A variant of the integrate-and-fire model to simulate the adaptive neural firing pattern

The integrate-and-fire (IF) based modeling technique has been long employed to study the neural firing activities. This paper introduces a variant of the IF model in order to simulate the adaptive neural firing pattern. An inductor branch is integrated into the IF model to track the variance of the external stimulus, and subsequently control the decrease of the instantaneous firing rate in response to the sustained stimulation. Simulation results demonstrated that the proposed model was able to reproduce the adaptive neural firing pattern. Besides, the inductor branch might adjust the decay rate of the adaptive firing curve and the prominent firing rate upon the onset of the adaptation. The proposed model is characterized by its structure simplicity and simulation efficiency, which would be helpful for the analysis and prediction of the adaptive firing responses of the sensory neurons.     

Noise in attractor networks in the brain produced by graded firing rate representations

Representations in the cortex are often distributed with graded firing rates in the neuronal populations. The firing rate probability distribution of each neuron to a set of stimuli is often exponential or gamma. In processes in the brain, such as decision-making, that are influenced by the noise produced by the close to random spike timings of each neuron for a given mean rate, the noise with this graded type of representation may be larger than with the binary firing rate distribution that is usually investigated. In integrate-and-fire simulations of an attractor decision-making network, we show that the noise is indeed greater for a given sparseness of the representation for graded, exponential, than for binary firing rate distributions. The greater noise was measured by faster escaping times from the spontaneous firing rate state when the decision cues are applied, and this corresponds to faster decision or reaction times. The greater noise was also evident as less stability of the spontaneous firing state before the decision cues are applied. The implication is that spiking-related noise will continue to be a factor that influences processes such as decision-making, signal detection, short-term memory, and memory recall even with the quite large networks found in the cerebral cortex. In these networks there are several thousand recurrent collateral synapses onto each neuron. The greater noise with graded firing rate distributions has the advantage that it can increase the speed of operation of cortical circuitry.     

Dynamic Excitatory and Inhibitory Gain Modulation Can Produce Flexible,Robust and Optimal Decision-making

Behavioural and neurophysiological studies in primates have increasingly shown the involvement of urgency signals during the temporal integration of sensory evidence in perceptual decision-making. Neuronal correlates of such signals have been found in the parietal cortex, and in separate studies, demonstrated attention-induced gain modulation of both excitatory and inhibitory neurons. Although previous computational models of decision-making have incorporated gain modulation, their abstract forms do not permit an understanding of the contribution of inhibitory gain modulation. Thus, the effects of co-modulating both excitatory and inhibitory neuronal gains on decision-making dynamics and behavioural performance remain unclear. In this work, we incorporate time-dependent co-modulation of the gains of both excitatory and inhibitory neurons into our previous biologically based decision circuit model. We base our computational study in the context of two classic motion-discrimination tasks performed in animals. Our model shows that by simultaneously increasing the gains of both excitatory and inhibitory neurons, a variety of the observed dynamic neuronal firing activities can be replicated. In particular, the model can exhibit winner-take-all decision-making behaviour with higher firing rates and within a significantly more robust model parameter range. It also exhibits short-tailed reaction time distributions even when operating near a dynamical bifurcation point. The model further shows that neuronal gain modulation can compensate for weaker recurrent excitation in a decision neural circuit, and support decision formation and storage. Higher neuronal gain is also suggested in the more cognitively demanding reaction time than in the fixed delay version of the task. Using the exact temporal delays from the animal experiments, fast recruitment of gain co-modulation is shown to maximize reward rate, with a timescale that is surprisingly near the experimentally fitted value. Our work provides insights into the simultaneous and rapid modulation of excitatory and inhibitory neuronal gains, which enables flexible, robust, and optimal decision-making.     

Asymmetric life-history decision-making in butterfly larvae

In temperate environments, insects appearing in several generations in the growth season typically have to decide during the larval period whether to develop into adulthood, or to postpone adult emergence until next season by entering a species-specific diapause stage. This decision is typically guided by environmental cues experienced during development. An early decision makes it possible to adjust growth rate, which would allow the growing larva to respond to time stress involved in direct development, whereas a last-minute decision would instead allow the larva to use up-to-date information about which developmental pathway is the most favourable under the current circumstances. We study the timing of the larval pathway decision-making between entering pupal winter diapause and direct development in three distantly related butterflies (Pieris napi, Araschnia levana and Pararge aegeria). We pinpoint the timing of the larval diapause decision by transferring larvae from first to last instars from long daylength (inducing direct development) to short daylength conditions (inducing diapause), and vice versa. Results show that the pathway decision is typically made in the late instars in all three species, and that the ability to switch developmental pathway late in juvenile life is conditional; larvae more freely switched from diapause to direct development than in the opposite direction. We contend that this asymmetry is influenced by the additional physiological preparations needed to survive the long and cold winter period, and that the reluctance to make a late decision to enter diapause has the potential to be a general trait among temperate insects.     

Risky Decisions and Their Consequences: Neural Processing by Boys with Antisocial Substance Disorder

Background

Adolescents with conduct and substance problems (“Antisocial Substance Disorder” (ASD)) repeatedly engage in risky antisocial and drug-using behaviors. We hypothesized that, during processing of risky decisions and resulting rewards and punishments, brain activation would differ between abstinent ASD boys and comparison boys.

Methodology/Principal Findings

We compared 20 abstinent adolescent male patients in treatment for ASD with 20 community controls, examining rapid event-related blood-oxygen-level-dependent (BOLD) responses during functional magnetic resonance imaging. In 90 decision trials participants chose to make either a cautious response that earned one cent, or a risky response that would either gain 5 cents or lose 10 cents; odds of losing increased as the game progressed. We also examined those times when subjects experienced wins, or separately losses, from their risky choices. We contrasted decision trials against very similar comparison trials requiring no decisions, using whole-brain BOLD-response analyses of group differences, corrected for multiple comparisons. During decision-making ASD boys showed hypoactivation in numerous brain regions robustly activated by controls, including orbitofrontal and dorsolateral prefrontal cortices, anterior cingulate, basal ganglia, insula, amygdala, hippocampus, and cerebellum. While experiencing wins, ASD boys had significantly less activity than controls in anterior cingulate, temporal regions, and cerebellum, with more activity nowhere. During losses ASD boys had significantly more activity than controls in orbitofrontal cortex, dorsolateral prefrontal cortex, brain stem, and cerebellum, with less activity nowhere.

Conclusions/Significance

Adolescent boys with ASD had extensive neural hypoactivity during risky decision-making, coupled with decreased activity during reward and increased activity during loss. These neural patterns may underlie the dangerous, excessive, sustained risk-taking of such boys. The findings suggest that the dysphoria, reward insensitivity, and suppressed neural activity observed among older addicted persons also characterize youths early in the development of substance use disorders.     

Time course of perceptual discrimination and single neuron reliability

The reliability of identification of a visual target increases with time available for inspection of the stimulus. We suggest that the neural basis of this improvement is the existence of a mechanism for integrating a noisy firing rate over some period, leading to a reduction in mean firing rate variance with available processing time. We have determined the experimental time course of the improvement in reliability in a parallel search task where the available inspection time is limited by the presentation of a mask at various times after a brief stimulus. We compare the resulting psychometric functions with the predictions of a model based on Signal Detection Theory. The model is based on the assumption that the reliability of the observer's response is limited by the variability of the responses of individual neurons. The reliability of the discrimination between two stimuli at the neuronal level is then directly related to the ratio of the difference between their integrated mean responses (over many trials) to the response standard deviation. This reliability increases with inspection time. To demonstrate application of the model to electrophysiological data, neurometric functions are derived from the firing rates of a monkeyV1 cortical neuron. The data were obtained while the animal was active in a discrimination task. The results correspond qualitatively to our observed human psychometric functions.     

Spatial response properties of homing pigeon hippocampal neurons: correlations with goal locations,movement between goals,and environmental context in a radial-arm arena

The amniote hippocampal formation plays an evolutionarily-conserved role in the neural representation of environmental space. However, species differences in spatial ecology nurture the expectation of species differences in how hippocampal neurons represent space. To determine the spatial response properties of homing pigeon (Columba livia) HFneurons, we recorded from isolated units in birds freely navigating a radial arena in search of food present at four goal locations. Fifty of 76 neurons displayed firing rate variations that could be placed into three response categories. Location cells (n=25) displayed higher firing rates at restricted locations in the arena space, often in proximity to goal locations. Path cells (n=13) displayed higher firing rates as a pigeon moved between a subset of goal locations. Arena-off cells (n=12) were more active when a pigeon was in a baseline holding space compared to inside the arena. Overall, reliability and coherence scores of the recorded neurons were lower compared to rat place cells. The differences in the spatial response profiles of pigeon hippocampal formation neurons, when compared to rats, provide a departure point for better understanding the relationship between spatial behavior and how hippocampal formation neurons participate in the representation of space.     

Neural differentiation of expected reward and risk in human subcortical structures

In decision-making under uncertainty, economic studies emphasize the importance of risk in addition to expected reward. Studies in neuroscience focus on expected reward and learning rather than risk. We combined functional imaging with a simple gambling task to vary expected reward and risk simultaneously and in an uncorrelated manner. Drawing on financial decision theory, we modeled expected reward as mathematical expectation of reward, and risk as reward variance. Activations in dopaminoceptive structures correlated with both mathematical parameters. These activations differentiated spatially and temporally. Temporally, the activation related to expected reward was immediate, while the activation related to risk was delayed. Analyses confirmed that our paradigm minimized confounds from learning, motivation, and salience. These results suggest that the primary task of the dopaminergic system is to convey signals of upcoming stochastic rewards, such as expected reward and risk, beyond its role in learning, motivation, and salience.     

Candidate codes in the gustatory system of caterpillars

Larvae of tobacco hornworms offer unique opportunities to relate the electrophysiological output of identified chemosensory neurons to specific behavioral responses. Larvae can discriminate among three preferred plants with only eight functioning gustatory receptors. They can be induced to prefer any one of the plants, and these preferences can be reversed. All eight neurons respond to each plant sap. Two fire too infrequently to permit detailed analysis. Analyses of the remaining six show that all electrophysiological responses consist of phasic and tonic components. Only the "salt best" cell fires during the phasic period. Temporal analysis of the spike train during this period shows that tomato and tobacco could be distinguished from Jerusalem cherry but not from each other by a rate code. Measurements of behavioral response times together with the nonspecificity of this with respect of food plants, unacceptable plants, and sodium chloride eliminate a phasic period rate code as a probable mechanism for complex discrimination. Events occurring in the tonic period, when all cells are firing, suggest a major role for this period. Analyses of variance in the interval frequencies of the large and medium spikes suggest that a variance code could allow discrimination among the three plants as long as both cells were firing at the same time. Evidence has been found for temporal patterning in the tonic response of the "salt best" cell to Jerusalem cherry but is absent elsewhere. The most likely basis for coding the difference between each of the three plants is across- fiber patterning in which the relative rates of firing and the variances of all the sensory neurons in the tonic phase are critical.     

Improved dimensionally-reduced visual cortical network using stochastic noise modeling

In this paper, we extend our framework for constructing low-dimensional dynamical system models of large-scale neuronal networks of mammalian primary visual cortex. Our dimensional reduction procedure consists of performing a suitable linear change of variables and then systematically truncating the new set of equations. The extended framework includes modeling the effect of neglected modes as a stochastic process. By parametrizing and including stochasticity in one of two ways we show that we can improve the systems-level characterization of our dimensionally reduced neuronal network model. We examined orientation selectivity maps calculated from the firing rate distribution of large-scale simulations and stochastic dimensionally reduced models and found that by using stochastic processes to model the neglected modes, we were able to better reproduce the mean and variance of firing rates in the original large-scale simulations while still accurately predicting the orientation preference distribution.     

In vivo approach to the cellular mechanisms for sensory processing in sleep and wakefulness

1. The present review analyzes sensory processing during sleep and wakefulness from a single neuronal viewpoint. Our premises are that processing changes throughout the sleep–wakefulness cycle may be at least partially evidenced in single neurons by (a) changes in the phase locking of the response to the hippocampal theta rhythm, (b) changes in the discharge rate and firing pattern of the response to sound, and (c) changes in the effects of the neurotransmitters involved in the afferent and efferent pathways.2. The first part of our report is based on the hypothesis that the encoding of sensory information needs a timer in order to be processed and stored, and that the hippocampal theta rhythm could contribute to the temporal organization. We have demonstrated that the guinea pig's auditory and visual neuronal discharge exhibits a temporal relationship (phase locking) to the hippocampal theta waves during wakefulness and sleep phases.3. The concept that the neural network organization during sleep versus wakefulness is different and can be modulated by sensory signals and vice versa, and that the sensory input may be influenced by the CNS state, i.e., asleep or awake, is introduced. During sleep the evoked firing of auditory units increases, decreases, or remains similar to that observed during quiet wakefulness. However, there has been no auditory unit yet that stops firing as the guinea pig enters sleep. Approximately half of the cortical neurons studied did not change firing rate when passing into sleep while others increased or decreased. Thus, the system is continuously aware of the environment. We postulate that those neurons that changed their evoked firing during sleep are also related to still unknown sleep processes.4. Excitatory amino acid neurotransmitters participate in the synaptic transmission of the afferent and efferent pathways in the auditory system. In the inferior colliculus, however, the effects of glutamate's mediating the response to sound and the efferent excitation evoked by cortical stimulation failed to show differences in sleep and wakefulness.5. Considering that neonates and also infants spend most of the time asleep, the continuous arrival of sensory information to the brain during both sleep phases may serve to sculpt the brain by activity-dependent mechanisms of neural development, as has been postulated for wakefulness.     

Amplification of trial-to-trial response variability by neurons in visual cortex

The visual cortex responds to repeated presentations of the same stimulus with high variability. Because the firing mechanism is remarkably noiseless, the source of this variability is thought to lie in the membrane potential fluctuations that result from summated synaptic input. Here this hypothesis is tested through measurements of membrane potential during visual stimulation. Surprisingly, trial-to-trial variability of membrane potential is found to be low. The ratio of variance to mean is much lower for membrane potential than for firing rate. The high variability of firing rate is explained by the threshold present in the function that converts inputs into firing rates. Given an input with small, constant noise, this function produces a firing rate with a large variance that grows with the mean. This model is validated on responses recorded both intracellularly and extracellularly. In neurons of visual cortex, thus, a simple deterministic mechanism amplifies the low variability of summated synaptic inputs into the large variability of firing rate. The computational advantages provided by this amplification are not known.     

Acetylcholine-gated current translates wake neuronal firing rate information into a spike timing-based code in Non-REM sleep,stabilizing neural network dynamics during memory consolidation

Sleep is critical for memory consolidation, although the exact mechanisms mediating this process are unknown. Combining reduced network models and analysis of in vivo recordings, we tested the hypothesis that neuromodulatory changes in acetylcholine (ACh) levels during non-rapid eye movement (NREM) sleep mediate stabilization of network-wide firing patterns, with temporal order of neurons’ firing dependent on their mean firing rate during wake. In both reduced models and in vivo recordings from mouse hippocampus, we find that the relative order of firing among neurons during NREM sleep reflects their relative firing rates during prior wake. Our modeling results show that this remapping of wake-associated, firing frequency-based representations is based on NREM-associated changes in neuronal excitability mediated by ACh-gated potassium current. We also show that learning-dependent reordering of sequential firing during NREM sleep, together with spike timing-dependent plasticity (STDP), reconfigures neuronal firing rates across the network. This rescaling of firing rates has been reported in multiple brain circuits across periods of sleep. Our model and experimental data both suggest that this effect is amplified in neural circuits following learning. Together our data suggest that sleep may bias neural networks from firing rate-based towards phase-based information encoding to consolidate memories.     

神经放电起步点对电场刺激反应的“临界敏感”现象

在大鼠坐骨神经慢性压迫模型的放电起步点上,记录单纤维放电的峰峰间期(ISIs)序列。在无钙条件下,ISIs序列进入加周期分岔过程后,通过调定灌流液乙二醇双四乙酸(Ethylene Glycol—bis(β—aminoethyl Ether)N,N,N’,N’-Tetracetic Acid,EGTA,一种钙离子螯合剂)的浓度,使。ISIs序列分别稳定于远离分岔点的周期阶段(称周期阶段)或邻近分岔点的阶段(称临界阶段),分析电场刺激反应与分岔动力学状态的关系。实验观察到,相同强度的电场刺激可使周期阶段和临界阶段的放电频率增加,但后者的增加幅度比前者显著,并伴有放电模式的转化。在周期阶段,随电场刺激强度增大,放电频率近似线性增加,放电模式不变;在临界阶段,当电场刺激达到一定强度时,放电频率增加的斜率显著增大,此时,放电模式也发生转化。结果提示邻近分岔点的临界阶段对电场刺激的反应较周期阶段敏感,称之为“临界敏感”现象。     

Nonlinear sequence-dependent structure of nigral dopamine neuron interspike interval firing patterns.

Firing patterns of 15 dopamine neurons in the rat substantia nigra were studied. These cells alternated between two firing modes, single-spike and bursting, which interwove to produce irregular, aperiodic interspike interval (ISI) patterns. When examined by linear autocorrelation analysis, these patterns appeared to reflect a primarily stochastic or random process. However, dynamical analysis revealed that the sequential behavior of a majority of these cells expressed "higher-dimensional" nonlinear deterministic structure. Dimensionality refers to the number of degrees of freedom or complexity of a time series. Bursting was statistically associated with some aspects of nonlinear ISI sequence dependence. Controlling for the effects of nonstationarity substantially increased overall predictability of ISI sequences. We hypothesize that the nonlinear deterministic structure of ISI firing patterns reflects the neuron's response to coordinated synaptic inputs emerging from neural circuit interactions.     

Dynamics of the Instantaneous Firing Rate in Response to Changes in Input Statistics

We review and extend recent results on the instantaneous firing rate dynamics of simplified models of spiking neurons in response to noisy current inputs. It has been shown recently that the response of the instantaneous firing rate to small amplitude oscillations in the mean inputs depends in the large frequency limit f on the spike initiation dynamics. A particular simplified model, the exponential integrate-and-fire (EIF) model, has a response that decays as 1/f in the large frequency limit and describes very well the response of conductance-based models with a Hodgkin-Huxley type fast sodium current. Here, we show that the response of the EIF instantaneous firing rate also decays as 1/f in the case of an oscillation in the variance of the inputs for both white and colored noise. We then compute the initial transient response of the firing rate of the EIF model to a step change in its mean inputs and/or in the variance of its inputs. We show that in both cases the response speed is proportional to the neuron stationary firing rate and inversely proportional to a spike slope factor _T that controls the sharpness of spike initiation: as 1/_T for a step change in mean inputs, and as 1/_T² for a step change in the variance in the inputs.     

Responses of pulmonary stretch receptors during ramp inflations of the lung

Studies were conducted in anesthetized paralyzed dogs to determine how the dynamic and proportional sensitivity of pulmonary stretch receptors change during lung inflation. The firing of each receptor was examined at multiple levels of static transpulmonary pressure and during multiple identical inflations at each of several rates. The averaged response of the receptor was computed and receptor activity related to transpulmonary pressure. On the basis of a quantitative criterion, employed to distinguish type I from type II receptors, the receptors could not be divided into distinct subpopulations. Thus all receptors were treated as coming from a single population. For all receptors we observed that their proportional sensitivity (increases in firing produced by increases in lung expansion at a constant rate of inflation) declined as the lung was inflated. In contrast, the dynamic sensitivity (increases in firing produced by increased rates of inflation at constant transpulmonary pressure) increased or remained relatively constant with increasing lung expansion. Thus, as inflation volume increases, the pulmonary stretch receptor acts increasingly as a rate receptor. The rate of inflation may have a more important role in control of the inspiratory duration than previously realized.     

Phase-of-firing coding of natural visual stimuli in primary visual cortex

We investigated the hypothesis that neurons encode rich naturalistic stimuli in terms of their spike times relative to the phase of ongoing network fluctuations rather than only in terms of their spike count. We recorded local field potentials (LFPs) and multiunit spikes from the primary visual cortex of anaesthetized macaques while binocularly presenting a color movie. We found that both the spike counts and the low-frequency LFP phase were reliably modulated by the movie and thus conveyed information about it. Moreover, movie periods eliciting higher firing rates also elicited a higher reliability of LFP phase across trials. To establish whether the LFP phase at which spikes were emitted conveyed visual information that could not be extracted by spike rates alone, we compared the Shannon information about the movie carried by spike counts to that carried by the phase of firing. We found that at low LFP frequencies, the phase of firing conveyed 54% additional information beyond that conveyed by spike counts. The extra information available in the phase of firing was crucial for the disambiguation between stimuli eliciting high spike rates of similar magnitude. Thus, phase coding may allow primary cortical neurons to represent several effective stimuli in an easily decodable format.     

Stochastic analogues of deterministic single-species population models

Although single-species deterministic difference equations have long been used in modeling the dynamics of animal populations, little attention has been paid to how stochasticity should be incorporated into these models. By deriving stochastic analogues to difference equations from first principles, we show that the form of these models depends on whether noise in the population process is demographic or environmental. When noise is demographic, we argue that variance around the expectation is proportional to the expectation. When noise is environmental the variance depends in a non-trivial way on how variation enters into model parameters, but we argue that if the environment affects the population multiplicatively then variance is proportional to the square of the expectation. We compare various stochastic analogues of the Ricker map model by fitting them, using maximum likelihood estimation, to data generated from an individual-based model and the weevil data of Utida. Our demographic models are significantly better than our environmental models at fitting noise generated by population processes where noise is mainly demographic. However, the traditionally chosen stochastic analogues to deterministic models--additive normally distributed noise and multiplicative lognormally distributed noise--generally fit all data sets well. Thus, the form of the variance does play a role in the fitting of models to ecological time series, but may not be important in practice as first supposed.