A nonlinear cascade model for action potential encoding in an insect sensory neuron.

Action potential encoding in the cockroach tactile spine neuron can be represented as a single-input single-output nonlinear dynamic process. We have used a new functional expansion method to characterize the nonlinear behavior of the neural encoder. This method, which yields similar kernels to the Wiener method, is more accurate than the latter and is efficient enough to obtain reasonable kernels in less than 15 min using a personal computer. The input stimulus was band-limited white Gaussian noise and the output consisted of the resulting train of action potentials, which were unitized to give binary values. The kernels and the system input-output signals were used to identify a model for encoding comprising a cascade of dynamic linear, static nonlinear, and dynamic linear components. The two dynamic linear components had repeatable and distinctive forms with the first being low-pass and the second being high-pass. The static nonlinearity was fitted with a fifth-order polynomial function over several input amplitude ranges and had the form of a half-wave rectifier. The complete model gave a good approximation to the output of the neuron when both were subjected to the same novel white noise input signal.     

The dynamic nonlinear behavior of fly photoreceptors evoked by a wide range of light intensities.

Fly photoreceptor cells were stimulated with steps of light over a wide intensity range. First- and second-order Volterra kernels were then computed from sequences of combined step responses. Diagonal values of the second-order Volterra kernels were much greater than the off-diagonal values, and the diagonal values were roughly proportional to the corresponding first-order kernels, suggesting that the response could be approximated by a static nonlinearity followed by a dynamic linear component (Hammerstein model). The amplitudes of the second-order kernels were much smaller in light-adapted than in dark-adapted photoreceptors. Hammerstein models constructed from the step input/output measurements gave reasonable approximations to the actual photoreceptor responses, with light-adapted responses being relatively better fitted. However, Hammerstein models could not account for several features of the photoreceptor behavior, including the dependence of the step response shape on step amplitude. A model containing an additional static nonlinearity after the dynamic linear component gave significantly better fits to the data. These results indicate that blowfly photoreceptors have a strong early gain control nonlinearity acting before the processes that create the characteristic time course of the response, in addition to the nonlinearities caused by membrane conductances.     

General methodology for nonlinear modeling of neural systems with Poisson point-process inputs

This paper presents a general methodological framework for the practical modeling of neural systems with point-process inputs (sequences of action potentials or, more broadly, identical events) based on the Volterra and Wiener theories of functional expansions and system identification. The paper clarifies the distinctions between Volterra and Wiener kernels obtained from Poisson point-process inputs. It shows that only the Wiener kernels can be estimated via cross-correlation, but must be defined as zero along the diagonals. The Volterra kernels can be estimated far more accurately (and from shorter data-records) by use of the Laguerre expansion technique adapted to point-process inputs, and they are independent of the mean rate of stimulation (unlike their P-W counterparts that depend on it). The Volterra kernels can also be estimated for broadband point-process inputs that are not Poisson. Useful applications of this modeling approach include cases where we seek to determine (model) the transfer characteristics between one neuronal axon (a point-process 'input') and another axon (a point-process 'output') or some other measure of neuronal activity (a continuous 'output', such as population activity) with which a causal link exists.     

On parsing the neural code in the prefrontal cortex of primates using principal dynamic modes

Nonlinear modeling of multi-input multi-output (MIMO) neuronal systems using Principal Dynamic Modes (PDMs) provides a novel method for analyzing the functional connectivity between neuronal groups. This paper presents the PDM-based modeling methodology and initial results from actual multi-unit recordings in the prefrontal cortex of non-human primates. We used the PDMs to analyze the dynamic transformations of spike train activity from Layer 2 (input) to Layer 5 (output) of the prefrontal cortex in primates performing a Delayed-Match-to-Sample task. The PDM-based models reduce the complexity of representing large-scale neural MIMO systems that involve large numbers of neurons, and also offer the prospect of improved biological/physiological interpretation of the obtained models. PDM analysis of neuronal connectivity in this system revealed “input–output channels of communication” corresponding to specific bands of neural rhythms that quantify the relative importance of these frequency-specific PDMs across a variety of different tasks. We found that behavioral performance during the Delayed-Match-to-Sample task (correct vs. incorrect outcome) was associated with differential activation of frequency-specific PDMs in the prefrontal cortex.     

Filter characteristics of cercal afferents in the cockroach

Summary The response dynamics of cercal afferents in the cockroach, Periplaneta americana, were determined by means of a cross-correlation technique using a Gaussian white noise modulation of wind as a stimulus. The white noise stimulus could evoke sustained firing activity in most of the afferents examined (Fig. 1). The spike discharges were unitized and then cross-correlated with the stimulus to compute 1st- and 2nd-order Weiner kernels. The Ist-order kernels from a total of 28 afferents were biphasic and closely matched the time differential of a pulse (Figs. 1, 3 and 4). The amplitude and waveform of the kernels depended on the stimulus angle in such a way that the kernels were the mirror image of those on the polar opposite side (Figs. 2 and 3). The 2nd-order kernels were also differential. They had 2 diagonal peaks and 2 off-diagonal valleys in a 2-dimensional plot with 2 time axes (Figs. 1, 5 and 6). This 4-eye configuration was basically invariant irrespective of the stimulus angle, although the kernels varied in amplitude when the stimulus angle was changed. The time between the peak and a following trough of the 1st-order kernel was constant and had a mean of 4.6±0.1 ms, whereas the time between 2 diagonal peaks of the 2nd-order kernels was 4.7±0.1 ms (Figs. 4 and 6), suggesting that wind receptors (filiform sensilla) on cerci act as a band-pass filter with a peak frequency of about 106 Hz. The peak time, however, varies from 2.3 to 6.9 ms in both kernels, which may reflect the spatial distribution of the corresponding hairs on the cercus. The summation of the 1st- (linear) and 2nd-order (nonlinear) models precisely predicted the timing of the spike firing (Fig. 8). Thus, these 2 lower-order kernels can totally characterize the response dynamics of the wind receptors. The nonlinear response explains the directional sensitivity of the sensory neurons, while the differentiating 1st-order kernel explains the velocity sensitivity of the neurons. The nonlinearity is a signal compression in which one of the diagonal peaks of the 2nd-order kernel always offsets the downward phase of the 1st-order kernel (Fig. 7) and obviously represents a half-wave rectification property of the wind receptors that are excited by hair movement in only one direction and inhibited by hair movement in the polar opposite direction.     

Calcium buffering and clearance in spider mechanosensory neurons

Spider VS-3 mechanoreceptor neurons have a low-voltage-activated Ca2+ current that raises intracellular calcium concentration [Ca2+] when they are depolarized by agonists of GABAA receptors or fire action potentials. The Ca2+ rise produces negative feedback by modulating the mechanoreceptor current and regulates Ca2+- and voltage-activated K+ currents. However, nothing is known about Ca2+ buffering in VS-3 neurons. Dynamic changes in VS-3 neuron intracellular [Ca2+] were measured using the fluorescent Ca2+ indicator Oregon Green BAPTA-1 (OG488) to understand Ca2+ buffering and clearance. Intracellular OG488 concentration increased slowly over more than 2 h as it diffused through a sharp intracellular microelectrode and spread through the cell. This slow increase was used to measure endogenous Ca2+ buffering and clearance by the added buffer technique, with OG488 acting as both added exogenous buffer and Ca2+ indicator. [Ca2+] was raised for brief periods by regular action potential firing, produced by pulsed electric current injection through the microelectrode. The resulting rise and fall of [Ca2+] were well fitted by the single compartment model of Ca2+ dynamics. With earlier ratiometric [Ca2+] estimates, these data gave an endogenous Ca2+ binding ratio of 684. Strong Ca2+ buffering may assist these neurons to deal with rapid changes in mechanical inputs.     

Parametric and non-parametric modeling of short-term synaptic plasticity. Part I: Computational study

Parametric and non-parametric modeling methods are combined to study the short-term plasticity (STP) of synapses in the central nervous system (CNS). The nonlinear dynamics of STP are modeled by means: (1) previously proposed parametric models based on mechanistic hypotheses and/or specific dynamical processes, and (2) non-parametric models (in the form of Volterra kernels) that transforms the presynaptic signals into postsynaptic signals. In order to synergistically use the two approaches, we estimate the Volterra kernels of the parametric models of STP for four types of synapses using synthetic broadband input–output data. Results show that the non-parametric models accurately and efficiently replicate the input–output transformations of the parametric models. Volterra kernels provide a general and quantitative representation of the STP.     

Intrinsic dendritic filtering gives low-pass power spectra of local field potentials

The local field potential (LFP) is among the most important experimental measures when probing neural population activity, but a proper understanding of the link between the underlying neural activity and the LFP signal is still missing. Here we investigate this link by mathematical modeling of contributions to the LFP from a single layer-5 pyramidal neuron and a single layer-4 stellate neuron receiving synaptic input. An intrinsic dendritic low-pass filtering effect of the LFP signal, previously demonstrated for extracellular signatures of action potentials, is seen to strongly affect the LFP power spectra, even for frequencies as low as 10 Hz for the example pyramidal neuron. Further, the LFP signal is found to depend sensitively on both the recording position and the position of the synaptic input: the LFP power spectra recorded close to the active synapse are typically found to be less low-pass filtered than spectra recorded further away. Some recording positions display striking band-pass characteristics of the LFP. The frequency dependence of the properties of the current dipole moment set up by the synaptic input current is found to qualitatively account for several salient features of the observed LFP. Two approximate schemes for calculating the LFP, the dipole approximation and the two-monopole approximation, are tested and found to be potentially useful for translating results from large-scale neural network models into predictions for results from electroencephalographic (EEG) or electrocorticographic (ECoG) recordings.     

Association of Brain-Derived Neurotrophic Factor Gene Val66Met Polymorphism with Primary Dysmenorrhea

Primary dysmenorrhea (PDM), the most prevalent menstrual cycle-related problem in women of reproductive age, is associated with negative moods. Whether the menstrual pain and negative moods have a genetic basis remains unknown. Brain-derived neurotrophic factor (BDNF) plays a key role in the production of central sensitization and contributes to chronic pain conditions. BDNF has also been implicated in stress-related mood disorders. We screened and genotyped the BDNF Val66Met polymorphism (rs6265) in 99 Taiwanese (Asian) PDMs (20–30 years old) and 101 age-matched healthy female controls. We found that there was a significantly higher frequency of the Met allele of the BDNF Val66Met polymorphism in the PDM group. Furthermore, BDNF Met/Met homozygosity had a significantly stronger association with PDM compared with Val carrier status. Subsequent behavioral/hormonal assessments of sub-groups (PDMs = 78, controls = 81; eligible for longitudinal multimodal neuroimaging battery studies) revealed that the BDNF Met/Met homozygous PDMs exhibited a higher menstrual pain score (sensory dimension) and a more anxious mood than the Val carrier PDMs during the menstrual phase. Although preliminary, our study suggests that the BDNF Val66Met polymorphism is associated with PDM in Taiwanese (Asian) people, and BDNF Met/Met homozygosity may be associated with an increased risk of PDM. Our data also suggest the BDNF Val66Met polymorphism as a possible regulator of menstrual pain and pain-related emotions in PDM. Absence of thermal hypersensitivity may connote an ethnic attribution. The presentation of our findings calls for further genetic and neuroscientific investigations of PDM.     

Slow adaptation in spider mechanoreceptor neurons

Slow adaptation of action potential firing is a common but poorly understood property of sensory neurons. We quantified slow adaptation in a cuticular mechanoreceptor organ of the spider, Cupiennius salei, by stimulating with continuous pseudorandom mechanical displacements while recording action potentials intracellularly from the cell bodies. Firing rate declined over a period of several minutes before reaching a steady level at about half the initial rate. This slow adaptation was fitted by an exponential decay with mean time constant of 18.5 s. Recovery from slow adaptation was also fitted by an exponential process, but with a longer time constant of 167 s. The receptor potential produced by the same stimulation protocol did not change its amplitude or dynamics, showing that slow adaptation occurs during action potential encoding from the receptor potential. Experiments with chemical blockers of calcium entry or the known potassium currents failed to reduce the slow adaptation. The Na⁺/K⁺ pump blocker Ouabain decreased the time constant of slow adaptation, suggesting that ion accumulation is involved. In some experiments, a second class of small action potentials were observed, which were tentatively attributed to failed conduction from the sensory dendrite through the soma to the axon.     

Positron Emission Tomography of the Human Brain in Relation to Psychological Defense Mechanisms in Patients with Multiple Sclerosis

Neurophysiological correlates of psychological defense mechanisms (PDMs) were studied in patients with multiple sclerosis. PDM scores (the Lifestyle Index test) were compared with the relative glucose metabolic rate (GMR) estimated by positron emission tomography. The results testified that the combined metabolic activity of the limbic system and the frontal and temporal brain areas of the right hemisphere plays a predominant role in the functioning of the PDM system. An increase or decrease in PDM activity was associated with changes in GMR in several brain structures of the parietal and frontal regions.     

Electrical properties of the dendrite in an insect mechanoreceptor: Effects of antidromic or direct electrical stimulation

A study of the negative phase of the spikes recorded extra cellularly from insect mechanoreceptor has been performed in order to characterize some electrical properties of the dendrite which contains the transducing part of the sensory neuron. These properties have been investigated in mechanoreceptors of the metathoracic leg of the locust Schistocerca gregaria by firing antidromic action potentials both at rest and during mechanical or electrical stimulation. The amplitude of the negative phase of the spike appears to be correlated with the polarization of the dendritic membrane, although when bursts of action potentials are applied, the relation is more complex, including a depressive influence of a given spike on the following spike. The receptor potential and the antidromic dendritic spikes both originate in the same region of the dendrite but they involve different ionic processes. Our results indicate that the dendrite is electrically excitable. The spike which originates in the dendrite has an initial negative phase with a small superimposed positive component. A spike of this shape is never observed under natural stimulation. It is proposed that the negative phase of the antidromic impulse provides a suitable means for studying the variations in electrical polarization of the dendrite which cannot be recorded directly.     

From spiking neuron models to linear-nonlinear models

Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.     

Third-order reverse correlation analysis of muscle spindle primary afferent fiber responses to random muscle stretch

 The response of primary muscle spindle afferent fibers to muscle stretch is nonlinear. Now spindle responses (trains of action potentials) to band-limited Gaussian white noise length perturbations of the gastrocnemius muscles (input signal) are described in cats. The input noise upper cutoff frequency was clearly above the frequency range of physiological length changes in cat hindleg muscles. The input–output relation was analyzed by means of peri-spike averages (PSAs), which could be shown to correspond to the kernels of Wiener’s white noise approach to systems identification. The present approach (the reverse correlation analysis) was applied up to the third order. An experiment consisted of two recordings: one (the source recording) to determine PSAs and the other (the test recording) to provide an input signal for predicting responses. The predictions of different orders were compared with the actual neuronal response (the observation) of the test recording. Four different approximation procedures were developed to adapt prediction and observation and to determine weighting factors for the predictions of different orders. The approximations also yielded the value of the power density P of the input noise signal: at a variety of stimulus parameters, P from approximations had the same magnitude as P determined directly from the input signal amplitude spectrum. The prediction of a sequence of action potentials improved the higher the order of components. 37 of 42 action potentials of a test recording (the observation) could be confidently predicted from PSAs or kernels. Compared with the size of the linear first-order prediction curve, the relative sizes of the second and third-order prediction curves were: 1.0 : 0.47 : 0.26. Received: 15 November 1994/Accepted in revised form: 23 May 1995     

Intracellular recording from a spider vibration receptor

The present study introduces a new preparation of a spider vibration receptor that allows intracellular recording of responses to natural mechanical or electrical stimulation of the associated mechanoreceptor cells. The spider vibration receptor is a lyriform slit sense organ made up of 21 cuticular slits located on the distal end of the metatarsus of each walking leg. The organ is stimulated when the tarsus receives substrate vibrations, which it transmits to the organ’s cuticular structures, reducing the displacement to about one tenth due to geometrical reasons. Current clamp recording was used to record action potentials generated by electrical or mechanical stimuli. Square pulse stimulation identified two groups of sensory cells, the first being single-spike cells which generated only one or two action potentials and the second being multi-spike cells which produced bursts of action potentials. When the more natural mechanical sinusoidal stimulation was applied, differences in adaptation rate between the two cell types remained. In agreement with prior extracellular recordings, both cell types showed a decrease in the threshold tarsus deflection with increasing stimulus frequency. Off-responses to mechanical stimuli have also been seen in the metatarsal organ for the first time.     

Dynamics of Intrinsic Dendritic Calcium Signaling during Tonic Firing of Thalamic Reticular Neurons

The GABAergic neurons of the nucleus reticularis thalami that control the communication between thalamus and cortex are interconnected not only through axo-dendritic synapses but also through gap junctions and dendro-dendritic synapses. It is still unknown whether these dendritic communication processes may be triggered both by the tonic and the T-type Ca²⁺ channel-dependent high frequency burst firing of action potentials displayed by nucleus reticularis neurons during wakefulness and sleep, respectively. Indeed, while it is known that activation of T-type Ca²⁺ channels actively propagates throughout the dendritic tree, it is still unclear whether tonic action potential firing can also invade the dendritic arborization. Here, using two-photon microscopy, we demonstrated that dendritic Ca²⁺ responses following somatically evoked action potentials that mimic wake-related tonic firing are detected throughout the dendritic arborization. Calcium influx temporally summates to produce dendritic Ca²⁺ accumulations that are linearly related to the duration of the action potential trains. Increasing the firing frequency facilitates Ca²⁺ influx in the proximal but not in the distal dendritic compartments suggesting that the dendritic arborization acts as a low-pass filter in respect to the back-propagating action potentials. In the more distal compartment of the dendritic tree, T-type Ca²⁺ channels play a crucial role in the action potential triggered Ca²⁺ influx suggesting that this Ca²⁺ influx may be controlled by slight changes in the local dendritic membrane potential that determine the T-type channels’ availability. We conclude that by mediating Ca²⁺ dynamic in the whole dendritic arborization, both tonic and burst firing of the nucleus reticularis thalami neurons might control their dendro-dendritic and electrical communications.     

Eigenschaften diskreter Ortsfilter

Summary Properties of discrete spatial filters are investigated. By introducing rectangular or oblique coordinates it is possible to design filters in a quadratic or hexagonal raster. The design of low-pass, high-pass and band-pass filters is shown. Their properties are evaluated by computing an example; different filters are compared. It is possible to design arbitrary filters; however, there are limitations due to quantization error and approximation of filters by a necessarily finite (and small) number of elements.     

Modeling the Afferent Dynamics of the Baroreflex Control System

In this study we develop a modeling framework for predicting baroreceptor firing rate as a function of blood pressure. We test models within this framework both quantitatively and qualitatively using data from rats. The models describe three components: arterial wall deformation, stimulation of mechanoreceptors located in the BR nerve-endings, and modulation of the action potential frequency. The three sub-systems are modeled individually following well-established biological principles. The first submodel, predicting arterial wall deformation, uses blood pressure as an input and outputs circumferential strain. The mechanoreceptor stimulation model, uses circumferential strain as an input, predicting receptor deformation as an output. Finally, the neural model takes receptor deformation as an input predicting the BR firing rate as an output. Our results show that nonlinear dependence of firing rate on pressure can be accounted for by taking into account the nonlinear elastic properties of the artery wall. This was observed when testing the models using multiple experiments with a single set of parameters. We find that to model the response to a square pressure stimulus, giving rise to post-excitatory depression, it is necessary to include an integrate-and-fire model, which allows the firing rate to cease when the stimulus falls below a given threshold. We show that our modeling framework in combination with sensitivity analysis and parameter estimation can be used to test and compare models. Finally, we demonstrate that our preferred model can exhibit all known dynamics and that it is advantageous to combine qualitative and quantitative analysis methods.     

Spike discharges of skeletomotor neurons during random noise modulated transmembrane current stimulation and muscle stretch

 Spike discharges of skeletomotor neurons innervating triceps surae muscles elicited by white noise modulated transmembrane current stimulation and muscle stretch were studied in decerebrated cats. The white noise modulated current intensity ranged from 4.3 to 63.2 nA peak-to-peak, while muscle stretches ranged from 100 μm to 4.26 mm peak-to-peak. The neuronal responses were studied by averaging the muscle length records centered at the skeletomotor action potentials (peri-spike average, PSA) and by Wiener analysis. Skeletomotor spikes appeared after a sharp peak in PSA of the injected current, preceded by a longer-lasting smaller wavelet of either depolarizing or hyperpolarizing direction. The PSA amplitude was not related to the injected current amplitude nor showed any differences related to the motor unit type. The PSA amplitudes were virtually independent of the stretching amplitude σ, after an initial increase with stretching amplitudes in the range of 15–40 μm (S.D.), or 100–270 μm peak-to-peak.Analyses of cross-spectra indicated a small or absent increase in gain with frequency in response to injected current, but about 20 dB/decade in the range 10–100 Hz in response to muscle stretch. The peaks of both Wiener kernels in response to current injection appear to decrease with the amplitude of injected current, but this decrease was not statistically significant. The narrow first-order kernels suggest that the transfer function between the current input and spike discharge is lowpass with a wide passband, i.e. there is very little change in dynamics. The values of the second-order kernels appear to be nonzero only along the main diagonal. This is characteristic of a simple Hammerstein type cascade, i.e. a zero memory nonlinearity followed by a linear system. Small values of second-order kernels away from the origin and narrow first-order kernels suggest that the linear cascade contributes very little to the overall dynamic response.In contrast to Wiener kernels found in response to current injection, the Wiener kernels in response to stretch showed a decreasing trend with stretch amplitude. The size of the second-order kernels decreased to a somewhat larger extent with input amplitude than that of the first-order kernels, indicating an amplitude-dependent nonlinearity. Overall, the transformation between length and spike output was described as an LNNL cascade with second-order nonlinearities. Received: 1 April 1993/Accepted in revised form: 24 March 1994