Identifying and Tracking Simulated Synaptic Inputs from Neuronal Firing: Insights from In Vitro Experiments

Accurately describing synaptic interactions between neurons and how interactions change over time are key challenges for systems neuroscience. Although intracellular electrophysiology is a powerful tool for studying synaptic integration and plasticity, it is limited by the small number of neurons that can be recorded simultaneously in vitro and by the technical difficulty of intracellular recording in vivo. One way around these difficulties may be to use large-scale extracellular recording of spike trains and apply statistical methods to model and infer functional connections between neurons. These techniques have the potential to reveal large-scale connectivity structure based on the spike timing alone. However, the interpretation of functional connectivity is often approximate, since only a small fraction of presynaptic inputs are typically observed. Here we use in vitro current injection in layer 2/3 pyramidal neurons to validate methods for inferring functional connectivity in a setting where input to the neuron is controlled. In experiments with partially-defined input, we inject a single simulated input with known amplitude on a background of fluctuating noise. In a fully-defined input paradigm, we then control the synaptic weights and timing of many simulated presynaptic neurons. By analyzing the firing of neurons in response to these artificial inputs, we ask 1) How does functional connectivity inferred from spikes relate to simulated synaptic input? and 2) What are the limitations of connectivity inference? We find that individual current-based synaptic inputs are detectable over a broad range of amplitudes and conditions. Detectability depends on input amplitude and output firing rate, and excitatory inputs are detected more readily than inhibitory. Moreover, as we model increasing numbers of presynaptic inputs, we are able to estimate connection strengths more accurately and detect the presence of connections more quickly. These results illustrate the possibilities and outline the limits of inferring synaptic input from spikes.     

Enhanced Sensitivity to Rapid Input Fluctuations by Nonlinear Threshold Dynamics in Neocortical Pyramidal Neurons

The way in which single neurons transform input into output spike trains has fundamental consequences for network coding. Theories and modeling studies based on standard Integrate-and-Fire models implicitly assume that, in response to increasingly strong inputs, neurons modify their coding strategy by progressively reducing their selective sensitivity to rapid input fluctuations. Combining mathematical modeling with in vitro experiments, we demonstrate that, in L5 pyramidal neurons, the firing threshold dynamics adaptively adjust the effective timescale of somatic integration in order to preserve sensitivity to rapid signals over a broad range of input statistics. For that, a new Generalized Integrate-and-Fire model featuring nonlinear firing threshold dynamics and conductance-based adaptation is introduced that outperforms state-of-the-art neuron models in predicting the spiking activity of neurons responding to a variety of in vivo-like fluctuating currents. Our model allows for efficient parameter extraction and can be analytically mapped to a Generalized Linear Model in which both the input filter—describing somatic integration—and the spike-history filter—accounting for spike-frequency adaptation—dynamically adapt to the input statistics, as experimentally observed. Overall, our results provide new insights on the computational role of different biophysical processes known to underlie adaptive coding in single neurons and support previous theoretical findings indicating that the nonlinear dynamics of the firing threshold due to Na⁺-channel inactivation regulate the sensitivity to rapid input fluctuations.     

Processing of behaviorally relevant temporal parameters of acoustic stimuli by single neurons in the superior olivary nucleus of the leopard frog

Summary Response characteristics of 130 single neurons in the superior olivary nucleus of the northern leopard frog (Rana pipiens pipiens) were examined to determine their selectivity to various behaviorally relevant temporal parameters [rise-fall time, duration, and amplitude modulation (AM) rate of acoustic signals. Response functions were constructed with respect to each of these variables. Neurons with different temporal firing patterns such as tonic, phasic or phasic-burst firing patterns, participated in time domain analysis in specific manners. Phasic neurons manifested preferences for signals with short rise-fall times, thus possessing low-pass response functions with respect to this stimulus parameter; conversely, tonic and phasic-burst units were non-selective and possessed all-pass response functions. A distinction between temporal firing patterns was also observed for duration coding. Whereas phasic units showed no change in the mean spike count with a change in stimulus duration (i.e., all-pass duration response functions), tonic and phasic-burst units gave higher mean spike counts with an increase in stimulus duration (i.e., primary-like high-pass response functions). Phasic units manifested greater response selectivity for AM rate than did tonic or phasic-burst units, and many phasic units were tuned to a narrow range of modulation rates (i.e., band-pass). The results suggest that SON neurons play an important role in the processing of complex acoustic patterns; they perform extensive computations on AM rate as well as other temporal parameters of complex sounds. Moreover, the response selectivities for rise-fall time, duration, and AM rate could often be shown to contribute to the differential responses to complex synthetic and natural sounds.Abbreviations SON superior olivary nucleus - DMN dorsal medullary nucleus - TS torus semicircularis - FTC frequency threshold curve - BF best excitatory frequency - PAM pulsatile amplitude modulation - SAM sinusoidal amplitude modulation - SQAM square-wave amplitude modulation - MTF modulation transfer function - PSTH peri-stimulus time histogram     

Offset response of the olfactory projection neurons in the moth antennal lobe

We investigated a population activity of central olfactory neurons after the termination of odor input. Olfactory response of projection neurons in the moth primary olfactory center was characterized using in vivo intracellular recording and staining techniques. The population activity changed rapidly to the different states after the stimulus offset. The response after stimulus offset represents information regarding odor identity. We analyzed the spatial distribution of offset-activated glomeruli in a virtual neuronal population that was reconstructed using accumulated individual recordings obtained from different specimens. The offset-activated glomeruli tended to be widely distributed, whereas the onset-activated glomeruli were relatively clustered. These results suggest the importance of lateral interaction in shaping the offset olfactory response.     

Frequency entrainment of squid axon membrane

Summary Sinusoidally varying stimulating currents were applied to space-clamped squid giant axon membranes in a double sucrose gap apparatus. Stimulus parameters varied were peak-to-peak current amplitude, frequency, and DC offset bias. In response to these stimuli, the membranes produced action potentials in varying patterns, according to variation of input stimulus parameters. For some stimulus parameters the output patterns were stable and obviously periodic with the periods being simple multiples of the input period; for other stimulus parameters no obvious periodicity was manifest in the output. The experimental results were compared with simulations using a computer model which was modified in several ways from the Hodgkin-Huxley model to make it more representative of our preparation. The model takes into account K⁺ accumulation in the periaxonal space, features of Na⁺ inactivation which are anomalous to the Hodgkin-Huxley model, sucrose gap hyperpolarization current, and membrane current noise. Many aspects of the experiments are successfully simulated but some are not, possibly because some very slow process present in the preparation is not included in the model.     

Context-dependent coding in single neurons

The linear-nonlinear cascade model (LN model) has proven very useful in representing a neural system’s encoding properties, but has proven less successful in reproducing the firing patterns of individual neurons whose behavior is strongly dependent on prior firing history. While the cell’s behavior can still usefully be considered as feature detection acting on a fluctuating input, some of the coding capacity of the cell is taken up by the increased firing rate due to a constant “driving” direct current (DC) stimulus. Furthermore, both the DC input and the post-spike refractory period generate regular firing, reducing the spike-timing entropy available for encoding time-varying fluctuations. In this paper, we address these issues, focusing on the example of motoneurons in which an afterhyperpolarization (AHP) current plays a dominant role regularizing firing behavior. We explore the accuracy and generalizability of several alternative models for single neurons under changes in DC and variance of the stimulus input. We use a motoneuron simulation to compare coding models in neurons with and without the AHP current. Finally, we quantify the tradeoff between instantaneously encoding information about fluctuations and about the DC.     

The Possible Role of Spike Patterns in Cortical Information Processing

When the same visual stimulus is presented across many trials, neurons in the visual cortex receive stimulus-related synaptic inputs that are reproducible across trials (S) and inputs that are not (N). The variability of spike trains recorded in the visual cortex and their apparent lack of spike-to-spike correlations beyond that implied by firing rate fluctuations, has been taken as evidence for a low S/N ratio. A recent re-analysis of in vivo cortical data revealed evidence for spike-to-spike correlations in the form of spike patterns. We examine neural dynamics at a higher S/N in order to determine what possible role spike patterns could play in cortical information processing. In vivo-like spike patterns were obtained in model simulations. Superpositions of multiple sinusoidal driving currents were especially effective in producing stable long-lasting patterns. By applying current pulses that were either short and strong or long and weak, neurons could be made to switch from one pattern to another. Cortical neurons with similar stimulus preferences are located near each other, have similar biophysical properties and receive a large number of common synaptic inputs. Hence, recordings of a single neuron across multiple trials are usually interpreted as the response of an ensemble of these neurons during one trial. In the presence of distinct spike patterns across trials there is ambiguity in what would be the corresponding ensemble, it could consist of the same spike pattern for each neuron or a set of patterns across neurons. We found that the spiking response of a neuron receiving these ensemble inputs was determined by the spike-pattern composition, which, in turn, could be modulated dynamically as a means for cortical information processing.     

Stochastically Gating Ion Channels Enable Patterned Spike Firing through Activity-Dependent Modulation of Spike Probability

The transformation of synaptic input into patterns of spike output is a fundamental operation that is determined by the particular complement of ion channels that a neuron expresses. Although it is well established that individual ion channel proteins make stochastic transitions between conducting and non-conducting states, most models of synaptic integration are deterministic, and relatively little is known about the functional consequences of interactions between stochastically gating ion channels. Here, we show that a model of stellate neurons from layer II of the medial entorhinal cortex implemented with either stochastic or deterministically gating ion channels can reproduce the resting membrane properties of stellate neurons, but only the stochastic version of the model can fully account for perithreshold membrane potential fluctuations and clustered patterns of spike output that are recorded from stellate neurons during depolarized states. We demonstrate that the stochastic model implements an example of a general mechanism for patterning of neuronal output through activity-dependent changes in the probability of spike firing. Unlike deterministic mechanisms that generate spike patterns through slow changes in the state of model parameters, this general stochastic mechanism does not require retention of information beyond the duration of a single spike and its associated afterhyperpolarization. Instead, clustered patterns of spikes emerge in the stochastic model of stellate neurons as a result of a transient increase in firing probability driven by activation of HCN channels during recovery from the spike afterhyperpolarization. Using this model, we infer conditions in which stochastic ion channel gating may influence firing patterns in vivo and predict consequences of modifications of HCN channel function for in vivo firing patterns.     

Adaptive Spike Threshold Enables Robust and Temporally Precise Neuronal Encoding

Neural processing rests on the intracellular transformation of information as synaptic inputs are translated into action potentials. This transformation is governed by the spike threshold, which depends on the history of the membrane potential on many temporal scales. While the adaptation of the threshold after spiking activity has been addressed before both theoretically and experimentally, it has only recently been demonstrated that the subthreshold membrane state also influences the effective spike threshold. The consequences for neural computation are not well understood yet. We address this question here using neural simulations and whole cell intracellular recordings in combination with information theoretic analysis. We show that an adaptive spike threshold leads to better stimulus discrimination for tight input correlations than would be achieved otherwise, independent from whether the stimulus is encoded in the rate or pattern of action potentials. The time scales of input selectivity are jointly governed by membrane and threshold dynamics. Encoding information using adaptive thresholds further ensures robust information transmission across cortical states i.e. decoding from different states is less state dependent in the adaptive threshold case, if the decoding is performed in reference to the timing of the population response. Results from in vitro neural recordings were consistent with simulations from adaptive threshold neurons. In summary, the adaptive spike threshold reduces information loss during intracellular information transfer, improves stimulus discriminability and ensures robust decoding across membrane states in a regime of highly correlated inputs, similar to those seen in sensory nuclei during the encoding of sensory information.     

Diversity of Intrinsic Frequency Encoding Patterns in Rat Cortical Neurons—Mechanisms and Possible Functions

Extracellular recordings of single neurons in primary and secondary somatosensory cortices of monkeys in vivo have shown that their firing rate can increase, decrease, or remain constant in different cells, as the external stimulus frequency increases. We observed similar intrinsic firing patterns (increasing, decreasing or constant) in rat somatosensory cortex in vitro, when stimulated with oscillatory input using conductance injection (dynamic clamp). The underlying mechanism of this observation is not obvious, and presents a challenge for mathematical modelling. We propose a simple principle for describing this phenomenon using a leaky integrate-and-fire model with sinusoidal input, an intrinsic oscillation and Poisson noise. Additional enhancement of the gain of encoding could be achieved by local network connections amongst diverse intrinsic response patterns. Our work sheds light on the possible cellular and network mechanisms underlying these opposing neuronal responses, which serve to enhance signal detection.     

Resonating vector strength: what happens when we vary the “probing” frequency while keeping the spike times fixed

The synchrony vector, whose length stands for the vector strength (VS), is a means to quantify the amount of periodicity in a neuronal response to a given periodic signal, say, the stimulus. One usually chooses the input angular frequency and evaluates the synchrony vector as a weighted sum of exponentials taken at given experimental spike times of the neuronal response in combination with the driving input frequency. Given the experimental spike times, we replace the stimulus frequency by a variable probing frequency, study the synchrony vector in dependence upon this probing frequency, i.e., as a function of the frequency as a real variable, and exhibit both mathematically and experimentally a resonance behavior once the variable frequency is in the neighborhood of the stimulus frequency. Furthermore, a “resonating” VS is shown to be quite useful since one need not know the external frequency but can simply stick to the given spike times and analyze the ensuing resonance as the frequency varies, for example, to determine at the same time a “best” frequency and the corresponding VS. Finally, it is straightforward to determine the corresponding phase originating from, say, a delay as well.     

Activity-dependent enhancement in the reliability of correlated spike timings in cultured cortical neurons

To study the use-dependent modification of activity in neural networks, we investigated the spike timing by simultaneously recording activity at multiple sites in a network of cultured cortical neurons. We used dynamical analysis to study the temporal structure of spike trains and the activity-dependent changes in the reliability and reproducibility of spike patterns evoked by a stimulus. We also used cross-correlation analysis to evaluate the interactions of neuron pairs. Our main conclusions are that even when no obvious change in spike numbers can be seen, use-dependent modification occurs, either enhancing or reducing in the reliability and reproducibility of spike trains evoked by a stimulus, and the fine temporal structure of stimulus-evoked spike trains and interactions between neurons are also modified by tetanic stimulation. Received: 25 February 1998 / Accepted in revised form: 24 August 1998     

M-channels modulate the intrinsic excitability and synaptic responses of layer 2/3 pyramidal neurons in auditory cortex

Neurons in the auditory cortex are believed to utilize temporal patterns of neural activity to accurately process auditory information but the intrinsic neuronal mechanism underlying the control of auditory neural activity is not known. The slowly activating, persistent K⁺ channel, also called M-channel that belongs to the Kv7 family, is already known to be important in regulating subthreshold neural excitability and synaptic summation in neocortical and hippocampal pyramidal neurons. However, its functional role in the primary auditory cortex (A1) has never been characterized. In this study, we investigated the roles of M-channels on neuronal excitability, short-term plasticity, and synaptic summation of A1 layer 2/3 regular spiking pyramidal neurons with whole-cell current-clamp recordings in vitro. We found that blocking M-channels with a selective M-channel blocker, XE991, significantly increased neural excitability of A1 layer 2/3 pyramidal neurons. Furthermore, M-channels controled synaptic responses of intralaminar-evoked excitatory postsynaptic potentials (EPSPs); XE991 significantly increased EPSP amplitude, decreased the rate of short-term depression, and increased the synaptic summation. These results suggest that M-channels are involved in controlling spike output patterns and synaptic responses of A1 layer 2/3 pyramidal neurons, which would have important implications in auditory information processing.     

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.     

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.     

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.     

Spike-Threshold Adaptation Predicted by Membrane Potential Dynamics In Vivo

Neurons encode information in sequences of spikes, which are triggered when their membrane potential crosses a threshold. In vivo, the spiking threshold displays large variability suggesting that threshold dynamics have a profound influence on how the combined input of a neuron is encoded in the spiking. Threshold variability could be explained by adaptation to the membrane potential. However, it could also be the case that most threshold variability reflects noise and processes other than threshold adaptation. Here, we investigated threshold variation in auditory neurons responses recorded in vivo in barn owls. We found that spike threshold is quantitatively predicted by a model in which the threshold adapts, tracking the membrane potential at a short timescale. As a result, in these neurons, slow voltage fluctuations do not contribute to spiking because they are filtered by threshold adaptation. More importantly, these neurons can only respond to input spikes arriving together on a millisecond timescale. These results demonstrate that fast adaptation to the membrane potential captures spike threshold variability in vivo.     

Receptive field properties of neurons in the electrosensory lateral line lobe of the weakly electric fish, <Emphasis Type="Italic">Gnathonemus petersii</Emphasis>

The receptive field of a sensory neuron is known as that region in sensory space where a stimulus will alter the response of the neuron. We determined the spatial dimensions and the shape of receptive fields of electrosensitive neurons in the medial zone of the electrosensory lateral line lobe of the African weakly electric fish, Gnathonemus petersii, by using single cell recordings. The medial zone receives input from sensory cells which encode the stimulus amplitude. We analysed the receptive fields of 71 neurons. The size and shape of the receptive fields were determined as a function of spike rate and first spike latency and showed differences for the two analysis methods used. Spatial diameters ranged from 2 to 36 mm (spike rate) and from 2.45 to 14.12 mm (first spike latency). Some of the receptive fields were simple consisting only of one uniform centre, whereas most receptive fields showed a complex and antagonistic centre-surround organisation. Several units had a very complex structure with multiple centres and surrounding-areas. While receptive field size did not correlate with peripheral receptor location, the complexity of the receptive fields increased from rostral to caudal along the fish's body.     

Dynamics of cockroach ocellar neurons

The incremental responses from the second-order neurons of the ocellus of the cockroach, Periplaneta americana, have been measured. The stimulus was a white-noise-modulated light with various mean illuminances. The kernels, obtained by cross-correlating the white-noise input against the resulting response, provided a measure of incremental sensitivity as well as of response dynamics. We found that the incremental sensitivity of the second-order neurons was an exact Weber-Fechner function; white-noise-evoked responses from second-order neurons were linear; the dynamics of second-order neurons remain unchanged over a mean illuminance range of 4 log units; the small nonlinearity in the response of the second-order neuron was a simple amplitude compression; and the correlation between the white-noise input and spike discharges of the second-order neurons produced a first-order kernel similar to that of the cell's slow potential. We conclude that signal processing in the cockroach ocellus is simple but different from that in other visual systems, including vertebrate retinas and insect compound eyes, in which the system's dynamics depend on the mean illuminance.     

Processing of sensory signals by a non-spiking neuron in the leech

The non-spiking neurons 151 are present as bilateral pairs in each midbody ganglion of the leech nervous system and they are electrically coupled to several motorneurons. Intracellular recordings were used to investigate how these neurons process input from the mechanosensory P neurons in isolated ganglia. Induction of spike trains (15 Hz) in single P cells evoked responses that combined depolarizing and hyperpolarizing phases in cells 151. The phasic depolarizations, transmitted through spiking interneurons, reversed at around -20 mV. The hyperpolarization had two components, both reversing at around -65 mV, and which were inhibited by strychnine (10 micromol l(-1)). The faster component was transmitted through spiking interneurons and the slower component through a direct P-151 interaction. Short trains (<400 ms) of P cell spikes (15 Hz) evoked the phasic depolarizations superimposed on the hyperpolarization, while long spike trains (>500 ms) produced a succession of depolarizations that masked the hyperpolarizing phase. The amplitude and duration of the hyperpolarization reached their maximum at the initial spikes in a train, while the depolarizations persisted throughout the duration of the stimulus train. Both phases of the response were relatively unaffected by the spike frequency (5-25 Hz). The non-spiking neurons 151 processed the sensory signals in the temporal rather than in the amplitude domain.