Membrane potential fluctuations determine the precision of spike timing and synchronous activity: a model study

High-Precision Fast-Spiking Basket Cell Discharges during Complex Events in the Human Neocortex

In the human neocortex, solitary action potentials in some layer 2–3 pyramidal cells (PCs) trigger brief episodes of network activity known as complex events through strong excitatory synapses that specifically innervate GABAergic interneurons. Yet, how these “master PCs” configure the local network activity is not well understood. We report that single spikes in the PCs, studied here in synaptically connected cell pairs in frontal or temporal neocortical areas of both males and females, elicit firing of fast-spiking basket cells (FSBCs) with a short delay (on average 2.7 ms). The FSBC discharge is triggered by 13 mV (on average) monosynaptic EPSPs, and the action potential is time locked to the master PC spike with high temporal precision, showing little jitter in delay. In the complex events, the FSBC discharge occurs in the beginning of the activity episode, forming the first wave of the complex event activity. Firing of FSBCs generates GABAergic IPSCs with fast kinetics in layer 2–3 PCs, and similar IPSCs regularly occur time locked to master PC spikes in the beginning of the complex events with high probability and short (median 4.1 ms) delay with little jitter. In comparison, discharge of nonfast spiking interneurons (non-FSINs) investigated here appears inconsistently in the complex events and shows low probability. Thus, firing of layer 2–3 FSBCs with high temporal fidelity characterizes early phase of the complex events in the human neocortex.

Frequency-dependent signal processing in apical dendrites of hippocampal CA1 pyramidal cells

Depending on an animal's behavioral state, hippocampal CA1 pyramidal cells receive distinct patterns of excitatory and inhibitory synaptic inputs. The time-dependent changes in the frequencies of these inputs and the nonuniform distribution of voltage-gated channels lead to dynamic fluctuations in membrane conductance. In this study, using a whole-cell patch-clamp method, we attempted to record and analyze the frequency dependencies of membrane responsiveness in Wistar rat hippocampal CA1 pyramidal cells following noise current injection directly into dendrites and somata under pharmacological blockade of all synaptic inputs. To estimate the frequency-dependent properties of membrane potential, membrane impedance was determined from the voltage response divided by the input current in the frequency domain. The cell membrane of most neurons showed low-pass filtering properties in all regions. In particular, the properties were strongly expressed in the somata or proximal dendrites. Moreover, the data revealed nonuniform distribution of dendritic impedance, which was high in the intermediate segment of the apical dendritic shaft (∼220-260μm from the soma). The low-pass filtering properties in the apical dendrites were more enhanced by membrane depolarization than those in the somata. Coherence spectral analysis revealed high coherence between the input signal and the output voltage response in the theta-gamma frequency range, and large lags emerged in the distal dendrites in the gamma frequency range. Our results suggest that apical dendrites of hippocampal CA1 pyramidal cells integrate synaptic inputs according to the frequency components of the input signal along the dendritic segments receiving the inputs.

Impact and sources of neuronal variability in the fly's motion vision pathway

Nervous systems encode information about dynamically changing sensory input by changes in neuronal activity. Neuronal activity changes, however, also arise from noise sources within and outside the nervous system or from changes of the animal's behavioral state. The resulting variability of neuronal responses in representing sensory stimuli limits the reliability with which animals can respond to stimuli and may thus even affect the chances for survival in certain situations. Relevant sources of noise arising at different stages along the motion vision pathway have been investigated from the sensory input to the initiation of behavioral reactions. Here, we concentrate on the reliability of processing visual motion information in flies. Flies rely on visual motion information to guide their locomotion. They are among the best established model systems for the processing of visual motion information allowing us to bridge the gap between behavioral performance and underlying neuronal computations. It has been possible to directly assess the consequences of noise at major stages of the fly's visual motion processing system on the reliability of neuronal signals. Responses of motion sensitive neurons and their variability have been related to optomotor movements as indicators for the overall performance of visual motion computation. We address whether and how noise already inherent in the stimulus, e.g. photon noise for the visual system, influences later processing stages and to what extent variability at the output level of the sensory system limits behavioral performance. Recent advances in circuit analysis and the progress in monitoring neuronal activity in behaving animals should now be applied to understand how the animal meets the requirements of fast and reliable manoeuvres in naturalistic situations.

The effect of neural noise on spike time precision in a detailed CA3 neuron model

Experimental and computational studies emphasize the role of the millisecond precision of neuronal spike times as an important coding mechanism for transmitting and representing information in the central nervous system. We investigate the spike time precision of a multicompartmental pyramidal neuron model of the CA3 region of the hippocampus under the influence of various sources of neuronal noise. We describe differences in the contribution to noise originating from voltage-gated ion channels, synaptic vesicle release, and vesicle quantal size. We analyze the effect of interspike intervals and the voltage course preceding the firing of spikes on the spike-timing jitter. The main finding of this study is the ranking of different noise sources according to their contribution to spike time precision. The most influential is synaptic vesicle release noise, causing the spike jitter to vary from 1 ms to 7 ms of a mean value 2.5 ms. Of second importance was the noise incurred by vesicle quantal size variation causing the spike time jitter to vary from 0.03 ms to 0.6 ms. Least influential was the voltage-gated channel noise generating spike jitter from 0.02 ms to 0.15 ms.

Distinct intrinsic membrane properties determine differential information processing between main and accessory olfactory bulb mitral cells

Most mammals rely on semiochemicals, such as pheromones, to mediate their social interactions. Recent studies found that semiochemicals are perceived by at least two distinct chemosensory systems: the main and accessory olfactory systems, which share many molecular, cellular, and anatomical features. Nevertheless, the division of labor between these systems remained unclear. Previously we suggested that the two olfactory systems differ in the way they process sensory information. In this study we found that mitral cells of the main and accessory olfactory bulbs, the first brain stations of both systems, display markedly different passive and active intrinsic properties which permit distinct types of information processing. Moreover, we found that accessory olfactory bulb mitral cells are divided into three neuronal sub-populations with distinct firing properties. These neuronal sub-populations can be integrated in a simulated neuronal network that neglects episodic stimuli while amplifying reaction to long-lasting signals.

Difference in response reliability predicted by spectrotemporal tuning in the cochlear nuclei of barn owls

The brainstem auditory pathway is obligatory for all aural information. Brainstem auditory neurons must encode the level and timing of sounds, as well as their time-dependent spectral properties, the fine structure, and envelope, which are essential for sound discrimination. This study focused on envelope coding in the two cochlear nuclei of the barn owl, nucleus angularis (NA) and nucleus magnocellularis (NM). NA and NM receive input from bifurcating auditory nerve fibers and initiate processing pathways specialized in encoding interaural time (ITD) and level (ILD) differences, respectively. We found that NA neurons, although unable to accurately encode stimulus phase, lock more strongly to the stimulus envelope than NM units. The spectrotemporal receptive fields (STRFs) of NA neurons exhibit a pre-excitatory suppressive field. Using multilinear regression analysis and computational modeling, we show that this feature of STRFs can account for enhanced across-trial response reliability, by locking spikes to the stimulus envelope. Our findings indicate a dichotomy in envelope coding between the time and intensity processing pathways as early as at the level of the cochlear nuclei. This allows the ILD processing pathway to encode envelope information with greater fidelity than the ITD processing pathway. Furthermore, we demonstrate that the properties of the STRFs of the neurons can be quantitatively related to spike timing reliability.

Distributed dendritic processing facilitates object detection: a computational analysis on the visual system of the fly

Background

Detecting objects is an important task when moving through a natural environment. Flies, for example, may land on salient objects or may avoid collisions with them. The neuronal ensemble of Figure Detection cells (FD-cells) in the visual system of the fly is likely to be involved in controlling these behaviours, as these cells are more sensitive to objects than to extended background structures. Until now the computations in the presynaptic neuronal network of FD-cells and, in particular, the functional significance of the experimentally established distributed dendritic processing of excitatory and inhibitory inputs is not understood.

Methodology/Principal Findings

We use model simulations to analyse the neuronal computations responsible for the preference of FD-cells for small objects. We employed a new modelling approach which allowed us to account for the spatial spread of electrical signals in the dendrites while avoiding detailed compartmental modelling. The models are based on available physiological and anatomical data. Three models were tested each implementing an inhibitory neural circuit, but differing by the spatial arrangement of the inhibitory interaction. Parameter optimisation with an evolutionary algorithm revealed that only distributed dendritic processing satisfies the constraints arising from electrophysiological experiments. In contrast to a direct dendro-dendritic inhibition of the FD-cell (Direct Distributed Inhibition model), an inhibition of its presynaptic retinotopic elements (Indirect Distributed Inhibition model) requires smaller changes in input resistance in the inhibited neurons during visual stimulation.

Conclusions/Significance

Distributed dendritic inhibition of retinotopic elements as implemented in our Indirect Distributed Inhibition model is the most plausible wiring scheme for the neuronal circuit of FD-cells. This microcircuit is computationally similar to lateral inhibition between the retinotopic elements. Hence, distributed inhibition might be an alternative explanation of perceptual phenomena currently explained by lateral inhibition networks.

Synapses in the fly motion-vision pathway: evidence for a broad range of signal amplitudes and dynamics

Synapses are generally considered to operate efficiently only when their signaling range matches the spectrum of prevailing presynaptic signals in terms of both amplitudes and dynamics. However, the prerequisites for optimally matching the signaling ranges may differ between spike-mediated and graded synaptic transmission. This poses a problem for synapses that convey both graded and spike signals at the same time. We addressed this issue by tracing transmission systematically in vivo in the blowfly's visual-motion pathway by recording from single neurons that receive mixed potential signals consisting of rather slow graded fluctuations superimposed with highly variable spikes from a small number of presynaptic elements. Both pre- and postsynaptic neurons were previously shown to represent preferred-direction motion velocity reliably and linearly at low fluctuation frequencies. To selectively assess the performance of individual synapses and to precisely control presynaptic signals, we voltage clamped one of the presynaptic neurons. Results showed that synapses can effectively convey signals over a much larger amplitude and frequency range than is normally used during graded transmission of visual signals. An explanation for this unexpected finding might lie in the transmission of the spike component that reaches larger amplitudes and contains higher frequencies than graded signals.

Implications of functionally different synaptic inputs for neuronal gain and computational properties of fly visual interneurons

Neurons embedded in networks are thought to receive synaptic inputs that do not drive them on their own, but modulate the responsiveness to driving input. Although studies on brain slices have led to detailed knowledge of how nondriving input affects dendritic integration, its origin and functional implications remain unclear. We tackle this issue using an ensemble of fly wide-field visual interneurons. These neurons offer the opportunity not only to combine in vivo recording techniques and natural sensory stimulation but also to interpret electrophysiological results in a behavioral context. By targeted manipulation of the animal's visual input we find a pronounced modulating impact of nondriving input, whereas functionally important cellular properties like direction tuning and the coding of pattern velocity are left almost unaffected. We propose that the integration of functionally different synaptic inputs is a mechanism that immanently equalizes the ensemble's sensitivity irrespective of the specific stimulus conditions.

Intrinsic noise in cultured hippocampal neurons: experiment and modeling

Ion channels open and close stochastically. The fluctuation of these channels represents an intrinsic source of noise that affects the input-output properties of the neuron. We combined whole-cell measurements with biophysical modeling to characterize the intrinsic stochastic and electrical properties of single neurons as observed at the soma. We measured current and voltage noise in 18 d postembryonic cultured neurons from the rat hippocampus, at various subthreshold and near-threshold holding potentials in the presence of synaptic blockers. The observed current noise increased with depolarization, as ion channels were activated, and its spectrum demonstrated generalized 1/f behavior. Exposure to TTX removed a significant contribution from Na+ channels to the noise spectrum, particularly at depolarized potentials, and the resulting spectrum was now dominated by a single Lorentzian (1/f2) component. By replacing the intracellular K+ with Cs+, we demonstrated that a major portion of the observed noise was attributable to K+ channels. We compared the measured power spectral densities to a 1-D cable model of channel fluctuations based on Markov kinetics. We found that a somatic compartment, in combination with a single equivalent cylinder, described the effective geometry from the viewpoint of the soma. Four distinct channel populations were distributed in the membrane and modeled as Lorentzian current noise sources. Using the NEURON simulation program, we summed up the contributions from the spatially distributed current noise sources and calculated the total voltage and current noise. Our quantitative model reproduces important voltage- and frequency-dependent features of the data, accounting for the 1/f behavior, as well as the effects of various blockers.

Analysis and simulation of gain control and precision in crayfish visual interneurons

Impulse trains in sustaining and dimming fibers of crayfish optic lobe (in situ) were elicited with sinusoidal extrinsic current and sine-wave illumination. Extrinsic currents and currents derived from postsynaptic potentials (PSPs) were used to compute the time course of the spike train with an adaptive integrate-and-fire model. The neurons exhibit variations in gain and spike timing precision related to the frequency of stimulation. These phenomena are influenced by spike-frequency adaptation and nonlinearities in the PSP. Dimming fibers exhibit relatively strong spike-frequency adaptation and an associated increase in gain with the frequency of sinusoidal extrinsic current and sine-wave illumination. The dimming fiber IPSP promotes spike train rectification, and rectification contributes to spike timing precision. Sustaining fibers exhibit weaker spike-frequency adaptation and the gain of the current-elicited response is less sensitive to stimulus frequency. The sustaining fiber excitatory PSP, however, exhibits a strong frequency-dependent nonlinearity that influences the frequency response. Spike timing precision is a function of stimulus frequency in all cells and it is enhanced by rectification of the discharge and/or resonance. In rectified responses the jitter in spike times is closely related to the variance in the times the membrane potential reaches spike threshold. These gain and spike timing results are well approximated by the simulated responses. Because the nonlinearity of the sustaining fiber PSP entails a high rate of depolarization, the PSP can increase the precision of spike timing by 10- to 100-fold compared with the response to pure sine-wave stimuli. This enhanced precision has implications for crayfish oculomotor reflexes that are driven by sustaining fibers and highly sensitive to impulse timing during transient excitation.

Reliable control of spike rate and spike timing by rapid input transients in cerebellar stellate cells

Granule cell activity in cerebellar cortex directly excites Purkinje cells via parallel fibers, but it also inhibits Purkinje cells via cerebellar cortical interneurons. This contribution of inhibitory interneurons to cerebellar cortical processing remains poorly understood. In the present study we examined the response properties of stellate cells in vitro to input patterns that may result from granule cell activity in vivo. We constructed input waveforms that represented the sum of inputs from all individual synapses and applied these waveforms to the soma of stellate cells during whole cell recordings in acute brain slices. The stimulus waveforms contained fluctuations in a broad range of frequencies and were applied at different amplitudes. To determine the contribution of synaptic shunting to stellate cell spike responses we applied the same input waveforms either as a simulated synaptic conductance using dynamic clamping or as a direct current injection stimulus. Only the dynamic clamp stimulus has the shunting properties of real synapses, i.e. leads to different-sized synaptic current as a function of membrane potential. We found that stellate cells spike with millisecond precision in response to fast temporal fluctuations in the total synaptic input. Transient increases in excitatory input frequency led to pronounced stellate cell spike responses, indicating that this pathway may be very responsive to even small assemblies of co-activated granule cells. This was observed regardless of whether the input waveform was applied as a conductance with dynamic clamping, or as a direct current injection. Thus the shunting properties of a conductance input did not play a major role in determining the control of precisely timed spiking. In contrast, a more tonic increase in excitatory conductance did not lead to a sustained spike response as obtained with prolonged positive current injection. However, even with tonic current injection the precision of spiking was lost, as previously observed. Overall, the synaptic response function of stellate cells suggests that this cell type may pick out transients in granule cell activity, and may generate precisely timed inhibition of Purkinje cells during behavior.

Encoder adaptation modulates the visual responses of crayfish interneurons

The responses of sustaining and dimming fibers were characterized by the time varying firing rates elicited by extrinsic current and flashes of light. These data were simulated by an adaptive integrate-and-fire model. A postimpulse shunt conductance simulated spike-frequency adaptation. The correlation between observed and model current-elicited impulse rates was 0.94-0.98. However, except for a difference in input resistance (both measured and simulated), the voltage to impulse encoders of the two cell groups was similar and exhibited comparable degrees of spike-frequency adaptation (40 to 45%). The encoder model derived from current-elicited responses (with fixed parameters) was used to simulate visual responses elicited by light flashes. These simulations included a synaptic current derived from the time course of the postsynaptic potential (PSP). The sustaining fiber visual response consisted of a large excitatory PSP and high-frequency transient burst that adapted (by approximately 80%) to a low-frequency plateau discharge. The simulations indicated that spike-frequency adaptation had no effect on the transient discharge but reduced the plateau firing rate by approximately 60%. Encoder adaptation enhances the sustaining fiber response to the time derivative of the stimulus. In dimming fibers, the light flash elicits an inhibitory PSP that interrupts the "dark discharge" and an off response following the end of the flash. The simulations indicated that spike-frequency adaptation reduces the firing rate of both the dark discharge and the off response. Thus the model suggests that different effects of encoder adaptation on the two cell types arise from the same encoder mechanisms, but different actions are determined by differences in impulse rate and the time course of the discharge.

Synaptic transfer of dynamic motion information between identified neurons in the visual system of the blowfly

Synaptic transmission is usually studied in vitro with electrical stimulation replacing the natural input of the system. In contrast, we analyzed in vivo transfer of visual motion information from graded-potential presynaptic to spiking postsynaptic neurons in the fly. Motion in the null direction leads to hyperpolarization of the presynaptic neuron but does not much influence the postsynaptic cell, because its firing rate is already low during rest, giving only little scope for further reductions. In contrast, preferred-direction motion leads to presynaptic depolarizations and increases the postsynaptic spike rate. Signal transfer to the postsynaptic cell is linear and reliable for presynaptic graded membrane potential fluctuations of up to approximately 10 Hz. This frequency range covers the dynamic range of velocities that is encoded with a high gain by visual motion-sensitive neurons. Hence, information about preferred-direction motion is transmitted largely undistorted ensuring a consistent dependency of neuronal signals on stimulus parameters, such as motion velocity. Postsynaptic spikes are often elicited by rapid presynaptic spike-like depolarizations which superimpose the graded membrane potential. Although the timing of most of these spike-like depolarizations is set by noise and not by the motion stimulus, it is preserved at the synapse with millisecond precision.

Spike generating dynamics and the conditions for spike-time precision in cortical neurons

Temporal precision of spiking response in cortical neurons has been a subject of intense debate. Using a canonical model of spike generation, we explore the conditions for precise and reliable spike timing in the presence of Gaussian white noise. In agreement with previous results we find that constant stimuli lead to imprecise timing, while aperiodic stimuli yield precise spike timing. Under constant stimulus the neuron is a noise perturbed oscillator, the spike times follow renewal statistics and are imprecise. Under an aperiodic stimulus sequence, the neuron acts as a threshold element; the firing times are precisely determined by the dynamics of the stimulus. We further study the dependence of spike-time precision on the input stimulus frequency and find a non-linear tuning whose width can be related to the locking modes of the neuron. We conclude that viewing the neuron as a non-linear oscillator is the key for understanding spike-time precision.

Variability of postsynaptic responses depends non-linearly on the number of synaptic inputs

A conductance-based model for synaptic transmission and postsynaptic integration reveals how postsynaptic responses and their variability depend on the number of synaptic inputs. With increasing number of balanced stochastic excitatory and inhibitory inputs, the postsynaptic responses and their variance first increase and then decrease again. This non-linearity can be attributed to an anti-correlation between the total excitatory and inhibitory currents. The anti-correlation, which occurs even though the conductances of the individual synapses vary independently of each other, is determined by the total synaptic conductance and grows with the number of inputs. As the number of inputs increases, the membrane potential comes increasingly closer to the resting level.

Tuning neocortical pyramidal neurons between integrators and coincidence detectors

Do cortical neurons operate as integrators or as coincidence detectors? Despite the importance of this question, no definite answer has been given yet, because each of these two views can find its own experimental support. Here we investigated this question using models of morphologically-reconstructed neocortical pyramidal neurons under in vivo like conditions. In agreement with experiments we find that the cell is capable of operating in a continuum between coincidence detection and temporal integration, depending on the characteristics of the synaptic inputs. Moreover, the presence of synaptic background activity at a level comparable to intracellular measurements in vivo can modulate the operating mode of the cell, and act as a switch between temporal integration and coincidence detection. These results suggest that background activity can be viewed as an important determinant of the integrative mode of pyramidal neurons. Thus, background activity not only sharpens cortical responses but it can also be used to tune an entire network between integration and coincidence detection modes.

Interspike interval correlations, memory, adaptation, and refractoriness in a leaky integrate-and-fire model with threshold fatigue

Neuronal adaptation as well as interdischarge interval correlations have been shown to be functionally important properties of physiological neurons. We explore the dynamics of a modified leaky integrate-and-fire (LIF) neuron, referred to as the LIF with threshold fatigue, and show that it reproduces these properties. In this model, the postdischarge threshold reset depends on the preceding sequence of discharge times. We show that in response to various classes of stimuli, namely, constant currents, step currents, white gaussian noise, and sinusoidal currents, the model exhibits new behavior compared with the standard LIF neuron. More precisely, (1) step currents lead to adaptation, that is, a progressive decrease of the discharge rate following the stimulus onset, while in the standard LIF, no such patterns are possible; (2) a saturation in the firing rate occurs in certain regimes, a behavior not seen in the LIF neuron; (3) interspike intervals of the noise-driven modified LIF under constant current are correlated in a way reminiscent of experimental observations, while those of the standard LIF are independent of one another; (4) the magnitude of the correlation coefficients decreases as a function of noise intensity; and (5) the dynamics of the sinusoidally forced modified LIF are described by iterates of an annulus map, an extension to the circle map dynamics displayed by the LIF model. Under certain conditions, this map can give rise to sensitivity to initial conditions and thus chaotic behavior.

Attractor reliability reveals deterministic structure in neuronal spike trains

When periodic current is injected into an integrate-and-fire model neuron, the voltage as a function of time converges from different initial conditions to an attractor that produces reproducible sequences of spikes. The attractor reliability is a measure of the stability of spike trains against intrinsic noise and is quantified here as the inverse of the number of distinct spike trains obtained in response to repeated presentations of the same stimulus. High reliability characterizes neurons that can support a spike-time code, unlike neurons with discharges forming a renewal process (such as a Poisson process). These two classes of responses cannot be distinguished using measures based on the spike-time histogram, but they can be identified by the attractor dynamics of spike trains, as shown here using a new method for calculating the attractor reliability. We applied these methods to spike trains obtained from current injection into cortical neurons recorded in vitro. These spike trains did not form a renewal process and had a higher reliability compared to renewal-like processes with the same spike-time histogram.

Precision and reliability of periodically and quasiperiodically driven integrate-and-fire neurons

Neurons in the brain communicate via trains of all-or-none electric events known as spikes. How the brain encodes information using spikes-the neural code-remains elusive. Here the robustness against noise of stimulus-induced neural spike trains is studied in terms of attractors and bifurcations. The dynamics of model neurons converges after a transient onto an attractor yielding a reproducible sequence of spike times. At a bifurcation point the spike times on the attractor change discontinuously when a parameter is varied. Reliability, the stability of the attractor against noise, is reduced when the neuron operates close to a bifurcation point. We determined using analytical spike-time maps the attractor and bifurcation structure of an integrate-and-fire model neuron driven by a periodic or a quasiperiodic piecewise constant current and investigated the stability of attractors against noise. The integrate-and-fire model neuron became mode locked to the periodic current with a rational winding number p/q and produced p spikes per q cycles. There were q attractors. p:q mode-locking regions formed Arnold tongues. In the model, reliability was the highest during 1:1 mode locking when there was only one attractor, as was also observed in recent experiments. The quasiperiodically driven neuron mode locked to either one of the two drive periods, or to a linear combination of both of them. Mode-locking regions were organized in Arnold tongues and reliability was again highest when there was only one attractor. These results show that neuronal reliability in response to the rhythmic drive generated by synchronized networks of neurons is profoundly influenced by the location of the Arnold tongues in parameter space.

Spike timing, synchronization and information processing on the sensory side of the central nervous system

To what extent is the variability of the neuronal responses compatible with the use of spike timing for sensory information processing by the central nervous system? In reviewing the state of the art of this question, I first analyze the characteristics of this variability with its three elements: synaptic noise, impact of ongoing activity and possible fluctuations in evoked responses. I then review the recent literature on the various sensory modalities: somato-sensory, olfactory, gustatory and visual and auditory processing. I emphasize that the conditions in which precise timing, at the millisecond level, is usually obtained, are conditions that usually require dynamic stimulation or sharp changes in the stimuli. By contrast, situations in which stimulation not belonging to the temporal domain is temporally encoded lead to much coarser temporal coding; although in both cases, neural networks transmit the signals with similarly high precision. Synchronization among neurons is an important tool in information processing in both cases but again seems to act either at millisecond or tens of millisecond levels. Information theory applied to both situations confirms that the average rate of information transmission is much higher in dynamic than in static situations. These facts suggest that channels of precise temporal encoding may exist in the brain but imply populations of neurons working in a yet to be discovered way.

Neural coding with graded membrane potential changes and spikes

The neural encoding of sensory stimuli is usually investigated for spike responses, although many neurons are known to convey information by graded membrane potential changes. We compare by model simulations how well different dynamical stimuli can be discriminated on the basis of spiking or graded responses. Although a continuously varying membrane potential contains more information than binary spike trains, we find situations where different stimuli can be better discriminated on the basis of spike responses than on the basis of graded responses. Spikes can be superior to graded membrane potential fluctuations if spikes sharpen the temporal structure of neuronal responses by amplifying fast transients of the membrane potential. Such fast membrane potential changes can be induced deterministically by the stimulus or can be due to membrane potential noise that is influenced in its statistical properties by the stimulus. The graded response mode is superior for discrimination between stimuli on a fine time scale.

Reliability of a fly motion-sensitive neuron depends on stimulus parameters

The variability of responses of sensory neurons constrains how reliably animals can respond to stimuli in the outside world. We show for a motion-sensitive visual interneuron of the fly that the variability of spike trains depends on the properties of the motion stimulus, although differently for different stimulus parameters. (1) The spike count variances of responses to constant and to dynamic stimuli lie in the same range. (2) With increasing stimulus size, the variance may slightly decrease. (3) Increasing pattern contrast reduces the variance considerably. For all stimulus conditions, the spike count variance is much smaller than the mean spike count and does not depend much on the mean activity apart from very low activities. Using a model of spike generation, we analyzed how the spike count variance depends on the membrane potential noise and the deterministic membrane potential fluctuations at the spike initiation zone of the neuron. In a physiologically plausible range, the variance is affected only weakly by changes in the dynamics or the amplitude of the deterministic membrane potential fluctuations. In contrast, the amplitude and dynamics of the membrane potential noise strongly influence the spike count variance. The membrane potential noise underlying the variability of the spike responses in the motion-sensitive neuron is concluded to be affected considerably by the contrast of the stimulus but by neither its dynamics nor its size.