Search

Neural circuits can produce similar activity patterns from vastly different combinations of channel and synaptic conductances. These conductances are tuned for specific activity patterns but might also reflect additional constraints, such as metabolic cost or robustness to perturbations. How do such constraints influence the range of permissible conductances? Here we investigate how metabolic cost affects the parameters of neural circuits with similar activity in a model of the pyloric network of the crab Cancer borealis. We present a machine learning method that can identify a range of network models that generate activity patterns matching experimental data and find that neural circuits can consume largely different amounts of energy despite similar circuit activity. Furthermore, a reduced but still significant range of circuit parameters gives rise to energy-efficient circuits. We then examine the space of parameters of energy-efficient circuits and identify potential tuning strategies for low metabolic cost. Finally, we investigate the interaction between metabolic cost and temperature robustness. We show that metabolic cost can vary across temperatures but that robustness to temperature changes does not necessarily incur an increased metabolic cost. Our analyses show that despite metabolic efficiency and temperature robustness constraining circuit parameters, neural systems can generate functional, efficient, and robust network activity with widely disparate sets of conductances. [ABSTRACT FROM AUTHOR]

In this paper, an efficient procedure based on the multiquadric radial basis functions (RBFs) collocation method is applied for the numerical solution of the singularly perturbed differentialdifference (SPDDE) equation. The method is coupled with the Residual subsampling algorithm for support adaptivity. The problem considered in this paper shows turning point behavior which is added to the complexity in the construction of numerical approximation to the solution of the problem. The proposed algorithm is very simple to perform. Some numerical examples are given to validate the computational efficacy of the suggested numerical scheme. [ABSTRACT FROM AUTHOR]

Stroke is a complex event on both behavioral and neuronal grounds. Recent investigations evidence the central role of subcortical damage on the post-stroke brain and behavior reorganization. We have conducted an exploratory study combining anatomical lesion analysis, functional analysis of resting state fMRI, and behavioral assessment with focus on exploration as represented by SEEKING. 24 stroke inpatients were studied immediately after their clinical stabilization post-stroke; neuronal variability in fMRI along with behavioral outcomes were assessed. These outcomes were compared with a control group of 22 healthy subjects. First, we observed predominant subcortical lesions in our sample with all stroke patients showing subcortical lesions and only some exhibiting additional cortical lesions. Second, we observed significantly reduced neuronal variability in the posterior cingulate cortex (PCC) that did not show any structural damage. Third, our stroke subjects showed reduced SEEKING which was related to reduced PCC neuronal variability in an abnormal way (compared to healthy subjects). This last outcome was assessed by considering the subset of 11 stroke subjects for which fMRI and behavioral outcomes were jointly measured. Taken together, our findings suggest that damage in subcortical regions may play a central role in abnormalities in both cortical activity (PCC) and associated behavior of post-stroke reorganization. Accounting for these aspects may have significant implications to optimize multidisciplinary rehabilitation processes, particularly during the early steps of recovery, reducing the impact of stroke on the patient and caregiver quality of life. [ABSTRACT FROM AUTHOR]

In this study, we consider the network of noisy leaky integrate-and-fire (NNLIF) model, which governs by a second-order nonlinear time-dependent partial differential equation (PDE). This equation uses the probability density approach to describe the behavior of neurons with refractory states and the transmission delays. A numerical approximation based on the discontinuous Galerkin (DG) method is used for the spatial discretization with the analysis of stability. The strong stability-preserving explicit Runge–Kutta (SSPERK) method is performed for the temporal discretization. Finally, some test examples and numerical simulations are given to examine the behavior of the solution. The execution of the constructed scheme is measured by the quantitative comparison with the existing finite difference technique, namely weighted essentially nonoscillatory (WENO) scheme. [ABSTRACT FROM AUTHOR]

Cortical responses to repeated presentations of a sensory stimulus are variable. This variability is sensitive to several stimulus dimensions, suggesting that it may carry useful information beyond the average firing rate. Many experimental manipulations that affect response variability are also known to engage divisive normalization, a widespread operation that describes neuronal activity as the ratio of a numerator (representing the excitatory stimulus drive) and denominator (the normalization signal). Although it has been suggested that normalization affects response variability, we lack a quantitative framework to determine the relation between the two. Here we extend the standard normalization model, by treating the numerator and the normalization signal as variable quantities. The resulting model predicts a general stabilizing effect of normalization on neuronal responses, and allows us to infer the single-trial normalization strength, a quantity that cannot be measured directly. We test the model on neuronal responses to stimuli of varying contrast, recorded in primary visual cortex of male macaques. We find that neurons that are more strongly normalized fire more reliably, and response variability and pairwise noise correlations are reduced during trials in which normalization is inferred to be strong. Our results thus suggest a novel functional role for normalization, namely, modulating response variability. Our framework could enable a direct quantification of the impact of single-trial normalization strength on the accuracy of perceptual judgments, and can be readily applied to other sensory and nonsensory factors. [ABSTRACT FROM AUTHOR]

Abstract In this article, we study the excitatory and inhibitory population density model based on leaky integrate-and-fire neuron model. The time evolution of population density is determined by a hyperbolic partial differential equation. There are two factors which might cause difficulties to find the solution. First one is the presence of point-wise delta type source term and second one is the presence of the non-local terms of the voltage of a neuron. We design a high accurate scheme based on WENO-finite volume approximation for spatial discretization. The time evolution is done by SSP-Runge Kutta scheme. To check the efficiency of the designed scheme, we compare the results with the existing scheme in literature. Finally, we remove the non-local terms by diffusion approximation and simulate the model equation. The diffusion approximation is tackled with the Strang splitting method. Some test examples are reported. The performance of the designed scheme is shown by the convergence results. [ABSTRACT FROM AUTHOR]

Affective temperaments have been described since the early 20th century and may play a central role in psychiatric illnesses, such as bipolar disorder (BD). However, the neuronal basis of temperament is still unclear. We investigated the relationship of temperament with neuronal variability in the resting state signal—measured by fractional standard deviation (fSD) of Blood‐Oxygen‐Level Dependent signal—of the different large‐scale networks, that is, sensorimotor network (SMN), along with default‐mode, salience and central executive networks, in standard frequency band (SFB) and its sub‐frequencies slow4 and slow5, in a large sample of healthy subject (HC, n = 109), as well as in the various temperamental subgroups (i.e., cyclothymic, hyperthymic, depressive, and irritable). A replication study on an independent dataset of 121 HC was then performed. SMN fSD positively correlated with cyclothymic z‐score and was significantly increased in the cyclothymic temperament compared to the depressive temperament subgroups, in both SFB and slow4. We replicated our findings in the independent dataset. A relationship between cyclothymic temperament and neuronal variability, an index of intrinsic neuronal activity, in the SMN was found. Cyclothymic and depressive temperaments were associated with opposite changes in the SMN variability, resembling changes previously described in manic and depressive phases of BD. These findings shed a novel light on the neural basis of affective temperament and also carry important implications for the understanding of a potential dimensional continuum between affective temperaments and BD, on both psychological and neuronal levels. [ABSTRACT FROM AUTHOR]

Abstract Background Despite the great number of resting state functional connectivity studies on Eating Disorders (ED), no biomarkers could be detected yet. Therefore, we here focus on a different measure of resting state activity that is neuronal variability. The objective of this study was to investigate neuronal variability in the resting state of women with ED and to correlate possible differences with clinical and psychopathological indices. Methods 58 women respectively 25 with Anorexia Nervosa (AN), 16 with Bulimia Nervosa (BN) and 17 matched healthy controls (CN) were enrolled for the study. All participants were tested with a battery of psychometric tests and underwent a functional Magnetic Resonance Imaging (fMRI) resting state scanning. We investigated topographical patterns of variability measured by the Standard Deviation (SD) of the Blood-Oxygen-Level-Dependent (BOLD) signal (as a measure of neuronal variability) in the resting-state and their relationship to clinical and psychopathological indices. Results Neuronal variability was increased in both anorectic and bulimic subjects specifically in the Ventral Attention Network (VAN) compared to healthy controls. No significant differences were found in the other networks. Significant correlations were found between neuronal variability of VAN and various clinical and psychopathological indices. Conclusions We here show increased neuronal variability of VAN in ED patients. As the VAN is relevant for switching between endogenous and exogenous stimuli, our results showing increased neuronal variability suggest unstable balance between body attention and attention to external world. These results offer new perspective on the neurobiological basis of ED. Clinical and therapeutic implication will be discussed. [ABSTRACT FROM AUTHOR]

We consider a noisy leaky integrate-and-fire (NLIF) neuron model. The resulting nonlinear time-dependent partial differential equation (PDE) is a Fokker-Planck Equation (FPE) which describes the evolution of the probability density. The finite element method (FEM) has been proposed to solve the governing PDE. In the realistic neural network, the irregular space is always determined. Thus, FEM can be used to tackle those situations whereas other numerical schemes are restricted to the problems with only a finite regular space. The stability of the proposed scheme is also discussed. A comparison with the existing Weighted Essentially Non-Oscillatory (WENO) finite difference approximation is also provided. The numerical results reveal that FEM may be a better scheme for the solution of such types of model problems. The numerical scheme also reduces computational time in comparison with time required by other schemes.

Time is an essential feature in bipolar disorder (BP). Manic and depressed BP patients perceive the speed of time as either too fast or too slow. The present article combines theoretical and empirical approaches to integrate phenomenological, psychological, and neuroscientific accounts of abnormal time perception in BP. Phenomenology distinguishes between perception of inner time, ie, self-time, and outer time, ie, world-time, that desynchronize or dissociate from each other in BP: inner time speed is abnormally slow (as in depression) or fast (as in mania) and, by taking on the role as default-mode function, impacts and modulates the perception of outer time speed in an opposite way, ie, as too fast in depression and too slow in mania. Complementing, psychological investigation show opposite results in time perception, ie, time estimation and reproduction, in manic and depressed BP. Neuronally, time speed can be indexed by neuronal variability, ie, SD. Our own empirical data show opposite changes in manic and depressed BP (and major depressive disorder [MDD]) with abnormal SD balance, ie, SD ratio, between somatomotor and sensory networks that can be associated with inner and outer time. Taken together, our combined theoretical-empirical approach demonstrates that desynchronization or dissociation between inner and outer time in BP can be traced to opposite neuronal variability patterns in somatomotor and sensory networks. This opens the door for individualized therapeutic "normalization" of neuronal variability pattern in somatomotor and sensory networks by stimulation with TMS and/or tDCS. [ABSTRACT FROM AUTHOR]

The cortical layer 1 contains mainly small interneurons, which have traditionally been classified according to their axonal morphology. The dendritic morphology of these cells, however, has received little attention and remains ill defined. Very little is known about how the dendritic morphology and spatial distribution of these cells may relate to functional neuronal properties. We used biocytin labeling and whole cell patch clamp recordings, associated with digital reconstruction and quantitative morphological analysis, to assess correlations between dendritic morphology, spatial distribution and membrane properties of rat layer 1 neurons. A total of 106 cells were recorded, labeled and subjected to morphological analysis. Based on the quantitative patterns of their dendritic arbor, cells were divided into four major morphotypes: horizontal, radial, ascendant, and descendant cells. Descendant cells exhibited a highly distinct spatial distribution in relation to other morphotypes, suggesting that they may have a distinct function in these cortical circuits. A significant difference was also found in the distribution of firing patterns between each morphotype and between the neuronal populations of each sublayer. Passive membrane properties were, however, statistically homogeneous among all subgroups. We speculate that the differences observed in active membrane properties might be related to differences in the synaptic input of specific types of afferent fibers and to differences in the computational roles of each morphotype in layer 1 circuits. Our findings provide new insights into dendritic morphology and neuronal spatial distribution in layer 1 circuits, indicating that variations in these properties may be correlated with distinct physiological functions.

Depressive and manic phases in bipolar disorder show opposite constellations of affective, cognitive, and psychomotor symptoms. At a neural level, these may be related to topographical disbalance between large-scale networks, such as the default mode network (DMN) and sensorimotor network (SMN). We investigated topographical patterns of variability in the resting-state signal--measured by fractional SD (fSD) of the BOLD signal--of the DMN and SMN (and other networks) in two frequency bands (Slow5 and Slow4) with their ratio and clinical correlations in depressed (n = 20), manic (n = 20), euthymic (n = 20) patients, and healthy controls (n = 40). After controlling for global signal changes, the topographical balance between the DMN and SMN, specifically in the lowest frequency band, as calculated by the Slow5 fSD DMN/SMN ratio, was significantly increased in depression, whereas the same ratio was significantly decreased in mania. Additionally, Slow5 variability was increased in the DMN and decreased in the SMN in depressed patients, whereas the opposite topographical pattern was observed in mania. Finally, the Slow5 fSD DMN/SMN ratio correlated positively with clinical scores of depressive symptoms and negatively with those of mania. Results were replicated in a smaller independent bipolar disorder sample. We demonstrated topographical abnormalities in frequency-specific resting-state variability in the balance between DMN and SMN with opposing patterns in depression and mania. The Slow5 DMN/SMN ratio was tilted toward the DMN in depression but was shifted toward the SMN in mania. The Slow5 fSD DMN/SMN pattern could constitute a state-biomarker in diagnosis and therapy. [ABSTRACT FROM AUTHOR]

The ability to discriminate between similar sensory stimuli relies on the amount of information encoded in sensory neuronal populations. Such information can be substantially reduced by correlated trial-to-trial variability. Noise correlations have been measured across a wide range of areas in the brain, but their origin is still far from clear. Here we show analytically and with simulations that optimal computation on inputs with limited information creates patterns of noise correlations that account for a broad range of experimental observations while at same time causing information to saturate in large neural populations. With the example of a network of V1 neurons extracting orientation from a noisy image, we illustrate to our knowledge the first generative model of noise correlations that is consistent both with neurophysiology and with behavioral thresholds, without invoking suboptimal encoding or decoding or internal sources of variability such as stochastic network dynamics or cortical state fluctuations. We further show that when information is limited at the input, both suboptimal connectivity and internal fluctuations could similarly reduce the asymptotic information, but they have qualitatively different effects on correlations leading to specific experimental predictions. Our study indicates that noise at the sensory periphery could have a major effect on cortical representations in widely studied discrimination tasks. It also provides an analytical framework to understand the functional relevance of different sources of experimentally measured correlations. [ABSTRACT FROM AUTHOR]

Introduction: The cortical midline structures seem to be involved in the modulation of different resting state networks, such as the default mode network (DMN) and salience network (SN). Alterations in these systems, in particular in the perigenual anterior cingulate cortex (PACC), seem to play a central role in bipolar disorder (BD). However, the exact role of the PACC, and its functional connections to other midline regions (within and outside DMN) still remains unclear in BD. Methods: We investigated functional connectivity (FC), standard deviation (SD, as a measure of neuronal variability) and their correlation in bipolar patients ( n = 40) versus healthy controls ( n = 40), in the PACC and in its connections in different frequency bands (standard: 0.01-0.10 Hz; Slow-5: 0.01-0.027 Hz; Slow-4: 0.027-0.073 Hz). Finally, we studied the correlations between FC alterations and clinical-neuropsychological parameters and we explored whether subgroups of patients in different phases of the illness present different patterns of FC abnormalities. Results: We found in BD decreased FC (especially in Slow-5) from the PACC to other regions located predominantly in the posterior DMN (such as the posterior cingulate cortex (PCC) and inferior temporal gyrus) and in the SN (such as the supragenual anterior cingulate cortex and ventrolateral prefrontal cortex). Second, we found in BD a decoupling between PACC-based FC and variability in the various target regions (without alteration in variability itself). Finally, in our subgroups explorative analysis, we found a decrease in FC between the PACC and supragenual ACC (in depressive phase) and between the PACC and PCC (in manic phase). Conclusions: These findings suggest that in BD the communication, that is, information transfer, between the different cortical midline regions within the cingulate gyrus does not seem to work properly. This may result in dysbalance between different resting state networks like the DMN and SN. A deficit in the anterior DMN-SN connectivity could lead to an abnormal shifting toward the DMN, while a deficit in the anterior DMN-posterior DMN connectivity could lead to an abnormal shifting toward the SN, resulting in excessive focusing on internal contents and reduced transition from idea to action or in excessive focusing on external contents and increased transition from idea to action, respectively, which could represent central dimensions of depression and mania. If confirmed, they could represent diagnostic markers in BD. Hum Brain Mapp 36:666-682, 2015. © 2014 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Abstract: Nervous systems encode information about dynamically changing sensory input by changes in neuronal activity. Neuronal activity changes, however, also arise from noise sources within and outside the nervous system or from changes of the animal’s behavioral state. The resulting variability of neuronal responses in representing sensory stimuli limits the reliability with which animals can respond to stimuli and may thus even affect the chances for survival in certain situations. Relevant sources of noise arising at different stages along the motion vision pathway have been investigated from the sensory input to the initiation of behavioral reactions. Here, we concentrate on the reliability of processing visual motion information in flies. Flies rely on visual motion information to guide their locomotion. They are among the best established model systems for the processing of visual motion information allowing us to bridge the gap between behavioral performance and underlying neuronal computations. It has been possible to directly assess the consequences of noise at major stages of the fly’s visual motion processing system on the reliability of neuronal signals. Responses of motion sensitive neurons and their variability have been related to optomotor movements as indicators for the overall performance of visual motion computation. We address whether and how noise already inherent in the stimulus, e.g. photon noise for the visual system, influences later processing stages and to what extent variability at the output level of the sensory system limits behavioral performance. Recent advances in circuit analysis and the progress in monitoring neuronal activity in behaving animals should now be applied to understand how the animal meets the requirements of fast and reliable manoeuvres in naturalistic situations. [Copyright &y& Elsevier]

Abstract: The objective of this paper is to present a numerical study of a class of boundary value problems of singularly perturbed differential difference equations (SPDDE) which arise in computational neuroscience in particular in the modeling of neuronal variability. The mathematical modeling of the determination of the expected time for the generation of action potential in the nerve cells by random synaptic inputs in dendrites includes a general boundary-value problem for singularly perturbed differential difference equation with shifts. The problem considered in this paper exhibit turning point behavior which add to the complexity in the construction of numerical approximation to the solution of the problem as well as in obtaining theoretical estimates on the solution. Exponentially fitted finite difference scheme based on Il’in-Allen-Southwell fitting is used on a specially designed mesh. Some numerical examples are given to validate convergence and computational efficiency of the proposed numerical scheme. Effect of the shifts on the layer structure is illuminated for the considered examples. [Copyright &y& Elsevier]

I summarize recent computational and experimental work that addresses the inherent variability in the synaptic and intrinsic conductances in normal healthy brains and shows that multiple solutions (sets of parameters) can produce similar circuit performance. I then discuss a number of issues raised by this observation, such as which parameter variations arise from compensatory mechanisms and which reflect insensitivity to those particular parameters. I ask whether networks with different sets of underlying parameters can nonetheless respond reliably to neuromodulation and other global perturbations. At the computational level, I describe a paradigm shift in which it is becoming increasingly common to develop families of models that reflect the variance in the biological data that the models are intended to illuminate rather than single, highly tuned models. On the experimental side, I discuss the inherent limitations of overreliance on mean data and suggest that it is important to look for compensations and correlations among as many system parameters as possible, and between each system parameter and circuit performance. This second paradigm shift will require moving away from measurements of each system component in isolation but should reveal important previously undescribed principles in the organization of complex systems such as brains. [ABSTRACT FROM AUTHOR]

Renewed calls for a systems biology reflect the hope hat enduring biological questions at single-cell and cell-population scales will be resolved as modern molecular biology, with its reductionist program, approaches a nearly-complete characterization of the molecular mechanisms of specific cellular processes. Due to the confounding complexity of biological organization across these scales, computational science is sought to complement the intuition of experimentalists. However, with respect to the molecular basis of cellular processes during development and disease, a gulf between feasible simulations and realistic biology persists. Formidable are the mathematical and computational challenges to conducting and validating cell population-scale simulations, drawn from single-cell level and molecular level details. Nonetheless, in some biological contexts, a focus on core processes crafted by evolution can yield coarse-grained mathematical models that retain explanatory potential despite drastic simplification of known biochemical kinetics. In this article, we bring this modeling philosophy to bear on the nature of neural progenitor cell decision making during mammalian cerebral cortical development. Specifically, we present the computational component to a research program addressing developmental links between (i) the cellular response to endogenous DNA damage, (ii) primary mechanisms of neuronal genetic heterogeneity, or mosaicism, and (iii) the cell fate decision making that defines the population kinetics of neurogenesis. [ABSTRACT FROM AUTHOR]

In this study, based on the view of statistical inference, we investigate the robustness of neural codes, i.e., the sensitivity of neural responses to noise, and its implication on the construction of neural coding. We first identify the key factors that influence the sensitivity of neural responses, and find that the overlap between neural receptive fields plays a critical role. We then construct a robust coding scheme, which enforces the neural responses not only to encode external inputs well, but also to have small variability. Based on this scheme, we find that the optimal basis functions for encoding natural images resemble the receptive fields of simple cells in the striate cortex. We also apply this scheme to identify the important features in the representation of face images and Chinese characters. [ABSTRACT FROM AUTHOR]

Recordings from the visual cortex of anaesthetized monkeys taken with a 30-fold multimicroelectrode demonstrate that the neuronal variability, defined as the change in response strength over time spans of a few seconds to several minutes, is highly correlated within groups of neurones. Several such groups exhibiting independent variability between groups, coexist within the area recorded. This within-group covariance suggests that a major part of neuronal variability is due not to a noise process in the cells, but rather to additional inputs to the neurones, which are not under control of the experimenter. [ABSTRACT FROM AUTHOR]

We consider a noisy leaky integrate-and-fire (NLIF) neuron model. The resulting nonlinear time-dependent partial differential equation (PDE) is a Fokker-Planck Equation (FPE) which describes the evolution of the probability density. The finite element method (FEM) has been proposed to solve the governing PDE. In the realistic neural network, the irregular space is always determined. Thus, FEM can be used to tackle those situations whereas other numerical schemes are restricted to the problems with only a finite regular space. The stability of the proposed scheme is also discussed. A comparison with the existing Weighted Essentially Non-Oscillatory (WENO) finite difference approximation is also provided. The numerical results reveal that FEM may be a better scheme for the solution of such types of model problems. The numerical scheme also reduces computational time in comparison with time required by other schemes. [ABSTRACT FROM AUTHOR]

Summary Trial-to-trial variability is a reflection of the circuitry and cellular physiology that make up a neuronal network. A pervasive yet puzzling feature of cortical circuits is that despite their complex wiring, population-wide shared spiking variability is low dimensional. Previous model cortical networks cannot explain this global variability, and rather assume it is from external sources. We show that if the spatial and temporal scales of inhibitory coupling match known physiology, networks of model spiking neurons internally generate low-dimensional shared variability that captures population activity recorded in vivo. Shifting spatial attention into the receptive field of visual neurons has been shown to differentially modulate shared variability within and between brain areas. A top-down modulation of inhibitory neurons in our network provides a parsimonious mechanism for this attentional modulation. Our work provides a critical link between observed cortical circuit structure and realistic shared neuronal variability and its modulation. Highlights • Low-dimensional shared variability can be generated in spatial network models • Synaptic spatial and temporal scales determine the dimensions of shared variability • Depolarizing inhibitory neurons suppresses the population-wide fluctuations • Modeling the attentional modulation of variability within and between brain areas Population-wide fluctuations of neural population activity are widely observed in cortical recordings. Huang et al. show that turbulent dynamics in spatially ordered recurrent networks give rise to low-dimensional shared variability, which can be suppressed by depolarizing inhibitory neurons. [ABSTRACT FROM AUTHOR]