Chaotic Balanced State in a Model of Cortical Circuits

The nature and origin of the temporal irregularity in the electrical activity of cortical neurons in vivo are not well understood. We consider the hypothesis that this irregularity is due to a balance of excitatory and inhibitory currents into the cortical cells. We study a network model with excitatory and inhibitory populations of simple binary units. The internal feedback is mediated by relatively large synaptic strengths, so that the magnitude of the total excitatory and inhibitory feedback is much larger than the neuronal threshold. The connectivity is random and sparse. The mean number of connections per unit is large, though small compared to the total number of cells in the network. The network also receives a large, temporally regular input from external sources. We present an analytical solution of the mean-field theory of this model, which is exact in the limit of large network size. This theory reveals a new cooperative stationary state of large networks, which we term a balanced state. In this state, a balance between the excitatory and inhibitory inputs emerges dynamically for a wide range of parameters, resulting in a net input whose temporal fluctuations are of the same order as its mean. The internal synaptic inputs act as a strong negative feedback, which linearizes the population responses to the external drive despite the strong nonlinearity of the individual cells. This feedback also greatly stabilizes the system's state and enables it to track a time-dependent input on time scales much shorter than the time constant of a single cell. The spatiotemporal statistics of the balanced state are calculated. It is shown that the autocorrelations decay on a short time scale, yielding an approximate Poissonian temporal statistics. The activity levels of single cells are broadly distributed, and their distribution exhibits a skewed shape with a long power-law tail. The chaotic nature of the balanced state is revealed by showing that the evolution of the microscopic state of the network is extremely sensitive to small deviations in its initial conditions. The balanced state generated by the sparse, strong connections is an asynchronous chaotic state. It is accompanied by weak spatial cross-correlations, the strength of which vanishes in the limit of large network size. This is in contrast to the synchronized chaotic states exhibited by more conventional network models with high connectivity of weak synapses.

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Possible Effects of Depolarizing GABAA Conductance on the Neuronal Input–Output Relationship: A Modeling Study

Journal of Neurophysiology ◽

10.1152/jn.00988.2004 ◽

2005 ◽

Vol 93 (6) ◽

pp. 3504-3523 ◽

Cited By ~ 9

Author(s):

Kenji Morita ◽

Kunichika Tsumoto ◽

Kazuyuki Aihara

Keyword(s):

Firing Rate ◽

Cortical Neurons ◽

Reversal Potential ◽

Pyramidal Cells ◽

Resting Potential ◽

Input Output ◽

Wide Range ◽

The Relationship

Recent in vitro experiments revealed that the GABAA reversal potential is about 10 mV higher than the resting potential in mature mammalian neocortical pyramidal cells; thus GABAergic inputs could have facilitatory, rather than inhibitory, effects on action potential generation under certain conditions. However, how the relationship between excitatory input conductances and the output firing rate is modulated by such depolarizing GABAergic inputs under in vivo circumstances has not yet been understood. We examine herewith the input–output relationship in a simple conductance-based model of cortical neurons with the depolarized GABAA reversal potential, and show that a tonic depolarizing GABAergic conductance up to a certain amount does not change the relationship between a tonic glutamatergic driving conductance and the output firing rate, whereas a higher GABAergic conductance prevents spike generation. When the tonic glutamatergic and GABAergic conductances are replaced by in vivo–like highly fluctuating inputs, on the other hand, the effect of depolarizing GABAergic inputs on the input–output relationship critically depends on the degree of coincidence between glutamatergic input events and GABAergic ones. Although a wide range of depolarizing GABAergic inputs hardly changes the firing rate of a neuron driven by noncoincident glutamatergic inputs, a certain range of these inputs considerably decreases the firing rate if a large number of driving glutamatergic inputs are coincident with them. These results raise the possibility that the depolarized GABAA reversal potential is not a paradoxical mystery, but is instead a sophisticated device for discriminative firing rate modulation.

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Scalings of first-return time for random walks on generalized and weighted transfractal networks

International Journal of Modern Physics B ◽

10.1142/s0217979219503065 ◽

2019 ◽

Vol 33 (26) ◽

pp. 1950306

Author(s):

Qin Liu ◽

Weigang Sun ◽

Suyu Liu

Keyword(s):

Random Walks ◽

Large Scale ◽

Probability Generating Function ◽

Return Time ◽

Network Size ◽

Large Network ◽

Large Scale Network ◽

Scale Network ◽

The Mean ◽

First Return Time

The first-return time (FRT) is an effective measurement of random walks. Presently, it has attracted considerable attention with a focus on its scalings with regard to network size. In this paper, we propose a family of generalized and weighted transfractal networks and obtain the scalings of the FRT for a prescribed initial hub node. By employing the self-similarity of our networks, we calculate the first and second moments of FRT by the probability generating function and obtain the scalings of the mean and variance of FRT with regard to network size. For a large network, the mean FRT scales with the network size at the sublinear rate. Further, the efficiency of random walks relates strongly with the weight factor. The smaller the weight, the better the efficiency bears. Finally, we show that the variance of FRT decreases with more number of initial nodes, implying that our method is more effective for large-scale network size and the estimation of the mean FRT is more reliable.

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Optogenetic activators of apoptosis, necroptosis and pyroptosis for probing cell death dynamics and bystander cell responses

10.1101/2021.08.31.458313 ◽

2021 ◽

Author(s):

Kateryna Shkarina ◽

Eva Hasel de Carvalho ◽

José Carlos Santos ◽

Maria Leptin ◽

Petr Broz

Keyword(s):

Cell Death ◽

Apoptotic Cell ◽

Single Cells ◽

Proof Of Concept ◽

Cell Responses ◽

Or Groups ◽

Wide Range ◽

Specific Induction

AbstractTargeted and specific induction of cell death in individual or groups of cells holds the potential for new insights into the response of tissues or organisms to different forms of death. Here we report the development of optogenetically-controlled cell death effectors (optoCDEs), a novel class of optogenetic tools that enables light-mediated induction of three types of programmed cell death (PCD) – apoptosis, pyroptosis and necroptosis – using Arabidopsis thaliana photosensitive protein Cryptochrome2. OptoCDEs enable rapid and highly specific induction of PCD in human, mouse and zebrafish cells and are suitable for a wide range of applications, such as sub-lethal cell death induction or precise elimination of single cells or cell populations in vitro and in vivo. As the proof-of-concept, we utilize optoCDEs to assess the differences in the neighboring cell response to apoptotic or necrotic PCD, revealing a new role for shingosine-1-phosphate signaling in regulating the efferocytosis of apoptotic cell by epithelia.

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Exploiting variability of single cells to uncover the in vivo hierarchy of miRNA targets

10.1101/035097 ◽

2015 ◽

Cited By ~ 2

Author(s):

Andrzej Jerzy Rzepiela ◽

Arnau Vina-Vilaseca ◽

Jeremie Breda ◽

Souvik Ghosh ◽

Afzal P Syed ◽

...

Keyword(s):

Gene Expression ◽

Single Cell ◽

Single Cells ◽

Human Embryonic Kidney Cells ◽

Mirna Targets ◽

Wide Range ◽

Gene Expression Dynamics ◽

Cell To Cell Variability ◽

First Time

MiRNAs are post-transcriptional repressors of gene expression that may additionally reduce the cell-to-cell variability in protein expression, induce correlations between target expression levels and provide a layer through which targets can influence each other's expression as 'competing RNAs' (ceRNAs). Here we combined single cell sequencing of human embryonic kidney cells in which the expression of two distinct miRNAs was induced over a wide range, with mathematical modeling, to estimate Michaelis-Menten (KM)-type constants for hundreds of evolutionarily conserved miRNA targets. These parameters, which we inferred here for the first time in the context of the entire network of endogenous miRNA targets, vary over ~2 orders of magnitude. They reveal an in vivo hierarchy of miRNA targets, defined by the concentration of miRNA-Argonaute complexes at which the targets are most sensitively down-regulated. The data further reveals miRNA-induced correlations in target expression at the single cell level, as well as the response of target noise to the miRNA concentration. The approach is generalizable to other miRNAs and post-transcriptional regulators and provides a deeper understanding of gene expression dynamics.

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KCC2-dependent Steady-state Intracellular Chloride Concentration and pH in Cortical Layer 2/3 Neurons of Anesthetized and Awake Mice

10.1101/234476 ◽

2017 ◽

Author(s):

Juan Carlos Boffi ◽

Johannes Knabbe ◽

Michaela Kaiser ◽

Thomas Kuner

Keyword(s):

Steady State ◽

Cortical Neurons ◽

Chloride Concentration ◽

Cortical Layer ◽

Model Systems ◽

Adult Mice ◽

Neuronal Inhibition ◽

Wide Range ◽

Intracellular Chloride Concentration

AbstractNeuronal intracellular Cl- concentration ([Cl-]i) influences a wide range of processes such as neuronal inhibition, membrane potential dynamics, intracellular pH (pHi) or cell volume. Up to date, neuronal [Cl-]i has predominantly been studied in model systems of reduced complexity. Here, we implemented the genetically encoded ratiometric Cl- indicator Superclomeleon (SCLM) to estimate the steady-state [Cl-]i in cortical neurons from anesthetized and awake mice using 2-photon microscopy. Additionally, we implemented superecliptic pHluorin as a ratiometric sensor to estimate the intracellular steady-state pH (pHi) of mouse cortical neurons in vivo. We estimated an average resting [Cl-]i of 6 ± 2 mM with no evidence of subcellular gradients in the proximal somato-dendritic domain and an average somatic pHi of 7.1 ± 0.1. Neither [Cl-]i nor pHi were affected by isoflurane anesthesia. We deleted the cation-Cl- co-transporter KCC2 in single identified neurons of adult mice and found an increase of [Cl-]i to approximately 26 ± 8 mM, demonstrating that under in vivo conditions KCC2 produces low [Cl-]i in adult mouse neurons. In summary, neurons of the brain of awake adult mice exhibit a low and evenly distributed [Cl-]i in the proximal somato-dendritic compartment that is independent of anesthesia and requires KCC2 expression for its maintenance.

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Quantum dot/antibody conjugates for in vivo cytometric imaging in mice

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1421632111 ◽

2015 ◽

Vol 112 (5) ◽

pp. 1350-1355 ◽

Cited By ~ 71

Author(s):

Hee-Sun Han ◽

Elisabeth Niemeyer ◽

Yuhui Huang ◽

Walid S. Kamoun ◽

John D. Martin ◽

...

Keyword(s):

Bone Marrow ◽

Quantum Dot ◽

Single Cells ◽

High Specificity ◽

Cell Labeling ◽

Hydrodynamic Diameter ◽

Calvarial Bone ◽

Hematopoietic Stem ◽

Wide Range

Multiplexed, phenotypic, intravital cytometric imaging requires novel fluorophore conjugates that have an appropriate size for long circulation and diffusion and show virtually no nonspecific binding to cells/serum while binding to cells of interest with high specificity. In addition, these conjugates must be stable and maintain a high quantum yield in the in vivo environments. Here, we show that this can be achieved using compact (∼15 nm in hydrodynamic diameter) and biocompatible quantum dot (QD) -Ab conjugates. We developed these conjugates by coupling whole mAbs to QDs coated with norbornene-displaying polyimidazole ligands using tetrazine–norbornene cycloaddition. Our QD immunoconstructs were used for in vivo single-cell labeling in bone marrow. The intravital imaging studies using a chronic calvarial bone window showed that our QD-Ab conjugates diffuse into the entire bone marrow and efficiently label single cells belonging to rare populations of hematopoietic stem and progenitor cells (Sca1+c-Kit+ cells). This in vivo cytometric technique may be useful in a wide range of structural and functional imaging to study the interactions between cells and between a cell and its environment in intact and diseased tissues.

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Multiple Time Scales of Temporal Response in Pyramidal and Fast Spiking Cortical Neurons

Journal of Neurophysiology ◽

10.1152/jn.00453.2006 ◽

2006 ◽

Vol 96 (6) ◽

pp. 3448-3464 ◽

Cited By ~ 69

Author(s):

Giancarlo La Camera ◽

Alexander Rauch ◽

David Thurbon ◽

Hans-R. Lüscher ◽

Walter Senn ◽

...

Keyword(s):

Time Scales ◽

Cortical Neurons ◽

Time Course ◽

Sensory Stimulation ◽

Multiple Time Scales ◽

Multiple Time ◽

Wide Range ◽

Fast Spiking

Neural dynamic processes correlated over several time scales are found in vivo, in stimulus-evoked as well as spontaneous activity, and are thought to affect the way sensory stimulation is processed. Despite their potential computational consequences, a systematic description of the presence of multiple time scales in single cortical neurons is lacking. In this study, we injected fast spiking and pyramidal (PYR) neurons in vitro with long-lasting episodes of step-like and noisy, in-vivo-like current. Several processes shaped the time course of the instantaneous spike frequency, which could be reduced to a small number (1–4) of phenomenological mechanisms, either reducing (adapting) or increasing (facilitating) the neuron's firing rate over time. The different adaptation/facilitation processes cover a wide range of time scales, ranging from initial adaptation (<10 ms, PYR neurons only), to fast adaptation (<300 ms), early facilitation (0.5–1 s, PYR only), and slow (or late) adaptation (order of seconds). These processes are characterized by broad distributions of their magnitudes and time constants across cells, showing that multiple time scales are at play in cortical neurons, even in response to stationary stimuli and in the presence of input fluctuations. These processes might be part of a cascade of processes responsible for the power-law behavior of adaptation observed in several preparations, and may have far-reaching computational consequences that have been recently described.

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Mean field dynamics of a Wilson–Cowan neuronal network with nonlinear coupling term

Stochastics and Dynamics ◽

10.1142/s0219493718500466 ◽

2018 ◽

Vol 18 (06) ◽

pp. 1850046

Author(s):

James MacLaurin ◽

Jamil Salhi ◽

Salwa Toumi

Keyword(s):

Mean Field ◽

Network Size ◽

Large Network ◽

Propagation Of Chaos ◽

Synaptic Connections ◽

Coupling Term ◽

Field Equations ◽

Mean Field Equations ◽

Different Populations ◽

The Mean

In this paper we prove the propagation of chaos property for an ensemble of interacting neurons subject to independent Brownian noise. The propagation of chaos property means that in the large network size limit, the neurons behave as if they are probabilistically independent. The model for the internal dynamics of the neurons is taken to be that of Wilson and Cowan, and we consider there to be multiple different populations. The synaptic connections are modeled with a nonlinear “electrical” model. The nonlinearity of the synaptic connections means that our model lies outside the scope of classical propagation of chaos results. We obtain the propagation of chaos result by taking advantage of the fact that the mean-field equations are Gaussian, which allows us to use Borell’s Inequality to prove that its tails decay exponentially.

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Tritium effect in peroxidation of ehtanol by liver catalase

Biochemical Journal ◽

10.1042/bj1670077 ◽

1977 ◽

Vol 167 (1) ◽

pp. 77-86 ◽

Cited By ~ 6

Author(s):

S E Damgaard

Keyword(s):

Isotope Effect ◽

Ethanol Concentration ◽

Mean Value ◽

Wide Range ◽

H2o2 Generation ◽

State Generation ◽

The Mean ◽

Galactose Dehydrogenase

1. Simultaneous determination of the rate of appearance of 3H in water from [(1R)-1-3H1] ethanol and the rate of acetaldehyde formation in the presence of rat or ox liver catalase under conditions of steady-state generation of H2O2 allowed calculation of the 3H isotope effect. The mean value of 2.52 obtained for rat liver catalase at 37 degrees C and pH 6.3-7.7 was independent of both ethanol concentration and the rate of H2O2 generation over a wide range. At 25 degrees C a slightly lower mean value of 2.40 was obtained with the ox liver catalase. 2. Neither the product, acetaldehyde, nor 4-methylpyrazole influenced the two rates measured in the assay. 3. Relating the value obtained for the 3H isotope effect to a known value for the 2H isotope effect strongly supports the view that both values are close to the true isotope effect with the respective substituted compounds on the rate constant in the catalytic step involving scission of the C-H bond. 4. The constancy of the isotope effect under various conditions makes it possible to use it for interpretations in vivo. 5. It was established that beta-D-galactose dehydrogenase exhibits B-specificity towards the nicotinamide ring in NAD.

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Intercomparison of snow density measurements: bias, precision and spatial resolution

The Cryosphere Discussions ◽

10.5194/tcd-9-3581-2015 ◽

2015 ◽

Vol 9 (4) ◽

pp. 3581-3616 ◽

Cited By ~ 2

Author(s):

M. Proksch ◽

N. Rutter ◽

C. Fierz ◽

M. Schneebeli

Keyword(s):

Initial Conditions ◽

Fundamental Property ◽

Density Variation ◽

Measurement Methods ◽

Micro Computed Tomography ◽

Snow Density ◽

Density Measurements ◽

Wide Range ◽

The Mean ◽

Ct Density

Abstract. Density is a fundamental property of porous media such as snow. A wide range of snow properties and physical processes are linked to density, but few studies have addressed the uncertainty in snow density measurements. No study has yet considered the recent advances in snow measurement methods such as micro-computed tomography (CT). During the MicroSnow Davos 2014 workshop different approaches to measure snow density were applied in a controlled laboratory environment and in the field. Overall, the agreement between CT and gravimetric methods (density cutters) was 5 to 9 %, with a bias of −5 to 2 %, expressed as percentage of the mean CT density. In the field, the density cutters tend to overestimate (1 to 6 %) densities below and underestimate (1 to 6 %) densities above 296 to 350 kg m−3, respectively, depending on the cutter type. Using the mean per layer of all measurement methods applied in the field (CT, box, wedge and cylinder cutter) and ignoring ice layers, the variation of layer density between the methods was 2 to 5 % with a bias of −1 to 1 %. In general, our result suggests that snow densities measured by different methods agree within 9 %. However, the density profiles resolved by the measurement methods differed considerably. In particular, the millimeter scale density variations revealed by the high resolution CT contrasted the thick layers with sharp boundaries introduced by the observer. In this respect, the unresolved variation, i.e. the density variation within a layer, which is lost by sampling with lower resolution or layer aggregation, is critical when snow density measurements are used as boundary or initial conditions in numerical simulations.

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