Counting statistics of 1/f fluctuations in neuronal spike trains

The mesencephalic reticular formation (MRF) neurons are regarded as contributing to the activation of the celebral cortex. In this paper, the statistical features of single neuronal activities in MRF of cat during dream sleep are investigated; the neuronal spike train exhibits 1/f fluctuations. Counting statistics is applied to the neuronal spike train giving rise to a variance/mean curve which follows at -law. For an interpretation of these findings, the clustering Poisson process is applied which not only gives rise to at -law but also suggests a generation mechanism. The MRF neuronal activities are closely fitted by the clustering Poisson process and the underlying statistical parameters can be estimated. These findings strongly suggest that neuronal activities can be interpreted as superposition of randomly occuring clusters ( = bursts of spikes).     

Further study on 1/f fluctuations observed in central single neurons during REM sleep

Recently, 1/f fluctuations have been discovered in the single-unit activity of mesencephalic reticular formation (MRF) neurons during REM sleep. In a previous paper, such behavior could satisfyingly be interpreted on the basis of the clustering Poisson process. The question of applicability of this model to other MRF neurons remained unanswered. The present paper reports on 1/f fluctuations in 12 MRF neurons all of which can satisfyingly be modeled by the clustering Poisson process.     

Simulation study on dynamics transition in neuronal activity during sleep cycle by using asynchronous and symmetry neural network model

We have found that single neuronal activities in different regions in the brain commonly exhibit the distinct dynamics transition during sleep-waking cycle in cats. Especially, power spectral densities of single neuronal activities change their profiles from the white to the 1/f along with sleep cycle from slow wave sleep (SWS) to paradoxical sleep (PS). Each region has different neural network structure and physiological function. This suggests a globally working mechanism may be underlying the dynamics transition we concern. Pharmacological studies have shown that a change in a wide-spread serotonergic input to these regions possibly causes the neuronal dynamics transition during sleep cycle. In this paper, based on these experimental results, an asynchronous and symmetry neural network model including inhibitory input, which represents the role of the serotonergic system, is utilized to examine the reality of our idea that the inhibitory input level varying during sleep cycle induce that transition. Simulation results show that the globally applied inhibitory input can control the dynamics of single neuronal state evolution in the artificial neural network: 1/f-like power spectral density profiles result under weak inhibition, which possibly corresponds to PS, and white profiles under strong inhibition, which possibly corresponds to SWS. An asynchronous neural network is known to change its state according to its energy function. The geometrical structure of network energy function is thought to vary along with the change in inhibitory level, which is expected to cause the dynamics transition of neuronal state evolution in the network model. These simulation results support the possibility that the serotonergic system is essential for the dynamics transition of single neuronal activities during sleep cycle.     

Slow oscillations in neural networks with facilitating synapses

The synchronous oscillatory activity characterizing many neurons in a network is often considered to be a mechanism for representing, binding, conveying, and organizing information. A number of models have been proposed to explain high-frequency oscillations, but the mechanisms that underlie slow oscillations are still unclear. Here, we show by means of analytical solutions and simulations that facilitating excitatory (E _f) synapses onto interneurons in a neural network play a fundamental role, not only in shaping the frequency of slow oscillations, but also in determining the form of the up and down states observed in electrophysiological measurements. Short time constants and strong E _f synapse-connectivity were found to induce rapid alternations between up and down states, whereas long time constants and weak E _f synapse connectivity prolonged the time between up states and increased the up state duration. These results suggest a novel role for facilitating excitatory synapses onto interneurons in controlling the form and frequency of slow oscillations in neuronal circuits.     

Simulated power spectral density (PSD) of background electrocorticogram (ECoG)

The ECoG background activity of cerebral cortex in states of rest and slow wave sleep resembles broadband noise. The power spectral density (PSD) then may often conform to a power-law distribution: a straight line in coordinates of log power vs. log frequency. The exponent, x, of the distribution, 1/f^x, ranges between 2 and 4. These findings are explained with a model of the neural source of the background activity in mutual excitation among pyramidal cells. The dendritic response of a population of interactive excitatory neurons to an impulse input is a rapid exponential rise and a slow exponential decay, which can be fitted with the sum of two exponential terms. When that function is convolved as the kernel with pulses from a Poisson process and summed, the resulting “brown” or “black noise conforms to the ECoG time series and the PSD in rest and sleep. The PSD slope is dependent on the rate of rise. The variation in the observed slope is attributed to variation in the level of the background activity that is homeostatically regulated by the refractory periods of the excitatory neurons. Departures in behavior from rest and sleep to action are accompanied by local peaks in the PSD, which manifest emergent nonrandom structure in the ECoG, and which prevent reliable estimation of the 1/f^x exponents in active states. We conclude that the resting ECoG truly is low-dimensional noise, and that the resting state is an optimal starting point for defining and measuring both artifactual and physiological structures emergent in the activated ECoG.     

Steady State of Photosynthetic Electron Transport in Cells of the Cyanophyti Synechocystis PCC 6714 Having Different Stoichiometry between PS I and PS II: Analysis of Flash-Induced Oxidation-Reduction of Cytochrome f and P700 under Steady State of Photosynthesis

The steady state of photosynthetic electron transport drivenby two photosystems was studied with cells of the cyanophyteSynechocystis PCC 6714 by analyzing the flash-induced oxidation-reductionof Cyt f and P700 under continuous background illumination.We first analyzed the spectra and the kinetics of flash-inducedabsorption changes in the 400 to 440 nm wavelength region anddefined the absorption changes due to oxidation-reduction ofCyt f and P700. Results indicated that the flash-induced absorptionchanges at 420 and 435 nm are due to the oxidation-reductionof Cyt f and P700, respectively. Determination of the steadystate of Cyt f (420 nm) and P700 (435 nm) was made for the cellsgrown under a weak orange light exciting mainly PS II (PS IIlight) and having a high ratio of PS I to PS II (PS I/PS II),and those grown under a weak red light exciting preferentiallyPS I (PS I light) and having a low PS I/PS II. The steady stateof electron transport in cells of the two types were comparedunder PS I and PS II lights. The results indicated that: (1)under the light conditions used for growth (both red and orangelight), the intermediate electron pool between the two photosystemsremained in a redox state so as to keep both photosystems inthe open state. (2) When shifted to PS I light, the intermediatepool and PS I in cells of high PS I/PS II became extremely electron-poor,and so most of the PS I reaction centers were closed. (3) Theintermediate pool in cells of low PS I/PS II became extremelyelectron-rich when shifted to PS II light, and most of the PSII reaction centers were closed. The electron transport stateis released from such biased states by regulation of PS I/PSII. Results supported our previously proposed hypothesis thatthe stoichiometry between PS I and PS II is regulated so asto keep the two photosystems in the open state. The relationshipbetween the steady state of electron transport and the regulationof PS I/PS II is discussed. (Received August 2, 1990; Accepted December 10, 1990)     

Coexistence of memory patterns and mixed states in a sparsely encoded associative memory model storing ultrametric patterns

Analyzing the coexistence of memory patterns and mixed states gives important information for constructing a model for the face responsive neurons of the monkey inferior-temporal cortex. We analyzed whether the memory patterns coexist with mixed states when the sparse coding scheme is used for the associative memory model storing ultrametric patterns. For memory patterns and mixed states to coexist, there must be sufficient capacity for storing them and their threshold values must be the same. We determined that the storage capacities for all mixed states composed of correlated memory patterns diverge as 1/|flogf| (where f is the firing rate) even when the correlation of the memory patterns is infinitesimally small. We also determined that the memory patterns and the mixed states can become the equilibrium state of the model in the same threshold value. These results mean that they can coexist in this model. These findings should contribute to research on face responsive neurons in the monkey inferior-temporal cortex.     

Simple method for isolation of oxygen evolving photosystem 2 core complex free of cytochrome <Emphasis Type="Italic">f</Emphasis> contamination

This communication presents a simple method for isolation of oxygen evolving photosystem 2 (PS 2) core complex by solubilisation of PS 2 membranes with the nonionic detergent octyl-β-D-thioglucopyranoside (OTG). This complex was free of cytochrome (Cyt) f contamination and also lacked the 22 and 10 kDa proteins that may not be directly required for primary photochemistry of the PS 2 complex and water oxidation. OTG could also remove the Cyt f contamination from the PS 2-core complex isolated using octyl-β-D-glucopyranoside (OGP). The Cyt f contamination in the PS 2 complexes could potentially interfere with spectrophotometric determinations of redox states of Cyt _b559 and its stoichiometry in the PS 2 complex.     

A Markov model for interspike interval distributions of auditory cortical neurons that do not show periodic firings

Spontaneous firing properties of individual auditory cortical neurons are interpreted in terms of local and global order present in functioning brain networks, such as alternating “up” and “down” states. A four-state modulated Markov process is used to model neuronal firings. The system alternates between a bound and an unbound state, both with Poisson-distributed lifetimes. During the unbound state, active and closed states alternate with Poisson-distributed lifetimes. Inside the active state, spikes are generated as a realization of a Poisson process. This combination of processes constitutes a four-state modulated Markov process, determined by five independent parameters. Analytical expressions for the probability density functions (pdfs) that describe the interspike interval (ISI) distribution and autocorrelation function are derived. The pdf for the ISI distribution is shown to be a linear combination of three exponential functions and is expressed through the five system parameters. Through fitting experimental ISI histograms by the theoretical ones, numerical values of the system parameters are obtained for the individual neurons. Both Monte Carlo simulations and goodness-of-fit tests are used to validate the fitting procedure. The values of the estimated system parameters related to the active-closed and bound–unbound processes and their independence on the neurons’ mean firing rate suggest that the underlying quasi-periodic processes reflect properties of the network in which the neurons are embedded. The characteristic times of autocorrelations, determined by the bound–unbound and active-closed processes, are also independent of the neuron’s firing rate. The agreement between experimental and theoretical ISI histograms and autocorrelation functions allows interpretation of the system parameters of the individual neurons in terms of slow and delta waves, and high-frequency oscillations observed in cortical networks. This procedure can identify and track the influence of changing brain states on the single-unit firing patterns in experimental animals.     

Cytochrome b 6 f complex: Dynamic molecular organization,function and acclimation

The cytochrome b ₆ f complex occupies a central position in photosynthetic electron transport and proton translocation by linking PS II to PS I in linear electron flow from water to NADP⁺, and around PS I for cyclic electron flow. Cytochrome b ₆ f complexes are uniquely located in three membrane domains: the appressed granal membranes, the non-appressed stroma thylakoids and end grana membranes, and also the non-appressed grana margins, in contrast to the marked lateral heterogeneity of the localization of all other thylakoid multiprotein complexes. In addition to its vital role in vectorial electron transfer and proton translocation across the membrane, cytochrome b ₆ f complex is also involved in the regulation of balanced light excitation energy distribution between the photosystems, since its redox state governs the activation of LHC II kinase (the kinase that phosphorylates the mobile peripheral fraction of the chlorophyll a/b-proteins of LHC II of PS II). Hence, cytochrome b ₆ f complex is the molecular link in the interactive co-regulation of light-harvesting and electron transfer.The importance of a highly dynamic, yet flexible organization of the thylakoid membranes of plants and green algae has been highlighted by the exciting discovery that a lateral reorganization of some cytochrome b ₆ f complexes occurs in the state transition mechanism both in vivo and in vitro (Vallon et al. 1991). The lateral redistribution of phosphorylated LHC II from stacked granal membrane regions is accompanied by a concomitant movement of some cytochrome b ₆ f complexes from the granal membranes out to the PS I-containing stroma thylakoids. Thus, the dynamic movement of cytochrome b ₆ f complex as a multiprotein complex is a molecular mechanism for short-term adaptation to changing light conditions. With the concept of different membrane domains for linear and cyclic electron flow gaining credence, it is thought that linear electron flow occurs in the granal compartments and cyclic electron flow is localised in the stroma thylakoids at non-limiting irradiances. It is postulated that dynamic lateral reversible redistribution of some cytochrome b ₆ f complexes are part of the molecular mechanism involved in the regulation of linear electron transfer (ATP and NADPH) and cyclic electron flow (ATP only). Finally, the molecular significance of the marked regulation of cytochrome b ₆ f complexes for long-term regulation and optimization of photosynthetic function under varying environmental conditions, particularly light acclimation, is discussed.Abbreviations Chl chlorophyll - cyt cytochrome - PS Photosystem     

The spatial distribution of neurons and glia in human cortex based on the poisson distribution

A method was devised that employs deviations from the Poisson distribution to analyze the spatial arrangement of neurons and glia in human cerebral cortex. A field of randomly distributed points equal in number of a sample field of neuronal or glial cells is generated by computer, and the proportion of cells in the sample field that are closer to the nearest neighboring cells than to the nearest randomly distributed point is determined. We call this proportion the "Poisson ratio." When the cells are randomly distributed, the Poisson ratio is equal to 0.5. If the Poisson ratio is less than 0.5, the cells are farther away from one another than a random distribution would predict (exclusionary pattern); if the Poisson ratio is greater than 0.5, the cells are closer to one another than a random distribution would predict (clustering). A simple nonparametric statistical test is used to determine the significance of differences in the ratios. This method was applied to samples of human cerebral cortex in order to test the hypothesis that patients with schizophrenic psychosis may have an altered pattern of neuronal clustering. The analysis revealed that there is no difference in the nearest-neighbor distribution of either neurons or glia between psychotic patients and controls. It was found, however, that there is a highly significant difference in the spatial distribution of neurons versus glia in human cerebral cortex. Neurons of layers II to VI in the human cortex show greater-than-expected distances among them and are distributed according to an exclusionary pattern, while neurons in layer I show a clustering pattern.(ABSTRACT TRUNCATED AT 250 WORDS)     

A model for the neuronal implementation of selective visual attention based on temporal correlation among neurons

We propose a model for the neuronal implementation of selective visual attention based on temporal correlation among groups of neurons. Neurons in primary visual cortex respond to visual stimuli with a Poisson distributed spike train with an appropriate, stimulus-dependent mean firing rate. The spike trains of neurons whose receptive fields donot overlap with the focus of attention are distributed according to homogeneous (time-independent) Poisson process with no correlation between action potentials of different neurons. In contrast, spike trains of neurons with receptive fields within the focus of attention are distributed according to non-homogeneous (time-dependent) Poisson processes. Since the short-term average spike rates of all neurons with receptive fields in the focus of attention covary, correlations between these spike trains are introduced which are detected by inhibitory interneurons in V4. These cells, modeled as modified integrate-and-fire neurons, function as coincidence detectors and suppress the response of V4 cells associated with non-attended visual stimuli. The model reproduces quantitatively experimental data obtained in cortical area V4 of monkey by Moran and Desimone (1985).     

The potential role of presenilin 1 in regulation of synaptic function

One of the earliest neuropathological symptoms of Alzheimer’s disease is the loss of synapses that precedes the formation of amyloid plaques and neurodegeneration. Although most cases of early-onset familial Alzheimer’s disease are caused by mutations in the presenilin 1 (PS1) gene, the functions of PS1 and its role in synaptic dysfunction are not yet completely understood. In this paper, we analyzed PS1 intra- and extracellular distribution in cultures of mouse cortical embryonic neurons. We found that PS1 was concentrated on the surface of the growth cone and neurite contact sites. PS1 was also found in synapses where it was colocalized with synaptophysin. We obtained independent evidence of PS1 involvement in synaptic function by transfection of neurons with GFP-PS1cDNA. GFP was colocalized with synaptophysin in transfected cultures. GFP-immunoprecepitates from transfected neurons contained N-cadherin. This finding represents additional evidence of PS1 participation in the synapse formation. To evaluate the role of PS1 inactivation in the synaptic functions, we compare the synaptic density in neuronal cell cultures from knockout mice PS1 (−/−) and wild type mice PS1 (+/+). Our results obviously show that PS1 (−/−) cultures displayed lower number of morphological synapses compared to wild type culture PS1 (+/+). In summary, our findings show the role of PS1 in synaptic function.     

Fast numerical methods for simulating large-scale integrate-and-fire neuronal networks

We discuss numerical methods for simulating large-scale, integrate-and-fire (I&F) neuronal networks. Important elements in our numerical methods are (i) a neurophysiologically inspired integrating factor which casts the solution as a numerically tractable integral equation, and allows us to obtain stable and accurate individual neuronal trajectories (i.e., voltage and conductance time-courses) even when the I&F neuronal equations are stiff, such as in strongly fluctuating, high-conductance states; (ii) an iterated process of spike-spike corrections within groups of strongly coupled neurons to account for spike-spike interactions within a single large numerical time-step; and (iii) a clustering procedure of firing events in the network to take advantage of localized architectures, such as spatial scales of strong local interactions, which are often present in large-scale computational models—for example, those of the primary visual cortex. (We note that the spike-spike corrections in our methods are more involved than the correction of single neuron spike-time via a polynomial interpolation as in the modified Runge-Kutta methods commonly used in simulations of I&F neuronal networks.) Our methods can evolve networks with relatively strong local interactions in an asymptotically optimal way such that each neuron fires approximately once in operations, where N is the number of neurons in the system. We note that quantifications used in computational modeling are often statistical, since measurements in a real experiment to characterize physiological systems are typically statistical, such as firing rate, interspike interval distributions, and spike-triggered voltage distributions. We emphasize that it takes much less computational effort to resolve statistical properties of certain I&F neuronal networks than to fully resolve trajectories of each and every neuron within the system. For networks operating in realistic dynamical regimes, such as strongly fluctuating, high-conductance states, our methods are designed to achieve statistical accuracy when very large time-steps are used. Moreover, our methods can also achieve trajectory-wise accuracy when small time-steps are used. Action Editor: Nicolas Brunel     

Regulation of Photosystem Stoichiometry in the Photosynthetic System of the Cyanophyte Synechocystis PCC 6714 in Response to Light-Intensity

Light-induced changes in stoichiometry among three thylakoidcomponents, PS I, PS II and Cyt b₆-f complexes, were studiedwith the cyanophyte Synechocystis PCC 6714. Special attentionwas paid to two aspects of the stoichiometric change; first,a comparison of the patterns of regulation in response to differencesin light-intensity with those induced by differences in light-quality,and second, the relationship between regulation of the stoichiometryand the steady state of the electron transport system. Resultsfor the former indicated that (1) the abundance of PS I on aper cell basis was reduced under white light at the intensityas high as that for light-saturation of photosynthesis, butPS I per cell was increased under low light-intensity, (2) PSII and Cyt b₆-f complexes remained fairly constant, and (3)changes in the abundance of PS I depended strictly on proteinsynthesis. The pattern was identical with that of chromaticregulation. For the second problem, the redox steady-statesof Cyt f and P700 under white light of various intensities weredetermined by flash-spectroscopy. Results indicated that (1)Cyt f and P700 in cells grown under low light-intensity [highratio of PS I to PS II (PS I/PS II)] were markedly oxidizedwhen the cells were exposed to high light-intensity, while theyremained in the reduced state under low light-intensity. (2)After a decrease in the abundance of PS I, most of P700 remainedin the reduced state even under high light-intensity, whilethe level of reduced Cyt f remained low. (3) Both Cyt f andP700 in cells of low PS I/PS II were fully reduced under lowlight-intensity, and Cyt f reduction following the flash wasrapid, which indicates that the turnover of PS I limits theoverall rate of electron flow. After an increase in the abundanceof PS I, the electron transport recovered from the biased state.(4) The redox steady-state of the Cyt b₆-f complex correlatedwell with the regulation of PS I/PS II while the state of thePQ pool did not. Based on these results, a working model ofthe regulation of assembly of the PS I complex, in which theredox steady-state of the Cyt b₆-f complex is closely relatedto the primary signal, is proposed. (Received August 2, 1990; Accepted December 10, 1990)     

Regulation of Electron Transport Composition in Cyanobacterial Photosynthetic System: Stoichiometry among Photosystem I and II Complexes and Their Light-Harvesting Antennae and Cytochrome b6/fComplex

This study was done to confirm our previous observation withthe pattern of changes in electron transport composition inducedby an imbalance of the electron transport state. Contents ofphotosystem (PS) I and II complexes and their antennae and Cytb₆/f complex were determined for systems of cyanobacterium SynechocystisPCC 6714 of different PS I/PS II ratios. The results indicatedthat (1) the observed changes in the PS I/PS II ratio are not-dueto regulation of the activities of the respective PS's but tochanges in their contents, (2) the molar ratio between PS IIand Cyt b₆/f complexes was fairly constant when marked changesoccurred in the PS I content, and (3) the PS II and Cyt b₆/fcontents per cell remained fairly constant while the PS I contentchanged markedly. These findings agree with our previous observationwith autotrophic cells of Anacystis nidulans Tx 20 and supportour argument that in cyanobacterial and red algal electron transportsystems, the content of the terminalcomponent(s), such as PSI complex, is regulated in order to maintain a balance betweenthe electron influx by PS II action to the system and the effluxby PS I action from it. (Received June 3, 1987; Accepted September 20, 1987)     

Localization of the Brainstem GABAergic Neurons Controlling Paradoxical (REM) Sleep

Paradoxical sleep (PS) is a state characterized by cortical activation, rapid eye movements and muscle atonia. Fifty years after its discovery, the neuronal network responsible for the genesis of PS has been only partially identified. We recently proposed that GABAergic neurons would have a pivotal role in that network. To localize these GABAergic neurons, we combined immunohistochemical detection of Fos with non-radioactive in situ hybridization of GAD67 mRNA (GABA synthesis enzyme) in control rats, rats deprived of PS for 72 h and rats allowed to recover after such deprivation. Here we show that GABAergic neurons gating PS (PS-off neurons) are principally located in the ventrolateral periaqueductal gray (vlPAG) and the dorsal part of the deep mesencephalic reticular nucleus immediately ventral to it (dDpMe). Furthermore, iontophoretic application of muscimol for 20 min in this area in head-restrained rats induced a strong and significant increase in PS quantities compared to saline. In addition, we found a large number of GABAergic PS-on neurons in the vlPAG/dDPMe region and the medullary reticular nuclei known to generate muscle atonia during PS. Finally, we showed that PS-on neurons triggering PS localized in the SLD are not GABAergic. Altogether, our results indicate that multiple populations of PS-on GABAergic neurons are distributed in the brainstem while only one population of PS-off GABAergic neurons localized in the vlPAG/dDpMe region exist. From these results, we propose a revised model for PS control in which GABAergic PS-on and PS-off neurons localized in the vlPAG/dDPMe region play leading roles.     

Prosaposin Overexpression following Kainic Acid-Induced Neurotoxicity

Because excessive glutamate release is believed to play a pivotal role in numerous neuropathological disorders, such as ischemia or seizure, we aimed to investigate whether intrinsic prosaposin (PS), a neuroprotective factor when supplied exogenously in vivo or in vitro, is up-regulated after the excitotoxicity induced by kainic acid (KA), a glutamate analog. In the present study, PS immunoreactivity and its mRNA expression in the hippocampal and cortical neurons showed significant increases on day 3 after KA injection, and high PS levels were maintained even after 3 weeks. The increase in PS, but not saposins, detected by immunoblot analysis suggests that the increase in PS-like immunoreactivity after KA injection was not due to an increase in saposins as lysosomal enzymes after neuronal damage, but rather to an increase in PS as a neurotrophic factor to improve neuronal survival. Furthermore, several neurons with slender nuclei inside/outside of the pyramidal layer showed more intense PS mRNA expression than other pyramidal neurons. Based on the results from double immunostaining using anti-PS and anti-GABA antibodies, these neurons were shown to be GABAergic interneurons in the extra- and intra-pyramidal layers. In the cerebral cortex, several large neurons in the V layer showed very intense PS mRNA expression 3 days after KA injection. The choroid plexus showed intense PS mRNA expression even in the normal rat, and the intensity increased significantly after KA injection. The present study indicates that inhibitory interneurons as well as stimulated hippocampal pyramidal and cortical neurons synthesize PS for neuronal survival, and the choroid plexus is highly activated to synthesize PS, which may prevent neurons from excitotoxic neuronal damage. To the best of our knowledge, this is the first study that demonstrates axonal transport and increased production of neurotrophic factor PS after KA injection.