Dynamics of neuronal firing modulated by high-frequency electrical pulse stimulations at axons in rat hippocampus

Objective. The development of electrical pulse stimulations in brain, including deep brain stimulation, is promising for treating various brain diseases. However, the mechanisms of brain stimulations are not yet fully understood. Previous studies have shown that the commonly used high-frequency stimulation (HFS) can increase the firing of neurons and modulate the pattern of neuronal firing. Because the generation of neuronal firing in brain is a nonlinear process, investigating the characteristics of nonlinear dynamics induced by HFS could be helpful to reveal more mechanisms of brain stimulations. The aim of present study is to investigate the fractal properties in the neuronal firing generated by HFS.Approach. HFS pulse sequences with a constant frequency 100 Hz were applied in the afferent fiber tracts of rat hippocampal CA1 region. Unit spikes of both the pyramidal cells and the interneurons in the downstream area of stimulations were recorded. Two fractal indexes-the Fano factor and Hurst exponent were calculated to evaluate the changes of long-range temporal correlations (LRTCs), a typical characteristic of fractal process, in spike sequences of neuronal firing.Mainresults. Neuronal firing at both baseline and during HFS exhibited LRTCs over multiple time scales. In addition, the LRTCs significantly increased during HFS, which was confirmed by simulation data of both randomly shuffled sequences and surrogate sequences.Conclusion. The purely periodic stimulation of HFS pulses, a non-fractal process without LRTCs, can increase rather than decrease the LRTCs in neuronal firing.Significance. The finding provides new nonlinear mechanisms of brain stimulation and suggests that LRTCs could be a new biomarker to evaluate the nonlinear effects of HFS.

Quantification of Microbial Robustness in Yeast

Stable cell performance in a fluctuating environment is essential for sustainable bioproduction and synthetic cell functionality; however, microbial robustness is rarely quantified. Here, we describe a high-throughput strategy for quantifying robustness of multiple cellular functions and strains in a perturbation space. We evaluated quantification theory on experimental data and concluded that the mean-normalized Fano factor allowed accurate, reliable, and standardized quantification. Our methodology applied to perturbations related to lignocellulosic bioethanol production showed that the industrial bioethanol producing strain Saccharomyces cerevisiae Ethanol Red exhibited both higher and more robust growth rates than the laboratory strain CEN.PK and industrial strain PE-2, while a more robust product yield traded off for lower mean levels. The methodology validated that robustness is function-specific and characterized by positive and negative function-specific trade-offs. Systematic quantification of robustness to end-use perturbations will be important to analyze and construct robust strains with more predictable functions.

Variability of neuronal responses in the posterior superior temporal sulcus predicts choice behavior during social interactions

Recent studies have shown that neural activity in a well-defined patch in the posterior superior temporal sulcus (the "gaze-following patch," GFP) of the primate brain is strongly modulated when the other's gaze attracts the observer's attention to locations/objects, the other is looking at. Changes of the mean discharge rate of neurons in the monkey GFP indicate that they are involved in two distinct computations: the allocation of spatial attention guided by the other's gaze vector and the suppression of gaze following if inappropriate in a given situation. Here, we asked if and how the discharge variability of neurons in the GFP is related to the task and if it carries information on behavioral performance. To this end, we calculated the Fano factor as a measure of across-trial discharge variability as a function of time. Our results show that all neurons exhibiting a task-related discharge-rate modulation also exhibit a stimulus onset-dependent drop in the Fano factor. Furthermore, the amplitude of the Fano factor reduction is modulated by task condition and the neuron's selectivity in this regard. We found that these effects are directly related to the monkeys' behavioral performance in that the Fano factor is predictive about upcoming correct or wrong decisions. Our results indicate that neuronal discharge variability as gauged by the Fano factor, hitherto primarily studied in the context of visual perception or motor control, is an informative measure also in studies of the neural underpinnings of complex social behavior.NEW & NOTEWORTHY Quenching of neural variability following stimulus onset is a widely accepted phenomenon. However, the relevance of quenching for the shaping of complex social behaviors remains to be explored. Here, we show that task selective neurons in the GFP exhibit a higher degree of variability quenching than their neighboring unselective neurons. Furthermore, we demonstrate that behavioral errors are not only associated with lower firing rates but also less variability quenching, suggesting that both facilitate optimal performance.

Trial-to-Trial Variability of Spiking Delay Activity in Prefrontal Cortex Constrains Burst-Coding Models of Working Memory

A hallmark neuronal correlate of working memory (WM) is stimulus-selective spiking activity of neurons in PFC during mnemonic delays. These observations have motivated an influential computational modeling framework in which WM is supported by persistent activity. Recently, this framework has been challenged by arguments that observed persistent activity may be an artifact of trial-averaging, which potentially masks high variability of delay activity at the single-trial level. In an alternative scenario, WM delay activity could be encoded in bursts of selective neuronal firing which occur intermittently across trials. However, this alternative proposal has not been tested on single-neuron spike-train data. Here, we developed a framework for addressing this issue by characterizing the trial-to-trial variability of neuronal spiking quantified by Fano factor (FF). By building a doubly stochastic Poisson spiking model, we first demonstrated that the burst-coding proposal implies a significant increase in FF positively correlated with firing rate, and thus loss of stability across trials during the delay. Simulation of spiking cortical circuit WM models further confirmed that FF is a sensitive measure that can well dissociate distinct WM mechanisms. We then tested these predictions on datasets of single-neuron recordings from macaque PFC during three WM tasks. In sharp contrast to the burst-coding model predictions, we only found a small fraction of neurons showing increased WM-dependent burstiness, and stability across trials during delay was strengthened in empirical data. Therefore, reduced trial-to-trial variability during delay provides strong constraints on the contribution of single-neuron intermittent bursting to WM maintenance.SIGNIFICANCE STATEMENT There are diverging classes of theoretical models explaining how information is maintained in working memory by cortical circuits. In an influential model class, neurons exhibit persistent elevated memorandum-selective firing, whereas a recently developed class of burst-coding models suggests that persistent activity is an artifact of trial-averaging, and spiking is sparse in each single trial, subserved by brief intermittent bursts. However, this alternative picture has not been characterized or tested on empirical spike-train data. Here we combine mathematical analysis, computational model simulation, and experimental data analysis to test empirically these two classes of models and show that the trial-to-trial variability of empirical spike trains is not consistent with burst coding. These findings provide constraints for theoretical models of working memory.

Unified Model of Shot Noise in the Tunneling Current in Sub-10 nm MOSFETs

A single unified analytical model is presented to predict the shot noise for both the source-to-drain (SD) and the gate tunneling current in sub-10 nm MOSFETs with ultrathin oxide. Based on the Landauer formula, the model is constructed from the sequential tunneling flows associated with number fluctuations. This approach provides the analytical formulation of the shot noise as a function of the applied voltages. The model performs well in predicting the Fano factor for shot noise in the SD and gate tunneling currents.

Interference effect on the Andreev reflections induced by Majorana bound states

We investigate the effect of quantum interference on the Andreev reflections (ARs) induced by Majorana bound states (MBSs), by considering their additional coupling via a quantum-dot molecule. It is found that due to the direct and indirect couplings of MBSs, a quantum ring is constructed in this system. Consequently, the interference effect makes important contribution to the ARs, especially in the presence of the local magnetic flux. All the results are manifested as the tight dependence of the differential conductance and Fano factors on the magnetic flux phase factor, dot-MBS couplings, and the dot level, respectively. Moreover, at the zero-bias limit, the magnitudes of the Fano factors and their relation can be efficiently altered by the interference properties. We believe that quantum interference is important for manipulating the Andreev reflection behaviors of the MBSs.

Fano Factor: A Potentially Useful Information

The Fano factor, defined as the variance-to-mean ratio of spike counts in a time window, is often used to measure the variability of neuronal spike trains. However, despite its transparent definition, careless use of the Fano factor can easily lead to distorted or even wrong results. One of the problems is the unclear dependence of the Fano factor on the spiking rate, which is often neglected or handled insufficiently. In this paper we aim to explore this problem in more detail and to study the possible solution, which is to evaluate the Fano factor in the operational time. We use equilibrium renewal and Markov renewal processes as spike train models to describe the method in detail, and we provide an illustration on experimental data.

Spiking Noise and Information Density of Neurons in Visual Area V2 of Infant Monkeys

Encoding of visual information requires precisely timed spiking activity in the network of cortical neurons; irregular spiking can interfere with information processing especially for low-contrast images. The vision of newborn infants is impoverished. An infant's contrast sensitivity is low and the ability to discriminate complex stimuli is poor. The neural mechanisms that limit the visual capacities of infants are a matter of debate. Here we asked whether noisy spiking and/or crude information processing in visual cortex limit infant vision. Since neurons beyond the primary visual cortex (V1) have rarely been studied in neonates or infants, we focused on the firing pattern of neurons in visual area V2, the earliest extrastriate visual area of both male and female macaque monkeys (Maccaca mulatta). For eight stimulus contrasts ranging from 0% to 80%, we analyzed spiking irregularity by calculating the square of the coefficient of variation (CV²) in interspike intervals, the trial-to-trial fluctuation in spiking (Fano factor), and the amount of information on contrast conveyed by each spiking (information density). While the contrast sensitivity of infant neurons was reduced as expected, spiking noise, both the magnitude of spiking irregularity and the trial-to-trial fluctuations, was much lower in the spike trains of infant V2 neurons compared with those of adults. However, information density for V2 neurons was significantly lower in infants. Our results suggest that poor contrast sensitivity combined with lower information density of extrastriate neurons, despite their lower spiking noise, may limit behaviorally determined contrast sensitivity soon after birth.SIGNIFICANCE STATEMENT Despite >50 years of investigations on the postnatal development of the primary visual cortex (V1), cortical mechanisms that may limit infant vision are still unclear. We investigated the quality and strength of neuronal firing in primate visual area V2 by analyzing contrast sensitivity, spiking variability, and the amount of information on contrast conveyed by each action potential (information density). Here we demonstrate that the firing rate, contrast sensitivity, and dynamic range of V2 neurons were depressed in infants compared with adults. Although spiking noise was less, information density was lower in infant V2. Impoverished neuronal drive and lower information density in extrastriate visual areas, despite lower spiking noise, largely explain the impoverished visual sensitivity of primates near birth.

Age Is Associated with Reduced Sharp-Wave Ripple Frequency and Altered Patterns of Neuronal Variability

Spatial and episodic memory performance declines with age, and the neural basis for this decline is not well understood. Sharp-wave ripples are brief (∼70 ms) high-frequency oscillatory events generated in the hippocampus and are associated with the consolidation of spatial memories. Given the connection between ripple oscillations and memory consolidation, we investigated whether the structure of ripple oscillations and ripple-triggered patterns of single-unit activity are altered in aged rats. Local field and single-unit activity surrounding sharp-wave ripple events were examined in the CA1 region of the hippocampus of old (n = 5) and young (n = 6) F344 rats during periods of rest preceding and following performance on a place-dependent eyeblink-conditioning task. Neural responses in aged rats differed from responses in young rats in several ways. First, compared with young rats, the rate of ripple occurrence (ripple density) is reduced in aged rats during postbehavior rest. Second, mean ripple frequency during prebehavior and postbehavior rest is lower in aged animals (aged: 132 Hz; young: 146 Hz). Third, single neurons in aged animals responded more consistently from ripple to ripple. Fourth, variability in interspike intervals was greater in aged rats. Finally, neurons were tuned to a narrower range of phases of the ripple oscillation relative to young animals. Together, these results suggest that the CA1 network in aged animals has a reduced "vocabulary" of available representational states.

SIGNIFICANCE STATEMENT

The hippocampus is a structure that is critical for the formation of episodic memories. Sharp-wave ripple events generated in the hippocampus have been implicated in memory consolidation processes critical to memory stabilization. We examine here whether these ripple oscillations are altered over the course of the life span, which could contribute to hippocampus-dependent memory deficits that occur during aging. This experiment used young and aged memory-impaired rats to examine age-related changes in ripple architecture, ripple-triggered spike variance, and spike-phase coherence. We found that there are, indeed, significant changes in characteristics of ripples in older animals that could impact consolidation processes and memory stabilization in the aged brain.

High-velocity stimulation evokes "dense" population response in layer 2/3 vibrissal cortex

Supragranular layers of sensory cortex are known to exhibit sparse firing. In rodent vibrissal cortex, a small fraction of neurons in layer 2 and 3 (L2/3) respond to whisker stimulation. In this study, we combined whole cell recording and two-photon imaging in anesthetized mice and quantified the synaptic response and spiking profile of L2/3 neurons. Previous literature has shown that neurons across layers of vibrissal cortex are tuned to the velocity of whisker movement. We therefore used a broad range of stimuli that included the standard range of velocities (0-1.2 deg/ms) and extended to a "sharp" high-velocity deflection (3.8 deg/ms). Consistent with previous literature, whole cell recording revealed a sparse response to the standard range of velocities: although all recorded cells showed tuning to velocity in their postsynaptic potentials, only a small fraction produced stimulus-evoked spikes. In contrast, the sharp stimulus evoked reliable spiking in the majority of neurons. The action potential threshold of spikes evoked by the sharp stimulus was significantly lower than that of the spontaneous spikes. Juxtacellular recordings confirmed that application of sharp stimulus to single or multiple whiskers produced temporally precise spiking with minimal trial-to-trial spike count variability (Fano factors equal or close to the theoretical minimum). Two-photon imaging further confirmed that most neurons that were not responsive to the standard deflections responded to the sharp stimulus. Altogether, our results indicate that sparseness in L2/3 cortex depends on the choice of stimulus: strong single- or multiwhisker stimulation can induce the transition from sparse to "dense" population response.NEW & NOTEWORTHY In superficial layers of sensory cortex, only a small fraction of neurons fire most of the spontaneous and sensory evoked spikes. However, the functional relevance of such "sparse" activity remains unknown. We found that a "dense" population response is evoked by high-velocity micromotions applied to whiskers. Our results suggest that flashes of precisely timed population response on an almost silent background can provide a high capacity for coding of ecologically salient stimuli.

Estimation of Fano factor in inorganic scintillators

The Fano factor of an integer-valued random variable is defined as the ratio of its variance to its mean. Correlation between the outputs of two photomultiplier tubes on opposite faces of a scintillation crystal was used to estimate the Fano factor of photoelectrons and scintillation photons. Correlations between the integrals of the detector outputs were used to estimate the photoelectron and photon Fano factor for YAP:Ce, SrI₂:Eu and CsI:Na scintillator crystals. At 662 keV, SrI₂:Eu was found to be sub-Poisson, while CsI:Na and YAP:Ce were found to be super-Poisson. An experiment setup inspired from the Hanbury Brown and Twiss experiment was used to measure the correlations as a function of time between the outputs of two photomultiplier tubes looking at the same scintillation event. A model of the scintillation and the detection processes was used to generate simulated detector outputs as a function of time for different values of Fano factor. The simulated outputs from the model for different Fano factors was compared to the experimentally measured detector outputs to estimate the Fano factor of the scintillation photons for YAP:Ce, LaBr₃:Ce scintillator crystals. At 662 keV, LaBr₃:Ce was found to be sub-Poisson, while YAP:Ce was found to be close to Poisson.

Lower neuronal variability in the monkey dorsolateral prefrontal than posterior parietal cortex

The dorsolateral prefrontal and posterior parietal cortex are two brain areas involved in cognitive functions such as spatial attention and working memory. When tested with identical tasks, only subtle differences in firing rate are present between neurons recorded in the two areas. In this article we report that major differences in neuronal variability characterize the two areas during working memory. The Fano factors of spike counts in dorsolateral prefrontal neurons were consistently lower than those of the posterior parietal cortex across a range of tasks, epochs, and conditions in the same monkeys. Variability differences were observed despite minor differences in firing rates between the two areas in the tasks tested and higher overall firing rate in the prefrontal than in the posterior parietal sample. Other measures of neuronal discharge variability, such as the coefficient of variation of the interspike interval, displayed the same pattern of lower prefrontal variability. Fano factor values were negatively correlated with performance in the working memory task, suggesting that higher neuronal variability was associated with diminished task performance. The results indicate that information involving remembered stimuli is more reliably represented in the prefrontal than the posterior parietal cortex based on the variability of neuronal responses, and suggest functional differentiation between the two areas beyond differences in firing rate.

Impact of the Fano Factor on Position and Energy Estimation in Scintillation Detectors

The Fano factor for an integer-valued random variable is defined as the ratio of its variance to its mean. Light from various scintillation crystals have been reported to have Fano factors from sub-Poisson (Fano factor < 1) to super-Poisson (Fano factor > 1). For a given mean, a smaller Fano factor implies a smaller variance and thus less noise. We investigated if lower noise in the scintillation light will result in better spatial and energy resolutions. The impact of Fano factor on the estimation of position of interaction and energy deposited in simple gamma-camera geometries is estimated by two methods - calculating the Cramér-Rao bound and estimating the variance of a maximum likelihood estimator. The methods are consistent with each other and indicate that when estimating the position of interaction and energy deposited by a gamma-ray photon, the Fano factor of a scintillator does not affect the spatial resolution. A smaller Fano factor results in a better energy resolution.

A model of synaptic vesicle-pool depletion and replenishment can account for the interspike interval distributions and nonrenewal properties of spontaneous spike trains of auditory-nerve fibers

In mammalian auditory systems, the spiking characteristics of each primary afferent (type I auditory-nerve fiber; ANF) are mainly determined by a single ribbon synapse in a single receptor cell (inner hair cell; IHC). ANF spike trains therefore provide a window into the operation of these synapses and cells. It was demonstrated previously (Heil et al., 2007) that the distribution of interspike intervals (ISIs) of cat ANFs during spontaneous activity can be modeled as resulting from refractoriness operating on a non-Poisson stochastic point process of excitation (transmitter release events from the IHC). Here, we investigate nonrenewal properties of these cat-ANF spontaneous spike trains, manifest as negative serial ISI correlations and reduced spike-count variability over short timescales. A previously discussed excitatory process, the constrained failure of events from a homogeneous Poisson point process, can account for these properties, but does not offer a parsimonious explanation for certain trends in the data. We then investigate a three-parameter model of vesicle-pool depletion and replenishment and find that it accounts for all experimental observations, including the ISI distributions, with only the release probability varying between spike trains. The maximum number of units (single vesicles or groups of simultaneously released vesicles) in the readily releasable pool and their replenishment time constant can be assumed to be constant (∼4 and 13.5 ms, respectively). We suggest that the organization of the IHC ribbon synapses not only enables sustained release of neurotransmitter but also imposes temporal regularity on the release process, particularly when operating at high rates.

Discharge properties of neurons recorded in the parvalbumin-positive (PV1) nucleus of the rat lateral hypothalamus

This study reports for the first time the extracellular activity recorded, in anesthetized rats, from cells located in an identified cluster of parvalbumin (PV)-positive neurons of the lateral hypothalamus forming the PV1-nucleus. Random-like firing characterized the majority (21/30) of the cells, termed regular cells, with a median firing rate of 1.7 spikes/s, Fano factor equal to 1, and evenly distributed along the rostro-caudal axis. Four cells exhibiting an oscillatory activity in the range 1.6-2.1Hz were observed only in the posterior part of the PV1-nucleus. The asynchronous activity of PV1 neurons is likely to produce a "network-driven" effect on their main target within the periaqueductal gray matter. The hypothesis is raised that background random-like firing of PV1-nucleus is associated with functional network activity likely to contribute dynamic information related to condition transitions of awareness and non-conscious perception.

Long-Range Temporal Correlations, Multifractality, and the Causal Relation between Neural Inputs and Movements

Understanding the causal relation between neural inputs and movements is very important for the success of brain-machine interfaces (BMIs). In this study, we analyze 104 neurons’ firings using statistical, information theoretic, and fractal analysis. The latter include Fano factor analysis, multifractal adaptive fractal analysis (MF-AFA), and wavelet multifractal analysis. We find neuronal firings are highly non-stationary, and Fano factor analysis always indicates long-range correlations in neuronal firings, irrespective of whether those firings are correlated with movement trajectory or not, and thus does not reveal any actual correlations between neural inputs and movements. On the other hand, MF-AFA and wavelet multifractal analysis clearly indicate that when neuronal firings are not well correlated with movement trajectory, they do not have or only have weak temporal correlations. When neuronal firings are well correlated with movements, they are characterized by very strong temporal correlations, up to a time scale comparable to the average time between two successive reaching tasks. This suggests that neurons well correlated with hand trajectory experienced a “re-setting” effect at the start of each reaching task, in the sense that within the movement correlated neurons the spike trains’ long-range dependences persisted about the length of time the monkey used to switch between task executions. A new task execution re-sets their activity, making them only weakly correlated with their prior activities on longer time scales. We further discuss the significance of the coalition of those important neurons in executing cortical control of prostheses.

Local interneurons and projection neurons in the antennal lobe from a spiking point of view

Local computation in microcircuits is an essential feature of distributed information processing in vertebrate and invertebrate brains. The insect antennal lobe represents a spatially confined local network that processes high-dimensional and redundant peripheral input to compute an efficient odor code. Social insects can rely on a particularly rich olfactory receptor repertoire, and they exhibit complex odor-guided behaviors. This corresponds with a high anatomical complexity of their antennal lobe network. In the honeybee, a large number of glomeruli that receive sensory input are interconnected by a dense network of local interneurons (LNs). Uniglomerular projection neurons (PNs) integrate sensory and recurrent local network input into an efficient spatio-temporal odor code. To investigate the specific computational roles of LNs and PNs, we measured several features of sub- and suprathreshold single-cell responses to in vivo odor stimulation. Using a semisupervised cluster analysis, we identified a combination of five characteristic features as sufficient to separate LNs and PNs from each other, independent of the applied odor-stimuli. The two clusters differed significantly in all these five features. PNs showed a higher spontaneous subthreshold activation, assumed higher peak response rates and a more regular spiking pattern. LNs reacted considerably faster to the onset of a stimulus, and their responses were more reliable across stimulus repetitions. We discuss possible mechanisms that can explain our results, and we interpret cell-type-specific characteristics with respect to their functional relevance.

On the precision of neural computation with interaural level differences in the lateral superior olive

Interaural level difference (ILD) is one of the basic binaural clues in the spatial localization of a sound source. Due to the acoustic shadow cast by the head, a sound source out of the medial plane results in an increased sound level at the nearer ear and a decreased level at the distant ear. In the mammalian auditory brainstem, the ILD is processed by a neuronal circuit of binaural neurons in the lateral superior olive (LSO). These neurons receive major excitatory projections from the ipsilateral side and major inhibitory projections from the contralateral side. As the sound level is encoded predominantly by the neuronal discharge rate, the principal function of LSO neurons is to estimate and encode the difference between the discharge rates of the excitatory and inhibitory inputs. Two general mechanisms of this operation are biologically plausible: (1) subtraction of firing rates integrated over longer time intervals, and (2) detection of coincidence of individual spikes within shorter time intervals. However, the exact mechanism of ILD evaluation is not known. Furthermore, given the stochastic nature of neuronal activity, it is not clear how the circuit achieves the remarkable precision of ILD assessment observed experimentally. We employ a probabilistic model and complementary computer simulations to investigate whether the two general mechanisms are capable of the desired performance. Introducing the concept of an ideal observer, we determine the theoretical ILD accuracy expressed by means of the just-noticeable difference (JND) in dependence on the statistics of the interacting spike trains, the overall firing rate, detection time, the number of converging fibers, and on the neural mechanism itself. We demonstrate that the JNDs rely on the precision of spike timing; however, with an appropriate parameter setting, the lowest theoretical values are similar or better than the experimental values. Furthermore, a mechanism based on excitatory and inhibitory coincidence detection may give better results than the subtraction of firing rates. This article is part of a Special Issue entitled Neural Coding 2012.

Neuronal variability of MSTd neurons changes differentially with eye movement and visually related variables

Neurons in macaque cortical area MSTd are driven by visual motion and eye movement related signals. This multimodal characteristic makes MSTd an ideal system for studying the dependence of neuronal activity on different variables. Here, we analyzed the temporal structure of spiking patterns during visual motion stimulation using 2 distinct behavioral paradigms: fixation (FIX) and optokinetic response. For the FIX condition, inter- and intra-trial variability of spiking activity decreased with increasing stimulus strength, complying with a recent neurophysiological study reporting stimulus-related decline of neuronal variability. In contrast, for the optokinetic condition variability increased together with increasing eye velocity while retinal image velocity remained low. Analysis of stimulus signal variability revealed a correlation between the normalized variance of image velocity and neuronal variability, but no correlation with normalized eye velocity variance. We further show that the observed difference in neuronal variability allows classifying spike trains according to the paradigm used, even when mean firing rates (FRs) were similar. The stimulus-dependence of neuronal variability may result from the local network structure and/or the variability characteristics of the input signals, but may also reflect additional timing-based mechanisms independent of the neuron's mean FR and related to the modality driving the neuron.