Reliability, synchrony and noise

Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience

The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also surprises in the dynamical complexity of the attractors that can robustly appear-for example, heteroclinic network attractors. In this review we present a set of mathematical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical framework for further successful applications of mathematics to understanding network dynamics in neuroscience.

Neurons as oscillators

Regularly spiking neurons can be described as oscillators. In this article we review some of the insights gained from this conceptualization and their relevance for systems neuroscience. First, we explain how a regularly spiking neuron can be viewed as an oscillator and how the phase-response curve (PRC) describes the response of the neuron's spike times to small perturbations. We then discuss the meaning of the PRC for a single neuron's spiking behavior and review the PRCs measured from a variety of neurons in a range of spiking regimes. Next, we show how the PRC can be related to a number of common measures used to quantify neuronal firing, such as the spike-triggered average and the peristimulus histogram. We further show that the response of a neuron to correlated inputs depends on the shape of the PRC. We then explain how the PRC of single neurons can be used to predict neural network behavior. Given the PRC, conduction delays, and the waveform and time course of the synaptic potentials, it is possible to predict neural population behavior such as synchronization. The PRC also allows us to quantify the robustness of the synchronization to heterogeneity and noise. We finally ask how to combine the measured PRCs and the predictions based on PRC to further the understanding of systems neuroscience. As an example, we discuss how the change of the PRC by the neuromodulator acetylcholine could lead to a destabilization of cortical network dynamics. Although all of these studies are grounded in mathematical abstractions that do not strictly hold in biology, they provide good estimates for the emergence of the brain's network activity from the properties of individual neurons. The study of neurons as oscillators can provide testable hypotheses and mechanistic explanations for systems neuroscience.

Bipolar disorder dynamics: affective instabilities, relaxation oscillations and noise

Bipolar disorder is a chronic, recurrent mental illness characterized by extreme episodes of depressed and manic mood, interspersed with less severe but highly variable mood fluctuations. Here, we develop a novel mathematical approach for exploring the dynamics of bipolar disorder. We investigate how the dynamics of subjective experience of mood in bipolar disorder can be understood using a relaxation oscillator (RO) framework and test the model against mood time-series fluctuations from a set of individuals with bipolar disorder. We show that variable mood fluctuations in individuals diagnosed with bipolar disorder can be driven by the coupled effects of deterministic dynamics (captured by ROs) and noise. Using a statistical likelihood-based approach, we show that, in general, mood dynamics are described by two independent ROs with differing levels of endogenous variability among individuals. We suggest that this sort of nonlinear approach to bipolar disorder has neurobiological, cognitive and clinical implications for understanding this mental illness through a mechacognitive framework.

Inferring Cortical Variability from Local Field Potentials

The responses of sensory neurons can be quite different to repeated presentations of the same stimulus. Here, we demonstrate a direct link between the trial-to-trial variability of cortical neuron responses and network activity that is reflected in local field potentials (LFPs). Spikes and LFPs were recorded with a multielectrode array from the middle temporal (MT) area of the visual cortex of macaques during the presentation of continuous optic flow stimuli. A maximum likelihood-based modeling framework was used to predict single-neuron spiking responses using the stimulus, the LFPs, and the activity of other recorded neurons. MT neuron responses were strongly linked to gamma oscillations (maximum at 40 Hz) as well as to lower-frequency delta oscillations (1-4 Hz), with consistent phase preferences across neurons. The predicted modulation associated with the LFP was largely complementary to that driven by visual stimulation, as well as the activity of other neurons, and accounted for nearly half of the trial-to-trial variability in the spiking responses. Moreover, the LFP model predictions accurately captured the temporal structure of noise correlations between pairs of simultaneously recorded neurons, and explained the variation in correlation magnitudes observed across the population. These results therefore identify signatures of network activity related to the variability of cortical neuron responses, and suggest their central role in sensory cortical function.

SIGNIFICANCE STATEMENT

The function of sensory neurons is nearly always cast in terms of representing sensory stimuli. However, recordings from visual cortex in awake animals show that a large fraction of neural activity is not predictable from the stimulus. We show that this variability is predictable given the simultaneously recorded measures of network activity, local field potentials. A model that combines elements of these signals with the stimulus processing of the neuron can predict neural responses dramatically better than current models, and can predict the structure of correlations across the cortical population. In identifying ways to understand stimulus processing in the context of ongoing network activity, this work thus provides a foundation to understand the role of sensory cortex in combining sensory and cognitive variables.

Integrative properties and transfer function of cortical neurons initiating absence seizures in a rat genetic model

KEY POINTS

Absence seizures are accompanied by spike-and-wave discharges in cortical electroencephalograms. These complex paroxysmal activities, affecting the thalamocortical networks, profoundly alter cognitive performances and preclude conscious perception. Here, using a well-recognized genetic model of absence epilepsy, we investigated in vivo how information processing was impaired in the ictogenic neurons, i.e. the population of cortical neurons responsible for seizure initiation. In between seizures, ictogenic neurons were more prone to generate bursting activity and their firing response to weak depolarizing events was considerably facilitated compared to control neurons. In the course of seizures, information processing became unstable in ictogenic cells, alternating between an increased and a decreased responsiveness to excitatory inputs, depending on the spike and wave patterns. The state-dependent modulation in the excitability of ictogenic neurons affects their inter-seizure transfer function and their time-to-time responsiveness to incoming inputs during absences.

ABSTRACT

Epileptic seizures result from aberrant cellular and/or synaptic properties that can alter the capacity of neurons to integrate and relay information. During absence seizures, spike-and-wave discharges (SWDs) interfere with incoming sensory inputs and preclude conscious experience. The Genetic Absence Epilepsy Rats from Strasbourg (GAERS), a well-established animal model of absence epilepsy, allows exploration of the cellular basis of this impaired information processing. Here, by combining in vivo electrocorticographic and intracellular recordings from GAERS and control animals, we investigated how the pro-ictogenic properties of seizure-initiating cortical neurons modify their integrative properties and input-output operation during inter-ictal periods and during the spike (S-) and wave (W-) cortical patterns alternating during seizures. In addition to a sustained depolarization and an excessive firing rate in between seizures, ictogenic neurons exhibited a pronounced hyperpolarization-activated depolarization compared to homotypic control neurons. Firing frequency versus injected current relations indicated an increased sensitivity of GAERS cells to weak excitatory inputs, without modifications in the trial-to-trial variability of current-induced firing. During SWDs, the W-component resulted in paradoxical effects in ictogenic neurons, associating an increased membrane input resistance with a reduction in the current-evoked firing responses. Conversely, the collapse of cell membrane resistance during the S-component was accompanied by an elevated current-evoked firing relative to W-sequences, which remained, however, lower compared to inter-ictal periods. These findings show a dynamic modulation of ictogenic neurons' intrinsic properties that may alter inter-seizure cortical function and participate in compromising information processing in cortical networks during absences.

Flexible models for spike count data with both over- and under- dispersion

A key observation in systems neuroscience is that neural responses vary, even in controlled settings where stimuli are held constant. Many statistical models assume that trial-to-trial spike count variability is Poisson, but there is considerable evidence that neurons can be substantially more or less variable than Poisson depending on the stimuli, attentional state, and brain area. Here we examine a set of spike count models based on the Conway-Maxwell-Poisson (COM-Poisson) distribution that can flexibly account for both over- and under-dispersion in spike count data. We illustrate applications of this noise model for Bayesian estimation of tuning curves and peri-stimulus time histograms. We find that COM-Poisson models with group/observation-level dispersion, where spike count variability is a function of time or stimulus, produce more accurate descriptions of spike counts compared to Poisson models as well as negative-binomial models often used as alternatives. Since dispersion is one determinant of parameter standard errors, COM-Poisson models are also likely to yield more accurate model comparison. More generally, these methods provide a useful, model-based framework for inferring both the mean and variability of neural responses.

Differential effects of white noise in cognitive and perceptual tasks

Beneficial effects of noise on higher cognition have recently attracted attention. Hypothesizing an involvement of the mesolimbic dopamine system and its functional interactions with cortical areas, the current study aimed to demonstrate a facilitation of dopamine-dependent attentional and mnemonic functions by externally applying white noise in five behavioral experiments including a total sample of 167 healthy human subjects. During working memory, acoustic white noise impaired accuracy when presented during the maintenance period (Experiments 1-3). In a reward based long-term memory task, white noise accelerated perceptual judgments for scene images during encoding but left subsequent recognition memory unaffected (Experiment 4). In a modified Posner task (Experiment 5), the benefit due to white noise in attentional orienting correlated weakly with reward dependence, a personality trait that has been associated with the dopaminergic system. These results suggest that white noise has no general effect on cognitive functions. Instead, they indicate differential effects on perception and cognition depending on a variety of factors such as task demands and timing of white noise presentation.

Anomalous neuronal responses to fluctuated inputs

The irregular firing of a cortical neuron is thought to result from a highly fluctuating drive that is generated by the balance of excitatory and inhibitory synaptic inputs. A previous study reported anomalous responses of the Hodgkin-Huxley neuron to the fluctuated inputs where an irregularity of spike trains is inversely proportional to an input irregularity. In the current study, we investigated the origin of these anomalous responses with the Hindmarsh-Rose neuron model, map-based models, and a simple mixture of interspike interval distributions. First, we specified the parameter regions for the bifurcations in the Hindmarsh-Rose model, and we confirmed that the model reproduced the anomalous responses in the dynamics of the saddle-node and subcritical Hopf bifurcations. For both bifurcations, the Hindmarsh-Rose model shows bistability in the resting state and the repetitive firing state, which indicated that the bistability was the origin of the anomalous input-output relationship. Similarly, the map-based model that contained bistability reproduced the anomalous responses, while the model without bistability did not. These results were supported by additional findings that the anomalous responses were reproduced by mimicking the bistable firing with a mixture of two different interspike interval distributions. Decorrelation of spike trains is important for neural information processing. For such spike train decorrelation, irregular firing is key. Our results indicated that irregular firing can emerge from fluctuating drives, even weak ones, under conditions involving bistability. The anomalous responses, therefore, contribute to efficient processing in the brain.

The neurophysiology of language: Insights from non-invasive brain stimulation in the healthy human brain

With the advent of non-invasive brain stimulation (NIBS), a new decade in the study of language has started. NIBS allows for testing the functional relevance of language-related brain activation and enables the researcher to investigate how neural activation changes in response to focal perturbations. This review focuses on the application of NIBS in the healthy brain. First, some basic mechanisms will be introduced and the prerequisites for carrying out NIBS studies of language are addressed. The next section outlines how NIBS can be used to characterize the contribution of the stimulated area to a task. In this context, novel approaches such as multifocal transcranial magnetic stimulation and the condition-and-perturb approach are discussed. The third part addresses the combination of NIBS and neuroimaging in the study of plasticity. These approaches are particularly suited to investigate short-term reorganization in the healthy brain and may inform models of language recovery in post-stroke aphasia.

Identification of neural firing patterns, frequency and temporal coding mechanisms in individual aortic baroreceptors

In rabbit depressor nerve fibers, an on-off firing pattern, period-1 firing, and integer multiple firing with quiescent state were observed as the static pressure level was increased. A bursting pattern with bursts at the systolic phase of blood pressure, continuous firing, and bursting with burst at diastolic phase and quiescent state at systolic phase were observed as the mean level of the dynamic blood pressure was increased. For both static and dynamic pressures, the firing frequency of the first two firing patterns increased and of the last firing pattern decreased due to the quiescent state. If the quiescent state is disregarded, the spike frequency becomes an increasing trend. The instantaneous spike frequency of the systolic phase bursting, continuous firing, and diastolic phase bursting can reflect the temporal process of the systolic phase, whole procedure, and diastolic phase of the dynamic blood pressure signal, respectively. With increasing the static current corresponding to pressure level, the deterministic Hodgkin-Huxley (HH) model manifests a process from a resting state first to period-1 firing via a subcritical Hopf bifurcation and then to a resting state via a supercritical Hopf bifurcation, and the firing frequency increases. The on-off firing and integer multiple firing were here identified as noise-induced firing patterns near the subcritical and supercritical Hopf bifurcation points, respectively, using the stochastic HH model. The systolic phase bursting and diastolic phase bursting were identified as pressure-induced firings near the subcritical and supercritical Hopf bifurcation points, respectively, using an HH model with a dynamic signal. The firing, spike frequency, and instantaneous spike frequency observed in the experiment were simulated and explained using HH models. The results illustrate the dynamics of different firing patterns and the frequency and temporal coding mechanisms of aortic baroreceptor.

Mutation of the Dyslexia-Associated Gene Dcdc2 Enhances Glutamatergic Synaptic Transmission Between Layer 4 Neurons in Mouse Neocortex

Variants in DCDC2 have been associated with reading disability in humans, and targeted mutation of Dcdc2 in mice causes impairments in both learning and sensory processing. In this study, we sought to determine whether Dcdc2 mutation affects functional synaptic circuitry in neocortex. We found mutation in Dcdc2 resulted in elevated spontaneous and evoked glutamate release from neurons in somatosensory cortex. The probability of release was decreased to wild-type level by acute application of N-methyl-d-aspartate receptor (NMDAR) antagonists when postsynaptic NMDARs were blocked by intracellular MK-801, and could not be explained by elevated ambient glutamate, suggesting altered, nonpostsynaptic NMDAR activation in the mutants. In addition, we determined that the increased excitatory transmission was present at layer 4-layer 4 but not thalamocortical connections in Dcdc2 mutants, and larger evoked synaptic release appeared to enhance the NMDAR-mediated effect. These results demonstrate an NMDAR activation-gated, increased functional excitatory connectivity between layer 4 lateral connections in somatosensory neocortex of the mutants, providing support for potential changes in cortical connectivity and activation resulting from mutation of dyslexia candidate gene Dcdc2.

Dynamics of on-off neural firing patterns and stochastic effects near a sub-critical Hopf bifurcation

On-off firing patterns, in which repetition of clusters of spikes are interspersed with epochs of subthreshold oscillations or quiescent states, have been observed in various nervous systems, but the dynamics of this event remain unclear. Here, we report that on-off firing patterns observed in three experimental models (rat sciatic nerve subject to chronic constrictive injury, rat CA1 pyramidal neuron, and rabbit blood pressure baroreceptor) appeared as an alternation between quiescent state and burst containing multiple period-1 spikes over time. Burst and quiescent state had various durations. The interspike interval (ISI) series of on-off firing pattern was suggested as stochastic using nonlinear prediction and autocorrelation function. The resting state was changed to a period-1 firing pattern via on-off firing pattern as the potassium concentration, static pressure, or depolarization current was changed. During the changing process, the burst duration of on-off firing pattern increased and the duration of the quiescent state decreased. Bistability of a limit cycle corresponding to period-1 firing and a focus corresponding to resting state was simulated near a sub-critical Hopf bifurcation point in the deterministic Morris-Lecar (ML) model. In the stochastic ML model, noise-induced transitions between the coexisting regimes formed an on-off firing pattern, which closely matched that observed in the experiment. In addition, noise-induced exponential change in the escape rate from the focus, and noise-induced coherence resonance were identified. The distinctions between the on-off firing pattern and stochastic firing patterns generated near three other types of bifurcations of equilibrium points, as well as other viewpoints on the dynamics of on-off firing pattern, are discussed. The results not only identify the on-off firing pattern as noise-induced stochastic firing pattern near a sub-critical Hopf bifurcation point, but also offer practical indicators to discriminate bifurcation types and neural excitability types.

Stochastic synchronization of neural activity waves

We demonstrate that waves in distinct layers of a neuronal network can become phase locked by common spatiotemporal noise. This phenomenon is studied for stationary bumps, traveling waves, and breathers. A weak noise expansion is used to derive an effective equation for the position of the wave in each layer, yielding a stochastic differential equation with multiplicative noise. Stability of the synchronous state is characterized by a Lyapunov exponent, which we can compute analytically from the reduced system. Our results extend previous work on limit-cycle oscillators, showing common noise can synchronize waves in a broad class of models.

Statistics of a neuron model driven by asymmetric colored noise

Irregular firing of neurons can be modeled as a stochastic process. Here we study the perfect integrate-and-fire neuron driven by dichotomous noise, a Markovian process that jumps between two states (i.e., possesses a non-Gaussian statistics) and exhibits nonvanishing temporal correlations (i.e., represents a colored noise). Specifically, we consider asymmetric dichotomous noise with two different transition rates. Using a first-passage-time formulation, we derive exact expressions for the probability density and the serial correlation coefficient of the interspike interval (time interval between two subsequent neural action potentials) and the power spectrum of the spike train. Furthermore, we extend the model by including additional Gaussian white noise, and we give approximations for the interspike interval (ISI) statistics in this case. Numerical simulations are used to validate the exact analytical results for pure dichotomous noise, and to test the approximations of the ISI statistics when Gaussian white noise is included. The results may help to understand how correlations and asymmetry of noise and signals in nerve cells shape neuronal firing statistics.

Characterizing nonlinear relationships in functional imaging data using eigenspace maximal information canonical correlation analysis (emiCCA)

Many important problems in the analysis of neuroimages can be formulated as discovering the relationship between two sets of variables, a task for which linear techniques such as canonical correlation analysis (CCA) have been commonly used. However, to further explore potential nonlinear processes that might co-exist with linear ones in brain function, a more flexible method is required. Here, we propose a new unsupervised and data-driven method, termed the eigenspace maximal information canonical correlation analysis (emiCCA), which is capable of automatically capturing the linear and/or nonlinear relationships between various data sets. A simulation confirmed the superior performance of emiCCA in comparison with linear CCA and kernel CCA (a nonlinear version of CCA). An emiCCA framework for functional magnetic resonance imaging (fMRI) data processing was designed and applied to data from a real motor execution fMRI experiment. This analysis uncovered one linear (in primary motor cortex) and a few nonlinear networks (e.g., in the supplementary motor area, bilateral insula, and cerebellum). This suggests that these various task-related brain areas are part of networks that also contribute to the execution of movements of the hand. These results suggest that emiCCA is a promising technique for exploring various data.

Learning modulation of odor representations: new findings from Arc-indexed networks

We first review our understanding of odor representations in rodent olfactory bulb (OB) and anterior piriform cortex (APC). We then consider learning-induced representation changes. Finally we describe the perspective on network representations gained from examining Arc-indexed odor networks of awake rats. Arc-indexed networks are sparse and distributed, consistent with current views. However Arc provides representations of repeated odors. Arc-indexed repeated odor representations are quite variable. Sparse representations are assumed to be compact and reliable memory codes. Arc suggests this is not necessarily the case. The variability seen is consistent with electrophysiology in awake animals and may reflect top-down cortical modulation of context. Arc-indexing shows that distinct odors share larger than predicted neuron pools. These may be low-threshold neuronal subsets. Learning’s effect on Arc-indexed representations is to increase the stable or overlapping component of rewarded odor representations. This component can decrease for similar odors when their discrimination is rewarded. The learning effects seen are supported by electrophysiology, but mechanisms remain to be elucidated.

Examination of rhythmicity of extracellularly recorded neurons in the entorhinal cortex

A number of studies have examined the theta-rhythmic modulation of neuronal firing in the hippocampal circuit. For extracellular recordings, this is often done by examining spectral properties of the spike-time autocorrelogram, most significantly, for validating the presence or absence of theta modulation across species. These techniques can show significant rhythmicity for high firing rate, highly rhythmic neurons; however, they are substantially biased by several factors including the peak firing rate of the neuron, the amount of time spent in the neuron's receptive field, and other temporal properties of the rhythmicity such as cycle-skipping. These limitations make it difficult to examine rhythmic modulation in neurons with low firing rates or when an animal has short dwell times within the firing field and difficult to compare rhythmicity under disparate experimental conditions when these factors frequently differ. Here, we describe in detail the challenges that researchers face when using these techniques and apply our findings to recent recordings from bat entorhinal grid cells, suggesting that they may have lacked enough data to examine theta rhythmicity robustly. We describe a more sensitive and statistically rigorous method using maximum likelihood estimation (MLE) of a parametric model of the lags within the autocorrelation window, which helps to alleviate some of the problems of traditional methods and was also unable to detect rhythmicity in bat grid cells. Using large batteries of simulated data, we explored the boundaries for which the MLE technique and the theta index can detect rhythmicity. The MLE technique is less sensitive to many features of the autocorrelogram and provides a framework for statistical testing to detect rhythmicity as well as changes in rhythmicity in individual sessions providing a substantial improvement over previous methods.

Noise-enhanced nonlinear response and the role of modular structure for signal detection in neuronal networks

We show that sensory noise can enhance the nonlinear response of neuronal networks, and when delivered together with a weak signal, it improves the signal detection by the network. We reveal this phenomenon in neuronal networks that are in a dynamical state preceding a saddle-node bifurcation corresponding to the appearance of sustained network oscillations. In this state, even a weak subthreshold pulse can evoke a large-amplitude oscillation of neuronal activity. The signal-to-noise ratio reaches a maximum at an optimum level of sensory noise, manifesting stochastic resonance (SR) at the population level. We demonstrate SR by use of simulations and numerical integration of rate equations in a cortical model. Using this model, we mimic the experiments of Gluckman et al. [Phys. Rev. Lett. 77, 4098 (1996)PRLTAO0031-900710.1103/PhysRevLett.77.4098] that have given evidence of SR in mammalian brain. We also study neuronal networks in which neurons are grouped in modules and every module works in the regime of SR. We find that even a few modules can strongly enhance the reliability of signal detection in comparison with the case when a modular organization is absent.

Low endogenous neural noise in autism

‘Heuristic’ theories of autism postulate that a single mechanism or process underpins the diverse psychological features of autism spectrum disorder. Although no such theory can offer a comprehensive account, the parsimonious descriptions they provide are powerful catalysts to autism research. One recent proposal holds that ‘noisy’ neuronal signalling explains not only some deficits in autism spectrum disorder, but also some superior abilities, due to ‘stochastic resonance’. Here, we discuss three distinct actions of noise in neural networks, arguing in each case that autism spectrum disorder symptoms reflect too little, rather than too much, neural noise. Such reduced noise, perhaps a function of atypical brainstem activation, would enhance detection and discrimination in autism spectrum disorder but at significant cost, foregoing the widespread benefits of noise in neural networks.

The dyslexia-associated gene DCDC2 is required for spike-timing precision in mouse neocortex

BACKGROUND

Variants in dyslexia-associated genes, including DCDC2, have been linked to altered neocortical activation, suggesting that dyslexia associated genes might play as yet unspecified roles in neuronal physiology.

METHODS

Whole-cell patch clamp recordings were used to compare the electrophysiological properties of regular spiking pyramidal neurons of neocortex in Dcdc2 knockout (KO) and wild-type mice. Ribonucleic acid sequencing and reverse transcriptase polymerase chain reaction were performed to identify and characterize changes in gene expression in Dcdc2 KOs.

RESULTS

Neurons in KOs showed increased excitability and decreased temporal precision in action potential firing. The RNA sequencing screen revealed that the N-methyl-D-aspartate receptor (NMDAR) subunit Grin2B was elevated in Dcdc2 KOs, and an electrophysiological assessment confirmed a functional increase in spontaneous NMDAR-mediated activity. Remarkably, the decreased action potential temporal precision could be restored in mutants by treatment with either the NMDAR antagonist (2R)-amino-5-phosphonovaleric acid or the NMDAR 2B subunit-specific antagonist Ro 25-6981.

CONCLUSIONS

These results link the function of the dyslexia-associated gene Dcdc2 to spike timing through activity of NMDAR.

Sensory optimization by stochastic tuning

Individually, visual neurons are each selective for several aspects of stimulation, such as stimulus location, frequency content, and speed. Collectively, the neurons implement the visual system's preferential sensitivity to some stimuli over others, manifested in behavioral sensitivity functions. We ask how the individual neurons are coordinated to optimize visual sensitivity. We model synaptic plasticity in a generic neural circuit and find that stochastic changes in strengths of synaptic connections entail fluctuations in parameters of neural receptive fields. The fluctuations correlate with uncertainty of sensory measurement in individual neurons: The higher the uncertainty the larger the amplitude of fluctuation. We show that this simple relationship is sufficient for the stochastic fluctuations to steer sensitivities of neurons toward a characteristic distribution, from which follows a sensitivity function observed in human psychophysics and which is predicted by a theory of optimal allocation of receptive fields. The optimal allocation arises in our simulations without supervision or feedback about system performance and independently of coupling between neurons, making the system highly adaptive and sensitive to prevailing stimulation.

Elevated serotonergic signaling amplifies synaptic noise and facilitates the emergence of epileptiform network oscillations

Serotonin fibers densely innervate the cortical sheath to regulate neuronal excitability, but its role in shaping network dynamics remains undetermined. We show that serotonin provides an excitatory tone to cortical neurons in the form of spontaneous synaptic noise through 5-HT3 receptors, which is persistent and can be augmented using fluoxetine, a selective serotonin re-uptake inhibitor. Augmented serotonin signaling also increases cortical network activity by enhancing synaptic excitation through activation of 5-HT2 receptors. This in turn facilitates the emergence of epileptiform network oscillations (10-16 Hz) known as fast runs. A computational model of cortical dynamics demonstrates that these two combined mechanisms, increased background synaptic noise and enhanced synaptic excitation, are sufficient to replicate the emergence fast runs and their statistics. Consistent with these findings, we show that blocking 5-HT2 receptors in vivo significantly raises the threshold for convulsant-induced seizures.

Long-term temporal imprecision of information coding in the anterior cingulate cortex of mice with peripheral inflammation or nerve injury

Temporal properties of spike firing in the central nervous system (CNS) are critical for neuronal coding and the precision of information storage. Chronic pain has been reported to affect cognitive and emotional functions, in addition to trigger long-term plasticity in sensory synapses and behavioral sensitization. Less is known about the possible changes in temporal precision of cortical neurons in chronic pain conditions. In the present study, we investigated the temporal precision of action potential firing in the anterior cingulate cortex (ACC) by using both in vivo and in vitro electrophysiological approaches. We found that peripheral inflammation caused by complete Freund's adjuvant (CFA) increased the standard deviation (SD) of spikes latency (also called jitter) of ∼51% of recorded neurons in the ACC of adult rats in vivo. Similar increases in jitter were found in ACC neurons using in vitro brain slices from adult mice with peripheral inflammation or nerve injury. Bath application of glutamate receptor antagonists CNQX and AP5 abolished the enhancement of jitter induced by CFA injection or nerve injury, suggesting that the increased jitter depends on the glutamatergic synaptic transmission. Activation of adenylyl cyclases (ACs) by bath application of forskolin increased jitter, whereas genetic deletion of AC1 abolished the change of jitter caused by CFA inflammation. Our study provides strong evidence for long-term changes of temporal precision of information coding in cortical neurons after peripheral injuries and explains neuronal mechanism for chronic pain caused cognitive and emotional impairment.

Enhanced corticomuscular coherence by external stochastic noise

Noise can have beneficial effects as shown by the stochastic resonance (SR) phenomenon which is characterized by performance improvement when an optimal noise is added. Modern attempts to improve human performance utilize this phenomenon. The purpose of the present study was to investigate whether performance improvement by addition of optimum noise (ON) is related to increased cortical motor spectral power (SP) and increased corticomuscular coherence. Eight subjects performed a visuomotor task requiring to compensate with the right index finger a static force (SF) generated by a manipulandum on which Gaussian noise was applied. The finger position was displayed on-line on a monitor as a small white dot which the subjects had to maintain in the center of a green bigger circle. Electroencephalogram from the contralateral motor area, electromyogram from active muscles and finger position were recorded. The performance was measured by the mean absolute deviation (MAD) of the white dot from the zero position. ON compared to the zero noise condition induced an improvement in motor accuracy together with an enhancement of cortical motor SP and corticomuscular coherence in beta-range. These data suggest that the improved sensorimotor performance via SR is consistent with an increase in the cortical motor SP and in the corticomuscular coherence.

Simultaneous EEG-fMRI: trial level spatio-temporal fusion for hierarchically reliable information discovery

Simultaneous electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) have been pursued in an effort to integrate complementary noninvasive information on brain activity. The primary goal involves better information discovery of the event-related neural activations at a spatial region of the BOLD fluctuation with the temporal resolution of the electrical signal. Many techniques and algorithms have been developed to integrate EEGs and fMRIs; however, the relative reliability of the integrated information is unclear. In this work, we propose a hierarchical framework to ensure the relative reliability of the integrated results and attempt to understand brain activation using this hierarchical ideal. First, spatial Independent Component Analysis (ICA) of fMRI and temporal ICA of EEG were performed to extract features at the trial level. Second, the maximal information coefficient (MIC) was adopted to temporally match them across the modalities for both linear and non-linear associations. Third, fMRI-constrained EEG source imaging was utilized to spatially match components across modalities. The simultaneously occurring events in the above two match steps provided EEG-fMRI spatial-temporal reliable integrated information, resulting in the most reliable components with high spatial and temporal resolution information. The other components discovered in the second or third steps provided second-level complementary information for flexible and cautious explanations. This paper contains two simulations and an example of real data, and the results indicate that the framework is a feasible approach to reveal cognitive processing in the human brain.

Excitability and responsiveness of rat barrel cortex neurons in the presence and absence of spontaneous synaptic activity in vivo

The amplitude and temporal dynamics of spontaneous synaptic activity in the cerebral cortex vary as a function of brain states. To directly assess the impact of different ongoing synaptic activities on neocortical function, we performed in vivo intracellular recordings from barrel cortex neurons in rats under two pharmacological conditions generating either oscillatory or tonic synaptic drive. Cortical neurons membrane excitability and firing responses were compared, in the same neurons, before and after complete suppression of background synaptic drive following systemic injection of a high dose of anaesthetic. Compared to the oscillatory state, the tonic pattern resulted in a more depolarized and less fluctuating membrane potential (Vm), a lower input resistance (Rm) and steeper relations of firing frequency versus injected current (F-I). Whatever their temporal dynamics, suppression of background synaptic activities increased mean Vm, without affecting Rm, and induced a rightward shift of F-I curves. Both types of synaptic drive generated a high variability in current-induced firing rate and patterns in cortical neurons, which was much reduced after removal of spontaneous activity. These findings suggest that oscillatory and tonic synaptic patterns differentially facilitate the input-output function of cortical neurons but result in a similar moment-to-moment variability in spike responses to incoming depolarizing inputs.

A spiking network model of decision making employing rewarded STDP

Reward-modulated spike timing dependent plasticity (STDP) combines unsupervised STDP with a reinforcement signal that modulates synaptic changes. It was proposed as a learning rule capable of solving the distal reward problem in reinforcement learning. Nonetheless, performance and limitations of this learning mechanism have yet to be tested for its ability to solve biological problems. In our work, rewarded STDP was implemented to model foraging behavior in a simulated environment. Over the course of training the network of spiking neurons developed the capability of producing highly successful decision-making. The network performance remained stable even after significant perturbations of synaptic structure. Rewarded STDP alone was insufficient to learn effective decision making due to the difficulty maintaining homeostatic equilibrium of synaptic weights and the development of local performance maxima. Our study predicts that successful learning requires stabilizing mechanisms that allow neurons to balance their input and output synapses as well as synaptic noise.

Heterogeneity of intrinsic biophysical properties among cochlear nucleus neurons improves the population coding of temporal information

Reliable representation of the spectrotemporal features of an acoustic stimulus is critical for sound recognition. However, if all neurons respond with identical firing to the same stimulus, redundancy in the activity patterns would reduce the information capacity of the population. We thus investigated spike reliability and temporal fluctuation coding in an ensemble of neurons recorded in vitro from the avian auditory brain stem. Sequential patch-clamp recordings were made from neurons of the cochlear nucleus angularis while injecting identical filtered Gaussian white noise currents, simulating synaptic drive. The spiking activity in neurons receiving these identically fluctuating stimuli was highly correlated, measured pairwise across neurons and as a pseudo-population. Two distinct uncorrelated noise stimuli could be discriminated using the temporal patterning, but not firing rate, of the spike trains in the neural ensemble, with best discrimination using information at time scales of 5-20 ms. Despite high cross-correlation values, the spike patterns observed in individual neurons were idiosyncratic, with notable heterogeneity across neurons. To investigate how temporal information is being encoded, we used optimal linear reconstruction to produce an estimate of the original current stimulus from the spike trains. Ensembles of trains sampled across the neural population could be used to predict >50% of the stimulus variation using optimal linear decoding, compared with ∼20% using the same number of spike trains recorded from single neurons. We conclude that heterogeneity in the intrinsic biophysical properties of cochlear nucleus neurons reduces firing pattern redundancy while enhancing representation of temporal information.

Cardiorespiratory coupling: common rhythms in cardiac, sympathetic, and respiratory activities

Cardiorespiratory coupling is an encompassing term describing more than the well-recognized influences of respiration on heart rate and blood pressure. Our data indicate that cardiorespiratory coupling reflects a reciprocal interaction between autonomic and respiratory control systems, and the cardiovascular system modulates the ventilatory pattern as well. For example, cardioventilatory coupling refers to the influence of heart beats and arterial pulse pressure on respiration and is the tendency for the next inspiration to start at a preferred latency after the last heart beat in expiration. Multiple complementary, well-described mechanisms mediate respiration's influence on cardiovascular function, whereas mechanisms mediating the cardiovascular system's influence on respiration may only be through the baroreceptors but are just being identified. Our review will describe a differential effect of conditioning rats with either chronic intermittent or sustained hypoxia on sympathetic nerve activity but also on ventilatory pattern variability. Both intermittent and sustained hypoxia increase sympathetic nerve activity after 2 weeks but affect sympatho-respiratory coupling differentially. Intermittent hypoxia enhances sympatho-respiratory coupling, which is associated with low variability in the ventilatory pattern. In contrast, after constant hypobaric hypoxia, 1-to-1 coupling between bursts of sympathetic and phrenic nerve activity is replaced by 2-to-3 coupling. This change in coupling pattern is associated with increased variability of the ventilatory pattern. After baro-denervating hypobaric hypoxic-conditioned rats, splanchnic sympathetic nerve activity becomes tonic (distinct bursts are absent) with decreases during phrenic nerve bursts and ventilatory pattern becomes regular. Thus, conditioning rats to either intermittent or sustained hypoxia accentuates the reciprocal nature of cardiorespiratory coupling. Finally, identifying a compelling physiologic purpose for cardiorespiratory coupling is the biggest barrier for recognizing its significance. Cardiorespiratory coupling has only a small effect on the efficiency of gas exchange; rather, we propose that cardiorespiratory control system may act as weakly coupled oscillator to maintain rhythms within a bounded variability.

Critical phenomena and noise-induced phase transitions in neuronal networks

We study numerically and analytically first- and second-order phase transitions in neuronal networks stimulated by shot noise (a flow of random spikes bombarding neurons). Using an exactly solvable cortical model of neuronal networks on classical random networks, we find critical phenomena accompanying the transitions and their dependence on the shot noise intensity. We show that a pattern of spontaneous neuronal activity near a critical point of a phase transition is a characteristic property that can be used to identify the bifurcation mechanism of the transition. We demonstrate that bursts and avalanches are precursors of a first-order phase transition, paroxysmal-like spikes of activity precede a second-order phase transition caused by a saddle-node bifurcation, while irregular spindle oscillations represent spontaneous activity near a second-order phase transition caused by a supercritical Hopf bifurcation. Our most interesting result is the observation of the paroxysmal-like spikes. We show that a paroxysmal-like spike is a single nonlinear event that appears instantly from a low background activity with a rapid onset, reaches a large amplitude, and ends up with an abrupt return to lower activity. These spikes are similar to single paroxysmal spikes and sharp waves observed in electroencephalographic (EEG) measurements. Our analysis shows that above the saddle-node bifurcation, sustained network oscillations appear with a large amplitude but a small frequency in contrast to network oscillations near the Hopf bifurcation that have a small amplitude but a large frequency. We discuss an amazing similarity between excitability of the cortical model stimulated by shot noise and excitability of the Morris-Lecar neuron stimulated by an applied current.

Channel-noise-induced stochastic facilitation in an auditory brainstem neuron model

Neuronal membrane potentials fluctuate stochastically due to conductance changes caused by random transitions between the open and closed states of ion channels. Although it has previously been shown that channel noise can nontrivially affect neuronal dynamics, it is unknown whether ion-channel noise is strong enough to act as a noise source for hypothesized noise-enhanced information processing in real neuronal systems, i.e., "stochastic facilitation". Here we demonstrate that biophysical models of channel noise can give rise to two kinds of recently discovered stochastic facilitation effects in a Hodgkin-Huxley-like model of auditory brainstem neurons. The first, known as slope-based stochastic resonance (SBSR), enables phasic neurons to emit action potentials that can encode the slope of inputs that vary slowly relative to key time constants in the model. The second, known as inverse stochastic resonance (ISR), occurs in tonically firing neurons when small levels of noise inhibit tonic firing and replace it with burstlike dynamics. Consistent with previous work, we conclude that channel noise can provide significant variability in firing dynamics, even for large numbers of channels. Moreover, our results show that possible associated computational benefits may occur due to channel noise in neurons of the auditory brainstem. This holds whether the firing dynamics in the model are phasic (SBSR can occur due to channel noise) or tonic (ISR can occur due to channel noise).

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

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

GABA networks destabilize genetic oscillations in the circadian pacemaker

Systems of coupled oscillators abound in nature. How they establish stable phase relationships under diverse conditions is fundamentally important. The mammalian suprachiasmatic nucleus (SCN) is a self-sustained, synchronized network of circadian oscillators that coordinates daily rhythms in physiology and behavior. To elucidate the underlying topology and signaling mechanisms that modulate circadian synchrony, we discriminated the firing of hundreds of SCN neurons continuously over days. Using an analysis method to identify functional interactions between neurons based on changes in their firing, we characterized a GABAergic network comprised of fast, excitatory, and inhibitory connections that is both stable over days and changes in strength with time of day. By monitoring PERIOD2 protein expression, we provide the first evidence that these millisecond-level interactions actively oppose circadian synchrony and inject jitter into daily rhythms. These results provide a mechanism by which circadian oscillators can tune their phase relationships under different environmental conditions.

Pharmacological investigation of the bioluminescence signaling pathway of the dinoflagellate Lingulodinium polyedrum: evidence for the role of stretch-activated ion channels

Dinoflagellate bioluminescence serves as a whole-cell reporter of mechanical stress, which activates a signaling pathway that appears to involve the opening of voltage-sensitive ion channels and release of calcium from intracellular stores. However, little else is known about the initial signaling events that facilitate the transduction of mechanical stimuli. In the present study using the red tide dinoflagellate Lingulodinium polyedrum (Stein) Dodge, two forms of dinoflagellate bioluminescence, mechanically stimulated and spontaneous flashes, were used as reporter systems to pharmacological treatments that targeted various predicted signaling events at the plasma membrane level of the signaling pathway. Pretreatment with 200 μM Gadolinium III (Gd(3+) ), a nonspecific blocker of stretch-activated and some voltage-gated ion channels, resulted in strong inhibition of both forms of bioluminescence. Pretreatment with 50 μM nifedipine, an inhibitor of L-type voltage-gated Ca(2+) channels that inhibits mechanically stimulated bioluminescence, did not inhibit spontaneous bioluminescence. Treatment with 1 mM benzyl alcohol, a membrane fluidizer, was very effective in stimulating bioluminescence. Benzyl alcohol-stimulated bioluminescence was inhibited by Gd(3+) but not by nifedipine, suggesting that its role is through stretch activation via a change in plasma membrane fluidity. These results are consistent with the presence of stretch-activated and voltage-gated ion channels in the bioluminescence mechanotransduction signaling pathway, with spontaneous flashing associated with a stretch-activated component at the plasma membrane.

Patterned Brain Stimulation, What a Framework with Rhythmic and Noisy Components Might Tell Us about Recovery Maximization

Brain stimulation is having remarkable impact on clinical neurology. Brain stimulation can modulate neuronal activity in functionally segregated circumscribed regions of the human brain. Polarity, frequency, and noise specific stimulation can induce specific manipulations on neural activity. In contrast to neocortical stimulation, deep-brain stimulation has become a tool that can dramatically improve the impact clinicians can possibly have on movement disorders. In contrast, neocortical brain stimulation is proving to be remarkably susceptible to intrinsic brain-states. Although evidence is accumulating that brain stimulation can facilitate recovery processes in patients with cerebral stroke, the high variability of results impedes successful clinical implementation. Interestingly, recent data in healthy subjects suggests that brain-state dependent patterned stimulation might help resolve some of the intrinsic variability found in previous studies. In parallel, other studies suggest that noisy “stochastic resonance” (SR)-like processes are a non-negligible component in non-invasive brain stimulation studies. The hypothesis developed in this manuscript is that stimulation patterning with noisy and oscillatory components will help patients recover from stroke related deficits more reliably. To address this hypothesis we focus on two factors common to both neural computation (intrinsic variables) as well as brain stimulation (extrinsic variables): noise and oscillation. We review diverse theoretical and experimental evidence that demonstrates that subject-function specific brain-states are associated with specific oscillatory activity patterns. These states are transient and can be maintained by noisy processes. The resulting control procedures can resemble homeostatic or SR processes. In this context we try to extend awareness for inter-individual differences and the use of individualized stimulation in the recovery maximization of stroke patients.

Measuring input synchrony in the Ornstein-Uhlenbeck neuronal model through input parameter estimation

We present a method of estimating the input parameters and through them, the input synchrony, of a stochastic leaky integrate-and-fire neuronal model based on the Ornstein-Uhlenbeck process when it is driven by time-dependent sinusoidal input signal and noise. By driving the neuron using sinusoidal inputs, we simulate the effects of periodic synchrony on the membrane voltage and the firing of the neuron, where the peaks of the sine wave represent volleys of synchronised input spikes. Our estimation methods allow us to measure the degree of synchrony driving the neuron in terms of the input sine wave parameters, using the output spikes of the model and the membrane potential. In particular, by estimating the frequency of the synchronous input volleys and averaging the estimates of the level of input activity at corresponding intervals of the input signal, we obtain fairly accurate estimates of the baseline and peak activity of the input, which in turn define the degrees of synchrony. The same procedure is also successfully applied in estimating the baseline and peak activity of the noise. This article is part of a Special Issue entitled Neural Coding 2012.

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.

Spontaneous and sensory-evoked activity in mouse olfactory sensory neurons with defined odorant receptors

Sensory systems need to tease out stimulation-evoked activity against a noisy background. In the olfactory system, the odor response profile of an olfactory sensory neuron (OSN) is dependent on the type of odorant receptor it expresses. OSNs also exhibit spontaneous activity, which plays a role in establishing proper synaptic connections and may also increase the sensitivity of the cells. However, where the spontaneous activity originates and whether it informs sensory-evoked activity remain unclear. We addressed these questions by examining patch-clamp recordings of genetically labeled mouse OSNs with defined odorant receptors in intact olfactory epithelia. We show that OSNs expressing different odorant receptors had significantly different rates of basal activity. Additionally, OSNs expressing an inactive mutant I7 receptor completely lacked spontaneous activity, despite being able to fire action potentials in response to current injection. This finding strongly suggests that the spontaneous firing of an OSN originates from the spontaneous activation of its G protein-coupled odorant receptor. Moreover, OSNs expressing the same receptor displayed considerable variation in their spontaneous activity, and the variation was broadened upon odor stimulation. Interestingly, there is no significant correlation between the spontaneous and sensory-evoked activity in these neurons. This study reveals that the odorant receptor type determines the spontaneous firing rate of OSNs, but the basal activity does not correlate with the activity induced by near-saturated odor stimulation. The implications of these findings on olfactory information processing are discussed.

Synaptic variability in a cortical neuromorphic circuit

Variable behavior has been observed in several mechanisms found in biological neurons, resulting in changes in neural behavior that might be useful to capture in neuromorphic circuits. This paper presents a neuromorphic cortical neuron with synaptic neurotransmitter-release variability, which is designed to be used in neural networks as part of the Biomimetic Real-Time Cortex project. This neuron has been designed and simulated using carbon nanotube (CNT) transistors, which is one of several nanotechnologies under consideration to meet the challenges of scale presented by the cortex. Some research results suggest that some instances of variability are stochastic, while others indicate that some instances of variability are chaotic. In this paper, both possible sources of variability are considered by embedding either Gaussian noise or a chaotic signal into the neuromorphic or synaptic circuit and observing the simulation results. In order to embed chaotic behavior into the neuromorphic circuit, a chaotic signal generator circuit is presented, implemented with CNT transistors that could be embedded in the electronic neural circuit, and simulated using CNT SPICE models. The circuit uses a chaotic piecewise linear 1-D map implemented by switched-current circuits. The simulation results presented in this paper illustrate that neurotransmitter-release variability plays a beneficial role in the reliability of spike generation. In an examination of this reliability, the precision of spike timing in the CNT circuit simulations is found to be dependent on stimulus (postsynaptic potential) transients. Postsynaptic potentials with low neurotransmitter release variability or without neurotransmitter release variability produce imprecise spike trains, whereas postsynaptic potentials with high neurotransmitter-release variability produce spike trains with reproducible timing.

Neural variability, or lack thereof

We do not claim that the brain is completely deterministic, and we agree that noise may be beneficial in some cases. But we suggest that neuronal variability may be often overestimated, due to uncontrolled internal variables, and/or the use of inappropriate reference times. These ideas are not new, but should be re-examined in the light of recent experimental findings: trial-to-trial variability is often correlated across neurons, across trials, greater for higher-order neurons, and reduced by attention, suggesting that "intrinsic" sources of noise can only account for a minimal part of it. While it is obviously difficult to control for all internal variables, the problem of reference time can be largely avoided by recording multiple neurons at the same time, and looking at statistical structures in relative latencies. These relative latencies have another major advantage: they are insensitive to the variability that is shared across neurons, which is often a significant part of the total variability. Thus, we suggest that signal-to-noise ratios in the brain may be much higher than usually thought, leading to reactive systems, economic in terms of number of neurons, and energy efficient.

Quantifying interactions between real oscillators with information theory and phase models: application to cardiorespiratory coupling

Interactions between oscillators can be investigated with standard tools of time series analysis. However, these methods are insensitive to the directionality of the coupling, i.e., the asymmetry of the interactions. An elegant alternative was proposed by Rosenblum and collaborators [M. G. Rosenblum, L. Cimponeriu, A. Bezerianos, A. Patzak, and R. Mrowka, Phys. Rev. E 65, 041909 (2002); M. G. Rosenblum and A. S. Pikovsky, Phys. Rev. E 64, 045202 (2001)] which consists in fitting the empirical phases to a generic model of two weakly coupled phase oscillators. This allows one to obtain the interaction functions defining the coupling and its directionality. A limitation of this approach is that a solution always exists in the least-squares sense, even in the absence of coupling. To preclude spurious results, we propose a three-step protocol: (1) Determine if a statistical dependency exists in the data by evaluating the mutual information of the phases; (2) if so, compute the interaction functions of the oscillators; and (3) validate the empirical oscillator model by comparing the joint probability of the phases obtained from simulating the model with that of the empirical phases. We apply this protocol to a model of two coupled Stuart-Landau oscillators and show that it reliably detects genuine coupling. We also apply this protocol to investigate cardiorespiratory coupling in anesthetized rats. We observe reciprocal coupling between respiration and heartbeat and that the influence of respiration on the heartbeat is generally much stronger than vice versa. In addition, we find that the vagus nerve mediates coupling in both directions.

Parameterized phase response curves for characterizing neuronal behaviors under transient conditions

Phase response curves (PRCs) are a simple model of how a neuron's spike time is affected by synaptic inputs. PRCs are useful in predicting how networks of neurons behave when connected. One challenge in estimating a neuron's PRCs experimentally is that many neurons do not have stationary firing rates. In this article we introduce a new method to estimate PRCs as a function of firing rate of the neuron. We call the resulting model a parameterized PRC (pPRC). Experimentally, we perturb the neuron applying a current with two parts: 1) a current held constant between spikes but changed at the onset of a spike, used to make the neuron fire at different rates, and 2) a pulse to emulate a synaptic input. A model of the applied constant current and the history is made to predict the interspike interval (ISI). A second model is then made to fit the modulation of the spike time from the expected ISI by the pulsatile stimulus. A polynomial with two independent variables, the stimulus phase and the expected ISI, is used to model the pPRC. The pPRC is validated in a computational model and applied to pyramidal neurons from the CA1 region of the hippocampal slices from rat. The pPRC can be used to model the effect of changing firing rates on network synchrony. It can also be used to characterize the effects of neuromodulators and genetic mutations (among other manipulations) on network synchrony. It can also easily be extended to account for more variables.

Biologically inspired information processing and synchronization in ensembles of non-identical threshold-potential nanostructures

Nanotechnology produces basic structures that show a significant variability in their individual physical properties. This experimental fact may constitute a serious limitation for most applications requiring nominally identical building blocks. On the other hand, biological diversity is found in most natural systems. We show that reliable information processing can be achieved with heterogeneous groups of non-identical nanostructures by using some conceptual schemes characteristic of biological networks (diversity, frequency-based signal processing, rate and rank order coding, and synchronization). To this end, we simulate the integrated response of an ensemble of single-electron transistors (SET) whose individual threshold potentials show a high variability. A particular experimental realization of a SET is a metal nanoparticle-based transistor that mimics biological spiking synapses and can be modeled as an integrate-and-fire oscillator. The different shape and size distributions of nanoparticles inherent to the nanoscale fabrication procedures result in a significant variability in the threshold potentials of the SET. The statistical distributions of the nanoparticle physical parameters are characterized by experimental average and distribution width values. We consider simple but general information processing schemes to draw conclusions that should be of relevance for other threshold-based nanostructures. Monte Carlo simulations show that ensembles of non-identical SET may show some advantages over ensembles of identical nanostructures concerning the processing of weak signals. The results obtained are also relevant for understanding the role of diversity in biophysical networks.

Transcranial stimulation and cognition

Noninvasive brain stimulation (NIBS) is a unique method for studying cognitive function. For the study of cognition, NIBS has gained popularity as a complementary method to functional neuroimaging. By bypassing the correlative approaches of standard imaging techniques, it is possible to establish a putative relationship between brain cognition. In fact, functional neuroimaging data cannot demonstrate the actual role of a particular cortical activation in a specific function because an activated area may simply be correlated with task performance, rather than being responsible for it. NIBS can induce a temporary modification of performance only if the stimulated area is causally engaged in the task. In analogy with lesion studies, NIBS can provide information about where and when a particular process occurs. Based on this assumption, NIBS has been used in many different cognitive domains. However, one of the most interesting questions in neuroscience may not be where and when, but how cognitive activity occurs. Beyond localization approaches, NIBS can be employed to study brain mechanisms. NIBS techniques have the potential to influence behavior transiently by altering neuronal activity, which may have facilitatory or inhibitory behavioral effects. NIBS techniques include transcranial magnetic stimulation (TMS) and transcranial electrical stimulation (tES). TMS has been shown transiently to modulate neural excitability in a manner that is dependent mainly on the timing and frequency of stimulation (high versus low). The mechanism underlying tES is a change in neuronal membrane potentials that appears to be dependent mainly on the direction of current flow (anodal versus cathodal). Nevertheless, the final effects induced by TMS or tES depend on many technical parameters used during stimulation, such as the intensity of stimulation, coil orientation, site of the reference electrode, and time of application. Moreover, an important factor is the possible interactions between these factors and the physiological and cognitive state of the subject. To use NIBS in cognition, it is important to understand not only how NIBS functions but also the brain mechanisms being studied and the features of the area of interest. To describe better the advanced knowledge provided by NIBS in cognition, we will treat each NIBS technique separately and underline the related hypotheses beyond applications.