate gamma oscillations. These high-frequency network oscillations correlate with attention and increase during cognitive tasks in healthy subjects, and this correlation is attenuated in affected individuals. This finding, along with other observations indicating impaired GABAergic function, has led to the idea that abnormal neural activity in the prefrontal cortex (PFC) in individuals with SCZ reflects a perturbation in the balance of excitation and inhibition. Here we review the current state of knowledge of D4R functions in the PFC and hippocampus, two major brain areas implicated in SCZ. Special emphasis is given to studies focusing on the potential role of D4Rs in modulating GABAergic transmission and to an emerging concept of a close synergistic relationship between dopamine/D4R and neuregulin/ErbB4 signaling pathways that tunes the activity of PV interneurons to regulate gamma frequency network oscillations and potentially cognitive processes.

Reliability of spike and burst firing in thalamocortical relay cells

The reliability and precision of the timing of spikes in a spike train is an important aspect of neuronal coding. We investigated reliability in thalamocortical relay (TCR) cells in the acute slice and also in a Morris-Lecar model with several extensions. A frozen Gaussian noise current, superimposed on a DC current, was injected into the TCR cell soma. The neuron responded with spike trains that showed trial-to-trial variability, due to amongst others slow changes in its internal state and the experimental setup. The DC current allowed to bring the neuron in different states, characterized by a well defined membrane voltage (between -80 and -50 mV) and by a specific firing regime that on depolarization gradually shifted from a predominantly bursting regime to a tonic spiking regime. The filtered frozen white noise generated a spike pattern output with a broad spike interval distribution. The coincidence factor and the Hunter and Milton measure were used as reliability measures of the output spike train. In the experimental TCR cell as well as the Morris-Lecar model cell the reliability depends on the shape (steepness) of the current input versus spike frequency output curve. The model also allowed to study the contribution of three relevant ionic membrane currents to reliability: a T-type calcium current, a cation selective h-current and a calcium dependent potassium current in order to allow bursting, investigate the consequences of a more complex current-frequency relation and produce realistic firing rates. The reliability of the output of the TCR cell increases with depolarization. In hyperpolarized states bursts are more reliable than single spikes. The analytically derived relations were capable to predict several of the experimentally recorded spike features.

Modifying spiking precision in conductance-based neuronal models

The temporal precision of a neuron's spiking can be characterized by calculating its "jitter," defined as the standard deviation of the timing of individual spikes in response to repeated presentations of a stimulus. Sub-millisecond jitters have been measured for neurons in a variety of experimental systems and appear to be functionally important in some instances. We have investigated how modifying a neuron's maximal conductances affects jitter using the leaky integrate-and-fire (LIF) model and an eight-conductance Hodgkin-Huxley type (HH8) model. We observed that jitter can be largely understood in the LIF model in terms of the neuron's filtering properties. In the HH8 model we found the role of individual conductances in determining jitter to be complicated and dependent on the model's spiking properties. Distinct behaviors were observed for populations with slow (<11.5 Hz) and fast (>11.5 Hz) spike rates and appear to be related to differences in a particular channel's activity at times just before spiking occurs.

Role of Ih in the firing pattern of mammalian cold thermoreceptor endings

Mammalian peripheral cold thermoreceptors respond to cooling of their sensory endings with an increase in firing rate and modification of their discharge pattern. We recently showed that cultured trigeminal cold-sensitive (CS) neurons express a prominent hyperpolarization-activated current ( Ih), mainly carried by HCN1 channels, supporting subthreshold resonance in the soma without participating in the response to acute cooling. However, peripheral pharmacological blockade of Ih, or characterization of HCN1−/− mice, reveals a deficit in acute cold detection. Here we investigated the role of Ih in CS nerve endings, where cold sensory transduction actually takes place. Corneal CS nerve endings in mice show a rhythmic spiking activity at neutral skin temperature that switches to bursting mode when the temperature is lowered. Ih blockers ZD7288 and ivabradine alter firing patterns of CS nerve endings, lengthening interspike intervals and inducing bursts at neutral skin temperature. We characterized the CS nerve endings from HCN1−/− mouse corneas and found that they behave similar to wild type, although with a lower slope in the firing frequency vs. temperature relationship, thus explaining the deficit in cold perception of HCN1−/− mice. The firing pattern of nerve endings from HCN1−/− mice was also affected by ZD7288, which we attribute to the presence of HCN2 channels in the place of HCN1. Mathematical modeling shows that the firing phenotype of CS nerve endings from HCN1−/− mice can be reproduced by replacing HCN1 channels with the slower HCN2 channels rather than by abolishing Ih. We propose that Ih carried by HCN1 channels helps tune the frequency of the oscillation and the length of bursts underlying regular spiking in cold thermoreceptors, having important implications for neural coding of cold sensation.

Fluctuating inhibitory inputs promote reliable spiking at theta frequencies in hippocampal interneurons

Theta-frequency (4–12 Hz) rhythms in the hippocampus play important roles in learning and memory. CA1 interneurons located at the stratum lacunosum-moleculare and radiatum junction (LM/RAD) are thought to contribute to hippocampal theta population activities by rhythmically pacing pyramidal cells with inhibitory postsynaptic potentials. This implies that LM/RAD cells need to fire reliably at theta frequencies in vivo. To determine whether this could occur, we use biophysically based LM/RAD model cells and apply different cholinergic and synaptic inputs to simulate in vivo-like network environments. We assess spike reliabilities and spiking frequencies, identifying biophysical properties and network conditions that best promote reliable theta spiking. We find that synaptic background activities that feature large inhibitory, but not excitatory, fluctuations are essential. This suggests that strong inhibitory input to these cells is vital for them to be able to contribute to population theta activities. Furthermore, we find that Type I-like oscillator models produced by augmented persistent sodium currents (I_NaP) or diminished A-type potassium currents (I_A) enhance reliable spiking at lower theta frequencies. These Type I-like models are also the most responsive to large inhibitory fluctuations and can fire more reliably under such conditions. In previous work, we showed that I_NaP and I_A are largely responsible for establishing LM/RAD cells’ subthreshold activities. Taken together with this study, we see that while both these currents are important for subthreshold theta fluctuations and reliable theta spiking, they contribute in different ways – I_NaP to reliable theta spiking and subthreshold activity generation, and I_A to subthreshold activities at theta frequencies. This suggests that linking subthreshold and suprathreshold activities should be done with consideration of both in vivo contexts and biophysical specifics.

Single neuron firing properties impact correlation-based population coding

Correlated spiking has been widely observed, but its impact on neural coding remains controversial. Correlation arising from comodulation of rates across neurons has been shown to vary with the firing rates of individual neurons. This translates into rate and correlation being equivalently tuned to the stimulus; under those conditions, correlated spiking does not provide information beyond that already available from individual neuron firing rates. Such correlations are irrelevant and can reduce coding efficiency by introducing redundancy. Using simulations and experiments in rat hippocampal neurons, we show here that pairs of neurons receiving correlated input also exhibit correlations arising from precise spike-time synchronization. Contrary to rate comodulation, spike-time synchronization is unaffected by firing rate, thus enabling synchrony- and rate-based coding to operate independently. The type of output correlation depends on whether intrinsic neuron properties promote integration or coincidence detection: "ideal" integrators (with spike generation sensitive to stimulus mean) exhibit rate comodulation, whereas ideal coincidence detectors (with spike generation sensitive to stimulus variance) exhibit precise spike-time synchronization. Pyramidal neurons are sensitive to both stimulus mean and variance, and thus exhibit both types of output correlation proportioned according to which operating mode is dominant. Our results explain how different types of correlations arise based on how individual neurons generate spikes, and why spike-time synchronization and rate comodulation can encode different stimulus properties. Our results also highlight the importance of neuronal properties for population-level coding insofar as neural networks can employ different coding schemes depending on the dominant operating mode of their constituent neurons.

The role of tonic and phasic dopamine for long-term synaptic plasticity in the prefrontal cortex: a computational model

This work presents a computational model of dopamine (DA) influence on long-term potentiation (LTP) and long-term depression (LTD) in the prefrontal cortex. Distinct properties of the model are a DA-concentration-dependent switch from depression to potentiation during induction of plasticity, and an inverted-U-shaped dependence of protein synthesis on the level of background DA. Protein synthesis is responsible for the maintenance of LTP/LTD in the model. Our simulations suggest that in vitro experimental data on prefrontal plasticity, induced by high-frequency stimulation, may be accounted for by a single synaptic mechanism that is slowly (on the timescale of minutes) activated in the presence of DA in a concentration-dependent manner. The activation value determines the direction of plasticity during induction, while it also modulates the magnitude of plasticity during maintenance. More generally, our results support the hypothesis that phasic release of endogenous DA is necessary for the maintenance of long-term changes in synaptic efficacy, while the concentration of tonic DA determines the direction and magnitude of these changes in the PFC.

Spike-train communities: finding groups of similar spike trains

Identifying similar spike-train patterns is a key element in understanding neural coding and computation. For single neurons, similar spike patterns evoked by stimuli are evidence of common coding. Across multiple neurons, similar spike trains indicate potential cell assemblies. As recording technology advances, so does the urgent need for grouping methods to make sense of large-scale datasets of spike trains. Existing methods require specifying the number of groups in advance, limiting their use in exploratory analyses. I derive a new method from network theory that solves this key difficulty: it self-determines the maximum number of groups in any set of spike trains, and groups them to maximize intragroup similarity. This method brings us revealing new insights into the encoding of aversive stimuli by dopaminergic neurons, and the organization of spontaneous neural activity in cortex. I show that the characteristic pause response of a rat's dopaminergic neuron depends on the state of the superior colliculus: when it is inactive, aversive stimuli invoke a single pattern of dopaminergic neuron spiking; when active, multiple patterns occur, yet the spike timing in each is reliable. In spontaneous multineuron activity from the cortex of anesthetized cat, I show the existence of neural ensembles that evolve in membership and characteristic timescale of organization during global slow oscillations. I validate these findings by showing that the method both is remarkably reliable at detecting known groups and can detect large-scale organization of dynamics in a model of the striatum.

GAD67-GFP+ neurons in the Nucleus of Roller. II. Subthreshold and firing resonance properties

In the companion paper we show that GAD67-GFP+ (GFP+) inhibitory neurons located in the Nucleus of Roller of the mouse brain stem can be classified into two main groups (tonic and phasic) based on their firing patterns in responses to injected depolarizing current steps. In this study we examined the responses of GFP+ cells to fluctuating sinusoidal ("chirp") current stimuli. Membrane impedance profiles in response to chirp stimulation showed that nearly all phasic cells exhibited subthreshold resonance, whereas the majority of tonic GFP+ cells were nonresonant. In general, subthreshold resonance was associated with a relatively fast passive membrane time constant and low input resistance. In response to suprathreshold chirp current stimulation at a holding potential just below spike threshold the majority of tonic GFP+ cells fired multiple action potentials per cycle at low input frequencies (<5 Hz) and either stopped firing or were not entrained by the chirp at higher input frequencies (= tonic low-pass cells). A smaller group of phasic GFP+ cells did not fire at low input frequency but were able to phase-lock 1:1 at intermediate chirp frequencies (= band-pass cells). Spike timing reliability was tested with repeated chirp stimuli and our results show that phasic cells were able to reliably fire when they phase-locked 1:1 over a relatively broad range of input frequencies. Most tonic low-pass cells showed low reliability and poor phase-locking ability. Computer modeling suggested that these different firing resonance properties among GFP+ cells are due to differences in passive and active membrane properties and spiking mechanisms. This heterogeneity of resonance properties might serve to selectively activate subgroups of interneurons.

Mechanisms for Phase Shifting in Cortical Networks and their Role in Communication through Coherence

In the primate visual cortex, the phase of spikes relative to oscillations in the local field potential (LFP) in the gamma frequency range (30-80 Hz) can be shifted by stimulus features such as orientation and thus the phase may carry information about stimulus identity. According to the principle of communication through coherence (CTC), the relative LFP phase between the LFPs in the sending and receiving circuits affects the effectiveness of the transmission. CTC predicts that phase shifting can be used for stimulus selection. We review and investigate phase shifting in models of periodically driven single neurons and compare it with phase shifting in models of cortical networks. In a single neuron, as the driving current is increased, the spike phase varies systematically while the firing rate remains constant. In a network model of reciprocally connected excitatory (E) and inhibitory (I) cells phase shifting occurs in response to both injection of constant depolarizing currents and to brief pulses to I cells. These simple models provide an account for phase-shifting observed experimentally and suggest a mechanism for implementing CTC. We discuss how this hypothesis can be tested experimentally using optogenetic techniques.

Rate maintenance and resonance in the entorhinal cortex

Throughout the brain, neurons encode information in fundamental units of spikes. Each spike represents the combined thresholding of synaptic inputs and intrinsic neuronal dynamics. Here, we address a basic question of spike train formation: how do perithreshold synaptic inputs perturb the output of a spiking neuron? We recorded from single entorhinal principal cells in vitro and drove them to spike steadily at ∼5 Hz (theta range) with direct current injection, then used a dynamic-clamp to superimpose strong excitatory conductance inputs at varying rates. Neurons spiked most reliably when the input rate matched the intrinsic neuronal firing rate. We also found a striking tendency of neurons to preserve their rates and coefficients of variation, independently of input rates. As mechanisms for this rate maintenance, we show that the efficacy of the conductance inputs varied with the relationship of input rate to neuronal firing rate, and with the arrival time of the input within the natural period. Using a novel method of spike classification, we developed a minimal Markov model that reproduced the measured statistics of the output spike trains and thus allowed us to identify and compare contributions to the rate maintenance and resonance. We suggest that the strength of rate maintenance may be used as a new categorization scheme for neuronal response and note that individual intrinsic spiking mechanisms may play a significant role in forming the rhythmic spike trains of activated neurons; in the entorhinal cortex, individual pacemakers may dominate production of the regional theta rhythm.

How synaptic release probability shapes neuronal transmission: information-theoretic analysis in a cerebellar granule cell

A nerve cell receives multiple inputs from upstream neurons by way of its synapses. Neuron processing functions are thus influenced by changes in the biophysical properties of the synapse, such as long-term potentiation (LTP) or depression (LTD). This observation has opened new perspectives on the biophysical basis of learning and memory, but its quantitative impact on the information transmission of a neuron remains partially elucidated. One major obstacle is the high dimensionality of the neuronal input-output space, which makes it unfeasible to perform a thorough computational analysis of a neuron with multiple synaptic inputs. In this work, information theory was employed to characterize the information transmission of a cerebellar granule cell over a region of its excitatory input space following synaptic changes. Granule cells have a small dendritic tree (on average, they receive only four mossy fiber afferents), which greatly bounds the input combinatorial space, reducing the complexity of information-theoretic calculations. Numerical simulations and LTP experiments quantified how changes in neurotransmitter release probability (p) modulated information transmission of a cerebellar granule cell. Numerical simulations showed that p shaped the neurotransmission landscape in unexpected ways. As p increased, the optimality of the information transmission of most stimuli did not increase strictly monotonically; instead it reached a plateau at intermediate p levels. Furthermore, our results showed that the spatiotemporal characteristics of the inputs determine the effect of p on neurotransmission, thus permitting the selection of distinctive preferred stimuli for different p values. These selective mechanisms may have important consequences on the encoding of cerebellar mossy fiber inputs and the plasticity and computation at the next circuit stage, including the parallel fiber-Purkinje cell synapses.

Analysis and modeling of ensemble recordings from respiratory pre-motor neurons indicate changes in functional network architecture after acute hypoxia

We have combined neurophysiologic recording, statistical analysis, and computational modeling to investigate the dynamics of the respiratory network in the brainstem. Using a multielectrode array, we recorded ensembles of respiratory neurons in perfused in situ rat preparations that produce spontaneous breathing patterns, focusing on inspiratory pre-motor neurons. We compared firing rates and neuronal synchronization among these neurons before and after a brief hypoxic stimulus. We observed a significant decrease in the number of spikes after stimulation, in part due to a transient slowing of the respiratory pattern. However, the median interspike interval did not change, suggesting that the firing threshold of the neurons was not affected but rather the synaptic input was. A bootstrap analysis of synchrony between spike trains revealed that both before and after brief hypoxia, up to 45% (but typically less than 5%) of coincident spikes across neuronal pairs was not explained by chance. Most likely, this synchrony resulted from common synaptic input to the pre-motor population, an example of stochastic synchronization. After brief hypoxia most pairs were less synchronized, although some were more, suggesting that the respiratory network was transiently “rewired” after the stimulus. To investigate this hypothesis, we created a simple computational model with feed-forward divergent connections along the inspiratory pathway. Assuming that (1) the number of divergent projections was not the same for all presynaptic cells, but rather spanned a wide range and (2) that the stimulus increased inhibition at the top of the network; this model reproduced the reduction in firing rate and bootstrap-corrected synchrony subsequent to hypoxic stimulation observed in our experimental data.

Consistency and diversity of spike dynamics in the neurons of bed nucleus of stria terminalis of the rat: a dynamic clamp study

Neurons display a high degree of variability and diversity in the expression and regulation of their voltage-dependent ionic channels. Under low level of synaptic background a number of physiologically distinct cell types can be identified in most brain areas that display different responses to standard forms of intracellular current stimulation. Nevertheless, it is not well understood how biophysically different neurons process synaptic inputs in natural conditions, i.e., when experiencing intense synaptic bombardment in vivo. While distinct cell types might process synaptic inputs into different patterns of action potentials representing specific “motifs” of network activity, standard methods of electrophysiology are not well suited to resolve such questions. In the current paper we performed dynamic clamp experiments with simulated synaptic inputs that were presented to three types of neurons in the juxtacapsular bed nucleus of stria terminalis (jcBNST) of the rat. Our analysis on the temporal structure of firing showed that the three types of jcBNST neurons did not produce qualitatively different spike responses under identical patterns of input. However, we observed consistent, cell type dependent variations in the fine structure of firing, at the level of single spikes. At the millisecond resolution structure of firing we found high degree of diversity across the entire spectrum of neurons irrespective of their type. Additionally, we identified a new cell type with intrinsic oscillatory properties that produced a rhythmic and regular firing under synaptic stimulation that distinguishes it from the previously described jcBNST cell types. Our findings suggest a sophisticated, cell type dependent regulation of spike dynamics of neurons when experiencing a complex synaptic background. The high degree of their dynamical diversity has implications to their cooperative dynamics and synchronization.

Cell type-specific control of neuronal responsiveness by gamma-band oscillatory inhibition

Neocortical networks are composed of diverse populations of cells that differ in their chemical content, electrophysiological characteristics, and connectivity. Gamma-frequency oscillatory activity of inhibitory subnetworks has been hypothesized to regulate information processing in the cortex as a whole. Inhibitory neurons in these subnetworks synchronize their firing and selectively innervate the perisomatic compartments of their target neurons, generating both tonic and rapidly fluctuating inhibition. How do different types of cortical neurons respond to changes in the level and structure of perisomatic inhibition? What accounts for response heterogeneity between cell types, and are these response properties fixed or flexible? To answer these questions, we use in vitro whole-cell recording and dynamic-clamp somatic current injection to study six distinct types of cortical neurons. We demonstrate that different types of neurons systematically vary in their receptiveness to fast changes in the structure of inhibition and the range over which changes in inhibitory tone affect their output. Using simple neuron models and model neuron hybrids (dynamic clamp), we determine which intrinsic differences between cell types lead to these variations in receptiveness. These results suggest important differences in the way cell types are affected by gamma-frequency inhibition, which may have important circuit level implications. Although intrinsic differences observed in vitro are useful for the elucidation of basic cellular properties and differences between cell types, we also investigate how the integrative properties of neurons are likely to be rapidly modulated in the context of active networks in vivo.

Control of the firing patterns of vibrissa motoneurons by modulatory and phasic synaptic inputs: a modeling study

Vibrissa motoneurons (vMNs) generate rhythmic firing that controls whisker movements, even without cortical, cerebellar, or sensory inputs. vMNs receive serotonergic modulation from brain stem areas, which mainly increases their persistent sodium conductance (g(NaP)) and, possibly, phasic input from a putative central pattern generator (CPG). In response to serotonergic modulation or just-suprathreshold current steps, vMNs fire at low rates, below the firing frequency of exploratory whisking. In response to periodic inputs, vMNs exhibit nonlinear suprathreshold resonance in frequency ranges of exploratory whisking. To determine how firing patterns of vMNs are determined by their 1) intrinsic ionic conductances and 2) responses to periodic input from a putative CPG and to serotonergic modulation, we construct and analyze a single-compartment, conductance-based model of vMNs. Low firing rates are supported in extended regimes by adaptation currents and the minimal firing rate decreases with g(NaP) and increases with M-potassium and h-cation conductances. Suprathreshold resonance results from the locking properties of vMN firing to stimuli and from reduction of firing rates at low frequencies by slow M and afterhyperpolarization potassium conductances. h conductance only slightly affects the suprathreshold resonance. When a vMN is subjected to a small periodic CPG input, serotonergically induced g(NaP) elevation may transfer the system from quiescence to a firing state that is highly locked to the CPG input. Thus we conclude that for vMNs, the CPG controls firing frequency and phase and enables bursting, whereas serotonergic modulation controls transitions from quiescence to firing unless the CPG input is sufficiently strong.

Mode-locked spike trains in responses of ventral cochlear nucleus chopper and onset neurons to periodic stimuli

We report evidence of mode-locking to the envelope of a periodic stimulus in chopper units of the ventral cochlear nucleus (VCN). Mode-locking is a generalized description of how responses in periodically forced nonlinear systems can be closely linked to the input envelope, while showing temporal patterns of higher order than seen during pure phase-locking. Re-analyzing a previously unpublished dataset in response to amplitude modulated tones, we find that of 55% of cells (6/11) demonstrated stochastic mode-locking in response to sinusoidally amplitude modulated (SAM) pure tones at 50% modulation depth. At 100% modulation depth SAM, most units (3/4) showed mode-locking. We use interspike interval (ISI) scattergrams to unravel the temporal structure present in chopper mode-locked responses. These responses compared well to a leaky integrate-and-fire model (LIF) model of chopper units. Thus the timing of spikes in chopper unit responses to periodic stimuli can be understood in terms of the complex dynamics of periodically forced nonlinear systems. A larger set of onset (33) and chopper units (24) of the VCN also shows mode-locked responses to steady-state vowels and cosine-phase harmonic complexes. However, while 80% of chopper responses to complex stimuli meet our criterion for the presence of mode-locking, only 40% of onset cells show similar complex-modes of spike patterns. We found a correlation between a unit's regularity and its tendency to display mode-locked spike trains as well as a correlation in the number of spikes per cycle and the presence of complex-modes of spike patterns. These spiking patterns are sensitive to the envelope as well as the fundamental frequency of complex sounds, suggesting that complex cell dynamics may play a role in encoding periodic stimuli and envelopes in the VCN.

Effects of XE991, retigabine, losigamone and ZD7288 on kainate-induced theta-like and gamma network oscillations in the rat hippocampus in vitro

Ion currents such as M-currents (I(M)), persistent sodium currents (I(NaP)) and H-currents (I(h)) have been observed in a variety of brain regions, including the hippocampal formation, where storage and retrieval of information are facilitated by oscillatory network activities. They have been suggested to play an important role in neuronal excitability, synaptic transmission, membrane oscillatory activity, and in shaping resonance. Resonance and membrane potential oscillations have been implied in the generation of theta but not gamma oscillations. Here, we performed extracellular field potential recordings in hippocampal slices from adult rats and applied either the I(M) blocker XE991, the I(M) activator retigabine, the I(NaP) blocker losigamone or the I(h) inhibitor ZD7288 to test if these currents contribute to the generation of network oscillations. Kainate application induced network theta-like frequency oscillations in coronal slices as well as network gamma frequency oscillations in horizontal slices, and these remained stable for up to 3h. Power spectrum analysis revealed that all agents dose-dependently reduced the network oscillations in both frequency bands in areas CA3 and CA1. In contrast, the peak oscillation frequency was affected differentially. These results confirm that theta-like frequency oscillations are induced in longitudinal slices while gamma frequency oscillations dominate in horizontal slices. They also suggest that modifying neuronal excitability and transmitter release alters hippocampal network oscillations which are thought to be crucial for memory processing.

Two distinct mechanisms shape the reliability of neural responses

Despite intrinsic noise sources, neurons can generate action potentials with remarkable reliability. This reliability is influenced by the characteristics of sensory or synaptic inputs, such as stimulus frequency. Here we use conductance-based models to study the frequency dependence of reliability in terms of the underlying single-cell properties. We are led to distinguish a mean-driven firing regime, where the stimulus mean is sufficient to elicit continuous firing, and a fluctuation-driven firing regime, where spikes are generated by transient stimulus fluctuations. In the mean-driven regime, the stimulus frequency that induces maximum reliability coincides with the firing rate of the cell, whereas in the fluctuation-driven regime, it is determined by the resonance properties of the subthreshold membrane potential. When the stimulus frequency does not match the optimal frequency, the two firing regimes exhibit different "symptoms" of decreased reliability: reduced spike-time precision and reduced spike probability, respectively. As a signature of stochastic resonance, reliable spike generation in the fluctuation-driven regime can benefit from intermediate amounts of noise that boost spike probability without significantly impairing spike-time precision. Our analysis supports the view that neurons are endowed with selection mechanisms that allow only certain stimulus frequencies to induce reliable spiking. By modulating the intrinsic cell properties, the nervous system can thus tune individual neurons to pick out specific input frequency bands with enhanced spike precision or spike probability.

Spike-rate coding and spike-time coding are affected oppositely by different adaptation mechanisms

Spike-frequency adaptation causes reduced spiking during prolonged stimulation, but the full impact of adaptation on neural coding is far more complex, especially if one takes into account the diversity of biophysical mechanisms mediating adaptation and the different ways in which neural information can be encoded. Here, we show that adaptation has opposite effects depending on the neural coding strategy and the biophysical mechanism responsible for adaptation. Under noisy conditions, calcium-activated K(+) current (I(AHP)) improved efficient spike-rate coding at the expense of spike-time coding by regularizing the spike train elicited by slow or constant inputs; noise power was increased at high frequencies but reduced at low frequencies, consistent with noise shaping that improves coding of low- frequency signals. In contrast, voltage-activated M-type K(+) current (I(M)) improved spike-time coding at the expense of spike-rate coding by stopping the neuron from spiking repetitively to slow inputs so that it could generate isolated, well timed spikes in response to fast inputs. Using dynamical systems analysis, we demonstrate how I(AHP) minimizes perturbation of the interspike interval caused by high- frequency noise, whereas I(M) minimizes disruption of spike-timing accuracy caused by repetitive spiking. The dichotomous outcomes are related directly to the distinct activation requirements for I(AHP) and I(M), which in turn dictate whether those currents mediate negative feedback onto spiking or membrane potential. Thus, based on their distinct activation properties, I(AHP) implements noise shaping that improves spike-rate coding of low-frequency signals, whereas I(M) implements high-pass filtering that improves spike-time coding of high- frequency signals.

Detection of subthreshold pulses in neurons with channel noise

Neurons are subject to various kinds of noise. In addition to synaptic noise, the stochastic opening and closing of ion channels represents an intrinsic source of noise that affects the signal-processing properties of the neuron. We study the response of a stochastic Hodgkin-Huxley neuron to transient input subthreshold pulses. It is found that the average response time decreases but variance increases as the amplitude of channel noise increases. In the case of single-pulse detection, we show that channel noise enables one neuron to detect the subthreshold signals and an optimal membrane area (or channel noise intensity) exists for a single neuron to achieve optimal performance. However, the detection ability of a single neuron is limited by large errors. Here, we test a simple neuronal network that can enhance the pulse-detecting abilities of neurons and find that dozens of neurons can perfectly detect subthreshold pulses. The phenomenon of intrinsic stochastic resonance is also found at both the level of single neurons and the level of networks. At the network level, the detection ability of networks can be optimized for the number of neurons comprising the network.

Subthreshold membrane-potential resonances shape spike-train patterns in the entorhinal cortex

Many neurons exhibit subthreshold membrane-potential resonances, such that the largest voltage responses occur at preferred stimulation frequencies. Because subthreshold resonances are known to influence the rhythmic activity at the network level, it is vital to understand how they affect spike generation on the single-cell level. We therefore investigated both resonant and nonresonant neurons of rat entorhinal cortex. A minimal resonate-and-fire type model based on measured physiological parameters captures fundamental properties of neuronal firing statistics surprisingly well and helps to shed light on the mechanisms that shape spike patterns: 1) subthreshold resonance together with a spike-induced reset of subthreshold oscillations leads to spike clustering and 2) spike-induced dynamics influence the fine structure of interspike interval (ISI) distributions and are responsible for ISI correlations appearing at higher firing rates (> or =3 Hz). Both mechanisms are likely to account for the specific discharge characteristics of various cell types.

Oscillations and synchrony in large-scale cortical network models

Intrinsic neuronal and circuit properties control the responses of large ensembles of neurons by creating spatiotemporal patterns of activity that are used for sensory processing, memory formation, and other cognitive tasks. The modeling of such systems requires computationally efficient single-neuron models capable of displaying realistic response properties. We developed a set of reduced models based on difference equations (map-based models) to simulate the intrinsic dynamics of biological neurons. These phenomenological models were designed to capture the main response properties of specific types of neurons while ensuring realistic model behavior across a sufficient dynamic range of inputs. This approach allows for fast simulations and efficient parameter space analysis of networks containing hundreds of thousands of neurons of different types using a conventional workstation. Drawing on results obtained using large-scale networks of map-based neurons, we discuss spatiotemporal cortical network dynamics as a function of parameters that affect synaptic interactions and intrinsic states of the neurons.

Rate-specific synchrony: using noisy oscillations to detect equally active neurons

Although gamma frequency oscillations are common in the brain, their functional contributions to neural computation are not understood. Here we report in vitro electrophysiological recordings to evaluate how noisy gamma frequency oscillatory input interacts with the overall activation level of a neuron to determine the precise timing of its action potentials. The experiments were designed to evaluate spike synchrony in a neural circuit architecture in which a population of neurons receives a common noisy gamma oscillatory synaptic drive while the firing rate of each individual neuron is determined by a slowly varying independent input. We demonstrate that similarity of firing rate is a major determinant of synchrony under common noisy oscillatory input: Near coincidence of spikes at similar rates gives way to substantial desynchronization at larger firing rate differences. Analysis of this rate-specific synchrony phenomenon reveals distinct spike timing "fingerprints" at different firing rates that emerge through a combination of phase shifting and abrupt changes in spike patterns. We further demonstrate that rate-specific synchrony permits robust detection of rate similarity in a population of neurons through synchronous activation of a postsynaptic neuron, supporting the biological plausibility of a Many Are Equal computation. Our results reveal that spatially coherent noisy oscillations, which are common throughout the brain, can generate previously unknown relationships among neural rate codes, noisy interspike intervals, and precise spike synchrony codes. All of these can coexist in a self-consistent manner because of rate-specific synchrony.

Noise in the nervous system

Noise--random disturbances of signals--poses a fundamental problem for information processing and affects all aspects of nervous-system function. However, the nature, amount and impact of noise in the nervous system have only recently been addressed in a quantitative manner. Experimental and computational methods have shown that multiple noise sources contribute to cellular and behavioural trial-to-trial variability. We review the sources of noise in the nervous system, from the molecular to the behavioural level, and show how noise contributes to trial-to-trial variability. We highlight how noise affects neuronal networks and the principles the nervous system applies to counter detrimental effects of noise, and briefly discuss noise's potential benefits.

Spike-firing resonance in hypoglossal motoneurons

During an inspiration the output of hypoglossal (XII) motoneurons (HMs) in vitro is characterized by synchronous oscillatory firing in the 20- to 40-Hz range. To maintain synchronicity it is important that the cells fire with high reliability and precision. It is not known whether the intrinsic properties of HMs are tuned to maintain synchronicity when stimulated with time-varying inputs. We intracellularly recorded from HMs in an in vitro brain stem slice preparation from juvenile mice. Cells were held at or near spike threshold and were stimulated with steady or swept sine-wave current functions (10-s duration; 0- to 40-Hz range). Peristimulus time histograms were constructed from spike times based on threshold crossings. Synaptic transmission was suppressed by including blockers of GABAergic, glycinergic, and glutamatergic neurotransmission in the bath solution. Cells responded to sine-wave stimulation with bursts of action potentials at low (<3- to 5-Hz) sine-wave frequency, whereas they phase-locked 1:1 to the stimulus at intermediate frequencies (3-25 Hz). Beyond the 1:1 frequency range cells were able to phase-lock to subharmonics (1:2, 1:3, or 1:4) of the input frequency. The 1:1 phase-locking range increased with increasing stimulus amplitude and membrane depolarization. Reliability and spike-timing precision were highest when the cells phase-locked 1:1 to the stimulus. Our findings suggest that the coding of time-varying inspiratory synaptic inputs by individual HMs is most reliable and precise at frequencies that are generally lower than the frequency of the synchronous inspiratory oscillatory activity recorded from the XII nerve.

Regulation of spike timing in visual cortical circuits

A train of action potentials (a spike train) can carry information in both the average firing rate and the pattern of spikes in the train. But can such a spike-pattern code be supported by cortical circuits? Neurons in vitro produce a spike pattern in response to the injection of a fluctuating current. However, cortical neurons in vivo are modulated by local oscillatory neuronal activity and by top-down inputs. In a cortical circuit, precise spike patterns thus reflect the interaction between internally generated activity and sensory information encoded by input spike trains. We review the evidence for precise and reliable spike timing in the cortex and discuss its computational role.

A binless correlation measure reduces the variability of memory reactivation estimates

The standard procedure for measuring correlations between pairs of spike trains is to count the numbers of spikes occurring within a specified set of time intervals partitioning the continuous time line into discrete bins of width w (seconds). One then computes the Pearson correlation between pairs of the bin occupancy vectors. This method introduces a form of quantization noise, similar to that in analog-to-digital signal processing devices, due to the arbitrary positioning of bin boundaries relative to pairs of spikes. Small changes in bin width and small uniform shifts in bin boundaries typically produce large variations in the apparent correlation. An alternative method of determining a correlation between pairs of spike trains was recently introduced. Rather than discretize the data in time, the original spike trains are convolved with a Gaussian kernel with parameter sigma chosen to give an effective width matching the bin width omega = square root 12 sigma . Calculating the Pearson correlation of the resulting smooth functions gives an estimate of the correlation between the spike trains matching that given by the bin-based procedure, without introducing the significant variability of the bin-based estimate. Measures of memory reactivation based on the partial correlations between ensembles of pairwise spike train correlations are biased downwards by the quantization noise present in the pairwise correlation estimates. Using a binless method to measure pairwise correlation, we find that the partial correlation (or explained variance) of rat hippocampal maze activity and post-maze sleep, taking into account pre-maze sleep correlations, increases significantly over estimates made with the standard bin-based procedure.

Modeling parkinsonian circuitry and the DBS electrode. I. Biophysical background and software

Deep brain stimulation (DBS) of the subthalamic nucleus (STN) for Parkinson's disease (PD) has become routine over the past decade, utilizing microelectrode recordings to ensure accurate placement of the stimulating electrodes. The clinical benefits of STN DBS for PD are well documented, but the mechanisms by which DBS achieves these results remain elusive. We have created a closed-form mathematical function of the potential field generated by a typical 4-contact DBS electrode and inserted this function into a computational model designed to simulate individual neurons and neural circuitry of significant portions of the basal ganglia. We present the mathematical function representing the potential field itself and the basis for the neural circuitry modeling in this paper.

Optimal time scale for spike-time reliability: theory, simulations, and experiments

Use of spike timing to encode information requires that neurons respond with high temporal precision and with high reliability. Fast fluctuating stimuli are known to result in highly reproducible spike times across trials, whereas constant stimuli result in variable spike times. Here, we first studied mathematically how spike-time reliability depends on the rapidness of aperiodic stimuli. Then, we tested our theoretical predictions in computer simulations of neuron models (Hodgkin-Huxley and modified quadratic integrate-and-fire), as well as in patch-clamp experiments with real neurons (mitral cells in the olfactory bulb and pyramidal cells in the neocortex). As predicted by our theory, we found that for firing frequencies in the beta/gamma range, spike-time reliability is maximal when the time scale of the input fluctuations (autocorrelation time) is in the range of a few milliseconds (2-5 ms), coinciding with the time scale of fast synapses, and decreases substantially for faster and slower inputs. Finally, we comment how these findings relate to mechanisms causing neuronal synchronization.

Signaling properties of stratum oriens interneurons in the hippocampus of transgenic mice expressing EGFP in a subset of somatostatin-containing cells

GABAergic interneurons constitute a heterogeneous group of cells that exert a powerful control on network excitability and are responsible for the oscillatory behavior crucial for information processing in the brain. These cells have been differently classified according to their morphological, neurochemical, and physiological characteristics. Here, whole cell patch clamp recordings were used to further characterize, in transgenic mice expressing EGFP in a subpopulation of GABAergic interneurons containing somatostatin (GIN mice), the functional properties of EGFP-positive cells in stratum oriens of the CA1 region of the hippocampus, in slice cultures obtained from P8 old animals. These cells showed passive and active membrane properties similar to those found in stratum oriens interneurons projecting to stratum lacunosum-moleculare. Moreover, they exhibited different firing patterns that were maintained upon membrane depolarization: irregular (48%), regular (30%), and clustered (22%). Trains of action potentials in interneurons evoked in a minority of principal cells (3/45) small amplitude GABAergic currents that at 20 Hz underwent short-term depression. In contrast, excitatory connections between principal cells and EGFP-positive interneurons were highly reliable (17/55) and exhibited a frequency and use-dependent facilitation particularly in the gamma band. In addition, recordings from paired of interconnected EGFP-positive cells revealed in 47% of the cases electrical coupling, which was abolished by carbenoxolone (200 microM). On average, the coupling coefficient was 0.21 +/- 0.07. When electrical coupling was particularly strong it acted as a powerful low-pass filter, thus contributing to alter the output of individual cells. In conclusion, it appears that the dynamic interaction between cells with various firing patterns could differently affect GABAergic signaling, leading, as suggested by simulation data, to a wide range of interneuronal communication within the hippocampal network.

Contributions of Ih to feature selectivity in layer II stellate cells of the entorhinal cortex

Abstract Stellate cells (SCs) of the entorhinal cortex generate prominent subthreshold oscillations that are believed to be important contributors to the hippocampal theta rhythm. The slow inward rectifier Ih is expressed prominently in SCs and has been suggested to be a dominant factor in their integrative properties. We studied the input-output relationships in stellate cells (SCs) of the entorhinal cortex, both in control conditions and in the presence of the Ih antagonist ZD7288. Our results show that Ih is responsible for SCs' subthreshold resonance, and contributes to enhanced spiking reliability to theta-rich stimuli. However, SCs still exhibit other traits of rhythmicity, such as subthreshold oscillations, under Ih blockade. To clarify the effects of Ih on SC spiking, we used a generalized form of principal component analysis to show that SCs select particular features with relevant temporal signatures from stimuli. The spike-selected mix of those features varies with the frequency content of the stimulus, emphasizing the inherent nonlinearity of SC responses. A number of controls confirmed that this selectivity represents a stimulus-induced change in the cellular input-output relationship rather than an artifact of the analysis technique. Sensitivity to slow features remained statistically significant in ZD7288. However, with Ih blocked, slow stimulus features were less predictive of spikes and spikes conveyed less information about the stimulus over long time scales. Together, these results suggest that Ih is an important contributor to the input-output relationships expressed by SCs, but that other factors in SCs also contribute to subthreshold oscillations and nonlinear selectivity to slow features.

Cross-intensity functions and the estimate of spike-time jitter

Correlation measures are important tools for the analysis of simultaneously recorded spike trains. A well-known measure with probabilistic interpretation is the cross-intensity function (CIF), which is an estimate of the conditional probability that a neuron spikes as a function of the time lag to spikes in another neuron. The non-commutative nature of the CIF is particularly useful when different neuron classes are studied that can be distinguished based on their anatomy or physiology. Here we explore the utility of the CIF for estimating spike-time jitter in synaptic interactions between neuron pairs of connected classes. When applied to spike train pairs from sleeping songbirds, we are able to distinguish fast synaptic interactions mediated primarily by AMPA receptors from slower interactions mediated by NMDA receptors. We also find that spike jitter increases with the time lag between spikes, reflecting the accumulation of noise in neural activity sequences, such as in synfire chains. In conclusion, we demonstrate some new utility of the CIF as a spike-train measure.

The Firing of an Excitable Neuron in the Presence of Stochastic Trains of Strong Synaptic Inputs

We consider a fast-slow excitable system subject to a stochastic excitatory input train and show that under general conditions, its long-term behavior is captured by an irreducible Markov chain with a limiting distribution. This limiting distribution allows for the analytical calculation of the system's probability of firing in response to each input, the expected number of response failures between firings, and the distribution of slow variable values between firings. Moreover, using this approach, it is possible to understand why the system will not have a stationary distribution and why Monte Carlo simulations do not converge under certain conditions. The analytical calculations involved can be performed whenever the distribution of interexcitation intervals and the recovery dynamics of the slow variable are known. The method can be extended to other models that feature a single variable that builds up to a threshold where an instantaneous spike and reset occur. We also discuss how the Markov chain analysis generalizes to any pair of input trains, excitatory or inhibitory and synaptic or not, such that the frequencies of the two trains are sufficiently different from each other. We illustrate this analysis on a model thalamocortical (TC) cell subject to two example distributions of excitatory synaptic inputs in the cases of constant and rhythmic inhibition. The analysis shows a drastic drop in the likelihood of firing just after inhibitory onset in the case of rhythmic inhibition, relative even to the case of elevated but constant inhibition. This observation provides support for a possible mechanism for the induction of motor symptoms in Parkinson's disease and for their relief by deep brain stimulation, analyzed in Rubin and Terman (2004).

Action potential timing precision in dorsal cochlear nucleus pyramidal cells

Many studies of the dorsal cochlear nucleus (DCN) have focused on the representation of acoustic stimuli in terms of average firing rate. However, recent studies have emphasized the role of spike timing in information encoding. We sought to ascertain whether DCN pyramidal cells might employ similar strategies and to what extent intrinsic excitability regulates spike timing. Gaussian distributed low-pass noise current was injected into pyramidal cells in a brain slice preparation. The shuffled autocorrelation-based analysis was used to compute a correlation index of spike times across trials. The noise causes the cells to fire with temporal precision (SD congruent with 1-2 ms) and high reproducibility. Increasing the coefficient of variation of the noise improved the reproducibility of the spike trains, whereas increasing the firing rate of the neuron decreased the neurons' ability to respond with predictable patterns of spikes. Simulated inhibitory postsynaptic potentials superimposed on the noise stimulus enhanced spike timing for >300 ms, although the enhancement was greatest during the first 100 ms. We also found that populations of pyramidal neurons respond to the same noise stimuli with correlated spike trains, suggesting that ensembles of neurons in the DCN receiving shared input can fire with similar timing. These results support the hypothesis that spike timing can be an important aspect of information coding in the DCN.