Detecting and estimating signals in noisy cable structure, I: neuronal noise sources

Behavioural stochastic resonance across the lifespan

Stochastic resonance (SR) is the phenomenon wherein the introduction of a suitable level of noise enhances the detection of subthreshold signals in non linear systems. It manifests across various physical and biological systems, including the human brain. Psychophysical experiments have confirmed the behavioural impact of stochastic resonance on auditory, somatic, and visual perception. Aging renders the brain more susceptible to noise, possibly causing differences in the  SR phenomenon between young and elderly individuals. This study investigates the impact of noise on motion detection accuracy throughout the lifespan, with 214 participants ranging in age from 18 to 82. Our objective was to determine the optimal noise level to induce an SR-like response in both young and old populations. Consistent with existing literature, our findings reveal a diminishing advantage with age, indicating that the efficacy of noise addition progressively diminishes. Additionally, as individuals age, peak performance is achieved with lower levels of noise. This study provides the first insight into how SR changes across the lifespan of healthy adults and establishes a foundation for understanding the pathological alterations in perceptual processes associated with aging.

Mechanisms of stationary voltage fluctuation in the neuromuscular junction endplate and corresponding denoising paradigms

The neuromuscular junction (NMJ) has an elaborate anatomy to ensure agile and accurate signal transmission. Based on our formerly obtained expressions of the thermal and conductance induced voltage fluctuations, in this paper, the mechanisms underlying the conductance-induced voltage fluctuation are characterized from two aspects: the scaling laws with respect to either of the two system-size factors, the number of receptors or the membrane area; and the "seesaw effect" with respect to the intensive parameter, the concentration of acetylcholine. According to these mechanisms, several aspects of the NMJ anatomy are explained from a denoising perspective. Finally, the power spectra of the two types of voltage fluctuations are characterized by their specific scaling laws, based on which we explain why the endplate noise has the low-frequency property that is described by the term "seashell sound".

Stochastic resonance in sparse neuronal network: functional role of ongoing activity to detect weak sensory input in awake auditory cortex of rat

The awake cortex is characterized by a higher level of ongoing spontaneous activity, but it has a better detectability of weak sensory inputs than the anesthetized cortex. However, the computational mechanism underlying this paradoxical nature of awake neuronal activity remains to be elucidated. Here, we propose a hypothetical stochastic resonance, which improves the signal-to-noise ratio (SNR) of weak sensory inputs through nonlinear relations between ongoing spontaneous activities and sensory-evoked activities. Prestimulus and tone-evoked activities were investigated via in vivo extracellular recording with a dense microelectrode array covering the entire auditory cortex in rats in both awake and anesthetized states. We found that tone-evoked activities increased supralinearly with the prestimulus activity level in the awake state and that the SNR of weak stimulus representation was optimized at an intermediate level of prestimulus ongoing activity. Furthermore, the temporally intermittent firing pattern, but not the trial-by-trial reliability or the fluctuation of local field potential, was identified as a relevant factor for SNR improvement. Since ongoing activity differs among neurons, hypothetical stochastic resonance or "sparse network stochastic resonance" might offer beneficial SNR improvement at the single-neuron level, which is compatible with the sparse representation in the sensory cortex.

Digitally embodied lifespan neurocognitive development and Tactile Internet: Transdisciplinary challenges and opportunities

Mechanisms underlying perceptual processing and inference undergo substantial changes across the lifespan. If utilized properly, technologies could support and buffer the relatively more limited neurocognitive functions in the still developing or aging brains. Over the past decade, a new type of digital communication infrastructure, known as the "Tactile Internet (TI)," is emerging in the fields of telecommunication, sensor and actuator technologies and machine learning. A key aim of the TI is to enable humans to experience and interact with remote and virtual environments through digitalized multimodal sensory signals that also include the haptic (tactile and kinesthetic) sense. Besides their applied focus, such technologies may offer new opportunities for the research tapping into mechanisms of digitally embodied perception and cognition as well as how they may differ across age cohorts. However, there are challenges in translating empirical findings and theories about neurocognitive mechanisms of perception and lifespan development into the day-to-day practices of engineering research and technological development. On the one hand, the capacity and efficiency of digital communication are affected by signal transmission noise according to Shannon's (1949) Information Theory. On the other hand, neurotransmitters, which have been postulated as means that regulate the signal-to-noise ratio of neural information processing (e.g., Servan-Schreiber et al., 1990), decline substantially during aging. Thus, here we highlight neuronal gain control of perceptual processing and perceptual inference to illustrate potential interfaces for developing age-adjusted technologies to enable plausible multisensory digital embodiments for perceptual and cognitive interactions in remote or virtual environments.

A framework for preparing a stochastic nonlinear integrate-and-fire model for integrated information theory

This paper presents a framework for spiking neural networks to be prepared for the Integrated Information Theory (IIT) analysis, using a stochastic nonlinear integrate-and-fire model. The model includes the crucial dynamics of the all-or-none law and after-spike refractoriness. The noise is modelled as an additive term in the system's equations. By preparing the model for the IIT analysis, it is meant to determine the length of the analysis time-window and the transition probability distributions required for the IIT 3.0. To this end, a system of differential equations is proposed to estimate the time evolution of the system's mean and covariance. Assuming the binary Fired/Silent activity as the possible states of each neuron, an algorithm is proposed to calculate the required probability distributions. As long as the Fired/Silent probabilities are only concerned, the Gaussian density assumption with the estimated moments is a reasonable estimate. The synaptic inputs are treated as random variables with low variances to avoid the costs of conditioning on the system's past activities. The Monte-Carlo simulation is used to validate the estimation methods. To increase the reliability of the inductive inference behind the Monte-Carlo method, various stimulation protocols are applied to evoke the dynamics of the equations.

How Neuronal Noises Influence the Spiking Neural Networks's Cognitive Learning Process: A Preliminary Study

In neuroscience, the Default Mode Network (DMN), also known as the default network or the default-state network, is a large-scale brain network known to have highly correlated activities that are distinct from other networks in the brain. Many studies have revealed that DMNs can influence other cognitive functions to some extent. This paper is motivated by this idea and intends to further explore on how DMNs could help Spiking Neural Networks (SNNs) on image classification problems through an experimental study. The approach emphasizes the bionic meaning on model selection and parameters settings. For modeling, we select Leaky Integrate-and-Fire (LIF) as the neuron model, Additive White Gaussian Noise (AWGN) as the input DMN, and design the learning algorithm based on Spike-Timing-Dependent Plasticity (STDP). Then, we experiment on a two-layer SNN to evaluate the influence of DMN on classification accuracy, and on a three-layer SNN to examine the influence of DMN on structure evolution, where the results both appear positive. Finally, we discuss possible directions for future works.

Theoretical Aspects of Resting-State Cardiomyocyte Communication for Multi-Nodal Nano-Actuator Pacemakers

The heart consists of billions of cardiac muscle cells-cardiomyocytes-that work in a coordinated fashion to supply oxygen and nutrients to the body. Inter-connected specialized cardiomyocytes form signaling channels through which the electrical signals are propagated throughout the heart, controlling the heart's beat to beat function of the other cardiac cells. In this paper, we study to what extent it is possible to use ordinary cardiomyocytes as communication channels between components of a recently proposed multi-nodal leadless pacemaker, to transmit data encoded in subthreshold membrane potentials. We analyze signal propagation in the cardiac infrastructure considering noise in the communication channel by performing numerical simulations based on the Luo-Rudy computational model. The Luo-Rudy model is an action potential model but describes the potential changes with time including membrane potential and action potential stages, separated by the thresholding mechanism. Demonstrating system performance, we show that cardiomyocytes can be used to establish an artificial communication system where data are reliably transmitted between 10 s of cells. The proposed subthreshold cardiac communication lays the foundation for a new intra-cardiac communication technique.

Low-rate firing limit for neurons with axon, soma and dendrites driven by spatially distributed stochastic synapses

Analytical forms for neuronal firing rates are important theoretical tools for the analysis of network states. Since the 1960s, the majority of approaches have treated neurons as being electrically compact and therefore isopotential. These approaches have yielded considerable insight into how single-cell properties affect network activity; however, many neuronal classes, such as cortical pyramidal cells, are electrically extended objects. Calculation of the complex flow of electrical activity driven by stochastic spatio-temporal synaptic input streams in these structures has presented a significant analytical challenge. Here we demonstrate that an extension of the level-crossing method of Rice, previously used for compact cells, provides a general framework for approximating the firing rate of neurons with spatial structure. Even for simple models, the analytical approximations derived demonstrate a surprising richness including: independence of the firing rate to the electrotonic length for certain models, but with a form distinct to the point-like leaky integrate-and-fire model; a non-monotonic dependence of the firing rate on the number of dendrites receiving synaptic drive; a significant effect of the axonal and somatic load on the firing rate; and the role that the trigger position on the axon for spike initiation has on firing properties. The approach necessitates only calculating the mean and variances of the non-thresholded voltage and its rate of change in neuronal structures subject to spatio-temporal synaptic fluctuations. The combination of simplicity and generality promises a framework that can be built upon to incorporate increasing levels of biophysical detail and extend beyond the low-rate firing limit treated in this paper.

Resonance induced by coupling diversity in globally coupled bistable oscillators

We investigate the collective response of an ensemble of bistable oscillators to an external periodic signal, where the coupling strength between oscillators is diverse. We find that there exists an optimal level of coupling diversity, at which the collective response of the system can be largely improved, i.e., resonance induced by coupling diversity. We also observe that the system splits into three oscillation clusters when this resonance happens. We finally propose a reduced model based on the three oscillation clusters, which can well predict the collective response of the system.

Dimensional reduction in networks of non-Markovian spiking neurons: Equivalence of synaptic filtering and heterogeneous propagation delays

Message passing between components of a distributed physical system is non-instantaneous and contributes to determine the time scales of the emerging collective dynamics. In biological neuron networks this is due in part to local synaptic filtering of exchanged spikes, and in part to the distribution of the axonal transmission delays. How differently these two kinds of communication protocols affect the network dynamics is still an open issue due to the difficulties in dealing with the non-Markovian nature of synaptic transmission. Here, we develop a mean-field dimensional reduction yielding to an effective Markovian dynamics of the population density of the neuronal membrane potential, valid under the hypothesis of small fluctuations of the synaptic current. Within this limit, the resulting theory allows us to prove the formal equivalence between the two transmission mechanisms, holding for any synaptic time scale, integrate-and-fire neuron model, spike emission regimes and for different network states even when the neuron number is finite. The equivalence holds even for larger fluctuations of the synaptic input, if white noise currents are incorporated to model other possible biological features such as ionic channel stochasticity.

Optimized Real-Time Biomimetic Neural Network on FPGA for Bio-hybridization

Neurological diseases can be studied by performing bio-hybrid experiments using a real-time biomimetic Spiking Neural Network (SNN) platform. The Hodgkin-Huxley model offers a set of equations including biophysical parameters which can serve as a base to represent different classes of neurons and affected cells. Also, connecting the artificial neurons to the biological cells would allow us to understand the effect of the SNN stimulation using different parameters on nerve cells. Thus, designing a real-time SNN could useful for the study of simulations of some part of the brain. Here, we present a different approach to optimize the Hodgkin-Huxley equations adapted for Field Programmable Gate Array (FPGA) implementation. The equations of the conductance have been unified to allow the use of same functions with different parameters for all ionic channels. The low resources and high-speed implementation also include features, such as synaptic noise using the Ornstein-Uhlenbeck process and different synapse receptors including AMPA, GABAa, GABAb, and NMDA receptors. The platform allows real-time modification of the neuron parameters and can output different cortical neuron families like Fast Spiking (FS), Regular Spiking (RS), Intrinsically Bursting (IB), and Low Threshold Spiking (LTS) neurons using a Digital to Analog Converter (DAC). Gaussian distribution of the synaptic noise highlights similarities with the biological noise. Also, cross-correlation between the implementation and the model shows strong correlations, and bifurcation analysis reproduces similar behavior compared to the original Hodgkin-Huxley model. The implementation of one core of calculation uses 3% of resources of the FPGA and computes in real-time 500 neurons with 25,000 synapses and synaptic noise which can be scaled up to 15,000 using all resources. This is the first step toward neuromorphic system which can be used for the simulation of bio-hybridization and for the study of neurological disorders or the advanced research on neuroprosthesis to regain lost function.

Neuronal variability and tuning are balanced to optimize naturalistic self-motion coding in primate vestibular pathways

It is commonly assumed that the brain's neural coding strategies are adapted to the statistics of natural stimuli. Specifically, to maximize information transmission, a sensory neuron's tuning function should effectively oppose the decaying stimulus spectral power, such that the neural response is temporally decorrelated (i.e. 'whitened'). However, theory predicts that the structure of neuronal variability also plays an essential role in determining how coding is optimized. Here, we provide experimental evidence supporting this view by recording from neurons in early vestibular pathways during naturalistic self-motion. We found that central vestibular neurons displayed temporally whitened responses that could not be explained by their tuning alone. Rather, computational modeling and analysis revealed that neuronal variability and tuning were matched to effectively complement natural stimulus statistics, thereby achieving temporal decorrelation and optimizing information transmission. Taken together, our findings reveal a novel strategy by which neural variability contributes to optimized processing of naturalistic stimuli.

Hidden Quantum Processes, Quantum Ion Channels, and 1/ fθ-Type Noise

In this letter, we perform a complete and in-depth analysis of Lorentzian noises, such as those arising from [Formula: see text] and [Formula: see text] channel kinetics, in order to identify the source of [Formula: see text]-type noise in neurological membranes. We prove that the autocovariance of Lorentzian noise depends solely on the eigenvalues (time constants) of the kinetic matrix but that the Lorentzian weighting coefficients depend entirely on the eigenvectors of this matrix. We then show that there are rotations of the kinetic eigenvectors that send any initial weights to any target weights without altering the time constants. In particular, we show there are target weights for which the resulting Lorenztian noise has an approximately [Formula: see text]-type spectrum. We justify these kinetic rotations by introducing a quantum mechanical formulation of membrane stochastics, called hidden quantum activated-measurement models, and prove that these quantum models are probabilistically indistinguishable from the classical hidden Markov models typically used for ion channel stochastics. The quantum dividend obtained by replacing classical with quantum membranes is that rotations of the Lorentzian weights become simple readjustments of the quantum state without any change to the laboratory-determined kinetic and conductance parameters. Moreover, the quantum formalism allows us to model the activation energy of a membrane, and we show that maximizing entropy under constrained activation energy yields the previous [Formula: see text]-type Lorentzian weights, in which the spectral exponent [Formula: see text] is a Lagrange multiplier for the energy constraint. Thus, we provide a plausible neurophysical mechanism by which channel and membrane kinetics can give rise to [Formula: see text]-type noise (something that has been occasionally denied in the literature), as well as a realistic and experimentally testable explanation for the numerical values of the spectral exponents. We also discuss applications of quantum membranes beyond [Formula: see text]-type -noise, including applications to animal models and possible impact on quantum foundations.

Differential receptive field organizations give rise to nearly identical neural correlations across three parallel sensory maps in weakly electric fish

Understanding how neural populations encode sensory information thereby leading to perception and behavior (i.e., the neural code) remains an important problem in neuroscience. When investigating the neural code, one must take into account the fact that neural activities are not independent but are actually correlated with one another. Such correlations are seen ubiquitously and have a strong impact on neural coding. Here we investigated how differences in the antagonistic center-surround receptive field (RF) organization across three parallel sensory maps influence correlations between the activities of electrosensory pyramidal neurons. Using a model based on known anatomical differences in receptive field center size and overlap, we initially predicted large differences in correlated activity across the maps. However, in vivo electrophysiological recordings showed that, contrary to modeling predictions, electrosensory pyramidal neurons across all three segments displayed nearly identical correlations. To explain this surprising result, we incorporated the effects of RF surround in our model. By systematically varying both the RF surround gain and size relative to that of the RF center, we found that multiple RF structures gave rise to similar levels of correlation. In particular, incorporating known physiological differences in RF structure between the three maps in our model gave rise to similar levels of correlation. Our results show that RF center overlap alone does not determine correlations which has important implications for understanding how RF structure influences correlated neural activity.

Growing evidence across nervous systems and species shows that the activities of neighboring neurons are not independent but are correlated with one another, which has important implications for neural coding. Such correlations are generally thought to be due to shared input. However, how this shared input is integrated by neurons in order to give rise to correlated activity is not well understood in general. Here we investigated how receptive field structure determines correlations between the activities of electrosensory pyramidal neurons in weakly electric fish. To do so, we used a combination of mathematical modeling of the known antagonistic center-surround RF structure as well as in vivo electrophysiological recordings. Our results show that the amount of receptive field center overlap alone is not sufficient to explain experimentally observed neural correlations in general. This is because our experimental data shows that pyramidal neurons with very different amounts of receptive field center overlap display almost identical correlations between their activities. Further, our modeling shows that both receptive field center and surround play important roles in determining correlated activity, such that very different combinations of relative RF surround strength and size can generate nearly identical correlations between neural activities. We discuss the implications of our results for sensory processing.

A stochastic-field description of finite-size spiking neural networks

Neural network dynamics are governed by the interaction of spiking neurons. Stochastic aspects of single-neuron dynamics propagate up to the network level and shape the dynamical and informational properties of the population. Mean-field models of population activity disregard the finite-size stochastic fluctuations of network dynamics and thus offer a deterministic description of the system. Here, we derive a stochastic partial differential equation (SPDE) describing the temporal evolution of the finite-size refractory density, which represents the proportion of neurons in a given refractory state at any given time. The population activity—the density of active neurons per unit time—is easily extracted from this refractory density. The SPDE includes finite-size effects through a two-dimensional Gaussian white noise that acts both in time and along the refractory dimension. For an infinite number of neurons the standard mean-field theory is recovered. A discretization of the SPDE along its characteristic curves allows direct simulations of the activity of large but finite spiking networks; this constitutes the main advantage of our approach. Linearizing the SPDE with respect to the deterministic asynchronous state allows the theoretical investigation of finite-size activity fluctuations. In particular, analytical expressions for the power spectrum and autocorrelation of activity fluctuations are obtained. Moreover, our approach can be adapted to incorporate multiple interacting populations and quasi-renewal single-neuron dynamics.

In the brain, information about stimuli is encoded in the timing of action potentials produced by neurons. An understanding of this neural code is facilitated by the use of a well-established method called mean-field theory. Over the last two decades or so, mean-field theory has brought an important added value to the study of emergent properties of neural circuits. Nonetheless, in the mean-field framework, the thermodynamic limit has to be taken, that is, to postulate the number of neurons to be infinite. Doing so, small fluctuations are neglected, and the randomness so present at the cellular level disappears from the description of the circuit dynamics. The origin and functional implications of variability at the network scale are ongoing questions of interest in neuroscience. It is therefore crucial to go beyond the mean-field approach and to propose a description that fully entails the stochastic aspects of network dynamics. In this manuscript, we address this issue by showing that the dynamics of finite-size networks can be represented by stochastic partial differential equations.

Comparison of mechanisms for contrast-invariance of orientation selectivity in simple cells

The simple cells of the visual cortex respond over a narrow range of stimulus orientations, and this tuning is invariant to the contrast at which the stimulus is presented. The inputs to a single cell derive from a population of thalamic cells that provide a bell-shaped tuning width and offset that increases with stimulus contrast. Synaptic depression, noise and inhibition have been proposed as feedforward mechanisms to explain why these increases do not appear in simple cells. The extent to which these three mechanisms contribute to contrast-invariant orientation tuning is unknown. Consequently, the aim was to test the hypothesis that these mechanisms do not contribute equally. Unlike previous studies, all mechanisms were examined using the same network model based on Banitt et al. (2007). The results showed that thalamocortical synaptic noise was essential and sufficient to widen tuning widths at low contrasts to that of higher contrasts but could not counteract the offset at higher contrasts. Thalamocortical synaptic depression could only be used to counteract a small fraction of the offset otherwise the relationship between contrast and response rate was disrupted. Only broadly tuned simple and complex cell inhibition could counteract the remaining offset for all stimulus contrasts but complex cell inhibition reduced the gain of the response. These results suggest unequal contributions of these feedforward mechanisms with thalamic synaptic noise widening tuning widths for low contrasts, synaptic depression counteracting a small component of the offset and synaptic inhibition completely removing the remaining offset to produce contrast-invariant orientation tuning.

Electrosensory neural responses to natural electro-communication stimuli are distributed along a continuum

Neural heterogeneities are seen ubiquitously within the brain and greatly complicate classification efforts. Here we tested whether the responses of an anatomically well-characterized sensory neuron population to natural stimuli could be used for functional classification. To do so, we recorded from pyramidal cells within the electrosensory lateral line lobe (ELL) of the weakly electric fish Apteronotus leptorhynchus in response to natural electro-communication stimuli as these cells can be anatomically classified into six different types. We then used two independent methodologies to functionally classify responses: one relies of reducing the dimensionality of a feature space while the other directly compares the responses themselves. Both methodologies gave rise to qualitatively similar results: while ON and OFF-type cells could easily be distinguished from one another, ELL pyramidal neuron responses are actually distributed along a continuum rather than forming distinct clusters due to heterogeneities. We discuss the implications of our results for neural coding and highlight some potential advantages.

Optimal causal filtering for 1 /fα-type noise in single-electrode EEG signals

Understanding the mode of generation and the statistical structure of neurological noise is one of the central problems of biomedical signal processing. We have developed a broad class of abstract biological noise sources we call hidden simplicial tissues. In the simplest cases, such tissue emits what we have named generalized van der Ziel-McWhorter (GVZM) noise which has a roughly 1/fα spectral roll-off. Our previous work focused on the statistical structure of GVZM frequency spectra. However, causality of processing operations (i.e., dependence only on the past) is an essential requirement for real-time applications to seizure detection and brain-computer interfacing. In this paper we outline the theoretical background for optimal causal time-domain filtering of deterministic signals embedded in GVZM noise. We present some of our early findings concerning the optimal filtering of EEG signals for the detection of steady-state visual evoked potential (SSVEP) responses and indicate the next steps in our ongoing research.

Digital hardware implementation of a stochastic two-dimensional neuron model

This study explores the feasibility of stochastic neuron simulation in digital systems (FPGA), which realizes an implementation of a two-dimensional neuron model. The stochasticity is added by a source of current noise in the silicon neuron using an Ornstein-Uhlenbeck process. This approach uses digital computation to emulate individual neuron behavior using fixed point arithmetic operation. The neuron model's computations are performed in arithmetic pipelines. It was designed in VHDL language and simulated prior to mapping in the FPGA. The experimental results confirmed the validity of the developed stochastic FPGA implementation, which makes the implementation of the silicon neuron more biologically plausible for future hybrid experiments.

Noise effects on robust synchronization of a small pacemaker neuronal ensemble via nonlinear controller: electronic circuit design

In this paper, we report on the synchronization of a pacemaker neuronal ensemble constituted of an AB neuron electrically coupled to two PD neurons. By the virtue of this electrical coupling, they can fire synchronous bursts of action potential. An external master neuron is used to induce to the whole system the desired dynamics, via a nonlinear controller. Such controller is obtained by a combination of sliding mode and feedback control. The proposed controller is able to offset uncertainties in the synchronized systems. We show how noise affects the synchronization of the pacemaker neuronal ensemble, and briefly discuss its potential benefits in our synchronization scheme. An extended Hindmarsh-Rose neuronal model is used to represent a single cell dynamic of the network. Numerical simulations and Pspice implementation of the synchronization scheme are presented. We found that, the proposed controller reduces the stochastic resonance of the network when its gain increases.

A New Statistical Model of Electroencephalogram Noise Spectra for Real-Time Brain-Computer Interfaces

OBJECTIVE

A characteristic of neurological signal processing is high levels of noise from subcellular ion channels up to whole-brain processes. In this paper, we propose a new model of electroencephalogram (EEG) background periodograms, based on a family of functions which we call generalized van der Ziel-McWhorter (GVZM) power spectral densities (PSDs). To the best of our knowledge, the GVZM PSD function is the only EEG noise model that has relatively few parameters, matches recorded EEG PSD's with high accuracy from 0 to over 30 Hz, and has approximately 1/f^θ behavior in the midfrequencies without infinities.

METHODS

We validate this model using three approaches. First, we show how GVZM PSDs can arise in a population of ion channels at maximum entropy equilibrium. Second, we present a class of mixed autoregressive models, which simulate brain background noise and whose periodograms are asymptotic to the GVZM PSD. Third, we present two real-time estimation algorithms for steady-state visual evoked potential (SSVEP) frequencies, and analyze their performance statistically.

RESULTS

In pairwise comparisons, the GVZM-based algorithms showed statistically significant accuracy improvement over two well-known and widely used SSVEP estimators.

CONCLUSION

The GVZM noise model can be a useful and reliable technique for EEG signal processing.

SIGNIFICANCE

Understanding EEG noise is essential for EEG-based neurology and applications such as real-time brain-computer interfaces, which must make accurate control decisions from very short data epochs. The GVZM approach represents a successful new paradigm for understanding and managing this neurological noise.

Theoretical connections between mathematical neuronal models corresponding to different expressions of noise

Identifying the right tools to express the stochastic aspects of neural activity has proven to be one of the biggest challenges in computational neuroscience. Even if there is no definitive answer to this issue, the most common procedure to express this randomness is the use of stochastic models. In accordance with the origin of variability, the sources of randomness are classified as intrinsic or extrinsic and give rise to distinct mathematical frameworks to track down the dynamics of the cell. While the external variability is generally treated by the use of a Wiener process in models such as the Integrate-and-Fire model, the internal variability is mostly expressed via a random firing process. In this paper, we investigate how those distinct expressions of variability can be related. To do so, we examine the probability density functions to the corresponding stochastic models and investigate in what way they can be mapped one to another via integral transforms. Our theoretical findings offer a new insight view into the particular categories of variability and it confirms that, despite their contrasting nature, the mathematical formalization of internal and external variability is strikingly similar.

Channel based generating function approach to the stochastic Hodgkin-Huxley neuronal system

Internal and external fluctuations, such as channel noise and synaptic noise, contribute to the generation of spontaneous action potentials in neurons. Many different Langevin approaches have been proposed to speed up the computation but with waning accuracy especially at small channel numbers. We apply a generating function approach to the master equation for the ion channel dynamics and further propose two accelerating algorithms, with an accuracy close to the Gillespie algorithm but with much higher efficiency, opening the door for expedited simulation of noisy action potential propagating along axons or other types of noisy signal transduction.

Encoding of yaw in the presence of distractor motion: studies in a fly motion sensitive neuron

Motion estimation is crucial for aerial animals such as the fly, which perform fast and complex maneuvers while flying through a 3-D environment. Motion-sensitive neurons in the lobula plate, a part of the visual brain, of the fly have been studied extensively for their specialized role in motion encoding. However, the visual stimuli used in such studies are typically highly simplified, often move in restricted ways, and do not represent the complexities of optic flow generated during actual flight. Here, we use combined rotations about different axes to study how H1, a wide-field motion-sensitive neuron, encodes preferred yaw motion in the presence of stimuli not aligned with its preferred direction. Our approach is an extension of "white noise" methods, providing a framework that is readily adaptable to quantitative studies into the coding of mixed dynamic stimuli in other systems. We find that the presence of a roll or pitch ("distractor") stimulus reduces information transmitted by H1 about yaw, with the amount of this reduction depending on the variance of the distractor. Spike generation is influenced by features of both yaw and the distractor, where the degree of influence is determined by their relative strengths. Certain distractor features may induce bidirectional responses, which are indicative of an imbalance between global excitation and inhibition resulting from complex optic flow. Further, the response is shaped by the dynamics of the combined stimulus. Our results provide intuition for plausible strategies involved in efficient coding of preferred motion from complex stimuli having multiple motion components.

Self-consistent determination of the spike-train power spectrum in a neural network with sparse connectivity

A major source of random variability in cortical networks is the quasi-random arrival of presynaptic action potentials from many other cells. In network studies as well as in the study of the response properties of single cells embedded in a network, synaptic background input is often approximated by Poissonian spike trains. However, the output statistics of the cells is in most cases far from being Poisson. This is inconsistent with the assumption of similar spike-train statistics for pre- and postsynaptic cells in a recurrent network. Here we tackle this problem for the popular class of integrate-and-fire neurons and study a self-consistent statistics of input and output spectra of neural spike trains. Instead of actually using a large network, we use an iterative scheme, in which we simulate a single neuron over several generations. In each of these generations, the neuron is stimulated with surrogate stochastic input that has a similar statistics as the output of the previous generation. For the surrogate input, we employ two distinct approximations: (i) a superposition of renewal spike trains with the same interspike interval density as observed in the previous generation and (ii) a Gaussian current with a power spectrum proportional to that observed in the previous generation. For input parameters that correspond to balanced input in the network, both the renewal and the Gaussian iteration procedure converge quickly and yield comparable results for the self-consistent spike-train power spectrum. We compare our results to large-scale simulations of a random sparsely connected network of leaky integrate-and-fire neurons (Brunel, 2000) and show that in the asynchronous regime close to a state of balanced synaptic input from the network, our iterative schemes provide an excellent approximations to the autocorrelation of spike trains in the recurrent network.

Volterra dendritic stimulus processors and biophysical spike generators with intrinsic noise sources

We consider a class of neural circuit models with internal noise sources arising in sensory systems. The basic neuron model in these circuits consists of a dendritic stimulus processor (DSP) cascaded with a biophysical spike generator (BSG). The dendritic stimulus processor is modeled as a set of nonlinear operators that are assumed to have a Volterra series representation. Biophysical point neuron models, such as the Hodgkin-Huxley neuron, are used to model the spike generator. We address the question of how intrinsic noise sources affect the precision in encoding and decoding of sensory stimuli and the functional identification of its sensory circuits. We investigate two intrinsic noise sources arising (i) in the active dendritic trees underlying the DSPs, and (ii) in the ion channels of the BSGs. Noise in dendritic stimulus processing arises from a combined effect of variability in synaptic transmission and dendritic interactions. Channel noise arises in the BSGs due to the fluctuation of the number of the active ion channels. Using a stochastic differential equations formalism we show that encoding with a neuron model consisting of a nonlinear DSP cascaded with a BSG with intrinsic noise sources can be treated as generalized sampling with noisy measurements. For single-input multi-output neural circuit models with feedforward, feedback and cross-feedback DSPs cascaded with BSGs we theoretically analyze the effect of noise sources on stimulus decoding. Building on a key duality property, the effect of noise parameters on the precision of the functional identification of the complete neural circuit with DSP/BSG neuron models is given. We demonstrate through extensive simulations the effects of noise on encoding stimuli with circuits that include neuron models that are akin to those commonly seen in sensory systems, e.g., complex cells in V1.

Systematic analysis of the contributions of stochastic voltage gated channels to neuronal noise

Electrical signaling in neurons is mediated by the opening and closing of large numbers of individual ion channels. The ion channels' state transitions are stochastic and introduce fluctuations in the macroscopic current through ion channel populations. This creates an unavoidable source of intrinsic electrical noise for the neuron, leading to fluctuations in the membrane potential and spontaneous spikes. While this effect is well known, the impact of channel noise on single neuron dynamics remains poorly understood. Most results are based on numerical simulations. There is no agreement, even in theoretical studies, on which ion channel type is the dominant noise source, nor how inclusion of additional ion channel types affects voltage noise. Here we describe a framework to calculate voltage noise directly from an arbitrary set of ion channel models, and discuss how this can be use to estimate spontaneous spike rates.

Prediction of human's ability in sound localization based on the statistical properties of spike trains along the brainstem auditory pathway

The minimum audible angle test which is commonly used for evaluating human localization ability depends on interaural time delay, interaural level differences, and spectral information about the acoustic stimulus. These physical properties are estimated at different stages along the brainstem auditory pathway. The interaural time delay is ambiguous at certain frequencies, thus confusion arises as to the source of these frequencies. It is assumed that in a typical minimum audible angle experiment, the brain acts as an unbiased optimal estimator and thus the human performance can be obtained by deriving optimal lower bounds. Two types of lower bounds are tested: the Cramer-Rao and the Barankin. The Cramer-Rao bound only takes into account the approximation of the true direction of the stimulus; the Barankin bound considers other possible directions that arise from the ambiguous phase information. These lower bounds are derived at the output of the auditory nerve and of the superior olivary complex where binaural cues are estimated. An agreement between human experimental data was obtained only when the superior olivary complex was considered and the Barankin lower bound was used. This result suggests that sound localization is estimated by the auditory nuclei using ambiguous binaural information.

A novel model incorporating two variability sources for describing motor evoked potentials

OBJECTIVE

Motor evoked potentials (MEPs) play a pivotal role in transcranial magnetic stimulation (TMS), e.g., for determining the motor threshold and probing cortical excitability. Sampled across the range of stimulation strengths, MEPs outline an input-output (IO) curve, which is often used to characterize the corticospinal tract. More detailed understanding of the signal generation and variability of MEPs would provide insight into the underlying physiology and aid correct statistical treatment of MEP data.

METHODS

A novel regression model is tested using measured IO data of twelve subjects. The model splits MEP variability into two independent contributions, acting on both sides of a strong sigmoidal nonlinearity that represents neural recruitment. Traditional sigmoidal regression with a single variability source after the nonlinearity is used for comparison.

RESULTS

The distribution of MEP amplitudes varied across different stimulation strengths, violating statistical assumptions in traditional regression models. In contrast to the conventional regression model, the dual variability source model better described the IO characteristics including phenomena such as changing distribution spread and skewness along the IO curve.

CONCLUSIONS

MEP variability is best described by two sources that most likely separate variability in the initial excitation process from effects occurring later on. The new model enables more accurate and sensitive estimation of the IO curve characteristics, enhancing its power as a detection tool, and may apply to other brain stimulation modalities. Furthermore, it extracts new information from the IO data concerning the neural variability-information that has previously been treated as noise.

Consequences of converting graded to action potentials upon neural information coding and energy efficiency

Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na(+) and K(+) channels, with generator potential and graded potential models lacking voltage-gated Na(+) channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na(+) channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a 'footprint' in the generator potential that obscures incoming signals. These three processes reduce information rates by ∼50% in generator potentials, to ∼3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation.

Channel noise from both slow adaptation currents and fast currents is required to explain spike-response variability in a sensory neuron

Spike-timing variability has a large effect on neural information processing. However, for many systems little is known about the noise sources causing the spike-response variability. Here we investigate potential sources of spike-response variability in auditory receptor neurons of locusts, a classic insect model system. At low-spike frequencies, our data show negative interspike-interval (ISI) correlations and ISI distributions that match the inverse Gaussian distribution. These findings can be explained by a white-noise source that interacts with an adaptation current. At higher spike frequencies, more strongly peaked distributions and positive ISI correlations appear, as expected from a canonical model of suprathreshold firing driven by temporally correlated (i.e., colored) noise. Simulations of a minimal conductance-based model of the auditory receptor neuron with stochastic ion channels exclude the delayed rectifier as a possible noise source. Our analysis suggests channel noise from an adaptation current and the receptor or sodium current as main sources for the colored and white noise, respectively. By comparing the ISI statistics with generic models, we find strong evidence for two distinct noise sources. Our approach does not involve any dendritic or somatic recordings that may harm the delicate workings of many sensory systems. It could be applied to various other types of neurons, in which channel noise dominates the fluctuations that shape the neuron's spike statistics.

Exact Event-Driven Implementation for Recurrent Networks of Stochastic Perfect Integrate-and-Fire Neurons

In vivo cortical recording reveals that indirectly driven neural assemblies can produce reliable and temporally precise spiking patterns in response to stereotyped stimulation. This suggests that despite being fundamentally noisy, the collective activity of neurons conveys information through temporal coding. Stochastic integrate-and-fire models delineate a natural theoretical framework to study the interplay of intrinsic neural noise and spike timing precision. However, there are inherent difficulties in simulating their networks’ dynamics in silico with standard numerical discretization schemes. Indeed, the well-posedness of the evolution of such networks requires temporally ordering every neuronal interaction, whereas the order of interactions is highly sensitive to the random variability of spiking times. Here, we answer these issues for perfect stochastic integrate-and-fire neurons by designing an exact event-driven algorithm for the simulation of recurrent networks, with delayed Dirac-like interactions. In addition to being exact from the mathematical standpoint, our proposed method is highly efficient numerically. We envision that our algorithm is especially indicated for studying the emergence of polychronized motifs in networks evolving under spike-timing-dependent plasticity with intrinsic noise.

Effects of noise on models of spiny dendrites

We study the effects of noise in two models of spiny dendrites. Through the introduction of different types of noise to both the Spike-diffuse-spike (SDS) and Baer-Rinzel (BR) models we investigate the change in behaviour of the travelling wave solution present in both deterministic systems, as noise intensity increases. We show that the speed of wave propagation in both the SDS and BR models respectively differs as the noise intensity in the spine heads increases. In contrast the cable is very robust to noise and as such the speed shows very little variation from the deterministic system. We introduce a space-dependent spine density, ρ(x), to the original Baer-Rinzel model and show how this modified model can mimic behaviour (under influence of noise) of both original systems, through variation of one parameter. We also show that the correlation time and length scales of the noise can enhance propagation of travelling wave solutions where the white noise dominates the underlying signal and produces noise induced phenomena.

Bursts and isolated spikes code for opposite movement directions in midbrain electrosensory neurons

Directional selectivity, in which neurons respond strongly to an object moving in a given direction but weakly or not at all to the same object moving in the opposite direction, is a crucial computation that is thought to provide a neural correlate of motion perception. However, directional selectivity has been traditionally quantified by using the full spike train, which does not take into account particular action potential patterns. We investigated how different action potential patterns, namely bursts (i.e. packets of action potentials followed by quiescence) and isolated spikes, contribute to movement direction coding in a mathematical model of midbrain electrosensory neurons. We found that bursts and isolated spikes could be selectively elicited when the same object moved in opposite directions. In particular, it was possible to find parameter values for which our model neuron did not display directional selectivity when the full spike train was considered but displayed strong directional selectivity when bursts or isolated spikes were instead considered. Further analysis of our model revealed that an intrinsic burst mechanism based on subthreshold T-type calcium channels was not required to observe parameter regimes for which bursts and isolated spikes code for opposite movement directions. However, this burst mechanism enhanced the range of parameter values for which such regimes were observed. Experimental recordings from midbrain neurons confirmed our modeling prediction that bursts and isolated spikes can indeed code for opposite movement directions. Finally, we quantified the performance of a plausible neural circuit and found that it could respond more or less selectively to isolated spikes for a wide range of parameter values when compared with an interspike interval threshold. Our results thus show for the first time that different action potential patterns can differentially encode movement and that traditional measures of directional selectivity need to be revised in such cases.

The effect of neural noise on spike time precision in a detailed CA3 neuron model

Experimental and computational studies emphasize the role of the millisecond precision of neuronal spike times as an important coding mechanism for transmitting and representing information in the central nervous system. We investigate the spike time precision of a multicompartmental pyramidal neuron model of the CA3 region of the hippocampus under the influence of various sources of neuronal noise. We describe differences in the contribution to noise originating from voltage-gated ion channels, synaptic vesicle release, and vesicle quantal size. We analyze the effect of interspike intervals and the voltage course preceding the firing of spikes on the spike-timing jitter. The main finding of this study is the ranking of different noise sources according to their contribution to spike time precision. The most influential is synaptic vesicle release noise, causing the spike jitter to vary from 1 ms to 7 ms of a mean value 2.5 ms. Of second importance was the noise incurred by vesicle quantal size variation causing the spike time jitter to vary from 0.03 ms to 0.6 ms. Least influential was the voltage-gated channel noise generating spike jitter from 0.02 ms to 0.15 ms.

Biophysical Neural Spiking, Bursting, and Excitability Dynamics in Reconfigurable Analog VLSI

We study a range of neural dynamics under variations in biophysical parameters underlying extended Morris-Lecar and Hodgkin-Huxley models in three gating variables. The extended models are implemented in NeuroDyn, a four neuron, twelve synapse continuous-time analog VLSI programmable neural emulation platform with generalized channel kinetics and biophysical membrane dynamics. The dynamics exhibit a wide range of time scales extending beyond 100 ms neglected in typical silicon models of tonic spiking neurons. Circuit simulations and measurements show transition from tonic spiking to tonic bursting dynamics through variation of a single conductance parameter governing calcium recovery. We similarly demonstrate transition from graded to all-or-none neural excitability in the onset of spiking dynamics through the variation of channel kinetic parameters governing the speed of potassium activation. Other combinations of variations in conductance and channel kinetic parameters give rise to phasic spiking and spike frequency adaptation dynamics. The NeuroDyn chip consumes 1.29 mW and occupies 3 mm × 3 mm in 0.5 μm CMOS, supporting emerging developments in neuromorphic silicon-neuron interfaces.

Neuronal homeostasis: time for a change?

Homeostatic processes that regulate electrical activity in neurones are now an established aspect of physiology and rest on a large body of experimental evidence that points to roles in development, learning and memory, and disease. However, the concepts underlying homeostasis are too often summarized in ways that restrict their explanatory power and obviate important subtleties. Here, we present a review of the underlying theory of homeostasis--control theory--in an attempt to reconcile some existing conceptual problems in the context of neuronal physiology. In addition to clarifying the underlying theory, this review highlights the remaining challenges posed when analysing homeostatic phenomena that underlie the regulation of neuronal excitability. Moreover, we suggest approaches for future experimental and computational work that will further our understanding of neuronal homeostasis and the fundamental neurophysiological functions it serves.

Coding movement direction by burst firing in electrosensory neurons

Directional selectivity, in which neurons respond strongly to an object moving in a given direction ("preferred") but respond weakly or not at all to an object moving in the opposite direction ("null"), is a critical computation achieved in brain circuits. Previous measures of direction selectivity have compared the numbers of action potentials elicited by each direction of movement, but most sensory neurons display patterning, such as bursting, in their spike trains. To examine the contribution of patterned responses to direction selectivity, we recorded from midbrain neurons in weakly electric fish and found that most neurons responded with a combination of both bursts and isolated spikes to moving object stimuli. In these neurons, we separated bursts and isolated spikes using an interspike interval (ISI) threshold. The directional bias of bursts was significantly higher than that of either the full spike train or the isolated spike train. To examine the encoding and decoding of bursts, we built biologically plausible models that examine 1) the upstream mechanisms that generate these spiking patterns and 2) downstream decoders of bursts. Our model of upstream mechanisms uses an interaction between afferent input and subthreshold calcium channels to give rise to burst firing that occurs preferentially for one direction of movement. We tested this model in vivo by application of calcium antagonists, which reduced burst firing and eliminated the differences in direction selectivity between bursts, isolated spikes, and the full spike train. Our model of downstream decoders used strong synaptic facilitation to achieve qualitatively similar results to those obtained using the ISI threshold criterion. This model shows that direction selective information carried by bursts can be decoded by downstream neurons using biophysically plausible mechanisms.

Suprathreshold stochastic resonance in neural processing tuned by correlation

Suprathreshold stochastic resonance (SSR) is examined in the context of integrate-and-fire neurons, with an emphasis on the role of correlation in the neuronal firing. We employed a model based on a network of spiking neurons which received synaptic inputs modeled by Poisson processes stimulated by a stepped input signal. The smoothed ensemble firing rate provided an output signal, and the mutual information between this signal and the input was calculated for networks with different noise levels and different numbers of neurons. It was found that an SSR effect was present in this context. We then examined a more biophysically plausible scenario where the noise was not controlled directly, but instead was tuned by the correlation between the inputs. The SSR effect remained present in this scenario with nonzero noise providing improved information transmission, and it was found that negative correlation between the inputs was optimal. Finally, an examination of SSR in the context of this model revealed its connection with more traditional stochastic resonance and showed a trade-off between supratheshold and subthreshold components. We discuss these results in the context of existing empirical evidence concerning correlations in neuronal firing.

In vivo conditions induce faithful encoding of stimuli by reducing nonlinear synchronization in vestibular sensory neurons

Previous studies have shown that neurons within the vestibular nuclei (VN) can faithfully encode the time course of sensory input through changes in firing rate in vivo. However, studies performed in vitro have shown that these same VN neurons often display nonlinear synchronization (i.e. phase locking) in their spiking activity to the local maxima of sensory input, thereby severely limiting their capacity for faithful encoding of said input through changes in firing rate. We investigated this apparent discrepancy by studying the effects of in vivo conditions on VN neuron activity in vitro using a simple, physiologically based, model of cellular dynamics. We found that membrane potential oscillations were evoked both in response to step and zap current injection for a wide range of channel conductance values. These oscillations gave rise to a resonance in the spiking activity that causes synchronization to sinusoidal current injection at frequencies below 25 Hz. We hypothesized that the apparent discrepancy between VN response dynamics measured in in vitro conditions (i.e., consistent with our modeling results) and the dynamics measured in vivo conditions could be explained by an increase in trial-to-trial variability under in vivo vs. in vitro conditions. Accordingly, we mimicked more physiologically realistic conditions in our model by introducing a noise current to match the levels of resting discharge variability seen in vivo as quantified by the coefficient of variation (CV). While low noise intensities corresponding to CV values in the range 0.04-0.24 only eliminated synchronization for low (<8 Hz) frequency stimulation but not high (>12 Hz) frequency stimulation, higher noise intensities corresponding to CV values in the range 0.5-0.7 almost completely eliminated synchronization for all frequencies. Our results thus predict that, under natural (i.e. in vivo) conditions, the vestibular system uses increased variability to promote fidelity of encoding by single neurons. This prediction can be tested experimentally in vitro.

Neuronal model with distributed delay: analysis and simulation study for gamma distribution memory kernel

A single neuronal model incorporating distributed delay (memory)is proposed. The stochastic model has been formulated as a Stochastic Integro-Differential Equation (SIDE) which results in the underlying process being non-Markovian. A detailed analysis of the model when the distributed delay kernel has exponential form (weak delay) has been carried out. The selection of exponential kernel has enabled the transformation of the non-Markovian model to a Markovian model in an extended state space. For the study of First Passage Time (FPT) with exponential delay kernel, the model has been transformed to a system of coupled Stochastic Differential Equations (SDEs) in two-dimensional state space. Simulation studies of the SDEs provide insight into the effect of weak delay kernel on the Inter-Spike Interval(ISI) distribution. A measure based on Jensen-Shannon divergence is proposed which can be used to make a choice between two competing models viz. distributed delay model vis-á-vis LIF model. An interesting feature of the model is that the behavior of (CV(t))((ISI)) (Coefficient of Variation) of the ISI distribution with respect to memory kernel time constant parameter η reveals that neuron can switch from a bursting state to non-bursting state as the noise intensity parameter changes. The membrane potential exhibits decaying auto-correlation structure with or without damped oscillatory behavior depending on the choice of parameters. This behavior is in agreement with empirically observed pattern of spike count in a fixed time window. The power spectral density derived from the auto-correlation function is found to exhibit single and double peaks. The model is also examined for the case of strong delay with memory kernel having the form of Gamma distribution. In contrast to fast decay of damped oscillations of the ISI distribution for the model with weak delay kernel, the decay of damped oscillations is found to be slower for the model with strong delay kernel.

Accurate and fast simulation of channel noise in conductance-based model neurons by diffusion approximation

Stochastic channel gating is the major source of intrinsic neuronal noise whose functional consequences at the microcircuit- and network-levels have been only partly explored. A systematic study of this channel noise in large ensembles of biophysically detailed model neurons calls for the availability of fast numerical methods. In fact, exact techniques employ the microscopic simulation of the random opening and closing of individual ion channels, usually based on Markov models, whose computational loads are prohibitive for next generation massive computer models of the brain. In this work, we operatively define a procedure for translating any Markov model describing voltage- or ligand-gated membrane ion-conductances into an effective stochastic version, whose computer simulation is efficient, without compromising accuracy. Our approximation is based on an improved Langevin-like approach, which employs stochastic differential equations and no Montecarlo methods. As opposed to an earlier proposal recently debated in the literature, our approximation reproduces accurately the statistical properties of the exact microscopic simulations, under a variety of conditions, from spontaneous to evoked response features. In addition, our method is not restricted to the Hodgkin-Huxley sodium and potassium currents and is general for a variety of voltage- and ligand-gated ion currents. As a by-product, the analysis of the properties emerging in exact Markov schemes by standard probability calculus enables us for the first time to analytically identify the sources of inaccuracy of the previous proposal, while providing solid ground for its modification and improvement we present here.

A possible approach to understanding the neuronal bases of the computational properties of the nervous system consists of modelling its basic building blocks, neurons and synapses, and then simulating their collective activity emerging in large networks. In developing such models, a satisfactory description level must be chosen as a compromise between simplicity and faithfulness in reproducing experimental data. Deterministic neuron models – i.e., models that upon repeated simulation with fixed parameter values provide the same results – are usually made up of ordinary differential equations and allow for relatively fast simulation times. By contrast, they do not describe accurately the underlying stochastic response properties arising from the microscopical correlate of neuronal excitability. Stochastic models are usually based on mathematical descriptions of individual ion channels, or on an effective macroscopic account of their random opening and closing. In this contribution we describe a general method to transform any deterministic neuron model into its effective stochastic version that accurately replicates the statistical properties of ion channels random kinetics.

In vivo conditions influence the coding of stimulus features by bursts of action potentials

The functional role of burst firing (i.e. the firing of packets of action potentials followed by quiescence) in sensory processing is still under debate. Should bursts be considered as unitary events that signal the presence of a particular feature in the sensory environment or is information about stimulus attributes contained within their temporal structure? We compared the coding of stimulus attributes by bursts in vivo and in vitro of electrosensory pyramidal neurons in weakly electric fish by computing correlations between burst and stimulus attributes. Our results show that, while these correlations were strong in magnitude and significant in vitro, they were actually much weaker in magnitude if at all significant in vivo. We used a mathematical model of pyramidal neuron activity in vivo and showed that such a model could reproduce the correlations seen in vitro, thereby suggesting that differences in burst coding were not due to differences in bursting seen in vivo and in vitro. We next tested whether variability in the baseline (i.e. without stimulation) activity of ELL pyramidal neurons could account for these differences. To do so, we injected noise into our model whose intensity was calibrated to mimic baseline activity variability as quantified by the coefficient of variation. We found that this noise caused significant decreases in the magnitude of correlations between burst and stimulus attributes and could account for differences between in vitro and in vivo conditions. We then tested this prediction experimentally by directly injecting noise in vitro through the recording electrode. Our results show that this caused a lowering in magnitude of the correlations between burst and stimulus attributes in vitro and gave rise to values that were quantitatively similar to those seen under in vivo conditions. While it is expected that noise in the form of baseline activity variability will lower correlations between burst and stimulus attributes, our results show that such variability can account for differences seen in vivo. Thus, the high variability seen under in vivo conditions has profound consequences on the coding of information by bursts in ELL pyramidal neurons. In particular, our results support the viewpoint that bursts serve as a detector of particular stimulus features but do not carry detailed information about such features in their structure.

Improved integral equation solution for the first passage time of leaky integrate-and-fire neurons

An accurate calculation of the first passage time probability density (FPTPD) is essential for computing the likelihood of solutions of the stochastic leaky integrate-and-fire model. The previously proposed numerical calculation of the FPTPD based on the integral equation method discretizes the probability current of the voltage crossing the threshold. While the method is accurate for high noise levels, we show that it results in large numerical errors for small noise. The problem is solved by analytically computing, in each time bin, the mean probability current. Efficiency is further improved by identifying and ignoring time bins with negligible mean probability current.

Analog VLSI Biophysical Neurons and Synapses With Programmable Membrane Channel Kinetics

We present and characterize an analog VLSI network of 4 spiking neurons and 12 conductance-based synapses, implementing a silicon model of biophysical membrane dynamics and detailed channel kinetics in 384 digitally programmable parameters. Each neuron in the analog VLSI chip (NeuroDyn) implements generalized Hodgkin-Huxley neural dynamics in 3 channel variables, each with 16 parameters defining channel conductance, reversal potential, and voltage-dependence profile of the channel kinetics. Likewise, 12 synaptic channel variables implement a rate-based first-order kinetic model of neurotransmitter and receptor dynamics, accounting for NMDA and non-NMDA type chemical synapses. The biophysical origin of all 384 parameters in 24 channel variables supports direct interpretation of the results of adapting/tuning the parameters in terms of neurobiology. We present experimental results from the chip characterizing single neuron dynamics, single synapse dynamics, and multi-neuron network dynamics showing phase-locking behavior as a function of synaptic coupling strength. Uniform temporal scaling of the dynamics of membrane and gating variables is demonstrated by tuning a single current parameter, yielding variable speed output exceeding real time. The 0.5 CMOS chip measures 3 mm 3 mm, and consumes 1.29 mW.