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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]

Neuronal systems maintain stable functions despite large variability in their physiological components. Ion channel expression, in particular, is highly variable in neurons exhibiting similar electrophysiological phenotypes, which raises questions regarding how specific ion channel subsets reliably shape intrinsic properties of neurons. Here, we use detailed conductance-based modeling to explore how stable neuronal function is achieved despite variability in channel composition among neurons. Using dimensionality reduction, we uncover two principal dimensions in the channel conductance space that capture most of the variance of the observed variability. These two dimensions correspond to two sources of variability that originate from distinct physiologically relevant mechanisms underlying the regulation of neuronal activity, providing quantitative insights into how channel composition is linked to the electrophysiological activity of neurons. These insights allow us to understand and design a model-independent, reliable neuromodulation rule for variable neuronal populations., (© The Author(s) 2024. Published by Oxford University Press on behalf of National Academy of Sciences.)

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]

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]

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: 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]

The editor discusses findings of a research which explores the challenges of developing computational tools and mathematical theories in understanding of stochastic neural dynamics. The research focuses on topics of synaptic coupling between auditory nerve fibers and inner hair cells, stochastic version of ion channel noise and qualify information transmission in a stochastic Hodgkin-Huxley neuron model. The editor also outlines the variability of stochastic technology for cellular mechanism.

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]

The occurrence of neuronal spikes recorded directly from sensory cortex is highly irregular within and between presentations of an invariant stimulus. The traditional solution has been to average responses across many trials. However, with this approach, response variability is downplayed as noise, so it is assumed that statistically controlling it will reveal the brain's true response to a stimulus. A mounting body of evidence suggests that this approach is inadequate. For example, experiments show that response variability itself varies as a function of stimulus dimensions like contrast and state dimensions like attention. In other words, response variability has structure, is therefore potentially informative and should be incorporated into models which try to explain neural encoding. In this article we provide commentary on a recently published study by Coen-Cagli and Solomon that incorporates spike variability in a quantitative model, by explaining it as a function of divisive normalization. We consider the potential role of neural oscillations in this process as a potential bridge between the current microscale findings and response variability at the mesoscale/macroscale level., Competing Interests: No competing interests were disclosed., (Copyright: © 2020 Ruddy KL et al.)

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]

The spiking activity of cortical neurons is highly variable. This variability is generally correlated among nearby neurons, an effect commonly interpreted to reflect the coactivation of neurons due to anatomically shared inputs. Recent findings, however, indicate that correlations can be dynamically modulated, suggesting that the underlying mechanisms are not well understood. Here, we investigate the hypothesis that correlations are dominated by neuronal coinactivation: the occurrence of brief silent periods during which all neurons in the local network stop firing. We recorded spiking activity from large populations of neurons in the auditory cortex of anesthetized rats across different brain states. During spontaneous activity, the reduction of correlation accompanying brain state desynchronization was largely explained by a decrease in the density of the silent periods. The presentation of a stimulus caused an initial drop of correlations followed by a rebound, a time course that was mimicked by the instantaneous silence density. We built a rate network model with fluctuation-driven transitions between a silent and an active attractor and assumed that neurons fired Poisson spike trains with a rate following the model dynamics. Variations of the network external input altered the transition rate into the silent attractor and reproduced the relation between correlation and silence density found in the data, both in spontaneous and evoked conditions. This suggests that the observed changes in correlation, occurring gradually with brain state variations or abruptly with sensory stimulation, are due to changes in the likeliness of the microcircuit to transiently cease firing.