Nonlinear interaction between shunting and adaptation controls a switch between integration and coincidence detection in pyramidal neurons

Downregulation of parvalbumin at cortical GABA synapses reduces network gamma oscillatory activity

Postmortem and functional imaging studies of patients with psychiatric disorders, including schizophrenia, are consistent with a dysfunction of interneurons leading to compromised inhibitory control of network activity. Parvalbumin (PV)-expressing, fast-spiking interneurons interacting with pyramidal neurons generate cortical gamma oscillations (30-80 Hz) that synchronize cortical activity during cognitive processing. In postmortem studies of schizophrenia patients, these interneurons show reduced PV and glutamic acid decarboxylase 67 (GAD67), an enzyme that synthesizes GABA, but the consequences of this downregulation are unclear. We developed a biophysically realistic and detailed computational model of a cortical circuit including asynchronous release from GABAergic interneurons to investigate how reductions in PV and GABA affect gamma oscillations induced by sensory stimuli. Networks with reduced GABA were disinhibited and had altered gamma oscillations in response to stimulation; PV-deficient GABA synapses had increased asynchronous release of GABA, which decreased the level of excitation and reduced gamma-band activity. Combined reductions of PV and GABA resulted in a diminished gamma-band oscillatory activity in response to stimuli, similar to that observed in schizophrenia patients. Our results suggest a mechanism by which reduced GAD67 and PV in fast-spiking interneurons may contribute to cortical dysfunction in schizophrenia and related psychiatric disorders.

Parameter extraction and classification of three cortical neuron types reveals two distinct adaptation mechanisms

Cortical information processing originates from the exchange of action potentials between many cell types. To capture the essence of these interactions, it is of critical importance to build mathematical models that reflect the characteristic features of spike generation in individual neurons. We propose a framework to automatically extract such features from current-clamp experiments, in particular the passive properties of a neuron (i.e., membrane time constant, reversal potential, and capacitance), the spike-triggered adaptation currents, as well as the dynamics of the action potential threshold. The stochastic model that results from our maximum likelihood approach accurately predicts the spike times, the subthreshold voltage, the firing patterns, and the type of frequency-current curve. Extracting the model parameters for three cortical cell types revealed that cell types show highly significant differences in the time course of the spike-triggered currents and moving threshold, that is, in their adaptation and refractory properties but not in their passive properties. In particular, GABAergic fast-spiking neurons mediate weak adaptation through spike-triggered currents only, whereas regular spiking excitatory neurons mediate adaptation with both moving threshold and spike-triggered currents. GABAergic nonfast-spiking neurons combine the two distinct adaptation mechanisms with reduced strength. Differences between cell types are large enough to enable automatic classification of neurons into three different classes. Parameter extraction is performed for individual neurons so that we find not only the mean parameter values for each neuron type but also the spread of parameters within a group of neurons, which will be useful for future large-scale computer simulations.

ClC-2 channels regulate neuronal excitability, not intracellular chloride levels

Synaptic inhibition by GABA(A) receptors requires a transmembrane chloride gradient. Hyperpolarization or shunting results from outward current produced by chloride flowing down this gradient, into the cell. Chloride influx necessarily depletes the chloride gradient. Therefore, mechanisms that replenish the gradient (by reducing intracellular chloride concentration, [Cl(-)](i)) are crucial for maintaining the efficacy of GABA(A) receptor-mediated inhibition. ClC-2 is an inward-rectifying chloride channel that is thought to help extrude chloride because inward rectification should, in principle, allow ClC-2 to act as a one-way chloride exit valve. But chloride efflux via ClC-2 nevertheless requires an appropriate driving force. Using computer modeling, we reproduced voltage-clamp experiments showing chloride efflux via ClC-2, but testing the same model under physiological conditions revealed that ClC-2 normally leaks chloride into the cell. The discrepancy is explained by the driving force conditions that exist under artificial versus physiological conditions, and by the fact that ClC-2 rectification is neither complete nor instantaneous. Thus, contrary to previous assertions that ClC-2 helps maintain synaptic inhibition by lowering [Cl(-)](i), our simulations show that ClC-2 mediates chloride influx, thus producing outward current and directly reducing excitability. To test how ClC-2 functions in real neurons, we used dynamic clamp to insert virtual ClC-2 channels into rat CA1 pyramidal cells with and without native ClC-2 channels blocked. Experiments confirmed that ClC-2 reduces spiking independently of inhibitory synaptic transmission. Our results highlight the importance of considering driving force when inferring how a channel functions under physiological conditions.

Topological basis of epileptogenesis in a model of severe cortical trauma

Epileptic activity often arises after a latent period following traumatic brain injury. Several factors contribute to the emergence of post-traumatic epilepsy, including disturbances to ionic homeostasis, pathological action of intrinsic and synaptic homeostatic plasticity, and remodeling of anatomical network synaptic connectivity. We simulated a large-scale, biophysically realistic computational model of cortical tissue to study the mechanisms underlying the genesis of post-traumatic paroxysmal epileptic-like activity in the deafferentation model of a severely traumatized cortical network. Post-traumatic generation of paroxysmal events did not require changes of the structural connectivity. Rather, network bursts were induced following the action of homeostatic synaptic plasticity, which selectively influenced functionally dominant groups of intact neurons with preserved inputs. This effect critically depended on the spatial density of intact neurons. Thus in the deafferentation model of post-traumatic epilepsy, a trauma-induced change in functional (rather than anatomical) connectivity might be sufficient for epileptogenesis.

Contributions of Kv7-mediated potassium current to sub- and suprathreshold responses of rat layer II/III neocortical pyramidal neurons

After block of Kv1- and Kv2-mediated K(+) currents in acutely dissociated neocortical pyramidal neurons from layers II/III of rat somatosensory and motor cortex, the remaining current is slowly activating and persistent. We used whole cell voltage clamp to show that the Kv7 blockers linopirdine and XE-991 blocked a current with similar kinetics to the current remaining after combined block of Kv1 and Kv2 channels. This current was sensitive to low doses of linopirdine and activated more slowly and at more negative potentials than Kv1- or Kv2-mediated current. The Kv7-mediated current decreased in amplitude with time in whole cell recordings, but in most cells the current was stable for several minutes. Current in response to a traditional M-current protocol was blocked by muscarine, linopirdine, and XE-991. Whole cell slice recordings revealed that the Q₁₀ for channel deactivation was ∼2.5. Sharp electrode current-clamp recordings from adult pyramidal cells demonstrated that block of Kv7-mediated current with XE-991 reduced rheobase, shortened the latency to firing to near rheobase current, induced more regular firing at low current intensity, and increased the rate of firing to a given current injection. XE-991 did not affect single action potentials or spike frequency adaptation. Application of XE-991 also eliminated subthreshold voltage oscillations and increased gain for low-frequency inputs (<10 Hz) without affecting gain for higher frequency inputs. These data suggest important roles for Kv7 channels in subthreshold regulation of excitability, generation of theta-frequency subthreshold oscillations, regulation of interspike intervals, and biasing selectivity toward higher frequency inputs.

Gap junctions and epileptic seizures--two sides of the same coin?

Electrical synapses (gap junctions) play a pivotal role in the synchronization of neuronal ensembles which also makes them likely agonists of pathological brain activity. Although large body of experimental data and theoretical considerations indicate that coupling neurons by electrical synapses promotes synchronous activity (and thus is potentially epileptogenic), some recent evidence questions the hypothesis of gap junctions being among purely epileptogenic factors. In particular, an expression of inter-neuronal gap junctions is often found to be higher after the experimentally induced seizures than before. Here we used a computational modeling approach to address the role of neuronal gap junctions in shaping the stability of a network to perturbations that are often associated with the onset of epileptic seizures. We show that under some circumstances, the addition of gap junctions can increase the dynamical stability of a network and thus suppress the collective electrical activity associated with seizures. This implies that the experimentally observed post-seizure additions of gap junctions could serve to prevent further escalations, suggesting furthermore that they are a consequence of an adaptive response of the neuronal network to the pathological activity. However, if the seizures are strong and persistent, our model predicts the existence of a critical tipping point after which additional gap junctions no longer suppress but strongly facilitate the escalation of epileptic seizures. Our results thus reveal a complex role of electrical coupling in relation to epileptiform events. Which dynamic scenario (seizure suppression or seizure escalation) is ultimately adopted by the network depends critically on the strength and duration of seizures, in turn emphasizing the importance of temporal and causal aspects when linking gap junctions with epilepsy.

Membrane voltage fluctuations reduce spike frequency adaptation and preserve output gain in CA1 pyramidal neurons in a high-conductance state

Modulating the gain of the input-output function of neurons is critical for processing of stimuli and network dynamics. Previous gain control mechanisms have suggested that voltage fluctuations play a key role in determining neuronal gain in vivo. Here we show that, under increased membrane conductance, voltage fluctuations restore Na(+) current and reduce spike frequency adaptation in rat hippocampal CA1 pyramidal neurons in vitro. As a consequence, membrane voltage fluctuations produce a leftward shift in the frequency-current relationship without a change in gain, relative to an increase in conductance alone. Furthermore, we show that these changes have important implications for the integration of inhibitory inputs. Due to the ability to restore Na(+) current, hyperpolarizing membrane voltage fluctuations mediated by GABA(A)-like inputs can increase firing rate in a high-conductance state. Finally, our data show that the effects on gain and synaptic integration are mediated by voltage fluctuations within a physiologically relevant range of frequencies (10-40 Hz).

Reduction of an afterhyperpolarization current increases excitability in striatal cholinergic interneurons in rat parkinsonism

Striatal cholinergic interneurons show tonic spiking activity in the intact and sliced brain, which stems from intrinsic mechanisms. Because of it, they are also known as "tonically active neurons" (TANs). Another hallmark of TAN electrophysiology is a pause response to appetitive and aversive events and to environmental cues that have predicted these events during learning. Notably, the pause response is lost after the degeneration of dopaminergic neurons in animal models of Parkinson's disease. Moreover, Parkinson's disease patients are in a hypercholinergic state and find some clinical benefit in anticholinergic drugs. Current theories propose that excitatory thalamic inputs conveying information about salient sensory stimuli trigger an intrinsic hyperpolarizing response in the striatal cholinergic interneurons. Moreover, it has been postulated that the loss of the pause response in Parkinson's disease is related to a diminution of I(sAHP), a slow outward current that mediates an afterhyperpolarization following a train of action potentials. Here we report that I(sAHP) induces a marked spike-frequency adaptation in adult rat striatal cholinergic interneurons, inducing an abrupt end of firing during sustained excitation. Chronic loss of dopaminergic neurons markedly reduces I(sAHP) and spike-frequency adaptation in cholinergic interneurons, allowing them to fire continuously and at higher rates during sustained excitation. These findings provide a plausible explanation for the hypercholinergic state in Parkinson's disease. Moreover, a reduction of I(sAHP) may alter synchronization of cholinergic interneurons with afferent inputs, thus contributing to the loss of the pause response in Parkinson's disease.

Using computer simulations to determine the limitations of dynamic clamp stimuli applied at the soma in mimicking distributed conductance sources

In previous studies we used the technique of dynamic clamp to study how temporal modulation of inhibitory and excitatory inputs control the frequency and precise timing of spikes in neurons of the deep cerebellar nuclei (DCN). Although this technique is now widely used, it is limited to interpreting conductance inputs as being location independent; i.e., all inputs that are biologically distributed across the dendritic tree are applied to the soma. We used computer simulations of a morphologically realistic model of DCN neurons to compare the effects of purely somatic vs. distributed dendritic inputs in this cell type. We applied the same conductance stimuli used in our published experiments to the model. To simulate variability in neuronal responses to repeated stimuli, we added a somatic white current noise to reproduce subthreshold fluctuations in the membrane potential. We were able to replicate our dynamic clamp results with respect to spike rates and spike precision for different patterns of background synaptic activity. We found only minor differences in the spike pattern generation between focal or distributed input in this cell type even when strong inhibitory or excitatory bursts were applied. However, the location dependence of dynamic clamp stimuli is likely to be different for each cell type examined, and the simulation approach developed in the present study will allow a careful assessment of location dependence in all cell types.

Synaptic scaling stabilizes persistent activity driven by asynchronous neurotransmitter release

Small networks of cultured hippocampal neurons respond to transient stimulation with rhythmic network activity (reverberation) that persists for several seconds, constituting an in vitro model of synchrony, working memory, and seizure. This mode of activity has been shown theoretically and experimentally to depend on asynchronous neurotransmitter release (an essential feature of the developing hippocampus) and is supported by a variety of developing neuronal networks despite variability in the size of populations (10-200 neurons) and in patterns of synaptic connectivity. It has previously been reported in computational models that "small-world" connection topology is ideal for the propagation of similar modes of network activity, although this has been shown only for neurons utilizing synchronous (phasic) synaptic transmission. We investigated how topological constraints on synaptic connectivity could shape the stability of reverberations in small networks that also use asynchronous synaptic transmission. We found that reverberation duration in such networks was resistant to changes in topology and scaled poorly with network size. However, normalization of synaptic drive, by reducing the variance of synaptic input across neurons, stabilized reverberation in such networks. Our results thus suggest that the stability of both normal and pathological states in developing networks might be shaped by variance-normalizing constraints on synaptic drive. We offer an experimental prediction for the consequences of such regulation on the behavior of small networks.

The dynamics of somatic input processing in spinal motoneurons in vivo

Uncovering how motoneurons utilize their voltage-sensitive conductances to systematically respond to a variety of inputs is paramount to understanding synaptic integration. In this study, we examine the input dynamics and frequency-dependent characteristics of active conductances in motoneurons as viewed from the soma in the decerebrate cat. We evaluated the somatic response of the motoneuron by superimposing a voltage sinus sweep (a sine wave in which frequency increases with time, which is often referred to as a zap or chirp) at a subset of membrane holding potentials during discontinuous, single-electrode, somatic voltage-clamp. Results from both experimental and modeling data indicate that ionic conductances can respond to a wide variety of input dynamics. Notably, it appears that there is a divergence between low input conductance type S and high input conductance type FF motoneurons in their response to input frequency. Type S motoneurons generate a larger response to lower frequency input dynamics (compared with their response to higher frequencies), whereas type FF generate a larger response to higher input frequency dynamics. Functionally, these results may indicate that motoneurons on the lower end of the motor pool (i.e., recruited first) may favor steady inputs, whereas motoneurons at the higher end (i.e., recruited later) may favor input transients in producing action potentials.

Neural adaptation facilitates oscillatory responses to static inputs in a recurrent network of ON and OFF cells

We investigate the role of adaptation in a neural field model, composed of ON and OFF cells, with delayed all-to-all recurrent connections. As external spatially profiled inputs drive the network, ON cells receive inputs directly, while OFF cells receive an inverted image of the original signals. Via global and delayed inhibitory connections, these signals can cause the system to enter states of sustained oscillatory activity. We perform a bifurcation analysis of our model to elucidate how neural adaptation influences the ability of the network to exhibit oscillatory activity. We show that slow adaptation encourages input-induced rhythmic states by decreasing the Andronov-Hopf bifurcation threshold. We further determine how the feedback and adaptation together shape the resonant properties of the ON and OFF cell network and how this affects the response to time-periodic input. By introducing an additional frequency in the system, adaptation alters the resonance frequency by shifting the peaks where the response is maximal. We support these results with numerical experiments of the neural field model. Although developed in the context of the circuitry of the electric sense, these results are applicable to any network of spontaneously firing cells with global inhibitory feedback to themselves, in which a fraction of these cells receive external input directly, while the remaining ones receive an inverted version of this input via feedforward di-synaptic inhibition. Thus the results are relevant beyond the many sensory systems where ON and OFF cells are usually identified, and provide the backbone for understanding dynamical network effects of lateral connections and various forms of ON/OFF responses.

Shunting inhibition controls the gain modulation mediated by asynchronous neurotransmitter release in early development

The sensitivity of a neuron to its input can be modulated in several ways. Changes in the slope of the neuronal input-output curve depend on factors such as shunting inhibition, background noise, frequency-dependent synaptic excitation, and balanced excitation and inhibition. However, in early development GABAergic interneurons are excitatory and other mechanisms such as asynchronous transmitter release might contribute to regulating neuronal sensitivity. We modeled both phasic and asynchronous synaptic transmission in early development to study the impact of activity-dependent noise and short-term plasticity on the synaptic gain. Asynchronous release decreased or increased the gain depending on the membrane conductance. In the high shunt regime, excitatory input due to asynchronous release was divisive, whereas in the low shunt regime it had a nearly multiplicative effect on the firing rate. In addition, sensitivity to correlated inputs was influenced by shunting and asynchronous release in opposite ways. Thus, asynchronous release can regulate the information flow at synapses and its impact can be flexibly modulated by the membrane conductance.

Phase-response curves and synchronized neural networks

We review the principal assumptions underlying the application of phase-response curves (PRCs) to synchronization in neuronal networks. The PRC measures how much a given synaptic input perturbs spike timing in a neural oscillator. Among other applications, PRCs make explicit predictions about whether a given network of interconnected neurons will synchronize, as is often observed in cortical structures. Regarding the assumptions of the PRC theory, we conclude: (i) The assumption of noise-tolerant cellular oscillations at or near the network frequency holds in some but not all cases. (ii) Reduced models for PRC-based analysis can be formally related to more realistic models. (iii) Spike-rate adaptation limits PRC-based analysis but does not invalidate it. (iv) The dependence of PRCs on synaptic location emphasizes the importance of improving methods of synaptic stimulation. (v) New methods can distinguish between oscillations that derive from mutual connections and those arising from common drive. (vi) It is helpful to assume linear summation of effects of synaptic inputs; experiments with trains of inputs call this assumption into question. (vii) Relatively subtle changes in network structure can invalidate PRC-based predictions. (viii) Heterogeneity in the preferred frequencies of component neurons does not invalidate PRC analysis, but can annihilate synchronous activity.

Neurophysiological and computational principles of cortical rhythms in cognition

Synchronous rhythms represent a core mechanism for sculpting temporal coordination of neural activity in the brain-wide network. This review focuses on oscillations in the cerebral cortex that occur during cognition, in alert behaving conditions. Over the last two decades, experimental and modeling work has made great strides in elucidating the detailed cellular and circuit basis of these rhythms, particularly gamma and theta rhythms. The underlying physiological mechanisms are diverse (ranging from resonance and pacemaker properties of single cells to multiple scenarios for population synchronization and wave propagation), but also exhibit unifying principles. A major conceptual advance was the realization that synaptic inhibition plays a fundamental role in rhythmogenesis, either in an interneuronal network or in a reciprocal excitatory-inhibitory loop. Computational functions of synchronous oscillations in cognition are still a matter of debate among systems neuroscientists, in part because the notion of regular oscillation seems to contradict the common observation that spiking discharges of individual neurons in the cortex are highly stochastic and far from being clocklike. However, recent findings have led to a framework that goes beyond the conventional theory of coupled oscillators and reconciles the apparent dichotomy between irregular single neuron activity and field potential oscillations. From this perspective, a plethora of studies will be reviewed on the involvement of long-distance neuronal coherence in cognitive functions such as multisensory integration, working memory, and selective attention. Finally, implications of abnormal neural synchronization are discussed as they relate to mental disorders like schizophrenia and autism.

Feature selection in simple neurons: how coding depends on spiking dynamics

The relationship between a neuron's complex inputs and its spiking output defines the neuron's coding strategy. This is frequently and effectively modeled phenomenologically by one or more linear filters that extract the components of the stimulus that are relevant for triggering spikes and a nonlinear function that relates stimulus to firing probability. In many sensory systems, these two components of the coding strategy are found to adapt to changes in the statistics of the inputs in such a way as to improve information transmission. Here, we show for two simple neuron models how feature selectivity as captured by the spike-triggered average depends on both the parameters of the model and the statistical characteristics of the input.

Cellular mechanisms of temporal sensitivity in visual cortex neurons

The ability of cortical neurons to accurately encode the temporal pattern of their inputs has important consequences for cortical function and perceptual acuity. Here we identify cellular mechanisms underlying the sensitivity of cortical neurons to the timing of sensory-evoked synaptic inputs. We find that temporally coincident inputs to layer 4 neurons in primary visual cortex evoke an increase in spike precision and supralinear spike summation. Underlying this nonlinear summation are changes in the evoked excitatory conductance and the associated membrane potential response, and a lengthening of the window between excitation and inhibition. Furthermore, fast-spiking inhibitory interneurons in layer 4 exhibit a shorter window of temporal sensitivity compared with excitatory neurons. In contrast to the enhanced response to synchronous inputs by layer 4 neurons, sensory input integration in downstream cortical layers is more linear and less sensitive to timing. Neurons in the input layer of cortex are thus uniquely optimized to detect and encode synchronous sensory-evoked inputs.

Gain control in CA1 pyramidal cells using changes in somatic conductance

Gain modulation is an important feature of neural activity. Previous work has focused on the ability of background synaptic noise to modulate the slope (i.e., gain) of the frequency-current (f-I) relationship in neurons. To date, demonstrations of gain control that are independent of synaptic noise have been limited. We investigated the effects of increasing somatic conductance in the form of tonic inhibition on the initial and steady-state f-I relationship of CA1 pyramidal cells. We find that increasing membrane conductance reduces the gain of the steady-state f-I relationship through a graded increase in the magnitude of spike frequency adaptation. Increased adaptation arises through a conductance-induced depolarization of spike voltage threshold. Thus, by increasing the magnitude of spike frequency adaptation, added conductance can reduce the gain of the steady-state f-I relationship in the absence of random background membrane fluctuations.

Olfactory information processing in Drosophila

In both insect and vertebrate olfactory systems only two synapses separate the sensory periphery from brain areas required for memory formation and the organisation of behaviour. In the Drosophila olfactory system, which is anatomically very similar to its vertebrate counterpart, there has been substantial recent progress in understanding the flow of information from experiments using molecular genetic, electrophysiological and optical imaging techniques. In this review, we shall focus on how olfactory information is processed and transformed in order to extract behaviourally relevant information. We follow the progress from olfactory receptor neurons, through the first processing area, the antennal lobe, to higher olfactory centres. We address both the underlying anatomy and mechanisms that govern the transformation of neural activity. We emphasise our emerging understanding of how different elementary computations, including signal averaging, gain control, decorrelation and integration, may be mapped onto different circuit elements.

Signal processing in local neuronal circuits based on activity-dependent noise and competition

We study the characteristics of weak signal detection by a recurrent neuronal network with plastic synaptic coupling. It is shown that in the presence of an asynchronous component in synaptic transmission, the network acquires selectivity with respect to the frequency of weak periodic stimuli. For nonperiodic frequency-modulated stimuli, the response is quantified by the mutual information between input (signal) and output (network's activity) and is optimized by synaptic depression. Introducing correlations in signal structure resulted in the decrease in input-output mutual information. Our results suggest that in neural systems with plastic connectivity, information is not merely carried passively by the signal; rather, the information content of the signal itself might determine the mode of its processing by a local neuronal circuit.

Functional phase response curves: a method for understanding synchronization of adapting neurons

Phase response curves (PRCs) for a single neuron are often used to predict the synchrony of mutually coupled neurons. Previous theoretical work on pulse-coupled oscillators used single-pulse perturbations. We propose an alternate method in which functional PRCs (fPRCs) are generated using a train of pulses applied at a fixed delay after each spike, with the PRC measured when the phasic relationship between the stimulus and the subsequent spike in the neuron has converged. The essential information is the dependence of the recovery time from pulse onset until the next spike as a function of the delay between the previous spike and the onset of the applied pulse. Experimental fPRCs in Aplysia pacemaker neurons were different from single-pulse PRCs, principally due to adaptation. In the biological neuron, convergence to the fully adapted recovery interval was slower at some phases than that at others because the change in the effective intrinsic period due to adaptation changes the effective phase resetting in a way that opposes and slows the effects of adaptation. The fPRCs for two isolated adapting model neurons were used to predict the existence and stability of 1:1 phase-locked network activity when the two neurons were coupled. A stability criterion was derived by linearizing a coupled map based on the fPRC and the existence and stability criteria were successfully tested in two-simulated-neuron networks with reciprocal inhibition or excitation. The fPRC is the first PRC-based tool that can account for adaptation in analyzing networks of neural oscillators.

Sensitivity of firing rate to input fluctuations depends on time scale separation between fast and slow variables in single neurons

Neuronal responses are often characterized by the firing rate as a function of the stimulus mean, or the f-I curve. We introduce a novel classification of neurons into Types A, B-, and B+ according to how f-I curves are modulated by input fluctuations. In Type A neurons, the f-I curves display little sensitivity to input fluctuations when the mean current is large. In contrast, Type B neurons display sensitivity to fluctuations throughout the entire range of input means. Type B- neurons do not fire repetitively for any constant input, whereas Type B+ neurons do. We show that Type B+ behavior results from a separation of time scales between a slow and fast variable. A voltage-dependent time constant for the recovery variable can facilitate sensitivity to input fluctuations. Type B+ firing rates can be approximated using a simple "energy barrier" model.

Reduction of spike afterdepolarization by increased leak conductance alters interspike interval variability

Data from neurons in vivo have shown that spike output can often sustain episodes of high variability. Theoretical studies have indicated that the high conductance state of neurons brought on by synaptic activity can contribute to an increase in the variability of spike output by decreasing the integration timescale of the neuron. In the present work, we were interested in understanding how background synaptic conductance activity alters the interspike interval (ISI) variability of layer III pyramidal cells of the medial entorhinal cortex. We compared ISI variability in pyramidal cells as a result of synaptic current- or conductance-mediated membrane fluctuations. We found that the effects of background synaptic conductance activity on ISI variability depend on the neuron type. In pyramidal cells lacking spike frequency adaptation, the variability increased in relation to a comparable synaptic current stimulus. In contrast, in pyramidal cells displaying spike frequency adaptation, the synaptic conductance stimulus produced lower ISI variability. To understand this result, we constructed a phenomenological model that reproduced the basic properties of these neurons under control and increased leak conductance. We found that leak can change the properties of the neuron by acting as a bifurcation parameter that reduces the afterdepolarization (ADP) and decreases the slope (gain) of the frequency-current relationship, particularly for transient stimuli. A lower gain with the added leak causes a reduction in ISI variability. We conclude that the ability of a high conductance state to increase ISI variability cannot be generalized and can depend on the spike ADP dynamics expressed by the neuron.

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.

Adaptation of firing rate and spike-timing precision in the avian cochlear nucleus

Adaptation is commonly defined as a decrease in response to a constant stimulus. In the auditory system such adaptation is seen at multiple levels. However, the first-order central neurons of the interaural time difference detection circuit encode information in the timing of spikes rather than the overall firing rate. We investigated adaptation during in vitro whole-cell recordings from chick nucleus magnocellularis neurons. Injection of noisy, depolarizing current caused an increase in firing rate and a decrease in spike time precision that developed over approximately 20 s. This adaptation depends on sustained depolarization, is independent of firing, and is eliminated by alpha-dendrotoxin (0.1 microM), implicating slow inactivation of low-threshold voltage-activated K+ channels as its mechanism. This process may alter both firing rate and spike-timing precision of phase-locked inputs to coincidence detector neurons in nucleus laminaris and thereby adjust the precision of sound localization.

Pyramidal neurons switch from integrators in vitro to resonators under in vivo-like conditions

During wakefulness, pyramidal neurons in the intact brain are bombarded by synaptic input that causes tonic depolarization, increased membrane conductance (i.e., shunting), and noisy fluctuations in membrane potential; by comparison, pyramidal neurons in acute slices typically experience little background input. Such differences in operating conditions can compromise extrapolation of in vitro data to explain neuronal operation in vivo. For instance, pyramidal neurons have been identified as integrators (i.e., class 1 neurons according to Hodgkin's classification of intrinsic excitability) based on in vitro experiments but that classification is inconsistent with the ability of hippocampal pyramidal neurons to oscillate/resonate at theta frequency since intrinsic oscillatory behavior is limited to class 2 neurons. Using long depolarizing stimuli and dynamic clamp to reproduce in vivo-like conditions in slice experiments, we show that CA1 hippocampal pyramidal cells switch from integrators to resonators, i.e., from class 1 to class 2 excitability. The switch is explained by increased outward current contributed by the M-type potassium current I(M), which shifts the balance of inward and outward currents active at perithreshold potentials and thereby converts the spike-initiating mechanism as predicted by dynamical analysis of our computational model. Perithreshold activation of I(M) is enhanced by the depolarizing shift in spike threshold caused by shunting and/or sodium channel inactivation secondary to tonic depolarization. Our conclusions were validated by multiple comparisons between simulation and experimental data. Thus even so-called "intrinsic" properties may differ qualitatively between in vitro and in vivo conditions.

Intrinsic gain modulation and adaptive neural coding

In many cases, the computation of a neural system can be reduced to a receptive field, or a set of linear filters, and a thresholding function, or gain curve, which determines the firing probability; this is known as a linear/nonlinear model. In some forms of sensory adaptation, these linear filters and gain curve adjust very rapidly to changes in the variance of a randomly varying driving input. An apparently similar but previously unrelated issue is the observation of gain control by background noise in cortical neurons: the slope of the firing rate versus current (f-I) curve changes with the variance of background random input. Here, we show a direct correspondence between these two observations by relating variance-dependent changes in the gain of f-I curves to characteristics of the changing empirical linear/nonlinear model obtained by sampling. In the case that the underlying system is fixed, we derive relationships relating the change of the gain with respect to both mean and variance with the receptive fields derived from reverse correlation on a white noise stimulus. Using two conductance-based model neurons that display distinct gain modulation properties through a simple change in parameters, we show that coding properties of both these models quantitatively satisfy the predicted relationships. Our results describe how both variance-dependent gain modulation and adaptive neural computation result from intrinsic nonlinearity.

Many neurons are known to achieve a wide dynamic range by adaptively changing their computational input/output function according to the input statistics. These adaptive changes can be very rapid, and it has been suggested that a component of this adaptation could be purely input-driven: even a fixed neural system can show apparent adaptive behavior since inputs with different statistics interact with the nonlinearity of the system in different ways. In this paper, we show how a single neuron's intrinsic computational function can dictate such input-driven changes in its response to varying input statistics, which begets a relationship between two different characterizations of neural function—in terms of mean firing rate and in terms of generating precise spike timing. We then apply our results to two biophysically defined model neurons, which have significantly different response patterns to inputs with various statistics. Our model of intrinsic adaptation explains their behaviors well. Contrary to the picture that neurons carry out a stereotyped computation on their inputs, our results show that even in the simplest cases they have simple yet effective mechanisms by which they can adapt to their input. Adaptation to stimulus statistics, therefore, is built into the most basic single neuron computations.

Parvalbumin-positive basket interneurons in monkey and rat prefrontal cortex

Differences in the developmental origin and relative proportions of biochemically distinct classes of cortical neurons have been found between rodents and primates. In addition, species differences in the properties of certain cell types, such as neurogliaform cells, have also been reported. Consequently, in this study we compared the anatomical and physiological properties of parvalbumin (PV)-positive basket interneurons in the prefrontal cortex of macaque monkeys and rats. The somal size, total dendritic length, and horizontal and vertical spans of the axonal arbor were similar in monkeys and rats. Physiologically, PV basket cells could be identified as fast-spiking interneurons in both species, based on their short spike and high-frequency firing without adaptation. However, important interspecies differences in the intrinsic physiological properties were found. In monkeys, basket cells had a higher input resistance and a lower firing threshold, and they generated more spikes at near-threshold current intensities than those in rats. Thus monkey basket cells appeared to be more excitable. In addition, rat basket cells consistently fired the first spike with a substantial delay and generated spike trains interrupted by quiescent periods more often than monkey basket cells. The frequency of miniature excitatory postsynaptic potentials in basket cells was considerably higher in rats than that in monkeys. These differences between rats and monkeys in the electrophysiological properties of PV-positive basket cells may contribute to the differential patterns of neuronal activation observed in rats and monkeys performing working-memory tasks.

Two computational regimes of a single-compartment neuron separated by a planar boundary in conductance space

Recent in vitro data show that neurons respond to input variance with varying sensitivities. Here we demonstrate that Hodgkin-Huxley (HH) neurons can operate in two computational regimes: one that is more sensitive to input variance (differentiating) and one that is less sensitive (integrating). A boundary plane in the 3D conductance space separates these two regimes. For a reduced HH model, this plane can be derived analytically from the V nullcline, thus suggesting a means of relating biophysical parameters to neural computation by analyzing the neuron's dynamical system.

Activity-dependent stochastic resonance in recurrent neuronal networks

We use a biophysical model of a local neuronal circuit to study the implications of synaptic plasticity for the detection of weak sensory stimuli. Networks with fast plastic coupling show behavior consistent with stochastic resonance. The addition of an additional slow coupling that accounts for the asynchronous release of neurotransmitter results in qualitatively different properties of signal detection, and also leads to the appearance of transient post-stimulus bistability. Our results suggest testable hypothesis with regard to the self-organization and dynamics of local neuronal circuits.

Two computational regimes of a single-compartment neuron separated by a planar boundary in conductance space

Recent in vitro data show that neurons respond to input variance with varying sensitivities. Here we demonstrate that Hodgkin-Huxley (HH) neurons can operate in two computational regimes: one that is more sensitive to input variance (differentiating) and one that is less sensitive (integrating). A boundary plane in the 3D conductance space separates these two regimes. For a reduced HH model, this plane can be derived analytically from the V nullcline, thus suggesting a means of relating biophysical parameters to neural computation by analyzing the neuron's dynamical system.

Sensory adaptation

Adaptation occurs in a variety of forms in all sensory systems, motivating the question: what is its purpose? A productive approach has been to hypothesize that adaptation helps neural systems to efficiently encode stimuli whose statistics vary in time. To encode efficiently, a neural system must change its coding strategy, or computation, as the distribution of stimuli changes. Information theoretic methods allow this efficient coding hypothesis to be tested quantitatively. Empirically, adaptive processes occur over a wide range of timescales. On short timescales, underlying mechanisms include the contribution of intrinsic nonlinearities. Over longer timescales, adaptation is often power-law-like, implying the coexistence of multiple timescales in a single adaptive process. Models demonstrate that this can result from mechanisms within a single neuron.

Electrophysiological differences between neurogliaform cells from monkey and rat prefrontal cortex

Current dogma holds that a canonical cortical circuit is formed by cellular elements that are basically identical across species. However, detailed and direct comparisons between species of specific elements of this circuit are limited in number. In this study, we compared the morphological and physiological properties of neurogliaform (NGF) inhibitory neurons in the prefrontal cortex (PFC) of macaque monkeys and rats. In both species, NGF cells were readily identified based on their distinctive morphological features. Indeed, monkey NGF cells had only a few morphological features that differed from rat, including a larger soma, a greater number of dendrites, and a more compact axonal field. In contrast, whole cell recordings of the responses to injected current steps revealed important differences between monkey and rat NGF cells. Monkey NGF cells consistently generated a short-latency first spike riding on an initial depolarizing hump, whereas in rat NGF cells, the first spike appeared after a substantial delay riding on a depolarizing ramp not seen in monkey NGF cells. Thus although rat NGF cells are traditionally classified as late-spiking cells, monkey NGF cells did not meet this physiological criterion. In addition, NGF cells in monkey appeared to be more excitable than those in rat because they displayed a higher input resistance, a lower spike threshold, and a higher firing frequency. Finally, NGF cells in monkey showed a more prominent spike-frequency adaptation as compared with rat. Our findings indicate that the canonical cortical circuit differs in at least some aspects of its constituent elements across species.