Do neocortical pyramidal neurons display stochastic resonance?

The stochastic nature of action potential backpropagation in apical tuft dendrites

In cortical pyramidal neurons, backpropagating action potentials (bAPs) supply Ca²⁺ to synaptic contacts on dendrites. To determine whether the efficacy of AP backpropagation into apical tuft dendrites is stable over time, we performed dendritic Ca²⁺ and voltage imaging in rat brain slices. We found that the amplitude of bAP-Ca²⁺ in apical tuft branches was unstable, given that it varied from trial to trial (termed "bAP-Ca²⁺ flickering"). Small perturbations in dendritic physiology, such as spontaneous synaptic inputs, channel inactivation, or temperature-induced changes in channel kinetics, can cause bAP flickering. In the tuft branches, the density of Na⁺ and K⁺ channels was sufficient to support local initiation of fast spikelets by glutamate iontophoresis. We quantified the time delay between the somatic AP burst and the peak of dendritic Ca²⁺ transient in the apical tuft, because this delay is important for induction of spike-timing dependent plasticity. Depending on the frequency of the somatic AP triplets, Ca²⁺ signals peaked in the apical tuft 20-50 ms after the 1st AP in the soma. Interestingly, at low frequency (<20 Hz), the Ca²⁺ peaked sooner than at high frequency, because only the 1st AP invaded tuft. Activation of dendritic voltage-gated Ca²⁺ channels is sensitive to the duration of the dendritic voltage transient. In apical tuft branches, small changes in the duration of bAP voltage waveforms cause disproportionately large increases in dendritic Ca²⁺ influx (bAP-Ca²⁺ flickering). The stochastic nature of bAP-Ca²⁺ adds a new perspective on the mechanisms by which pyramidal neurons combine inputs arriving at different cortical layers.NEW & NOTEWORTHY The bAP-Ca²⁺ signal amplitudes in some apical tuft branches randomly vary from moment to moment. In repetitive measurements, successful AP invasions are followed by complete failures. Passive spread of voltage from the apical trunk into the tuft occasionally reaches the threshold for local Na⁺ spike, resulting in stronger Ca²⁺ influx. During a burst of three somatic APs, the peak of dendritic Ca²⁺ in the apical tuft occurs with a delay of 20-50 ms depending on AP frequency.

Effects of Small-World Rewiring Probability and Noisy Synaptic Conductivity on Slow Waves: Cortical Network

Physiological rhythms play a critical role in the functional development of living beings. Many biological functions are executed with an interaction of rhythms produced by internal characteristics of scores of cells. While synchronized oscillations may be associated with normal brain functions, anomalies in these oscillations may cause or relate the emergence of some neurological or neuropsychological pathologies. This study was designed to investigate the effects of topological structure and synaptic conductivity noise on the spatial synchronization and temporal rhythmicity of the waves generated by cells in the network. Because of holding the ability of clustering and randomizing with change of parameters, small-world (SW) network topology was chosen. The oscillatory activity of network was tried out by manipulating an insulated SW, cortical network model whose morphology is very close to real world. According to the obtained results, it was observed that at the optimal probabilistic rates of conductivity noise and rewiring of SW, powerful synchronized oscillatory small waves are generated in relation to the internal dynamics of cells, which are in line with the network's input. These two parameters were observed to be quite effective on the excitation-inhibition balance of the network. Accordingly, it may be suggested that the topological dynamics of SW and noisy synaptic conductivity may be associated with the normal and abnormal development of neurobiological structure.

Corticothalamic Synaptic Noise as a Mechanism for Selective Attention in Thalamic Neurons

A reason why the thalamus is more than a passive gateway for sensory signals is that two-third of the synapses of thalamocortical neurons are directly or indirectly related to the activity of corticothalamic axons. While the responses of thalamocortical neurons evoked by sensory stimuli are well characterized, with ON- and OFF-center receptive field structures, the prevalence of synaptic noise resulting from neocortical feedback in intracellularly recorded thalamocortical neurons in vivo has attracted little attention. However, in vitro and modeling experiments point to its critical role for the integration of sensory signals. Here we combine our recent findings in a unified framework suggesting the hypothesis that corticothalamic synaptic activity is adapted to modulate the transfer efficiency of thalamocortical neurons during selective attention at three different levels: First, on ionic channels by interacting with intrinsic membrane properties, second at the neuron level by impacting on the input-output gain, and third even more effectively at the cell assembly level by boosting the information transfer of sensory features encoded in thalamic subnetworks. This top-down population control is achieved by tuning the correlations in subthreshold membrane potential fluctuations and is adapted to modulate the transfer of sensory features encoded by assemblies of thalamocortical relay neurons. We thus propose that cortically-controlled (de-)correlation of subthreshold noise is an efficient and swift dynamic mechanism for selective attention in the thalamus.

Restoring the encoding properties of a stochastic neuron model by an exogenous noise

Here we evaluate the possibility of improving the encoding properties of an impaired neuronal system by superimposing an exogenous noise to an external electric stimulation signal. The approach is based on the use of mathematical neuron models consisting of stochastic HH-like circuit, where the impairment of the endogenous presynaptic inputs is described as a subthreshold injected current and the exogenous stimulation signal is a sinusoidal voltage perturbation across the membrane. Our results indicate that a correlated Gaussian noise, added to the sinusoidal signal can significantly increase the encoding properties of the impaired system, through the Stochastic Resonance (SR) phenomenon. These results suggest that an exogenous noise, suitably tailored, could improve the efficacy of those stimulation techniques used in neuronal systems, where the presynaptic sensory neurons are impaired and have to be artificially bypassed.

Branch specific and spike-order specific action potential invasion in basal, oblique, and apical dendrites of cortical pyramidal neurons

In neocortical pyramidal neurons, action potentials (APs) propagate from the axon into the dendritic tree to influence distal synapses. Traditionally, AP backpropagation was studied in the thick apical trunk. Here, we used the principles of optical imaging developed by Cohen to investigate AP invasion into thin dendritic branches (basal, oblique, and tuft) of prefrontal cortical L5 pyramidal neurons. Multisite optical recordings from neighboring dendrites revealed a clear dichotomy between two seemingly equal dendritic branches belonging to the same cell ("sister branches"). We documented the variable efficacy of AP invasion in basal and oblique branches by revealing their AP voltage waveforms. Using fast multisite calcium imaging, we found that trains of APs are filtered differently between two apical tuft branches. Although one dendritic branch passes all spikes in an AP train, another branch belonging to the same neuron, same cortical layer, and same path distance from the cell body, experiences only one spike. Our data indicate that the vast differences in dendritic voltage and calcium transients, detected in dendrites of pyramidal neurons, arise from a nonuniform distribution of A-type [Formula: see text] conductance, an aggregate number of branch points in the path of the AP propagation and minute differences in dendritic diameter.

A review of methods for identifying stochastic resonance in simulations of single neuron models

Stochastic resonance (SR) is said to be observed when the presence of noise in a nonlinear system enables an output signal from the system to better represent some feature of an input signal than it does in the absence of noise. The effect has been observed in models of individual neurons, and in experiments performed on real neural systems. Despite the ubiquity of biophysical sources of stochastic noise in the nervous system, however, it has not yet been established whether neuronal computation mechanisms involved in performance of specific functions such as perception or learning might exploit such noise as an integral component, such that removal of the noise would diminish performance of these functions. In this paper we revisit the methods used to demonstrate stochastic resonance in models of single neurons. This includes a previously unreported observation in a multicompartmental model of a CA1-pyramidal cell. We also discuss, as a contrast to these classical studies, a form of 'stochastic facilitation', known as inverse stochastic resonance. We draw on the reviewed examples to argue why new approaches to studying 'stochastic facilitation' in neural systems need to be developed.

A transition to sharp timing in stochastic leaky integrate-and-fire neurons driven by frozen noisy input

The firing activity of intracellularly stimulated neurons in cortical slices has been demonstrated to be profoundly affected by the temporal structure of the injected current (Mainen & Sejnowski, 1995 ). This suggests that the timing features of the neural response may be controlled as much by its own biophysical characteristics as by how a neuron is wired within a circuit. Modeling studies have shown that the interplay between internal noise and the fluctuations of the driving input controls the reliability and the precision of neuronal spiking (Cecchi et al., 2000 ; Tiesinga, 2002 ; Fellous, Rudolph, Destexhe, & Sejnowski, 2003 ). In order to investigate this interplay, we focus on the stochastic leaky integrate-and-fire neuron and identify the Hölder exponent H of the integrated input as the key mathematical property dictating the regime of firing of a single-unit neuron. We have recently provided numerical evidence (Taillefumier & Magnasco, 2013 ) for the existence of a phase transition when [Formula: see text] becomes less than the statistical Hölder exponent associated with internal gaussian white noise (H=1/2). Here we describe the theoretical and numerical framework devised for the study of a neuron that is periodically driven by frozen noisy inputs with exponent H>0. In doing so, we account for the existence of a transition between two regimes of firing when H=1/2, and we show that spiking times have a continuous density when the Hölder exponent satisfies H>1/2. The transition at H=1/2 formally separates rate codes, for which the neural firing probability varies smoothly, from temporal codes, for which the neuron fires at sharply defined times regardless of the intensity of internal noise.

Cortically-controlled population stochastic facilitation as a plausible substrate for guiding sensory transfer across the thalamic gateway

The thalamus is the primary gateway that relays sensory information to the cerebral cortex. While a single recipient cortical cell receives the convergence of many principal relay cells of the thalamus, each thalamic cell in turn integrates a dense and distributed synaptic feedback from the cortex. During sensory processing, the influence of this functional loop remains largely ignored. Using dynamic-clamp techniques in thalamic slices in vitro, we combined theoretical and experimental approaches to implement a realistic hybrid retino-thalamo-cortical pathway mixing biological cells and simulated circuits. The synaptic bombardment of cortical origin was mimicked through the injection of a stochastic mixture of excitatory and inhibitory conductances, resulting in a gradable correlation level of afferent activity shared by thalamic cells. The study of the impact of the simulated cortical input on the global retinocortical signal transfer efficiency revealed a novel control mechanism resulting from the collective resonance of all thalamic relay neurons. We show here that the transfer efficiency of sensory input transmission depends on three key features: i) the number of thalamocortical cells involved in the many-to-one convergence from thalamus to cortex, ii) the statistics of the corticothalamic synaptic bombardment and iii) the level of correlation imposed between converging thalamic relay cells. In particular, our results demonstrate counterintuitively that the retinocortical signal transfer efficiency increases when the level of correlation across thalamic cells decreases. This suggests that the transfer efficiency of relay cells could be selectively amplified when they become simultaneously desynchronized by the cortical feedback. When applied to the intact brain, this network regulation mechanism could direct an attentional focus to specific thalamic subassemblies and select the appropriate input lines to the cortex according to the descending influence of cortically-defined “priors”.

Most of the sensory information in the early visual system is relayed from the retina to the primary visual cortex through principal relay cells in the thalamus. While relay cells receive ∼7–16% of their synapses from retina, they integrate the synaptic barrage of a dense cortical feedback, which accounts for more than 60% of their total input. This feedback is thought to carry some form of “prior” resulting from the computation performed in cortical areas, which influences the response of relay cells, presumably by regulating the transfer of sensory information to cortical areas. Nevertheless, its statistical nature (input synchronization, excitation/inhibition ratio, etc.) and the cellular mechanisms gating thalamic transfer are largely ignored. Here we implemented hybrid circuits (biological and modeled cells) reproducing the main features of the thalamic gate and explored the functional impact of various statistics of the cortical input. We found that the regulation of sensory information is critically determined by the statistical coherence of the cortical synaptic bombardment associated with a stochastic facilitation process. We propose that this tuning mechanism could operate in the intact brain to selectively filter the sensory information reaching cortical areas according to attended features predesignated by the cortical feedback.

Stochastic resonance induced by exogenous noise in a model of a neuronal network

This study investigates the possibility of using exogenous noise to restore the processing performances of neuronal systems where the endogenous noise is reduced due to the ageing or to degenerative diseases. This idea is based on the assumption, supported by theoretical studies, that the endogenous noise has a positive role in neuronal signal detection and that its reduction impairs the system function. Results, obtained on a two-layers feedforward network, show the onset of the Stochastic Resonance (SR) behavior, as long as the exogenous noise is properly tailored and filtered. The amount of noise to be furnished from the outside to optimize the system performance depends on the residual level of endogenous noise, indicating that both kinds of noise cooperate to the signal detection. These results support potentially new bioengineering applications where exogenous noise is furnished to enhance signal detectability.

Resonance in neocortical neurons and networks

Neocortical networks produce oscillations that often correspond to characteristic physiological or pathological patterns. However, the mechanisms underlying the generation of and the transitions between such oscillatory states remain poorly understood. In this study, we examined resonance in mouse layer V neocortical pyramidal neurons. To accomplish this, we employed standard electrophysiology to describe cellular resonance parameters. Bode plot analysis revealed a range of resonance magnitude values in layer V neurons and demonstrated that both magnitude and phase response characteristics of layer V neocortical pyramidal neurons are modulated by changes in the extracellular environment. Specifically, increased resonant frequencies and total inductive areas were observed at higher extracellular potassium concentrations and more hyperpolarised membrane potentials. Experiments using pharmacological agents suggested that current through hyperpolarization-activated cyclic nucleotide-gated channels (I(h) ) acts as the primary driver of resonance in these neurons, with other potassium currents, such as A-type potassium current and delayed-rectifier potassium current (Kv1.4 and Kv1.1, respectively), contributing auxiliary roles. The persistent sodium current was also shown to play a role in amplifying the magnitude of resonance without contributing significantly to the phase response. Although resonance effects in individual neurons are small, their properties embedded in large networks may significantly affect network behavior and may have potential implications for pathological processes.

Temporal order detection and coding in nervous systems

This letter discusses temporal order coding and detection in nervous systems. Detection of temporal order in the external world is an adaptive function of nervous systems. In addition, coding based on the temporal order of signals can be used as an internal code. Such temporal order coding is a subset of temporal coding. We discuss two examples of processing the temporal order of external events: the auditory location detection system in birds and the visual direction detection system in flies. We then discuss how somatosensory stimulus intensities are translated into a temporal order code in the human peripheral nervous system. We next turn our attention to input order coding in the mammalian cortex. We review work demonstrating the capabilities of cortical neurons for detecting input order. We then discuss research refuting and demonstrating the representation of stimulus features in the cortex by means of input order. After some general theoretical considerations on input order detection and coding, we conclude by discussing the existing and potential use of input order coding in neuromorphic engineering.

Optimal spike-based communication in excitable networks with strong-sparse and weak-dense links

The connectivity of complex networks and functional implications has been attracting much interest in many physical, biological and social systems. However, the significance of the weight distributions of network links remains largely unknown except for uniformly- or Gaussian-weighted links. Here, we show analytically and numerically, that recurrent neural networks can robustly generate internal noise optimal for spike transmission between neurons with the help of a long-tailed distribution in the weights of recurrent connections. The structure of spontaneous activity in such networks involves weak-dense connections that redistribute excitatory activity over the network as noise sources to optimally enhance the responses of individual neurons to input at sparse-strong connections, thus opening multiple signal transmission pathways. Electrophysiological experiments confirm the importance of a highly broad connectivity spectrum supported by the model. Our results identify a simple network mechanism for internal noise generation by highly inhomogeneous connection strengths supporting both stability and optimal communication.

Emergence of resonances in neural systems: the interplay between adaptive threshold and short-term synaptic plasticity

In this work we study the detection of weak stimuli by spiking (integrate-and-fire) neurons in the presence of certain level of noisy background neural activity. Our study has focused in the realistic assumption that the synapses in the network present activity-dependent processes, such as short-term synaptic depression and facilitation. Employing mean-field techniques as well as numerical simulations, we found that there are two possible noise levels which optimize signal transmission. This new finding is in contrast with the classical theory of stochastic resonance which is able to predict only one optimal level of noise. We found that the complex interplay between adaptive neuron threshold and activity-dependent synaptic mechanisms is responsible for this new phenomenology. Our main results are confirmed by employing a more realistic FitzHugh-Nagumo neuron model, which displays threshold variability, as well as by considering more realistic stochastic synaptic models and realistic signals such as poissonian spike trains.

Multimodal transition and stochastic antiresonance in squid giant axons

The experimental data of Takahashi [Physica D 43, 318 (1990)], on the response of squid giant axons stimulated by periodic sequence of short current pulses is interpreted within the Hodgkin-Huxley model. The minimum of the firing rate as a function of the stimulus amplitude I0 in the high-frequency regime is due to the multimodal transition. Below this singular point only odd multiples of the driving period remain and the system is sensitive to noise. The coefficient of variation has a maximum and the firing rate has a minimum as a function of the noise intensity, which is an indication of the stochastic coherence antiresonance. The model calculations reproduce the frequency of occurrence of the most common modes in the vicinity of the transition. A linear relation of output frequency vs I0 above the transition is also confirmed.

Diverse antiepileptic drugs increase the ratio of background synaptic inhibition to excitation and decrease neuronal excitability in neurones of the rat entorhinal cortex in vitro

Although most anti-epileptic drugs are considered to have a primary molecular target, it is clear that their actions are unlikely to be limited to effects on a single aspect of inhibitory synaptic transmission, excitatory transmission or voltage-gated ion channels. Systemically administered drugs can obviously simultaneously access all possible targets, so we have attempted to determine the overall effect of diverse agents on the balance between GABAergic inhibition, glutamatergic excitation and cellular excitability in neurones of the rat entorhinal cortex in vitro. We used an approach developed for estimating global background synaptic excitation and inhibition from fluctuations in membrane potential obtained by intracellular recordings. We have previously validated this approach in entorhinal cortical neurones [Greenhill and Jones (2007a) Neuroscience 147:884–892]. Using this approach, we found that, despite their differing pharmacology, the drugs tested (phenytoin, lamotrigine, valproate, gabapentin, felbamate, tiagabine) were unified in their ability to increase the ratio of background GABAergic inhibition to glutamatergic excitation. This could occur as a result of decreased excitation concurrent with increased inhibition (phenytoin, lamotrigine, valproate), a decrease in excitation alone (gabapentin, felbamate), or even with a differential increase in both (tiagabine). Additionally, we found that the effects on global synaptic conductances agreed well with whole cell patch recordings of spontaneous glutamate and GABA release (our previous studies and further data presented here). The consistency with which the synaptic inhibition:excitation ratio was increased by the antiepileptic drugs tested was matched by an ability of all drugs to concurrently reduce intrinsic neuronal excitability. Thus, it seems possible that specific molecular targets among antiepileptic drugs are less important than the ability to increase the inhibition:excitation ratio and reduce overall neuronal and network excitability.

Gap junctions between striatal fast-spiking interneurons regulate spiking activity and synchronization as a function of cortical activity

Striatal fast-spiking (FS) interneurons are interconnected by gap junctions into sparsely connected networks. As demonstrated for cortical FS interneurons, these gap junctions in the striatum may cause synchronized spiking, which would increase the influence that FS neurons have on spiking by the striatal medium spiny (MS) neurons. Dysfunction of the basal ganglia is characterized by changes in synchrony or periodicity, thus gap junctions between FS interneurons may modulate synchrony and thereby influence behavior such as reward learning and motor control. To explore the roles of gap junctions on activity and spike synchronization in a striatal FS population, we built a network model of FS interneurons. Each FS connects to 30-40% of its neighbors, as found experimentally, and each FS interneuron in the network is activated by simulated corticostriatal synaptic inputs. Our simulations show that the proportion of synchronous spikes in FS networks with gap junctions increases with increased conductance of the electrical synapse; however, the synchronization effects are moderate for experimentally estimated conductances. Instead, the main tendency is that the presence of gap junctions reduces the total number of spikes generated in response to synaptic inputs in the network. The reduction in spike firing is due to shunting through the gap junctions; which is minimized or absent when the neurons receive coincident inputs. Together these findings suggest that a population of electrically coupled FS interneurons may function collectively as input detectors that are especially sensitive to synchronized synaptic inputs received from the cortex.

Stochastic differential equation model for cerebellar granule cell excitability

Neurons in the brain express intrinsic dynamic behavior which is known to be stochastic in nature. A crucial question in building models of neuronal excitability is how to be able to mimic the dynamic behavior of the biological counterpart accurately and how to perform simulations in the fastest possible way. The well-established Hodgkin-Huxley formalism has formed to a large extent the basis for building biophysically and anatomically detailed models of neurons. However, the deterministic Hodgkin-Huxley formalism does not take into account the stochastic behavior of voltage-dependent ion channels. Ion channel stochasticity is shown to be important in adjusting the transmembrane voltage dynamics at or close to the threshold of action potential firing, at the very least in small neurons. In order to achieve a better understanding of the dynamic behavior of a neuron, a new modeling and simulation approach based on stochastic differential equations and Brownian motion is developed. The basis of the work is a deterministic one-compartmental multi-conductance model of the cerebellar granule cell. This model includes six different types of voltage-dependent conductances described by Hodgkin-Huxley formalism and simple calcium dynamics. A new model for the granule cell is developed by incorporating stochasticity inherently present in the ion channel function into the gating variables of conductances. With the new stochastic model, the irregular electrophysiological activity of an in vitro granule cell is reproduced accurately, with the same parameter values for which the membrane potential of the original deterministic model exhibits regular behavior. The irregular electrophysiological activity includes experimentally observed random subthreshold oscillations, occasional spontaneous spikes, and clusters of action potentials. As a conclusion, the new stochastic differential equation model of the cerebellar granule cell excitability is found to expand the range of dynamics in comparison to the original deterministic model. Inclusion of stochastic elements in the operation of voltage-dependent conductances should thus be emphasized more in modeling the dynamic behavior of small neurons. Furthermore, the presented approach is valuable in providing faster computation times compared to the Markov chain type of modeling approaches and more sophisticated theoretical analysis tools compared to previously presented stochastic modeling approaches.

Computational modeling is of importance in striving to understand the complex dynamic behavior of a neuron. In neuronal modeling, the function of the neuron's components, including the cell membrane and voltage-dependent ion channels, is typically described using deterministic ordinary differential equations that always provide the same model output when repeating computer simulations with fixed model parameter values. It is well known, however, that the behavior of neurons and voltage-dependent ion channels is stochastic in nature. A stochastic modeling approach based on probabilistically describing the transition rates of ion channels has therefore gained interest due to its ability to produce more accurate results than the deterministic approaches. These Markov chain type of models are, however, relatively time-consuming to simulate. Thus it is important to develop new modeling and simulation approaches that take into account the stochasticity inherently present in the function of ion channels. In this study, we seek new stochastic methods for modeling the dynamic behavior of neurons. We apply stochastic differential equations (SDEs) and Brownian motion that are also commonly used in the air space industry and in economics. An SDE is a differential equation in which one or more of the terms of the mathematical equation are stochastic processes. Computer simulations show that the irregular firing behavior of a small neuron, in our case the cerebellar granule cell, is reproduced more accurately in comparison to previous deterministic models. Furthermore, the computation is performed in a relatively fast manner compared to previous stochastic approaches. Additionally, the SDE method provides more sophisticated mathematical analysis tools compared to other, similar kinds of stochastic approaches. In the future, the new SDE model of the cerebellar granule cell can be used in studying the emergent behavior of cerebellar neural network circuitry.

Kinetic models of spike-timing dependent plasticity and their functional consequences in detecting correlations

Spike-timing dependent plasticity (STDP) is a type of synaptic modification found relatively recently, but the underlying biophysical mechanisms are still unclear. Several models of STDP have been proposed, and differ by their implementation, and in particular how synaptic weights saturate to their minimal and maximal values. We analyze here kinetic models of transmitter-receptor interaction and derive a series of STDP models. In general, such kinetic models predict progressive saturation of the weights. Various forms can be obtained depending on the hypotheses made in the kinetic model, and these include a simple linear dependence on the value of the weight ("soft bounds"), mixed soft and abrupt saturation ("hard bound"), or more complex forms. We analyze in more detail simple soft-bound models of Hebbian and anti-Hebbian STDPs, in which nonlinear spike interactions (triplets) are taken into account. We show that Hebbian STDPs can be used to selectively potentiate synapses that are correlated in time, while anti-Hebbian STDPs depress correlated synapses, despite the presence of nonlinear spike interactions. This correlation detection enables neurons to develop a selectivity to correlated inputs. We also examine different versions of kinetics-based STDP models and compare their sensitivity to correlations. We conclude that kinetic models generally predict soft-bound dynamics, and that such models seem ideal for detecting correlations among large numbers of inputs.

Simultaneous estimation of global background synaptic inhibition and excitation from membrane potential fluctuations in layer III neurons of the rat entorhinal cortex in vitro

It is becoming clear that the detection and integration of synaptic input and its conversion into an output signal in cortical neurons are strongly influenced by background synaptic activity or “noise.” The majority of this noise results from the spontaneous release of synaptic transmitters, interacting with ligand-gated ion channels in the postsynaptic neuron [Berretta N, Jones RSG (1996); A comparison of spontaneous synaptic EPSCs in layer V and layer II neurones in the rat entorhinal cortex in vitro. J Neurophysiol 76:1089–1110; Jones RSG, Woodhall GL (2005) Background synaptic activity in rat entorhinal cortical neurons: differential control of transmitter release by presynaptic receptors. J Physiol 562:107–120; LoTurco JJ, Mody I, Kriegstein AR (1990) Differential activation of glutamate receptors by spontaneously released transmitter in slices of neocortex. Neurosci Lett 114:265–271; Otis TS, Staley KJ, Mody I (1991) Perpetual inhibitory activity in mammalian brain slices generated by spontaneous GABA release. Brain Res 545:142–150; Ropert N, Miles R, Korn H (1990) Characteristics of miniature inhibitory postsynaptic currents in CA1 pyramidal neurones of rat hippocampus. J Physiol 428:707–722; Salin PA, Prince DA (1996) Spontaneous GABA_A receptor-mediated inhibitory currents in adult rat somatosensory cortex. J Neurophysiol 75:1573–1588; Staley KJ (1999) Quantal GABA release: noise or not? Nat Neurosci 2:494–495; Woodhall GL, Bailey SJ, Thompson SE, Evans DIP, Stacey AE, Jones RSG (2005) Fundamental differences in spontaneous synaptic inhibition between deep and superficial layers of the rat entorhinal cortex. Hippocampus 15:232–245]. The function of synaptic noise has been the subject of debate for some years, but there is increasing evidence that it modifies or controls neuronal excitability and, thus, the integrative properties of cortical neurons. In the present study we have investigated a novel approach [Rudolph M, Piwkowska Z, Badoual M, Bal T, Destexhe A (2004) A method to estimate synaptic conductances from membrane potential fluctuations. J Neurophysiol 91:2884–2896] to simultaneously quantify synaptic inhibitory and excitatory synaptic noise, together with postsynaptic excitability, in rat entorhinal cortical neurons in vitro. The results suggest that this is a viable and useful approach to the study of the function of synaptic noise in cortical networks.

Diversity of gain modulation by noise in neocortical neurons: regulation by the slow afterhyperpolarization conductance

Neuronal firing is known to depend on the variance of synaptic input as well as the mean input current. Several studies suggest that input variance, or "noise," has a divisive effect, reducing the slope or gain of the firing frequency-current (f-I) relationship. We measured the effects of current noise on f-I relationships in pyramidal neurons and fast-spiking (FS) interneurons in slices of rat sensorimotor cortex. In most pyramidal neurons, noise had a multiplicative effect on the steady-state f-I relationship, increasing gain. In contrast, noise reduced gain in FS interneurons. Gain enhancement in pyramidal neurons increased with stimulus duration and was correlated with the amplitude of the slow afterhyperpolarization (sAHP), a major mechanism of spike-frequency adaptation. The 5-HT2 receptor agonist alpha-methyl-5-HT reduced the sAHP and eliminated gain increases, whereas augmenting the sAHP conductance by spike-triggered dynamic-current clamp enhanced the gain increase. These results indicate that the effects of noise differ fundamentally between classes of neocortical neurons, depending on specific biophysical properties including the sAHP conductance. Thus, noise from background synaptic input may enhance network excitability by increasing gain in pyramidal neurons with large sAHPs and reducing gain in inhibitory FS interneurons.

Inferring network activity from synaptic noise

During intense network activity in vivo, cortical neurons are in a high-conductance state, in which the membrane potential (V(m)) is subject to a tremendous fluctuating activity. Clearly, this "synaptic noise" contains information about the activity of the network, but there are presently no methods available to extract this information. We focus here on this problem from a computational neuroscience perspective, with the aim of drawing methods to analyze experimental data. We start from models of cortical neurons, in which high-conductance states stem from the random release of thousands of excitatory and inhibitory synapses. This highly complex system can be simplified by using global synaptic conductances described by effective stochastic processes. The advantage of this approach is that one can derive analytically a number of properties from the statistics of resulting V(m) fluctuations. For example, the global excitatory and inhibitory conductances can be extracted from synaptic noise, and can be related to the mean activity of presynaptic neurons. We show here that extracting the variances of excitatory and inhibitory synaptic conductances can provide estimates of the mean temporal correlation-or level of synchrony-among thousands of neurons in the network. Thus, "probing the network" through intracellular V(m) activity is possible and constitutes a promising approach, but it will require a continuous effort combining theory, computational models and intracellular physiology.

Using potassium currents to solve signal-to-noise problems in inhibitory feedforward networks of the striatum

Fast-spiking (FS) interneurons provide the main route of feedforward inhibition from cortex to spiny projection neurons in the striatum. A steep current-firing frequency curve and a dense local axonal arbor suggest that even small excitatory inputs could translate into powerful feedforward inhibition, although such an arrangement is also sensitive to amplification of spurious synaptic inputs. We show that a transient potassium (KA) current allows the FS interneuron to strike a balance between sensitivity to correlated input and robustness to noise, thereby increasing its signal-to-noise ratio (SNR). First, a compartmental FS neuron model was created to match experimental data from striatal FS interneurons in cortex-striatum-substantia nigra organotypic cultures. Densities of sodium, delayed rectifier, and KA channels were optimized to replicate responses to somatic current injection. Spontaneous alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) and gamma-aminobutyric acid (GABA) synaptic currents were adjusted to the experimentally measured amplitude, rise time, and interevent interval histograms. Second, two additional adjustments were required to emulate the remaining experimental observations. GABA channels were localized closer to the soma than AMPA channels to match the synaptic population reversal potential. Correlation among inputs was required to produce the observed firing rate during up-states. In this final model, KA channels were essential for suppressing down-state spikes while allowing reliable spike generation during up-states. This mechanism was particularly important under conditions of high dopamine. Our results suggest that KA channels allow FS interneurons to operate without a decrease in SNR during conditions of increased dopamine, as occurs in response to reward or anticipated reward.

Stochastic resonance with differential code in feedforward network with intra-layer random connections

We examined stochastic resonance with a differential coding scheme using a multilayer feedforward neural network which is composed of intra-layer connections. We show that the network, with random synaptic connections in each layer, encodes an input signal into a spike coherence that represents temporal differences among the inputs. We also demonstrate that both internal and external noise enhance the detection of weak signals. Finally, we discuss how the feedforward network with intra-layer random connections is similar to a membrane in its sensitivity to and amplification of a change in stimulus and suggest that the intensity of internal noise may be tuned in a real brain.

Encoding and decoding target locations with waves in the turtle visual cortex

Visual stimuli elicit waves of activity that propagate across the visual cortex of turtles. An earlier study showed that these waves encode information about the positions of stimuli in visual space. This paper addresses the question of how this information can be decoded from the waves. Windowing techniques were used to temporally localize information contained in the wave. Sliding encoding windows were used to represent waves of activity as low dimensional temporal strands in an appropriate space. Expanding detection window (EDW) or sliding detection window (SDW) techniques were combined with statistical hypothesis testing to discriminate input stimuli. Detection based on an EDW was more reliable than detection based on a SDW. Detection performance improved at a very early stage of the cortical response as the length of the detection window is increased. The property of intrinsic noise was explicitly considered. Assuming that the noise is colored provided a more reliable estimate than did the assumption of a white noise in the cortical output.

Membrane resonance and stochastic resonance modulate firing patterns of thalamocortical neurons

We examined the interactions of subthreshold membrane resonance and stochastic resonance using whole-cell patch clamp recordings in thalamocortical neurons of rat brain slices, as well as with a Hodgkin-Huxley-type mathematical model of thalamocortical neurons. The neurons exhibited the subthreshold resonance when stimulated with small amplitude sine wave currents of varying frequency, and stochastic resonance when noise was added to sine wave inputs. Stochastic resonance was manifest as a maximum in signal-to-noise ratio of output response to subthreshold periodic input combined with noise. Stochastic resonance in conjunction with subthreshold resonance resulted in action potential patterns that showed frequency selectivity for periodic inputs. Stochastic resonance was maximal near subthreshold resonance frequency and a high noise level was required for detection of high frequency signals. We speculate that combined membrane and stochastic resonances have physiological utility in coupling synaptic activity to preferred firing frequency and in network synchronization under noise.

Impact of spatially correlated noise on neuronal firing

We explore the impact of spatially correlated noise on neuronal firing when uncoupled Hodgkin-Huxley model neurons are subjected to a common subthreshold signal. Noise can play a positive role in optimizing neuronal behavior. Although the output signal-to-noise ratio decreases with enhanced noise correlation, both the degree of synchronization among neurons and the spike timing precision are improved. This suggests that there can exist precisely synchronized firings in the presence of correlated noise and that the nervous system can exploit temporal patterns of neural activity to convey more information than just using rate codes. The mechanisms underlying these noise-induced effects are also discussed in detail.

Characterization of Subthreshold Voltage Fluctuations in Neuronal Membranes

Synaptic noise due to intense network activity can have a significant impact on the electrophysiological properties of individual neurons. This is the case for the cerebral cortex, where ongoing activity leads to strong barrages of synaptic inputs, which act as the main source of synaptic noise affecting on neuronal dynamics. Here, we characterize the sub-threshold behavior of neuronal models in which synaptic noise is represented by either additive or multiplicative noise, described by Ornstein-Uhlenbeck processes. We derive and solve the Fokker-Planck equation for this system, which describes the time evolution of the probability density function for the membrane potential. We obtain an analytic expression for the membrane potential distribution at steady state and compare this expression with the subthreshold activity obtained in Hodgkin-Huxley-type models with stochastic synaptic inputs. The differences between multiplicative and additive noise models suggest that multiplicative noise is adequate to describe the high-conductance states similar to in vivo conditions. Because the steady-state membrane potential distribution is easily obtained experimentally, this approach provides a possible method to estimate the mean and variance of synaptic conduct ancesinreal neurons.

Active dendrites and spike propagation in multi-compartment models of oriens-lacunosum/moleculare hippocampal interneurons

It is well known that interneurons are heterogeneous in their morphologies, biophysical properties, pharmacological sensitivities and electrophysiological responses, but it is unknown how best to understand this diversity. Given their critical roles in shaping brain output, it is important to try to understand the functionality of their computational characteristics. To do this, we focus on specific interneuron subtypes. In particular, it has recently been shown that long-term potentiation is induced specifically on oriens-lacunosum/moleculare (O-LM) interneurons in hippocampus CA1 and that the same cells contain the highest density of dendritic sodium and potassium conductances measured to date. We have created multi-compartment models of an O-LM hippocampal interneuron using passive properties, channel kinetics, densities and distributions specific to this cell type, and explored its signalling characteristics. We found that spike initiation depends on both location and amount of input, as well as the intrinsic properties of the interneuron. Distal synaptic input always produces strong back-propagating spikes whereas proximal input could produce both forward- and back-propagating spikes depending on the input strength. We speculate that the highly active dendrites of these interneurons endow them with a specialized function within the hippocampal circuitry by allowing them to regulate direct and indirect signalling pathways within the hippocampus.

The discharge variability of neocortical neurons during high-conductance states

In vivo recordings have shown that the discharge of cortical neurons is often highly variable and can have statistics similar to a Poisson process with a coefficient of variation around unity. To investigate the determinants of this high variability, we analyzed the spontaneous discharge of Hodgkin-Huxley type models of cortical neurons, in which in vivo-like synaptic background activity was modeled by random release events at excitatory and inhibitory synapses. By using compartmental models with active dendrites, or single compartment models with fluctuating conductances and fluctuating currents, we found that a high discharge variability was always paralleled with a high-conductance state, while some active and passive cellular properties had only a minor impact. Furthermore, a balance between excitation and inhibition was not a necessary condition for high discharge variability. We conclude that the fluctuating high-conductance state caused by the ongoing activity in the cortical network in vivo may be viewed as a natural determinant of the highly variable discharges of these neurons.

A novel mechanism for irregular firing of a neuron in response to periodic stimulation: irregularity in the absence of noise

Irregular firing of action potentials (AP's) is a characteristic feature of neurons in the brain. The variability has been attributed to noise from various sources. This study illustrates an alternative mechanism, namely, deterministic irregularity within a model of ionic conductances. Specifically, a model based on modern measurements of the Na+ and K+ current components from the squid giant axon fires irregularly in response to a continuous train of near-threshold current pulses. The interspike interval histogram from these simulations is multi-modal, a result which in other systems has been attributed to stochastic resonance. Moreover, the simulations exhibited short burst of spikes followed by relatively long quiescent periods, a result suggestive of patterned input to the model even though the input consisted of a train of regularly spaced current pulses. The variability of firing is attributable to variations in AP parameters, in particular AP amplitude. The action potential for squid giant axons is not all-or-none. Rather, it is fundamentally a continuous function of stimulus amplitude. That is, the membrane lacks a threshold. Variation in AP amplitude, and to a lesser extent, AP duration, can produce variations in the time to a subsequent AP, which represents a paradigm shift for understanding irregular neuronal firing. The emphasis is not as much on events prior to an AP as it is on the AP's themselves.

Optimal noise-aided signal transmission through populations of neurons

Metabolic considerations and neurophysiological measurements indicate that biological neural systems prefer information transmission via many parallel low intensity channels, compared to few high intensity ones [S. B. Laughlin et al., Nature Neurosci. 1, 36 (1998)]. Furthermore, cortical neurons are exposed to a considerable amount of synaptic background activity, which increases the neurons' conductance and leads to a fluctuating membrane potential that, on average, is close to the threshold [A. Destexhe and D. Paré, J. Neurophysiol. 81, 1531 (1999)]. Recent studies have shown that noise can improve the transmission of subthreshold signals in populations of neurons, e.g., if their response is pooled. In general, the optimal noise level depends on the stimulus distribution and on the number of neurons in the population. In this contribution we show that for a large enough number of neurons the latter dependency becomes weak, such that the optimal noise level becomes almost independent of the number of neurons in the population. First we investigate a binary threshold model of neurons. We derive an analytic expression for the optimal noise level at each single neuron, which-for a large enough population size-depends only on quantities that are locally available to a single neuron. Using numerical simulations, we then verify the weak dependence of the optimal noise level on population size in a more realistic framework using leaky integrate-and-fire as well as Hodgkin-Huxley-type model neurons. Next we construct a cost function, where quality of information transmission is traded against its metabolic costs. Again we find that-for subthreshold signals-there is an optimal noise level which maximizes this cost. This noise level, however, is almost independent of the number of neurons, even for small population sizes, as numerical simulations using the Hodgkin-Huxley model show. Since the dependence of the optimal noise level on population size is weak for large enough populations, local neural adaptation is sufficient to adjust the level of noise to its optimal value.

Tuning neocortical pyramidal neurons between integrators and coincidence detectors

Do cortical neurons operate as integrators or as coincidence detectors? Despite the importance of this question, no definite answer has been given yet, because each of these two views can find its own experimental support. Here we investigated this question using models of morphologically-reconstructed neocortical pyramidal neurons under in vivo like conditions. In agreement with experiments we find that the cell is capable of operating in a continuum between coincidence detection and temporal integration, depending on the characteristics of the synaptic inputs. Moreover, the presence of synaptic background activity at a level comparable to intracellular measurements in vivo can modulate the operating mode of the cell, and act as a switch between temporal integration and coincidence detection. These results suggest that background activity can be viewed as an important determinant of the integrative mode of pyramidal neurons. Thus, background activity not only sharpens cortical responses but it can also be used to tune an entire network between integration and coincidence detection modes.

Sequential movement representations based on correlated neuronal activity

We tested the hypothesis that sequential movements are represented in the correlated activity of motor cortical neurons. We simultaneously recorded multiple single neurons in the motor cortex while monkeys performed a two-segment movement sequence. Before any movement began the correlated spike firing between pairs of neurons differed when these sequences were planned as whole (planned) as compared to when they were planned one segment at a time (unplanned) even when the firing rates of these neurons did not distinguish between the two conditions. Moreover, the correlation strength was significantly larger when the directional preferences of the neurons matched the direction of the final segment of the sequence. Our results suggest that spatially distributed groups of MI neurons form dynamic correlation structures that distinguish different forms of sequential action.