Accuracy of neuronal interspike times calculated from a diffusion approximation

The theory of neuronal firing in Stein's model is outlined as well as the corresponding theory for a diffusion approximation which has the same first two infinitesimal moments. The diffusion approximation is derived from the discontinuous model in the limit of large input frequencies and small postsynaptic potential amplitudes. A comparison of the calculated mean interspike intervals is made for various values of the threshold for firing and various input frequencies. The diffusion approximation can underestimate the interspike interval by up to 100% or severely overestimate it, depending on the input frequencies and the threshold. A general relation between the predictions of the two models is deduced.     

Generalized Stein's model for anatomically complex neurons

A neuron with a large dendritic structure is considered. The number of synapses located on the dendrites is substantially higher than on the soma. The synaptic input effect on the neuronal excitability decreases with distance between a synapse ending and the trigger zone. Two areas are distinguished in accordance with the effect of synaptic input--dendritic and somatic. The dendritic area, when compared to the soma, is characterized by much higher intensity of its activation but the amplitudes of synaptically evoked changes of the membrane potential at the trigger zone are in general small. This situation is suitable for a diffusion approximation. However, on the soma, especially in the proximity of the trigger zone, the membrane potential changes are a large fraction of the threshold depolarization. The membrane potential at the trigger zone is modelled by a one-dimensional stochastic process. The diffusion Ornstein-Uhlenbeck process serves as a basis of the model; however, at the moments of somatic synapses activation its voltage changes in jumps. Their sizes represent the amplitudes of the evoked postsynaptic potentials. The unimodal histograms of interspike intervals can be explained by the model. The values of the coefficient of variation greater than one are connected with substantial inhibition.     

Ephaptic feedback in identified synapses of terrestrial snails

A hypothesis for the existence of the intrasynaptic ephaptic feedback (EFB) in the invertebrate central nervous sytem was tested. Excitatory postsynaptic potentials (EPSPs) and currents (EPSCs) evoked by the activation of the recently described monosynaptic connection between the identified snail neurons were recorded intracellularly. In case of the EFB presence, the postsynaptic tetanization with hyperpolarization pulses could activate presynaptic Ca2+ channels and enhance the EPSP amplitude, whereas a steady postsynaptic hyperpolarization should induce a "supralinear" increase in EPSC amplitudes as it has been found in the rat hippocampus. In the first series of the experiments, 10 trains of hyperpolarizing pulses (40-50 mV, 1 Hz, pulse duration 0.5 s, train duration 45 s) were delivered postsynaptically. No significant changes in EPSP amplitudes were found. In the second series of the experiments, the EPSC amplitudes were measured during varying postsynaptic hyperpolarization. At the membrane potential 100 mV, the EPSP amplitude was significantly higher than theoretically predicted from the classical linear dependence. Such a "supralinear" effect of postsynaptic depolarization can be explained by the presence of the EFB. This finding is the first evidence for the EFB existence in the invertebrate central nervous system.     

The TRPM7 ion channel functions in cholinergic synaptic vesicles and affects transmitter release

A longstanding hypothesis is that ion channels are present in the membranes of synaptic vesicles and might affect neurotransmitter release. Here we demonstrate that TRPM7, a member of the transient receptor potential (TRP) ion channel family, resides in the membrane of synaptic vesicles of sympathetic neurons, forms molecular complexes with the synaptic vesicle proteins synapsin I and synaptotagmin I, and directly interacts with synaptic vesicular snapin. In sympathetic neurons, changes in TRPM7 levels and channel activity alter acetylcholine release, as measured by EPSP amplitudes and decay times in postsynaptic neurons. TRPM7 affects EPSP quantal size, an intrinsic property of synaptic vesicle release. Targeted peptide interference of TRPM7's interaction with snapin affects the amplitudes and kinetics of postsynaptic EPSPs. Thus, vesicular TRPM7 channel activity is critical to neurotransmitter release in sympathetic neurons.     

Effects of maturation on synaptic potentials in the locust flight system

We have measured parameters of identified excitatory postsynaptic potentials from flight interneurons in immature and mature adult locusts (Locusta migratoria) to determine whether parameters change during imaginal maturation. The presynaptic cell was the forewing stretch receptor. The postsynaptic cells were flight interneurons that were filled with Lucifer Yellow and identified by their morphology. Excitatory postsynaptic potentials from different postsynaptic cells had characteristic amplitudes. The amplitude, time to peak, duration at half amplitude and the area above the baseline of excitatory postsynaptic potentials did not change with maturation. The latency from action potentials in the forewing stretch receptor to onset of excitatory postsynaptic potentials decreased significantly with maturation. We suggest this was due to an increase in conduction velocity of the forewing stretch receptor. We also measured morphological parameters of the postsynaptic cells and found that they increased in size with maturation. Growth of the postsynaptic cell should cause excitatory postsynaptic potential amplitude to decrease as a result of a decrease in input resistance, however, this was not the case. Excitatory postsynaptic potentials in immature locusts depress more than in mature locusts at high frequencies of presynaptic action potentials. This difference in frequency sensitivity of the immature excitatory postsynaptic potentials may account in part for maturation of the locust flight rhythm generator.Abbreviations EPSP excitatory postsynaptic potential - fSR forewing stretch receptor - IPSP inhibitory postsynaptic potential - SR stretch receptor     

Fast, automated implementation of temporally precise blind deconvolution of multiphasic excitatory postsynaptic currents

Records of excitatory postsynaptic currents (EPSCs) are often complex, with overlapping signals that display a large range of amplitudes. Statistical analysis of the kinetics and amplitudes of such complex EPSCs is nonetheless essential to the understanding of transmitter release. We therefore developed a maximum-likelihood blind deconvolution algorithm to detect exocytotic events in complex EPSC records. The algorithm is capable of characterizing the kinetics of the prototypical EPSC as well as delineating individual release events at higher temporal resolution than other extant methods. The approach also accommodates data with low signal-to-noise ratios and those with substantial overlaps between events. We demonstrated the algorithm's efficacy on paired whole-cell electrode recordings and synthetic data of high complexity. Using the algorithm to align EPSCs, we characterized their kinetics in a parameter-free way. Combining this approach with maximum-entropy deconvolution, we were able to identify independent release events in complex records at a temporal resolution of less than 250 μs. We determined that the increase in total postsynaptic current associated with depolarization of the presynaptic cell stems primarily from an increase in the rate of EPSCs rather than an increase in their amplitude. Finally, we found that fluctuations owing to postsynaptic receptor kinetics and experimental noise, as well as the model dependence of the deconvolution process, explain our inability to observe quantized peaks in histograms of EPSC amplitudes from physiological recordings.     

Evaluating the Accuracy of Diffusion MRI Models in White Matter

Models of diffusion MRI within a voxel are useful for making inferences about the properties of the tissue and inferring fiber orientation distribution used by tractography algorithms. A useful model must fit the data accurately. However, evaluations of model-accuracy of commonly used models have not been published before. Here, we evaluate model-accuracy of the two main classes of diffusion MRI models. The diffusion tensor model (DTM) summarizes diffusion as a 3-dimensional Gaussian distribution. Sparse fascicle models (SFM) summarize the signal as a sum of signals originating from a collection of fascicles oriented in different directions. We use cross-validation to assess model-accuracy at different gradient amplitudes (b-values) throughout the white matter. Specifically, we fit each model to all the white matter voxels in one data set and then use the model to predict a second, independent data set. This is the first evaluation of model-accuracy of these models. In most of the white matter the DTM predicts the data more accurately than test-retest reliability; SFM model-accuracy is higher than test-retest reliability and also higher than the DTM model-accuracy, particularly for measurements with (a) a b-value above 1000 in locations containing fiber crossings, and (b) in the regions of the brain surrounding the optic radiations. The SFM also has better parameter-validity: it more accurately estimates the fiber orientation distribution function (fODF) in each voxel, which is useful for fiber tracking.     

Synaptic transmission in a model for stochastic neural activity.

A stochastic model equation for nerve membrane depolarization is derived which incorporates properties of synaptic transmission with a Rail-Eccles circuit for a trigger zone. If input processes are Poisson the depolarization is a Markov process for which equations for the moments of the interspike interval can be written down. An analytic result for the mean interval is obtained in a special case. The effect of the excitatory reversal potential is considerable if it is not too far from threshold and if the interspike interval is long. Computer simulations were performed when inhibitory and excitatory inputs are active. A substantial amount of inhibition leads to an exceedingly long tail in the density of the interspike time. With excitation only the interspike interval is often an approximately lognormal random variable. A coefficient of variation greater than one is often a consequence of relatively strong inhibition. Inferences can be made on the nature of the synaptic input from the statistics and density of the time between spikes. The inhibitory reversal potential usually has a relatively small effect except when the frequency of inhibition is large. An appendix contains the model equations in the case of an arbitrary distribution of postsynaptic potential amplitudes.     

Quantitative simulation of endplate currents at neuromuscular junctions based on the reaction of acetylcholine with acetylcholine receptor and acetylcholinesterase.

Two kinetic models are introduced which predict amplitudes and time-courses of endplate currents and miniature endplate currents at neuromuscular junctions, at both normal and acetylcholinesterase-inhibited endplates. Appropriate differential rate equations reflecting interactions of acetylcholine with acetylcholine receptor and with esterase, diffusion of acetylcholine both within and from the synaptic cleft, and cooperativity between receptor site occupancy and ion channel opening are solved. Acetylcholine release into the cleft is assumed to be instantaneous. The simpler homogeneous reaction space model accurately predicts decay phase time constants are inaccurate. The two-reaction space model predicts amplitudes and time constants within a factor of two of those observed experimentally. The simulations indicate that the amplitudes and time-courses are primarily determined by the chemical reaction rates that characterize acetylcholine interactions with receptor and esterase and that these interactions occur under nonequilibrium conditions. Approximately 50% of the total ion channels in the initial reaction space are predicted to be opened at the peak endplate current. The cooperative opening of ion channels by acetylcholine requires that acetylcholine be introduced into the cleft in discrete, concentrated elements. Virtually all the open channels are confined to the initial reaction space, although acetylcholine-bound receptor sites can be much more widely distributed.     

A qualitative comparison of some diffusion models for neural activity via stochastic ordering

A number of diffusion processes have been proposed as a continuous analog of Stein's model for the subthreshold membrane potential of a neuron. Interspike intervals are then described as the first-passage-time of the corresponding diffusion model through a suitable threshold. Various biological considerations suggest the use of more sophisticated models in lieu of the Ornstein-Uhlenbeck model. However, the advantages of the additional complexity are not always clear. Comparisons among different models generally use numerical methods in specific examples without a general sensitivity analysis on the role of the model parameters. Here, we compare the distribution of interspike intervals from different models using the method of stochastic ordering. The qualitative comparison of the role of each parameter extends the results obtained from numerical simulations. One result on neurons with high positive net excitation is that the reversal potential models considered do not greatly differ from the Ornstein-Uhlenbeck model. For neurons with increased inhibition, the models give greater differences among the interspike interval distributions. In particular, when the mean trajectories are matched, the Feller model gives shorter times than the Ornstein-Uhlenbeck model but longer times than our double reversal potential model. Received: 5 August 1999 / Accepted in revised form: 8 May 2000     

Effects of rectification on synaptic efficacy.

We have investigated the effects of postsynaptic membrane properties on the shape of synaptic potentials generated by time-varying synaptic conductances. We used numerical simulation techniques to model cells of several different geometrical forms, from an isopotential sphere to a neuron with a soma and a dendritic tree. A variety of postsynaptic membrane properties were tested: (a) a passive resistance-capacitance membrane, (b) a membrane represented by the Hodgkin and Huxley (HH) equations, and (c) a membrane that was passive except for a delayed rectification represented by a voltage- and time-dependent increase in GK. In all cases we investigated the effects of these postsynaptic membrane properties on synaptic potentials produced by synaptic conductances that were fast or slow compared with the membrane time constant. In all cases the effects of postsynaptic rectification occurred on postsynaptic potentials of amplitudes as low as 1 mV. The HH model (compared with the passive model) produced an increased peak amplitude (from the increase in GNa) but a decreased half-width and a decreased time integral (from the increase in GK). These effects of the HH GK change were duplicated by a simple analytical rectifier model.     

锥体神经元的连接模式对突触后局部电位的依赖

脑皮层的功能连接模式与突触可塑性密切相关,受突触空间分布和刺激模式等多种因素的影响。尽管越来越多的证据表明突触可塑性不仅受突触后动作电位而且还受突触后局部树突电位的影响,但是目前尚不清楚神经元的功能连接模式是否和怎样依赖于突触后局部电位的。为此,本文建立了一个无需硬边界设置的、突触后局部膜电位依赖的可塑性模型。该模型具有突触强度的自平衡能力并且能够再现多种突触可塑性实验结果。基于该模型对两个锥体神经元的功能连接模式进行仿真的结果表明,当突触后局部电位都处于亚阈值时两个神经元无功能连接,如果一个神经元的突触后膜电位高于阈值电位则产生向该神经元的单向连接,当两个神经元的突触后膜电位都超过阈值电位时则产生双向连接,说明突触后局部膜电位分布是神经元功能连接模式形成的关键。研究结果加深了神经网络连接模式形成机制的理解,对学习和记忆的研究具有重要意义。     

Transmitter concentration profiles in the synaptic cleft: an analytical model of release and diffusion.

A three-dimensional model for release and diffusion of glutamate in the synaptic cleft was developed and solved analytically. The model consists of a source function describing transmitter release from the vesicle and a diffusion function describing the spread of transmitter in the cleft. Concentration profiles of transmitter at the postsynaptic side were calculated for different transmitter concentrations in a vesicle, release scenarios, and diffusion coefficients. From the concentration profiles the receptor occupancy could be determined using alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor kinetics. It turned out that saturation of receptors and sufficiently fast currents could only be obtained if the diffusion coefficient was one order of magnitude lower than generally assumed, and if the postsynaptic receptors formed clusters with a diameter of roughly 100 nm directly opposite the release sites. Under these circumstances the gradient of the transmitter concentration at the postsynaptic membrane outside the receptor clusters was steep, with minimal cross-talk among neighboring receptor clusters. These findings suggest that for each release site a corresponding receptor aggregate exists, subdividing an individual synapse into independent functional subunits without the need for specific lateral diffusion barriers.     

Mediator liberation at the myoneural junctions of the frog sartorius muscle when axoplasmic transport has been disrupted with colchicine]

Colchicine application to the nerve innervating the frog sartorius muscle leads to reduction of the differences in functional condition of the myoneural synapses of this muscle by the signs of quantum content of the end plate potential (EPP) and by the changes of the EPP amplitudes in high frequency stimulation. Along with this there occurs a rarefaction of the frequency of miniature potential of the end plate, and reduction of its amplitude. Apparently, the latter is caused by reduction of effective resistance of the postsynaptic membrane. Changes of the induced and spontaneous secretion of the mediator are connected with disturbances of the axoplasmic transport just in the somatic nerve fibers.     

The pharmacological and physiological profile of glutamate receptors at the Drosophila larval neuromuscular junction

Abstract.  Drosophila larval muscles are commonly used for developmental assessment in regard to various mutations of synaptically relevant molecules. In addition, the molecular sequence of the glutamate receptors on the muscle fibre have been described; however, the pharmacological profiles to known agonists and antagonists have yet to be reported. Here, the responses of N -methyl- d -aspartic acid, α-amino-3-hydroxy-5-methyl-4-isoxazole-propionate (AMPA), l -glutamate, kainate, quisqualic acid, NBQX, AP5 and DNQX are characterized with regard to synaptic transmission and direct effects on the muscle fibres. The muscle fibres depolarize to application of glutamate or quisqualate and the excitatory postsynaptic potential (EPSP) amplitudes are diminished. Kainate does not alter the muscle membrane potential but does reduce the EPSP amplitude. The known antagonists NBQX, AP5 and DNQX have no substantial effect on synaptic transmission at 1 m m , nor do they block the response of quisqualate. Kainate may be acting as a postsynaptic antagonist or via autoreceptors presynaptically to reduce evoked transmission.     

A general diffusion model for analyzing the efficacy of synaptic input to threshold neurons

We describe a general diffusion model for analyzing the efficacy of individual synaptic inputs to threshold neurons. A formal expression is obtained for the system propagator which, when given an arbitrary initial state for the cell, yields the conditional probability distribution for the state at all later times. The propagator for a cell with a finite threshold is written as a series expansion, such that each term in the series depends only on the infinite threshold propagator, which in the diffusion limit reduces to a Gaussian form. This procedure admits a graphical representation in terms of an infinite sequence of diagrams. To connect the theory to experiment, we construct an analytical expression for the primary correlation kernel (PCK) which profiles the change in the instantaneous firing rate produced by a single postsynaptic potential (PSP). Explicit solutions are obtained in the diffusion limit to first order in perturbation theory. Our approximate expression resembles the PCK obtained by computer simulation, with the accuracy depending strongly on the mode of firing. The theory is most accurate when the synaptic input drives the membrane potential to a mean level more than one standard deviation below the firing threshold, making such cells highly sensitive to synchronous synaptic input.     

An unusual electrooptical effect observed for DNA fragments and its apparent relation to a permanent electric moment associated with bent DNA

Dichroism decay curves of DNA fragments with chain lengths in the range of 179-256 bp show an amplitude inversion suggesting the existence of a positive dichroism component, when these fragments are dissolved at monovalent salt concentrations above approx. 5 mM and are exposed to field pulses with amplitudes and/or lengths above critical values. At the critical values, the unusual dichroism is reflected by an apparent acceleration of the decay curves, which can be fitted by single exponentials with time constants much below the values expected from the DNA contour lengths. The critical pulse amplitudes and lengths decrease with increasing DNA chain length and increasing salt concentration. The experimental data are consistent with results obtained by hydrodynamic and electric model calculations on smoothly bent DNA double helices. The DNA is represented by a string of overlapping beads, which is used to calculate the rotational diffusion tensor and the center of diffusion. The distribution of phosphate charges is asymmetric with respect to this center and thus gives rise to a substantial permanent dipole moment. The magnitude of this dipole moment is calculated as a function of DNA curvature and is used together with experimental values of polarizabilities for simulations of dichroism decay curves. The curves simulated for bent DNA show the same phenomenon as observed experimentally. The ionic strength dependence of the unusual dichroism is explained by an independently observed strong decrease of the polarizability with increasing salt concentration. The field strength dependence is probably due to field-induced bending of double helices driven by the change of the dipole moment. Although our calculations are on rigid models of DNA and thus any flexibility of the double helix has not been considered, we conclude that the essential part of our experimental results can be explained by our model.     

Refractoriness of sural nerve in humans

High-frequency stimulation of peripheral nerve bundles is frequently used in clinical tests and physiologic experiments to study presynaptic and postsynaptic effects. To understand the postsynaptic effects, it is important to ensure that each pulse in the train is equally effective in stimulating the presynaptic nerve bundle; however, the optimal interpulse interval (IPI) and the stimulus intensity at which each pulse is equally effective in stimulating the same number of axons are not known. The magnitude of the compound action potential produced by each pulse in a train was tested on the sural nerve of 4 healthy human subjects. The stimulus train (2-4 pulses) was applied to the sural nerve at the lateral malleolus, and neural responses were recorded from just below the knee. With 2-pulse trains, families of curves between IPIs (1-6 ms) and normalized amplitudes of the second response were plotted for different stimulus intensities. Visual inspection of the data showed that the curves fell into 2 groups: with stimulus intensities <2.5x perception threshold (Th), the test response appeared partially at longer IPIs, whereas with stimulus intensities >=3x Th, partial recovery of the test response was earlier. The interval for complete recovery was statistically the same for low- and high-intensity stimulation. With more than 2 pulses in a stimulus train (IPI = 5 ms), the amplitude of the compound action potential (CAP) was not affected significantly. These results are important in understanding both the presynaptic and postsynaptic responses when presynaptic axon bundles are stimulated at high frequencies.     

Presynaptic effects of biogenic amines modulating synaptic transmission between identified sensory neurons and giant interneurons in the first instar cockroach

Intracellular recording was used to investigate the modulatory effects of serotonin and octopamine on the identified synapses between filiform hair sensory afferents and giant interneurons in the first instar cockroach, Periplaneta americana. Serotonin at 10(-4) mol l(-1) to 10(-3) mol l(-1) reduced the amplitude of the lateral axon-to-ipsilateral giant interneuron 3 excitatory postsynaptic potentials. and octopamine at 10(-4) mol l(-1) increased their amplitude. Similar effects were seen on excitatory postsynaptic potentials in dorsal giant interneuron 6. Several lines of evidence suggest that both substances modulate the amplitude of excitatory postsynaptic potentials by acting presynaptically, rather than on the postsynaptic neuron. The fitting of simple binomial distributions to the postsynaptic potential amplitude histograms suggested that, for both serotonin and octopamine, the number of synaptic release sites was being modulated. Secondly, the amplitudes of miniature excitatory postsynaptic potentials recorded in the presence of tetrodotoxin were unaffected by either modulator. Finally, recordings from contralateral giant interneuron 3, which has two identifiable populations of synaptic inputs, showed that each modulator had a more pronounced effect on excitatory postsynaptic potentials evoked by the lateral axon than on those evoked by the medial axon. Immunocytochemistry confirmed that neuropilar processes containing serotonin are present in close proximity to these synapses.