Spike latency and jitter of neuronal membrane patches with stochastic Hodgkin-Huxley channels

Ion channel stochasticity can influence the voltage dynamics of neuronal membrane, with stronger effects for smaller patches of membrane because of the correspondingly smaller number of channels. We examine this question with respect to first spike statistics in response to a periodic input of membrane patches including stochastic Hodgkin-Huxley channels, comparing these responses to spontaneous firing. Without noise, firing threshold of the model depends on frequency—a sinusoidal stimulus is subthreshold for low and high frequencies and suprathreshold for intermediate frequencies. When channel noise is added, a stimulus in the lower range of subthreshold frequencies can influence spike output, while high subthreshold frequencies remain subthreshold. Both input frequency and channel noise strength influence spike timing. Specifically, spike latency and jitter have distinct minima as a function of input frequency, showing a resonance like behavior. With either no input, or low frequency subthreshold input, or input in the low or high suprathreshold frequency range, channel noise reduces latency and jitter, with the strongest impact for the lowest input frequencies. In contrast, for an intermediate range of suprathreshold frequencies, where an optimal input gives a minimum latency, the noise effect reverses, and spike latency and jitter increase with channel noise. Thus, a resonant minimum of the spike response as a function of frequency becomes more pronounced with less noise. Spike latency and jitter also depend on the initial phase of the input, resulting in minimal latencies at an optimal phase, and depend on the membrane time constant, with a longer time constant broadening frequency tuning for minimal latency and jitter. Taken together, these results suggest how stochasticity of ion channels may influence spike timing and thus coding for neurons with functionally localized concentrations of channels, such as in “hot spots” of dendrites, spines or axons.     

Stimulus sampling as an exploration mechanism for fast reinforcement learning

Reinforcement learning in neural networks requires a mechanism for exploring new network states in response to a single, nonspecific reward signal. Existing models have introduced synaptic or neuronal noise to drive this exploration. However, those types of noise tend to almost average out—precluding or significantly hindering learning —when coding in neuronal populations or by mean firing rates is considered. Furthermore, careful tuning is required to find the elusive balance between the often conflicting demands of speed and reliability of learning. Here we show that there is in fact no need to rely on intrinsic noise. Instead, ongoing synaptic plasticity triggered by the naturally occurring online sampling of a stimulus out of an entire stimulus set produces enough fluctuations in the synaptic efficacies for successful learning. By combining stimulus sampling with reward attenuation, we demonstrate that a simple Hebbian-like learning rule yields the performance that is very close to that of primates on visuomotor association tasks. In contrast, learning rules based on intrinsic noise (node and weight perturbation) are markedly slower. Furthermore, the performance advantage of our approach persists for more complex tasks and network architectures. We suggest that stimulus sampling and reward attenuation are two key components of a framework by which any single-cell supervised learning rule can be converted into a reinforcement learning rule for networks without requiring any intrinsic noise source. This work was supported by the Swiss National Science Foundation grant K-32K0-118084.     

P3 latency jitter assessed using 2 techniques. I. Simulated data and surface recordings in normal subjects

Latency variability measurement using cross-correlational techniques has the drawback of alignment to background noise not related to ERP activity. We compared latency jitter estimation in simulated and real P3 recordings using Woody's algorithm and a non-cross-correlational technique, the maximum likelihood technique (MLT). Simulated ERPs (with introduced latency jitter) were generated using either a 1/2 cycle 2 Hz sine wave or an averaged P3 ERP with 1 of 3 added noise types in 5 signal to noise ratios (SNRs): (i) white noise; (ii) a 10 Hz sine wave; (iii) a 7.5 Hz sine wave. Jitter measurement accuracy was assessed using mean square error (MSE) for 1 iteration of the Woody method and each of 4 iterations of the MLT. Lowest MSEs occurred for higher SNRs and 1 iteration of the MLT. The MLT and Woody method were applied to P3 ERPs of 13 subjects with SNRs greater than 0.4. P3 latency jitter was significantly lower for the MLT. Latency jitter (both methods) did not differ between homologous electrodes and was highest in posterior electrodes. In the latency corrected ERP data of subjects with persistent alpha activity periodic components occurred in the Woody corrected average (not seen in the conventional or the MLT corrected averages). Our data indicate that the MLT is the more accurate method for determining latency jitter.     

The modeling and simulation of visuospatial working memory

Camperi and Wang (Comput Neurosci 5:383–405, 1998) presented a network model for working memory that combines intrinsic cellular bistability with the recurrent network architecture of the neocortex. While Fall and Rinzel (Comput Neurosci 20:97–107, 2006) replaced this intrinsic bistability with a biological mechanism-Ca²⁺ release subsystem. In this study, we aim to further expand the above work. We integrate the traditional firing-rate network with Ca²⁺ subsystem-induced bistability, amend the synaptic weights and suggest that Ca²⁺ concentration only increase the efficacy of synaptic input but has nothing to do with the external input for the transient cue. We found that our network model maintained the persistent activity in response to a brief transient stimulus like that of the previous two models and the working memory performance was resistant to noise and distraction stimulus if Ca²⁺ subsystem was tuned to be bistable.     

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.     

An intracellular Ca2+ subsystem as a biologically plausible source of intrinsic conditional bistability in a network model of working memory

We have developed a firing rate network model for working memory that combines Mexican-hat-like synaptic coupling with intrinsic or cellular dynamics that are conditionally bistable. While our approach is in the spirit of Camperi and Wang (1998) we include a specific and plausible mechanism for the cellular bistability. Modulatory neurotransmitters are known to activate second messenger signaling systems, and our model includes an intracellular Ca²⁺ handling subsystem whose dynamics depend upon the level of the second messenger inositol 1,4,5 trisphosphate (IP3). This Ca²⁺ subsystem endows individual units with conditional intrinsic bistability for a range of IP3. The full “hybrid” network sustains IP3-dependent persistent (“bump”) activity in response to a brief transient stimulus. The bump response in our hybrid model, like that of Camperi-Wang, is resistant to noise – its position does not drift with time. Action Editor: Upinder Bhalla     

A Model of Visuospatial Working Memory in Prefrontal Cortex: Recurrent Network and Cellular Bistability

We report a computer simulation of the visuospatial delayed-response experiments of Funahashi et al. (1989), using a firing-rate model that combines intrinsic cellular bistability with the recurrent local network architecture of the neocortex. In our model, the visuospatial working memory is stored in the form of a continuum of network activity profiles that coexist with a spontaneous activity state. These neuronal firing patterns provide a population code for the cue position in a graded manner. We show that neuronal persistent activity and tuning curves of delay-period activity (memory fields) can be generated by an excitatory feedback circuit and recurrent synaptic inhibition. However, if the memory fields are constructed solely by network mechanisms, noise may induce a random drift over time in the encoded cue position, so that the working memory storage becomes unreliable. Furthermore, a distraction stimulus presented during the delay period produces a systematic shift in the encoded cue position. We found that the working memory performance can be rendered robust against noise and distraction stimuli if single neurons are endowed with cellular bistability (presumably due to intrinsic ion channel mechanisms) that is conditional and realized only with sustained synaptic inputs from the recurrent network. We discuss how cellular bistability at the single cell level may be detected by analysis of spike trains recorded during delay-period activity and how local modulation of intrinsic cell properties and/or synaptic transmission can alter the memory fields of individual neurons in the prefrontal cortex.     

ERPs to stimuli requiring response production and inhibition: effects of age,probability and visual noise

Sixty-six normal adults ranging in age from 20 to 85 years were presented with stimuli containing explicit instructions to initiate or to inhibit a motor response (the words ‘push’ or ‘wait’). In one task, the effect of stimulus probability was investigated by varying probability between 0.25 and 0.75 for both Go and No-go stimuli. In another task, the effect of visual noise was investigated by degrading the stimuli with ampersands on half of the trials. Regression analysis was used to examine the effects of age on P3 amplitude and latency for each stimulus type. The effects of stimulus variables on P3, independent of age, were examined by standardizing each subject's data to those expected for a 20 year old.P3 latency to all stimuli and RT to Go stimuli increased with age. The latency of P3s to No-go stimuli was less sensitive to age than Go stimuli. P3 amplitude at Cz and Pz (but not Fz) diminished with age. P3s to Go stimuli were maximal at Pz and earlier than P3s to No-go stimuli. P3s to No-go stimuli were maximal at Cz. These differences between Go and No-go stimuli remained true under visual noise and probability manipulations. Visual noise prolonged the latency of Go and No-go P3. Less probable Go and No-go stimuli elicited larger and later P3s than more probable stimuli. Decreasing the probability of the No-go stimulus enhanced its central distribution.     

Cross-intensity functions and the estimate of spike-time jitter

Correlation measures are important tools for the analysis of simultaneously recorded spike trains. A well-known measure with probabilistic interpretation is the cross-intensity function (CIF), which is an estimate of the conditional probability that a neuron spikes as a function of the time lag to spikes in another neuron. The non-commutative nature of the CIF is particularly useful when different neuron classes are studied that can be distinguished based on their anatomy or physiology. Here we explore the utility of the CIF for estimating spike-time jitter in synaptic interactions between neuron pairs of connected classes. When applied to spike train pairs from sleeping songbirds, we are able to distinguish fast synaptic interactions mediated primarily by AMPA receptors from slower interactions mediated by NMDA receptors. We also find that spike jitter increases with the time lag between spikes, reflecting the accumulation of noise in neural activity sequences, such as in synfire chains. In conclusion, we demonstrate some new utility of the CIF as a spike-train measure.     

Noise Normalizes Firing Output of Mouse Lateral Geniculate Nucleus Neurons

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

Synaptic limitations to contrast coding in the retina of the blowfly Calliphora

We investigate the effects of synaptic transmission on early visual processing by examining the passage of signals from photoreceptors to second order neurons (LMCS). We concentrate on the roles played by three properties of synaptic transmission: (1) the shape of the characteristic curve, relating pre- and postsynaptic signal amplitudes, (2) the dynamics of synaptic transmission and (3) the noise introduced during transmission. The characteristic curve is sigmoidal and follows a simple model of synaptic transmission (Appendix) in which transmitter release rises exponentially with presynaptic potential. According to this model a presynaptic depolarization of 1.50-1.86 mV produces an e-fold increase in postsynaptic conductance. The characteristic curve generates a sigmoidal relation between postsynaptic (LMC) response amplitude and stimulus contrast. The shape and slope of the characteristic curve is unaffected by the state of light adaptation. Retinal antagonism adjusts the characteristic curve to keep it centred on the mean level of receptor response generated by the background. Thus the photoreceptor synapses operate in the mid-region of the curve, where the slope or gain is highest and equals approximately 6. The dynamics of transmission of a signal from photoreceptor to second-order neuron approximates to the sum of two processes with exponential time courses. A momentary receptor depolarization generates a postsynaptic hyperpolarization of time constant 0.5-1.0 ms, followed by a slower and weaker depolarization. Light adaptation increases the relative amplitude of the depolarizing process and reduces its time constant from 80 ms to 1.5 ms. The hyperpolarizing process is too rapid to bandlimit receptor signals. The noise introduced during the passage of the signal from receptor to second-order neuron is measured by comparing signal:noise ratios and noise power spectra in the two cell types. Under daylight conditions from 50 to 70% of the total noise power is generated by events associated with the transmission of photoreceptor signals and the generation of LMC responses. According to the exponential model of transmitter release, the effects of synaptic noise are minimized when synaptic gain is maximized. Moreover, both retinal antagonism and the sigmoidal shape of the characteristic curve promote synaptic gain. We conclude that retinal antagonism and nonlinear synaptic amplification act in concert to protect receptor signals from contamination by synaptic noise. This action may explain the widespread occurrence of these processes in early visual processing.     

Theory of Threshold Fluctuations in Nerves: I. Relationships between Electrical Noise and Fluctuations in Axon Firing

Relations describing threshold fluctuation phenomena in nerves are derived by calculating the approximate response of the Hodgkin-Huxley (HH) axon to electrical noise. We use FitzHugh's reduced phase space approximation and describe the dynamics of a noisy nerve by a two-dimensional brownian motion. The theory predicts the functional form and parametric dependence of the relation between probability of firing and stimulus strength. Expressions are also obtained for the firing probability as a function of stimulus duration and for the distribution of latency times as a function of stimulus strength.     

The location of olfactory receptor sites. Inferences from latency measurements.

Excitatory responses recorded from vertebrate olfactory sensory neurons are characterized by long latencies compared with those from other sensory receptors. Explanations which assume free access of the stimuli to receptor molecules presumably located on the olfactory cilia necessarily imply an intrinsic delay in the transduction mechanism. In contrast, the possibility of restricted or delayed access due to diffusion of the stimulus to molecular receptors located on the dendritic know or proximal portions of the cilia suggests transduction processes having time courses similar to those in other sensory systems. We show that the threshold stimulus concentrations and the latency of the excitatory response of the salamander can be predicted primarily on the basis of a diffusional delay and that the receptor molecules are well below the surface of the mucus. Examination of response latencies for other species reported in the literature support the generality of diffusional delay. The predicted location of molecular receptor sites is largely insensitive to assumptions based on the mode of clearance of the stimuli. Additional access restrictions are discussed but are shown to generate qualitatively different latency functions than does diffusion, suggesting that they exert only minor influences on latency and threshold characteristics.     

Response of hippocampal synapses to natural stimulation patterns

We have studied the synaptic responses in hippocampal slices to stimulus patterns derived from in vivo recordings of place cell firing in a behaving rodent. We find that synaptic strength is strongly modulated during the presentation of these natural stimulus trains, varying 2-fold or more because of short-term plasticity. This modulation of synaptic strength is precise and deterministic, because the pattern of synaptic response amplitudes is nearly identical from one presentation of the train to the next. The mechanism of synaptic modulation is primarily a change in release probability rather than a change in the size of the elementary postsynaptic response. In addition, natural stimulus trains are effective in inducing long-term potentiation (LTP). We conclude that short-term synaptic plasticity--facilitation, augmentation, and depression--plays a prominent role in normal synaptic function.     

Spike-based synaptic plasticity and the emergence of direction selective simple cells: simulation results

Direction selectivity (DS) of simple cells in the primary visual cortex was recently suggested to arise from short-term synaptic depression in thalamocortical afferents (Chance F, Nelson S, Abbott L (1998), J. Neuroscience 18(12): 4785–4799). In the model, two groups of afferents with spatially displaced receptive fields project through either depressing and non-depressing synapses onto the V1 cell. The degree of synaptic depression determines the temporal phase advance of the response to drifting gratings. We show that the spatial displacement and the appropriate degree of synaptic depression required for DS can develop within an unbiased input scenario by means of temporally asymmetric spike-timing dependent plasticity (STDP) which modifies both the synaptic strength and the degree of synaptic depression. Moving stimuli of random velocities and directions break any initial receptive field symmetry and produce DS. Frequency tuning curves and subthreshold membrane potentials akin to those measured for non-directional simple cells are thereby changed into those measured for directional cells. If STDP is such that down-regulation dominates up-regulation the overall synaptic strength adapts in a self-organizing way such that eventually the postsynaptic response for the non-preferred direction becomes subthreshold. To prevent unlearning of the acquired DS by randomly changing stimulus directions an additional learning threshold is necessary. To further protect the development of the simple cell properties against noise in the stimulus, asynchronous and irregular synaptic inputs are required.     

Predictive features of persistent activity emergence in regular spiking and intrinsic bursting model neurons

Proper functioning of working memory involves the expression of stimulus-selective persistent activity in pyramidal neurons of the prefrontal cortex (PFC), which refers to neural activity that persists for seconds beyond the end of the stimulus. The mechanisms which PFC pyramidal neurons use to discriminate between preferred vs. neutral inputs at the cellular level are largely unknown. Moreover, the presence of pyramidal cell subtypes with different firing patterns, such as regular spiking and intrinsic bursting, raises the question as to what their distinct role might be in persistent firing in the PFC. Here, we use a compartmental modeling approach to search for discriminatory features in the properties of incoming stimuli to a PFC pyramidal neuron and/or its response that signal which of these stimuli will result in persistent activity emergence. Furthermore, we use our modeling approach to study cell-type specific differences in persistent activity properties, via implementing a regular spiking (RS) and an intrinsic bursting (IB) model neuron. We identify synaptic location within the basal dendrites as a feature of stimulus selectivity. Specifically, persistent activity-inducing stimuli consist of activated synapses that are located more distally from the soma compared to non-inducing stimuli, in both model cells. In addition, the action potential (AP) latency and the first few inter-spike-intervals of the neuronal response can be used to reliably detect inducing vs. non-inducing inputs, suggesting a potential mechanism by which downstream neurons can rapidly decode the upcoming emergence of persistent activity. While the two model neurons did not differ in the coding features of persistent activity emergence, the properties of persistent activity, such as the firing pattern and the duration of temporally-restricted persistent activity were distinct. Collectively, our results pinpoint to specific features of the neuronal response to a given stimulus that code for its ability to induce persistent activity and predict differential roles of RS and IB neurons in persistent activity expression.     

P3 latency jitter assessed using 2 techniques. II. Surface and sphenoidal recordings in subjects with focal epilepsy

We compared the latency variability in auditory P3s of 13 subjects with unilateral temporal lobe epilepsy (TLE) to that of normal controls. We predicted that increased latency jitter would occur in TLE subjects, particularly on the epileptic side. ERPs were recorded from scalp and sphenoidal sites relative to a balanced non-cephalic reference. Signal-to-noise ratios (SNRs) were calculated for each subject. Data were excluded if SNRs fell below 0.4. P3 latency jitter was estimated using 2 methods: Woody's algorithm and the maximum likelihood technique (MLT), a novel method of jitter assessment.SNRs were significantly higher in controls and were maximal posteriorly for both groups. P3 peak amplitude was significantly smaller in TLE subjects at temporal sites. Latency jitter (MLT method) was greatest in posterior sites and mirrored the jitter profiles of controls. Latency jitter was significantly higher in TLE subjects in bilateral frontal and temporal sites, but was not higher on the side of the focus and could not be attributed to lower SNRs. The increased bilateral latency jitter in these patients may be related to effects of anticonvulsants or the more extensive nature of the underlying epileptic disorder.     

A field test of the audibility of urban versus rural songs in mountain chickadees

Anthropogenic noise can mask avian vocalizations, and several urban‐dwelling species adjust frequency or amplitude of vocalizations in ways that appear to compensate for increased noise levels. Playback studies have investigated whether receivers differentiate between signals produced by rural and urban males, but it is difficult to determine whether differential response to stimulus reflects differences in audibility versus perceived differences in male signals/condition that result from urban settlement. Here, we performed paired‐playback trials to determine whether mountain chickadees (Poecile gambeli) differentiate urban versus rural songs when both stimuli were broadcast within noise. For each playback, stimuli were played in short bouts starting at a low signal‐to‐noise ratio and increasing in relative amplitude with each successive bout. If the primary function of adjusted urban songs is propagation in noise, we hypothesized that focal males would respond sooner to urban versus rural playbacks (detect at lower signal‐to‐noise ratios). If urban songs solely encode information about the male's condition (such as increased aggression), then we predicted only a differential aggressive response to playbacks once detected. If urban songs both increase propagation and embed information on male condition, we predicted a combination of both response types. We found no difference in latency to first response in urban versus rural songs, but some evidence for differential aggression to playback dependent on both stimulus type (urban vs. rural) and local ambient noise levels; focal males in noisy (urban) sites responded aggressively to both stimulus types, whereas focal males in quiet (rural) sites responded more aggressively to urban than to rural stimuli. This context‐dependent discrimination may be the result of increased aggression in urban habitats, improved communication in noisy habitats by urban signallers and receivers, or some combination of the two.