Spike timing and reliability in cortical pyramidal neurons: effects of EPSC kinetics, input synchronization and background noise on spike timing

In vivo studies have shown that neurons in the neocortex can generate action potentials at high temporal precision. The mechanisms controlling timing and reliability of action potential generation in neocortical neurons, however, are still poorly understood. Here we investigated the temporal precision and reliability of spike firing in cortical layer V pyramidal cells at near-threshold membrane potentials. Timing and reliability of spike responses were a function of EPSC kinetics, temporal jitter of population excitatory inputs, and of background synaptic noise. We used somatic current injection to mimic population synaptic input events and measured spike probability and spike time precision (STP), the latter defined as the time window (Deltat) holding 80% of response spikes. EPSC rise and decay times were varied over the known physiological spectrum. At spike threshold level, EPSC decay time had a stronger influence on STP than rise time. Generally, STP was highest (6 ms) triggered spikes at lower temporal precision (>or=6.58 ms). We found an overall linear relationship between STP and spike delay. The difference in STP between fast and slow compound EPSCs could be reduced by incrementing the amplitude of slow compound EPSCs. The introduction of a temporal jitter to compound EPSCs had a comparatively small effect on STP, with a tenfold increase in jitter resulting in only a five fold decrease in STP. In the presence of simulated synaptic background activity, precisely timed spikes could still be induced by fast EPSCs, but not by slow EPSCs.     

Relationships between amplitudes and kinetics of rapid cytosolic free calcium fluctuations in GH4C1 rat pituitary cells: roles for diffusion and calcium-induced calcium release.

We have examined statistical relationships between the amplitudes and the kinetics (rise times, fall times, and decay constants) of cytosolic free calcium fluctuations (spikes) in a population of 353 individual GH4C1 rat pituitary cells. The fast falling phase was approximated by a single exponential decay, and the decay time constant, tau, increased linearly with spike amplitude in 80% of the cells studied. The slope of the tau versus amplitude plot for each cell was inversely related to the cell's mean spike amplitude. Thus, some process responsible for prolonging the decay phase of spikes appeared to operate strongly in cells with spikes of low amplitude, but to become less prominent in cells with high amplitude spikes. Mean tau correlated more strongly with mean rise and fall times than with mean spike amplitude, indicating that the kinetic properties of spikes were not tightly coupled to spike amplitude. These findings are consistent with a model wherein the rise phase corresponds to entry of extracellular calcium via L-type calcium channels into localized sub-plasmalemmal domains, followed by diffusion of subplasmalemmal calcium into the cell interior; and the falling phase corresponds to further calcium diffusion combined with activation of cytoplasmic calcium-induced calcium release, which prolongs the falling phase.     

The role of individual spikes and spike patterns in population coding of stimulus location in rat somatosensory cortex

This report addresses the nature of population coding in sensory cortex by applying information theoretic analysis to data recorded simultaneously from neuron pairs located in primary somatosensory cortex of anaesthetised rats. We studied how cortical spike trains code for the location of a whisker stimulus on the rat's snout. We found that substantially more information was conveyed by 10 ms precision spike timing compared with that conveyed by the number of spikes counted over a 40 ms response interval. Most of this information was accounted for by the timing of individual spikes. In particular, it was the first post-stimulus spikes that were crucial. Spike patterns within individual cells played a smaller role; spike patterns across cells were negligible. This pattern of results was robust both to the exact nature of the stimulus set and to the precision at which spikes were binned.     

Axonal branching pattern and coupling mechanisms of the cerebral giant neurones in the snail,lymnaea stagnalis

The axonal branching pattern of the two cerebral giant neurones (CGCs) of Lymnaea stagnalis was studied with intrasomatically applied horseradish peroxidase. The cells are symmetrical. Each CGC projects to the ipsilateral n. labialis medius and n. arteriae labialis, the subcerebral commissure, and to all ipsi- and contralateral buccal nerves. The contralateral buccal nerves are reached via the ipsilateral cerebro-buccal connective and the buccal commissure. The CGC fire action potentials 1:1 in a driver-follower relationship. Each cell is capable of both driving and following. The relationship depends on the membrane potentials of the somata. In driving CGC spikes are initiated in a cerebral spike trigger zone located near the soma. In following cells spikes are initiated in a distal zone located in the buccal ganglia. The buccal zone is only affected by the partner CGC. CGC are synchronized by three coupling mechanisms: mutual excitatory chemical synapses, electrotonic coupling, and common input. The chemical and electrotonic connections are located in the buccal ganglia. All spikes are relayed to the partner cell via the chemical synapses. The electrotonic coupling improves the efficiency of the chemical synapses. The dual connection selectively synchronizes the CGC-axonal spikes from each side of the buccal mass. Common excitatory input affects the cerebral spike trigger zones and can initiate simultaneous spikes in both cells. This results in bilateral synchrony of spikes in the CGC-axons in both the buccal and the lip nerves.     

The temporal structure of transient ON/OFF ganglion cell responses and its relation to intra-retinal processing

A subpopulation of transient ON/OFF ganglion cells in the turtle retina transmits changes in stimulus intensity as series of distinct spike events. The temporal structure of these event sequences depends systematically on the stimulus and thus carries information about the preceding intensity change. To study the spike events' intra-retinal origins, we performed extracellular ganglion cell recordings and simultaneous intracellular recordings from horizontal and amacrine cells. Based on these data, we developed a computational retina model, reproducing spike event patterns with realistic intensity dependence under various experimental conditions. The model's main features are negative feedback from sustained amacrine onto bipolar cells, and a two-step cascade of ganglion cell suppression via a slow and a fast transient amacrine cell. Pharmacologically blocking glycinergic transmission results in disappearance of the spike event sequence, an effect predicted by the model if a single connection, namely suppression of the fast by the slow transient amacrine cell, is weakened. We suggest that the slow transient amacrine cell is glycinergic, whereas the other types release GABA. Thus, the interplay of amacrine cell mediated inhibition is likely to induce distinct temporal structure in ganglion cell responses, forming the basis for a temporal code. Action Editor: Jonathan D. Victor     

Population coding in somatosensory cortex

Computational analyses have begun to elucidate which components of somatosensory cortical population activity may encode basic stimulus features. Recent results from rat barrel cortex suggest that the essence of this code is not synergistic spike patterns, but rather the precise timing of single neuron's first post-stimulus spikes. This may form the basis for a fast, robust population code.     

Ion channel noise can explain firing correlation in auditory nerves

Sensory neurons code information about stimuli in their sequence of action potentials (spikes). Intuitively, the spikes should represent stimuli with high fidelity. However, generating and propagating spikes is a metabolically expensive process. It is therefore likely that neural codes have been selected to balance energy expenditure against encoding error. Our recently proposed optimal, energy-constrained neural coder (Jones et al. Frontiers in Computational Neuroscience, 9, 61 2015) postulates that neurons time spikes to minimize the trade-off between stimulus reconstruction error and expended energy by adjusting the spike threshold using a simple dynamic threshold. Here, we show that this proposed coding scheme is related to existing coding schemes, such as rate and temporal codes. We derive an instantaneous rate coder and show that the spike-rate depends on the signal and its derivative. In the limit of high spike rates the spike train maximizes fidelity given an energy constraint (average spike-rate), and the predicted interspike intervals are identical to those generated by our existing optimal coding neuron. The instantaneous rate coder is shown to closely match the spike-rates recorded from P-type primary afferents in weakly electric fish. In particular, the coder is a predictor of the peristimulus time histogram (PSTH). When tested against in vitro cortical pyramidal neuron recordings, the instantaneous spike-rate approximates DC step inputs, matching both the average spike-rate and the time-to-first-spike (a simple temporal code). Overall, the instantaneous rate coder relates optimal, energy-constrained encoding to the concepts of rate-coding and temporal-coding, suggesting a possible unifying principle of neural encoding of sensory signals.     

Timing Precision in Population Coding of Natural Scenes in the Early Visual System

The timing of spiking activity across neurons is a fundamental aspect of the neural population code. Individual neurons in the retina, thalamus, and cortex can have very precise and repeatable responses but exhibit degraded temporal precision in response to suboptimal stimuli. To investigate the functional implications for neural populations in natural conditions, we recorded in vivo the simultaneous responses, to movies of natural scenes, of multiple thalamic neurons likely converging to a common neuronal target in primary visual cortex. We show that the response of individual neurons is less precise at lower contrast, but that spike timing precision across neurons is relatively insensitive to global changes in visual contrast. Overall, spike timing precision within and across cells is on the order of 10 ms. Since closely timed spikes are more efficient in inducing a spike in downstream cortical neurons, and since fine temporal precision is necessary to represent the more slowly varying natural environment, we argue that preserving relative spike timing at a ~10-ms resolution is a crucial property of the neural code entering cortex.     

Population coding of stimulus location in rat somatosensory cortex.

This study explores the nature of population coding in sensory cortex by applying information theoretic analyses to neuron pairs recorded simultaneously from rat barrel cortex. We quantified the roles of individual spikes and spike patterns in encoding whisker stimulus location. 82%-85% of the total information was contained in the timing of individual spikes: first spike time was particularly crucial. Spike patterns within neurons accounted for the remaining 15%-18%. Neuron pairs located in the same barrel column coded redundantly, whereas pairs in neighboring barrel columns coded independently. The barrel cortical population code for stimulus location appears to be the time of single neurons' first poststimulus spikes-a fast, robust coding mechanism that does not rely on "synergy" in crossneuronal spike patterns.     

Membrane Potential Fluctuations Determine the Precision of Spike Timing and Synchronous Activity: A Model Study

It is much debated on what time scale information is encoded by neuronal spike activity. With a phenomenological model that transforms time-dependent membrane potential fluctuations into spike trains, we investigate constraints for the timing of spikes and for synchronous activity of neurons with common input. The model of spike generation has a variable threshold that depends on the time elapsed since the previous action potential and on the preceding membrane potential changes. To ensure that the model operates in a biologically meaningful range, the model was adjusted to fit the responses of a fly visual interneuron to motion stimuli. The dependence of spike timing on the membrane potential dynamics was analyzed. Fast membrane potential fluctuations are needed to trigger spikes with a high temporal precision. Slow fluctuations lead to spike activity with a rate about proportional to the membrane potential. Thus, for a given level of stochastic input, the frequency range of membrane potential fluctuations induced by a stimulus determines whether a neuron can use a rate code or a temporal code. The relationship between the steepness of membrane potential fluctuations and the timing of spikes has also implications for synchronous activity in neurons with common input. Fast membrane potential changes must be shared by the neurons to produce synchronous activity.     

Characteristics of activity of "fast" and "slow" Purkinje cells of the cerebellum

In the guinea pig cerebellar cortex, three types of Purkinje cells were identified according to the properties of complex spikes: fast, intermediate, and slow cells. Fast Purkinje cells have following properties as compared with slow Purkinje cells: (i) salient components with short intervals in complex impulses (on the average, five components with a period of about 2 ms versus two components with a period of about 4 ms); (ii) a short duration of simple spikes (in the average, 2.13 +/- 0.53 ms versus 3.9 +/- 0.65 ms) and a quick restoration of their amplitude after preceding simple spikes (in the mean, 2.83 +/- 0.75 ms versus 11.0 +/- 2.82 ms); and (iii) a more pronounced rebound in the auto-correlation histogram of simple spikes (3.09 +/- 2.12 versus 1.45 +/- 0.36) and a short-latency excitation of simple spikes after complex spikes (2.81 +/- 1.64 versus 1.26 +/- 0.52). A decrease of interspike intervals in simple spike activity of all Purkinje cells was revealed (5.25 +/- 2.71 ms versus 9.71 +/- 3.48 ms in activity fragments without complex spikes). It is supposed that the properties of complex spikes depend on the type of Purkinje cells and may be one of the basic factors determining the interactions between the inputs of climbing and parallel fibers in Purkinje cells.     

The temporal resolution of neural codes: does response latency have a unique role?

This article reviews the nature of the neural code in non-human primate cortex and assesses the potential for neurons to carry two or more signals simultaneously. Neurophysiological recordings from visual and motor systems indicate that the evidence for a role for precisely timed spikes relative to other spike times (ca. 1-10 ms resolution) is inconclusive. This indicates that the visual system does not carry a signal that identifies whether the responses were elicited when the stimulus was attended or not. Simulations show that the absence of such a signal reduces, but does not eliminate, the increased discrimination between stimuli that are attended compared with when the stimuli are unattended. The increased accuracy asymptotes with increased gain control, indicating limited benefit from increasing attention. The absence of a signal identifying the attentional state under which stimuli were viewed can produce the greatest discrimination between attended and unattended stimuli. Furthermore, the greatest reduction in discrimination errors occurs for a limited range of gain control, again indicating that attention effects are limited. By contrast to precisely timed patterns of spikes where the timing is relative to other spikes, response latency provides a fine temporal resolution signal (ca. 10 ms resolution) that carries information that is unavailable from coarse temporal response measures. Changes in response latency and changes in response magnitude can give rise to different predictions for the patterns of reaction times. The predictions are verified, and it is shown that the standard method for distinguishing executive and slave processes is only valid if the representations of interest, as evidenced by the neural code, are known. Overall, the data indicate that the signalling evident in neural signals is restricted to the spike count and the precise times of spikes relative to stimulus onset (response latency). These coding issues have implications for our understanding of cognitive models of attention and the roles of executive and slave systems.     

Characterization of Exocytotic Events From Single PC12 Cells: Amperometric Studies in Native PC12h, DA-Loaded PC12h and Bovine Adrenal Chromaffin Cells

Exocytotic events from rat pheochromocytoma (PC12) cells were characterized by amperometric analysis. For single-cell amperometric recordings, PC12h cells cultured onto poly-L-lysine corted glass-base dish were incubated with 1 mM dopamine (DA) for 60 min. Amperometric recordings, with a carbon fiber microelectrode (5 μm diameter), of catecholamine release from the individual cells were conducted under an inverted microscope at 25 ^∘C. To characterize a single exocytotic event that is detected as a single spike current, the spike number, spike parameters (rise time, middle width and area) and spike shape were analyzed. Exposure of DA-loaded PC12h cells to 60 mM KCl (1000 hps) for 5 min and for 4 s evoked a train of events with the event number of 114± 19 (spikes/response for 5 min) and 12± 3 (spikes/response for 15 s), respectively. We observed distinctive kinetics in the events (rise time = 0.83± 0.19 ms, middle width = 2.89± 0.62 ms, area = 62± 7.6 fC and the spikes with a “foot” = 15.4± 2.7% of total spikes). The number and mean height of the events were 3- to 4-fold higher than that in DA-unloaded cells, and the values of rise time and middle width in DA-loaded PC12h cells were approx. 5- and 10-fold less than those observed in cultured adrenal chromaffin cells. The successful application of amperometry to monitor DA released from secretory vesicles in DA-loaded PC12h cell suggest that this technique is applicable to characterize exocytotic events in neurons.     

Predictive Coding of Dynamical Variables in Balanced Spiking Networks

Two observations about the cortex have puzzled neuroscientists for a long time. First, neural responses are highly variable. Second, the level of excitation and inhibition received by each neuron is tightly balanced at all times. Here, we demonstrate that both properties are necessary consequences of neural networks that represent information efficiently in their spikes. We illustrate this insight with spiking networks that represent dynamical variables. Our approach is based on two assumptions: We assume that information about dynamical variables can be read out linearly from neural spike trains, and we assume that neurons only fire a spike if that improves the representation of the dynamical variables. Based on these assumptions, we derive a network of leaky integrate-and-fire neurons that is able to implement arbitrary linear dynamical systems. We show that the membrane voltage of the neurons is equivalent to a prediction error about a common population-level signal. Among other things, our approach allows us to construct an integrator network of spiking neurons that is robust against many perturbations. Most importantly, neural variability in our networks cannot be equated to noise. Despite exhibiting the same single unit properties as widely used population code models (e.g. tuning curves, Poisson distributed spike trains), balanced networks are orders of magnitudes more reliable. Our approach suggests that spikes do matter when considering how the brain computes, and that the reliability of cortical representations could have been strongly underestimated.     

Afterhyperpolarization improves spike programming through lowering threshold potentials and refractory periods mediated by voltage-gated sodium channels

Neurons program various patterns of sequential spikes as neural codes to guide animal behavior. Studies show that spike programming (capacity and timing precision) is influenced by inhibitory synaptic inputs and membrane afterhyperpolarization (AHP). Less is clear about how these inhibitory components regulate spike programming, which we investigated at the cortical neurons. Whole-cell current-clamp recording for action potentials and single channel recording for voltage-gated sodium channels (VGSC) were conducted at regular-spiking and fast-spiking neurons in the cortical slices. With quantifying the threshold potentials and refractory periods of sequential spikes, we found that fast-spiking neurons expressing AHP possess lower threshold potentials and shorter refractory periods, and the hyperpolarization pulse immediately after each of spikes lowers threshold potentials and shortens refractory periods at regular-spiking neurons. Moreover, the hyperpolarization pulses shorten the refractory periods for VGSC reactivation and threshold potentials for its sequential activation. Our data indicate that inhibitory components immediately after spikes, such as AHP and recurrent inhibition, improve spike capacity and timing precision via lowering the refractory periods and threshold potentials mediated by voltage-gated sodium channels.     

Cell responses to acoustic stimuli in the pterothoracic ganglion of two noctuoid moths

Summary The spike activity of various types of cell responses in the pterothoracic ganglion ofAscalapha odorata (Noctuidae) andEmpyreuma pugione (Arctiidae) was studied. Pure tones (16 kHz forA. odorata and 20 kHz forE. pugione, 45 ms pulses) were presented at a 1 Hz rate over 9 s and at intensities ranging from 25 to 95 dB SPL. The values of the latency period and the interspike intervals allowed us to describe the intensity-latency and intensity-response functions as well as the spike distribution during the responses, the latter being given by the instantaneous frequency, i.e., as the inverse value of the mean of the nine measurements of each interspike interval during the response time. Repeater (RA₁ and RA₂) is a type of cell response that shows a phasic-tonic spike distribution similar to that of the receptor cells (A₁ and A₂) (Fig. 3), but that differs from the latter in a longer (ca. 1.0 ms) latency period, a lower number of spikes per pulse, and a lower instantaneous frequency during the response time (Tables 1 and 2). Another repeater type of cell response (RA) differs from the receptors and the other two repeaters in the form of its intensity-latency function, having the widest dynamic range (from 40 to 50 dB), and exhibiting the highest maximal number of spikes per pulse of all the response types recorded (Fig. 2, Table 1). We recorded also strictly phasic responses (1 or 2 spikes per pulse), which are considered as pulse markers. Of these, one (PM₁ has a shorter latency period (ca. 10 ms) and higher sensitivity than the other (PM₂) (Fig. 4). Two other types of cell responses showed significant differences in their latency period and the number of spikes per pulse under binaural and monoaural stimulation and are assumed to be the consequence of binaural summation, one by inhibition (BSI) and the other by excitation (BSE) (Fig. 5); they also differ in the spike distribution during the response. For the other types of cell responses recorded we used names that reflect the form of their spike distribution: chopper, build, On-S, tonic, and suppression (Figs. 8–12). The spike distributions during the response time recorded in the pterothoracic ganglion of these two noctuoid moths are compared with the temporal patterns of discharge described in the auditory neurons of the first relay stations of birds and mammals. Our results suggest that in the auditory pathway of the two moth species there is divergence, which could facilitate the parallel processing of the sensory information, and convergence, that could play a role in the directional localization of the acoustic signals. The complexity of this central auditory processing in animals with only 2 receptors in each peripheral organ is considerable, and we discuss its possible biological meaning.     

Identifying temporal codes in spontaneously active sensory neurons

The manner in which information is encoded in neural signals is a major issue in Neuroscience. A common distinction is between rate codes, where information in neural responses is encoded as the number of spikes within a specified time frame (encoding window), and temporal codes, where the position of spikes within the encoding window carries some or all of the information about the stimulus. One test for the existence of a temporal code in neural responses is to add artificial time jitter to each spike in the response, and then assess whether or not information in the response has been degraded. If so, temporal encoding might be inferred, on the assumption that the jitter is small enough to alter the position, but not the number, of spikes within the encoding window. Here, the effects of artificial jitter on various spike train and information metrics were derived analytically, and this theory was validated using data from afferent neurons of the turtle vestibular and paddlefish electrosensory systems, and from model neurons. We demonstrate that the jitter procedure will degrade information content even when coding is known to be entirely by rate. For this and additional reasons, we conclude that the jitter procedure by itself is not sufficient to establish the presence of a temporal code.     

Coding with spike shapes and graded potentials in cortical networks

In cortical neurones, analogue dendritic potentials are thought to be encoded into patterns of digital spikes. According to this view, neuronal codes and computations are based on the temporal patterns of spikes: spike times, bursts or spike rates. Recently, we proposed an 'action potential waveform code' for cortical pyramidal neurones in which the spike shape carries information. Broader somatic action potentials are reliably produced in response to higher conductance input, allowing for four times more information transfer than spike times alone. This information is preserved during synaptic integration in a single neurone, as back-propagating action potentials of diverse shapes differentially shunt incoming postsynaptic potentials and so participate in the next round of spike generation. An open question has been whether the information in action potential waveforms can also survive axonal conduction and directly influence synaptic transmission to neighbouring neurones. Several new findings have now brought new light to this subject, showing cortical information processing that transcends the classical models.     

Determination of the precision of spike timing in the visual cortex of anaesthetised cats

Neuronal cortical spike trains contain precisely replicating patterns whose presence cannot be accounted for by chance production. A comparison of the number of triplets of spikes present two times with the number of doublets replicated three times in the same window duration gives a frequency-insensitive measure of this type of fine temporal organisation. By varying the tolerance with which such precisely replicating patterns are detected, one can evaluate the accuracy of spike timing in spike trains. In the sample of data here analysed, it was found that replicating patterns were best seen in the precision range 0.4–1.4 ms (a result evidently at variance with a simple ‘integrate and fire’ model of neurons). Surprisingly, the fine temporal structure of spike trains thus evidenced was stronger at relatively low firing rate discharges and was present in both the ‘spontaneous’ and ‘evoked’ responses.     

Rapid activation of the cardiac ryanodine receptor by submillisecond calcium stimuli

The local control concept of excitation-contraction coupling in the heart postulates that the activity of the sarcoplasmic reticulum ryanodine receptor channels (RyR) is controlled by Ca(2+) entry through adjoining sarcolemmal single dihydropyridine receptor channels (DHPRs). One unverified premise of this hypothesis is that the RyR must be fast enough to track the brief (<0.5 ms) Ca(2+) elevations accompanying single DHPR channel openings. To define the kinetic limits of effective trigger Ca(2+) signals, we recorded activity of single cardiac RyRs in lipid bilayers during rapid and transient increases in Ca(2+) generated by flash photolysis of DM-nitrophen. Application of such Ca(2+) spikes (amplitude approximately 10-30 microM, duration approximately 0.1-0.4 ms) resulted in activation of the RyRs with a probability that increased steeply (apparent Hill slope approximately 2.5) with spike amplitude. The time constants of RyR activation were 0.07-0.27 ms, decreasing with spike amplitude. To fit the rising portion of the open probability, a single exponential function had to be raised to a power n approximately 3. We show that these data could be adequately described with a gating scheme incorporating four sequential Ca(2+)-sensitive closed states between the resting and the first open states. These results provide evidence that brief Ca(2+) triggers are adequate to activate the RyR, and support the possibility that RyR channels are governed by single DHPR openings. They also provide evidence for the assumption that RyR activation requires binding of multiple Ca(2+) ions in accordance with the tetrameric organization of the channel protein.