The parameters of the stochastic leaky integrate-and-fire neuronal model

Five parameters of one of the most common neuronal models, the diffusion leaky integrate-and-fire model, also known as the Ornstein-Uhlenbeck neuronal model, were estimated on the basis of intracellular recording. These parameters can be classified into two categories. Three of them (the membrane time constant, the resting potential and the firing threshold) characterize the neuron itself. The remaining two characterize the neuronal input. The intracellular data were collected during spontaneous firing, which in this case is characterized by a Poisson process of interspike intervals. Two methods for the estimation were applied, the regression method and the maximum-likelihood method. Both methods permit to estimate the input parameters and the membrane time constant in a short time window (a single interspike interval). We found that, at least in our example, the regression method gave more consistent results than the maximum-likelihood method. The estimates of the input parameters show the asymptotical normality, which can be further used for statistical testing, under the condition that the data are collected in different experimental situations. The model neuron, as deduced from the determined parameters, works in a subthreshold regimen. This result was confirmed by both applied methods. The subthreshold regimen for this model is characterized by the Poissonian firing. This is in a complete agreement with the observed interspike interval data. Action Editor: Nicolas Brunel     

Regulation of discrete sub-populations of transmitter-identified neurones after inhibition of electrical activity in cultures of mouse spinal cord

Summary The effects of blockade of electrical activity by tetrodotoxin in cultures of mouse spinal cord and dorsal root ganglion on immunohistochemically-identified neuronal sub-populations have been investigated. Some spinal cord neuronal types, such as those storing methionine-enkephalin, substance P or calcitonin gene-related peptide were almost totally depleted after inhibition of electrical activity for 4 days. By contrast, putative substance P- and calcitonin gene-related peptide-immunoreactive dorsal root ganglion neurones were not significantly affected by such treatment. Several other neuronal types were reduced by about 30–40% after exposure to tetrodotoxin. The decrement in methionine-enkephalin-, substance P- and calcitonin generelated peptide-immunoreactive neurones caused by tetrodotoxin was reversible, and, in the case of methionine-enkephalin, could not be elicited after day 30 in culture. Radioimmunoassay of levels of methionine-enkephalin in cultures confirmed the immunohistochemical data. It is concluded, therefore, that exposure to tetrodotoxin selectively reduces peptide immunoreactivity in specific neuronal sub-populations, but that the selectivity is not based on a single known neuronal characteristic such as transmitter phenotype, or a particular structural protein. The action of tetrodotoxin on those cells most severely attenuated is an alteration in transmitter expression rather than a lethal effect. The diminution with time of the ability of tetrodotoxin to attenuate methionine-enkephalin levels may reflect a reduction in the activity-dependent regulation of peptide expression relative to other competing trophic influences.     

A new analytical method of studying post-synaptic currents.

A powerful methodology for analyzing post-synaptic currents recorded from central neurons is presented. An unknown quantity of transmitter molecules released from presynaptic terminals by electrical stimulation of nerve fibers generates a post-synaptic response at the synaptic site. The current induced at the synaptic junction is assumed to rise rapidly and decay slowly with its peak amplitude being proportional to the number of released transmitter molecules. The signal so generated is then distorted by the cable properties of the dendrite, modeled as a time-invariant, linear filter with unknown parameters. The response recorded from the cell body of the neuron following the electrical stimulation is contaminated by zero-mean, white, Gaussian noise. The parameters of the signal are then evaluated from the observation sequence using a quasi-profile likelihood estimation procedure. These parameter values are then employed to deconvolve each measured post-synaptic response to produce an optimal estimate of the transmembrane current flux. From these estimates we derive the amplitude of the synaptic current and the relative amount of transmitter molecules that elicited each response. The underlying amplitude fluctuations in the entire data sequence are investigated using a non-parametric technique based on kernel smoothing procedures. The effectiveness of the new methodology is illustrated in various simulation examples.     

The effects of geometrical parameters on synaptic transmission: a Monte Carlo simulation study

Monte Carlo simulations of transmitter diffusion and its interactions with postsynaptic receptors have been used to study properties of quantal responses at central synapses. Fast synaptic responses characteristic of those recorded at glycinergic junctions on the teleost Mauthner cell (time to peak approximately 0.3-0.4 ms and decay time constant approximately 3-6 ms) served as the initial reference, and smaller contacts with fewer postsynaptic receptors were also modeled. Consistent with experimental findings, diffusion, simulated using a random walk algorithm and assuming a diffusion coefficient of 0.5-1.0 x 10(-5) cm2 s(-1), was sufficiently fast to account for transmitter removal from the synaptic cleft. Transmitter-receptor interactions were modeled as a two-step binding process, with the double-bound state having opened and closed conformations. Addition of a third binding step only slightly decreased response amplitude but significantly slowed both its rising and decay phases. The model allowed us to assess the sources of response variability and the likelihood of postsynaptic saturation as functions of multiple kinetic and spatial parameters. The method of nonstationary fluctuation analysis, typically used to estimate the number of functional channels at a synapse and single channel current, proved unreliable, presumably because the receptors in the postsynaptic matrix are not uniformly exposed to the same profile of transmitter concentration. Thus, the time course of the probability of channel opening most likely varies among receptors. Finally, possible substrates for phenomena of synaptic plasticity, such as long-term potentiation, were explored, including the diameter of the contact zone, defined by the region of pre- and postsynaptic apposition, the number and distribution of the receptors, and the degree of vesicle filling. Surprisingly, response amplitude is quite sensitive to the size of the receptor-free annulus surrounding the receptor cluster, such that expansion of the contact zone could produce an appreciable increase in quantal size, normally attributed to either the presence of more receptors or the release of more transmitter molecules.     

Transient Responses to Rapid Changes in Mean and Variance in Spiking Models

The mean input and variance of the total synaptic input to a neuron can vary independently, suggesting two distinct information channels. Here we examine the impact of rapidly varying signals, delivered via these two information conduits, on the temporal dynamics of neuronal firing rate responses. We examine the responses of model neurons to step functions in either the mean or the variance of the input current. Our results show that the temporal dynamics governing response onset depends on the choice of model. Specifically, the existence of a hard threshold introduces an instantaneous component into the response onset of a leaky-integrate-and-fire model that is not present in other models studied here. Other response features, for example a decaying oscillatory approach to a new steady-state firing rate, appear to be more universal among neuronal models. The decay time constant of this approach is a power-law function of noise magnitude over a wide range of input parameters. Understanding how specific model properties underlie these response features is important for understanding how neurons will respond to rapidly varying signals, as the temporal dynamics of the response onset and response decay to new steady-state determine what range of signal frequencies a population of neurons can respond to and faithfully encode.     

A Radio-telemetric System to Monitor Cardiovascular Function in Rats with Spinal Cord Transection and Embryonic Neural Stem Cell Grafts

High thoracic or cervical spinal cord injury (SCI) can lead to cardiovascular dysfunction. To monitor cardiovascular parameters, we implanted a catheter connected to a radio transmitter into the femoral artery of rats that underwent a T4 spinal cord transection with or without grafting of embryonic brainstem-derived neural stem cells expressing green fluorescent protein. Compared to other methods such as cannula insertion or tail-cuff, telemetry is advantageous to continuously monitor blood pressure and heart rate in freely moving animals. It is also capable of long term multiple data acquisitions. In spinal cord injured rats, basal cardiovascular data under unrestrained condition and autonomic dysreflexia in response to colorectal distension were successfully recorded. In addition, cardiovascular parameters before and after SCI can be compared in the same rat if a transmitter is implanted before a spinal cord transection. One limitation of the described telemetry procedure is that implantation in the femoral artery may influence the blood supply to the ipsilateral hindlimb.     

Development and regulation of substance P in sensory neurons in vitro

Substance P (SP), the putative neuropeptide mediator of pain sensation, is contained in small dorsomedial sensory neurons of the dorsal root ganglion. Using different culture techniques and a sensitive radioimmunoassay for SP, we studied the ontogeny and regulation of this functionally important neurotransmitter in these neurons, obtained from neonatal rats. In ganglion explants grown by two different techniques, SP increased two- to threefold during the first week in culture. This rise was predominantly due to mechanisms intrinsic to the ganglion since it occurred in a fully defined medium, in the absence of added nerve growth factor (NGF). Blockade of protein synthesis with cycloheximide prevented the increase in SP suggesting that ongoing protein synthesis was necessary. Furthermore, depolarization with veratridine blocked the increase in SP, an effect which was reversed by tetrodotoxin, suggesting that transmitter characteristics in sensory neurons may be regulated by depolarization and/or transmembrane sodium flux. After a week in culture on a collagen substratum, supplementary NGF was necessary for the continued rise in SP. However, raising the dose of the trophic factor had no incremental effect on SP content, suggesting that NGF was acting primarily on neuronal survival. To approach such questions at the cellular level, ganglia were dissociated and grown in cell culture. In all cultures, SP increased 1.5-fold during the first day. In the absence of NGF, however, SP and cell numbers fell progressively after the second day. NGF elicited parallel increases in cell survival and SP content, supporting the suggestion that NGF acts primarily through neuronal survival to increase SP. Veratridine blocked the increase in SP in a tetrodotoxin-reversible manner, without affecting neuronal survival, indicating that the effects of these agents do not depend on normal ganglionic cellular architecture. Consequently, depolarization probably affects ganglionic sensory neurons directly. Our studies suggest that the development of transmitter characteristics in primary sensory neurons may be regulated by multiple factors, including neuronal activity as well as trophic agents such as NGF.     

Modulation of ion currents and regulation of transmitter release in short-term synaptic plasticity: The rise and fall of the action potential

Up and down-regulation of calcium and potassium conductances are associated with several forms of short-term synaptic modulation. Detailed investigation of synaptic plasticity in the marine gastropodAplysia, and in other mollusks, indicates that synaptic transmission can be influenced in a number of ways by modulatory neurotransmitters acting through several second-messenger cascades. Modulation at the synapse itself occurs by means of the regulation of calcium current as well as through effects on processes directly involved in transmitter mobilization and exocytosis. Modulation of potassium current plays a major role in controlling neuronal excitability and may contribute to a lesser extent to the regulation of transmitter release through actions on the resting potential and on action potential configuration.     

Differentiation of Nerve Terminals in the Crayfish Opener Muscle and Its Functional Significance

Junctional potentials (jp's) recorded from superficial distal fibers of the crayfish opener muscle are up to 50 times larger than jp' in superficial central fibers when the single motor axon that innervates the muscle is stimulated at a frequency of 1/sec or less. At 80/sec, in contrast, central jp's are up to four times larger than those observed in distal fibers. The tension produced by single muscle fibers of either type is directly proportional to the integral of the time-voltage curve minus an excitation-contraction coupling threshold of 3 mv. Distal fibers therefore produce almost all the total muscle tension at low frequencies of stimulation and central fibers add an increasingly greater contribution as their nerve endings begin to facilitate in response to increased rate of motor discharge. Differentiation of muscle membrane characteristics (input resistance, space constant, time constant) cannot account for these differences in facilitation ratios. The mechanism of neuronal differentiation is not based upon the size or effectiveness of transmitter quanta, since equal sized jp's have equal variances;: mjp sizes and variances are also equal. No differences were found between fiber types in rates of transmitter mobilization, density of innervation, or the relationship between transmitter release and terminal depolarization. Single terminals on distal fibers were found to release transmitter with a greater probability than central terminals. More effective invasion of distal terminals by the nerve impulse at low frequencies can account for the difference.     

Analysis of a model for transmitter kinetics

Neural transmitters can generally exist in several states: stored, released, in combination with receptors, and recycling to storage. A set of equations is proposed and analyzed for such a system. We have considered boundedness and stability of solutions, and we have discussed physiological effects such as response saturation and adaptation. We have investigated the effects of the model parameters on system behavior and we have indicated how the model can be extended to include phenomena such as transmitter mobilization, modulation if its release and receptor desensitization.     

Principal component analysis of the cytokine and chemokine response to human traumatic brain injury

There is a growing realisation that neuro-inflammation plays a fundamental role in the pathology of Traumatic Brain Injury (TBI). This has led to the search for biomarkers that reflect these underlying inflammatory processes using techniques such as cerebral microdialysis. The interpretation of such biomarker data has been limited by the statistical methods used. When analysing data of this sort the multiple putative interactions between mediators need to be considered as well as the timing of production and high degree of statistical co-variance in levels of these mediators. Here we present a cytokine and chemokine dataset from human brain following human traumatic brain injury and use principal component analysis and partial least squares discriminant analysis to demonstrate the pattern of production following TBI, distinct phases of the humoral inflammatory response and the differing patterns of response in brain and in peripheral blood. This technique has the added advantage of making no assumptions about the Relative Recovery (RR) of microdialysis derived parameters. Taken together these techniques can be used in complex microdialysis datasets to summarise the data succinctly and generate hypotheses for future study.     

Noise Normalizes Firing Output of Mouse Lateral Geniculate Nucleus Neurons

The output of individual neurons is dependent on both synaptic and intrinsic membrane properties. While it is clear that the response of an individual neuron can be facilitated or inhibited based on the summation of its constituent synaptic inputs, it is not clear whether subthreshold activity, (e.g. synaptic “noise”- fluctuations that do not change the mean membrane potential) also serve a function in the control of neuronal output. Here we studied this by making whole-cell patch-clamp recordings from 29 mouse thalamocortical relay (TC) neurons. For each neuron we measured neuronal gain in response to either injection of current noise, or activation of the metabotropic glutamate receptor-mediated cortical feedback network (synaptic noise). As expected, injection of current noise via the recording pipette induces shifts in neuronal gain that are dependent on the amplitude of current noise, such that larger shifts in gain are observed in response to larger amplitude noise injections. Importantly we show that shifts in neuronal gain are also dependent on the intrinsic sensitivity of the neuron tested, such that the gain of intrinsically sensitive neurons is attenuated divisively in response to current noise, while the gain of insensitive neurons is facilitated multiplicatively by injection of current noise- effectively normalizing the output of the dLGN as a whole. In contrast, when the cortical feedback network was activated, only multiplicative gain changes were observed. These network activation-dependent changes were associated with reductions in the slow afterhyperpolarization (sAHP), and were mediated at least in part, by T-type calcium channels. Together, this suggests that TC neurons have the machinery necessary to compute multiple output solutions to a given set of stimuli depending on the current level of network stimulation.     

Presynaptic uptake blockade hypothesis for LSD action at the lateral inhibitory synapse in Limulus

We investigated the action of LSD at the putative indoleaminergic lateral inhibitory synapse in the lateral eye of Limulus polyphemus. We recorded extracellular and intracellular voltage responses from eccentric cells while producing inhibition either by light or by antidromic stimulation of the optic nerve in the presence of LSD, serotonin (5-HT), chlorimipramine, or a bathing medium whose high Mg++ and low Ca++ concentrations partially or completely blocked synaptic transmission. We found (a) light-evoked and antidromically stimulated lateral inhibition is enhanced during superfusion of low (1-5 microM) concentrations of LSD and suppressed by higher (5-20 microM) concentrations; (b) these actions of LSD are markedly reduced by bathing the retina in a medium high in Mg++ and low in Ca++; (c) very low concentrations of chlorimipramine, a putative uptake blocker of serotonin, appear to mimic actions of LSD both on eccentric cell firing rate and on lateral inhibition; (d) superfused 5-HT depresses lateral inhibition at all superthreshold concentrations (0.1-25 microM). These results suggest that LSD's action may require an intact inhibitory transmitter release and postsynaptic response mechanism, whereas serotonin exerts a direct postsynaptic effect. We propose that LSD blocks presynaptic uptake of transmitter at the lateral inhibitory synapse. The concentration dependence of LSD's action can be accounted for as follows: low concentrations partially restrict transmitter reuptake, thereby prolonging the lifetime of the transmitter in the synaptic cleft and thus increasing the magnitude and duration of postsynaptic inhibition. Higher concentrations cause more presynaptic uptake sites to be blocked; this causes accumulation of transmitter in the synaptic cleft, which causes a functional blockade of the synapse because of postsynaptic desensitization. As an alternative, we propose a hypothesis based on LSD action at presynaptic autoreceptors. Similar hypotheses can account for many aspects of LSD's action in mammalian brain.     

Parameter Estimation Methods for Single Neuron Models

With the advancement in computer technology, it has become possible to fit complex models to neuronal data. In this work, we test how two methods can estimate parameters of simple neuron models (passive soma) to more complex ones (neuron with one dendritic cylinder and two active conductances). The first method uses classical voltage traces resulting from current pulses injection (time domain), while the second uses measures of the neuron's response to sinusoidal stimuli (frequency domain). Both methods estimate correctly the parameters in all cases studied. However, the time-domain method is slower and more prone to estimation errors in the cable parameters than the frequency-domain method. Because with noisy data the goodness of fit does not distinguish between different solutions, we suggest that running the estimation procedure a large number of times might help find a good solution and can provide information about the interactions between parameters. Also, because the formulation used for the model's response in the frequency domain is analytical, one can derive a local sensitivity analysis for each parameter. This analysis indicates how well a parameter is likely to be estimated and helps choose an optimal stimulation protocol. Finally, the tests suggest a strategy for fitting single-cell models using the two methods examined.     

Neuronal identification of signal periodicity by balanced inhibition

Many animals, including men, use periodicity information, e.g., amplitude modulations of acoustic stimuli, as a vital cue to auditory object formation. The underlying neuronal mechanisms, however, still remain a matter of debate. Here, we mathematically analyze a model for periodicity identification that relies on the interplay of excitation and delayed inhibition. Our analytical results show how the maximal response of such a system varies systematically with the time constants of excitation and inhibition. The model reliably identifies signal periodicity in the range from about ten to several hundred Hertz. Importantly, the model relies on biologically plausible parameters only. It works best for excitatory and inhibitory neuronal couplings of equal strength, the so-called ‘balanced inhibition’. We show how balanced inhibition can serve to identify low-frequency signal periodicity and how variation of a single parameter, the inhibitory time constant, can tune the system to different frequencies.     

Multi-scale detection of rate changes in spike trains with weak dependencies

The statistical analysis of neuronal spike trains by models of point processes often relies on the assumption of constant process parameters. However, it is a well-known problem that the parameters of empirical spike trains can be highly variable, such as for example the firing rate. In order to test the null hypothesis of a constant rate and to estimate the change points, a Multiple Filter Test (MFT) and a corresponding algorithm (MFA) have been proposed that can be applied under the assumption of independent inter spike intervals (ISIs). As empirical spike trains often show weak dependencies in the correlation structure of ISIs, we extend the MFT here to point processes associated with short range dependencies. By specifically estimating serial dependencies in the test statistic, we show that the new MFT can be applied to a variety of empirical firing patterns, including positive and negative serial correlations as well as tonic and bursty firing. The new MFT is applied to a data set of empirical spike trains with serial correlations, and simulations show improved performance against methods that assume independence. In case of positive correlations, our new MFT is necessary to reduce the number of false positives, which can be highly enhanced when falsely assuming independence. For the frequent case of negative correlations, the new MFT shows an improved detection probability of change points and thus, also a higher potential of signal extraction from noisy spike trains.     

Stable isotopic labeling by amino acids in cultured primary neurons: application to brain-derived neurotrophic factor-dependent phosphotyrosine-associated signaling

Cultured primary neurons are a well established model for the study of neuronal function in vitro. Here we demonstrated that stable isotope labeling by amino acids in cell culture (SILAC) can be applied to a differentiated, non-dividing cell type such as primary neurons, and we applied this technique to assess changes in the neuronal phosphotyrosine proteome in response to stimulation by brain-derived neurotrophic factor (BDNF), an important molecule for the development and regulation of neuronal connections. We found that 13 proteins had SILAC ratios above 1.50 or below 0.67 in phosphotyrosine immunoprecipitations comparing BDNF-treated and control samples, and an additional 18 proteins had ratios above 1.25 or below 0.80. These proteins include TrkB, the receptor tyrosine kinase for BDNF, and others such as hepatocyte growth factor-regulated tyrosine kinase substrate and signal-transducing adaptor molecule, which are proteins known to regulate intracellular trafficking of receptor tyrosine kinases. These results demonstrate that the combination of primary neuronal cell culture and SILAC can be a powerful tool for the study of the proteomes of neuronal molecular and cellular dynamics.     

Improved neuronal models for studying neural networks

Previous neuronal models used for the study of neural networks are considered. Equations are developed for a model which includes: 1) a normalized range of firing rates with decreased sensitivity at large excitatory or large inhibitory input levels, 2) a single rate constant for the increase in firing rate following step changes in the input, 3) one or more rate constants, as required to fit experimental data for the adaptation of firing rates to maintained inputs. Computed responses compare well with the types of neuronal responses observed experimentally. Depending on the parameters, overdamped increases and decreases, damped oscillatory or maintained oscillatory changes in firing rate are observed to step changes in the input. The integrodifferential equations describing the neuronal models can be represented by a set of first-order differential equations. Steady-state solutions for these equations can be obtained for constant inputs, as well as the stability of the solutions to small perturbations. The linear frequency response function is derived for sufficiently small time-varying inputs. The linear responses are also compared with the computed solutions for larger non-linear responses.     

Modeling of ionic channel properties and its role in shaping neuronal spike activity

An electronic analog of a neuron operating in real time is presented. The sequence of signal formation in the analog follows that of processes occurring at the synapse, postsynaptic membrane, and soma of the cell. Concepts of the synapse as a "key" and of the postsynaptic membrane as ionic channel with conductance changing under the action of transmitter and intracellular potential having been put into effect in the physical model, the neuronal analog could be set up along the same lines as a spike generator in which operation of the synaptic apparatus and the structure of neuronal dendrites could be reproduced. Spike train transformation processes typical of different types of neurons (such as motoneurons and Renshaw cells) were modeled by changing the parameters of membrane resistance and capacitance. Findings from research on simple neuronal networks have made it possible to use the analogs suggested to study the principles governing organization of neuronal structures as well as mechanisms underlying neuronal interaction, particularly those of the motor control system.I. P. Pavlov Institute of Physiology, Academy of Sciences of the USSR, Leningrad. Translated from Neirofiziologiya, Vol. 21, No. 3, pp. 379–389, May–June, 1989.     

Neuroprotective Strategies in Hippocampal Neurodegeneration Induced by the Neurotoxicant Trimethyltin

The selective vulnerability of specific neuronal subpopulations to trimethyltin (TMT), an organotin compound with neurotoxicant effects selectively involving the limbic system and especially marked in the hippocampus, makes it useful to obtain in vivo models of neurodegeneration associated with behavioural alterations, such as hyperactivity and aggression, cognitive impairment as well as temporal lobe epilepsy. TMT has been widely used to study neuronal and glial factors involved in selective neuronal death, as well as the molecular mechanisms leading to hippocampal neurodegeneration (including neuroinflammation, excitotoxicity, intracellular calcium overload, mitochondrial dysfunction and oxidative stress). It also offers a valuable instrument to study the cell–cell interactions and signalling pathways that modulate injury-induced neurogenesis, including the involvement of newly generated neurons in the possible repair processes. Since TMT appears to be a useful tool to damage the brain and study the various responses to damage, this review summarises current data from in vivo and in vitro studies on neuroprotective strategies to counteract TMT-induced neuronal death, that may be useful to elucidate the role of putative candidates for translational medical research on neurodegenerative diseases.