Lateral dendritic shunt inhibition can regularize mitral cell spike patterning

Mitral cells, the principal output neurons of the olfactory bulb, receive direct synaptic activation from primary sensory neurons. Shunting inhibitory inputs delivered by granule cell interneurons onto mitral cell lateral dendrites, while poorly positioned to prevent spike initiation, are believed to influence spike timing and underlie coordinated field potential oscillations. We investigated this phenomenon in a reduced compartmental mitral cell model suitable for incorporation into network simulations. Lateral dendritic shunt conductances delayed spiking to a degree dependent on both their electrotonic distance and phase of onset. Moreover, when the afferent activation of mitral cells was loosely coordinated in time, recurrent inhibition significantly narrowed the distribution of mitral cell spike times, illustrating a tendency towards coordinated synchronous activity. However, if mitral cell activity was initially disorganized, recurrent inhibition actually increased the variance in spike timing. This result suggests an essential role for early mechanisms of temporal coordination in olfaction, such as sniffing and the initial synchronization of mitral cell intrinsic oscillations by periglomerular cell-mediated inhibition.     

Functional significance of the A-current

This work considers the response to simulated synaptic inputs of an excitable membrane model. The model is essentially of the Hodgkin-Huxley type, but contains an A-current in addition to sodium and delayed-rectifier potassium channels. The results were compared with previous simulations in which the stimulus was an injected current. These two types of stimuli give somewhat different results because synaptic stimuli directly change the membrane resistance, whereas injected current does not. The results of synaptic stimulation were similar to injected current in that very low frequencies of action potentials were elicited only where the stimulus was slightly above threshold. For most of the range of synaptic inputs that produced oscillatory behavior, the A-current had little effect on oscillation frequency. With synaptic stimuli as with injected current, the model membrane's spiking behavior does not begin immediately when an excitatory stimulus is imposed on a quiescent state. The delay before spiking is closely related to the inactivation time of the A-current. The synaptic results were different from the injected current results in that when substantial inhibition was present, the ability to produce very-low-frequency spiking was absent, even just above the excitatory threshold. The higher the degree of inhibition, the narrower the range of spike frequencies that could be elicited by excitation. At very high inhibition, no degree of excitation could elicit spiking.     

State transitions through inhibitory interneurons in a cortical network model

Inhibitory interneurons shape the spiking characteristics and computational properties of cortical networks. Interneuron subtypes can precisely regulate cortical function but the roles of interneuron subtypes for promoting different regimes of cortical activity remains unclear. Therefore, we investigated the impact of fast spiking and non-fast spiking interneuron subtypes on cortical activity using a network model with connectivity and synaptic properties constrained by experimental data. We found that network properties were more sensitive to modulation of the fast spiking population, with reductions of fast spiking excitability generating strong spike correlations and network oscillations. Paradoxically, reduced fast spiking excitability produced a reduction of global excitation-inhibition balance and features of an inhibition stabilised network, in which firing rates were driven by the activity of excitatory neurons within the network. Further analysis revealed that the synaptic interactions and biophysical features associated with fast spiking interneurons, in particular their rapid intrinsic response properties and short synaptic latency, enabled this state transition by enhancing gain within the excitatory population. Therefore, fast spiking interneurons may be uniquely positioned to control the strength of recurrent excitatory connectivity and the transition to an inhibition stabilised regime. Overall, our results suggest that interneuron subtypes can exert selective control over excitatory gain allowing for differential modulation of global network state.     

Gap Junctions Are Essential for Generating the Correlated Spike Activity of Neighboring Retinal Ganglion Cells

Neurons throughout the brain show spike activity that is temporally correlated to that expressed by their neighbors, yet the generating mechanism(s) remains unclear. In the retina, ganglion cells (GCs) show robust, concerted spiking that shapes the information transmitted to central targets. Here we report the synaptic circuits responsible for generating the different types of concerted spiking of GC neighbors in the mouse retina. The most precise concerted spiking was generated by reciprocal electrical coupling of GC neighbors via gap junctions, whereas indirect electrical coupling to a common cohort of amacrine cells generated the correlated activity with medium precision. In contrast, the correlated spiking with the lowest temporal precision was produced by shared synaptic inputs carrying photoreceptor noise. Overall, our results demonstrate that different synaptic circuits generate the discrete types of GC correlated activity. Moreover, our findings expand our understanding of the roles of gap junctions in the retina, showing that they are essential for generating all forms of concerted GC activity transmitted to central brain targets.     

Regulation of somatic firing dynamics by backpropagating dendritic spikes

Pyramidal cells of the apteronotid ELL have been shown to display a characteristic mechanism of burst discharge, which has been shown to play an important role in sensory coding. This form of bursting depends on a reciprocal dendro-somatic interaction, in which discharge of a somatic spike causes a dendritic spike, which in turn contributes a dendro-somatic current flow to create a depolarizing afterpotential (DAP) in the soma. We review here our recent work showing how the timing of this DAP influences the somatic firing dynamics, and how the degree of inactivation of dendritic Na⁺ currents can cause an increased delay between somatic and dendritic spikes. This ultimately allows the DAP to become more effective at increasing the excitability of the somatic spike generating mechanism. Further, this delay between dendritic and somatic spiking can be regulated by strongly hyperpolarizing GABA_B mediated dendritic inhibition, allowing the burst dynamics to fall under synaptic regulation. In contrast, a weaker, shunting inhibition due to GABA_A mediated dendritic inhibition can regulate the dendritic spike waveform to decrease the dendro-somatic current flow and the resulting DAP. We therefore show that the qualitative behaviour of an individual cell can depend on the degree of synaptic input, and the exact timing of events across the spatial extent of the neuron. Thus, our results serve to illustrate the complex dynamics that can be observed in cells with significant dendritic arborisation, a nearly ubiquitous adaptation amongst principal neurons.     

Effects of active versus passive dendritic membranes on the transfer properties of a simulated neuron

In a simulated neuron with a dendritic tree, the relative effects of active and passive dendritic membranes on transfer properties were studied. The simulations were performed by means of a digital computer. The computations calculated the changes in transmembrane voltages of many compartments over time as a function of other biophysical variables. These variables were synaptic input intensity, critical firing threshold, rate of leakage of current across the membrane, and rate of longitudinal current spread between compartments. For both passive and active dendrites, the transfer properties of the soma studied for different rates of longitudinal current spread. With low rates of current spread, graded changes in firing threshold produced correspondingly graded changes in output discharge. With high rates of current spread, the neuron became a bistable operator where spiking was enhanced if the threshold was below a certain level and suppressed if the threshold was above that level. Since alterations in firing threshold were shown to have the same effect on firing rate as alterations in synaptic input intensity, the neuron can be said to change from graded to contrast-enhancing in its response to stimuli of different intensities. The presence or absence of dendritic spiking was found to have a significant effect on the integrative properties of the simulated neuron. In particular, contrast enhancement was considerably more pronounced in neurons with passive than with active dendrites in that somatic spike rates reached a higher maximum when dendrites were passive. With active dendrites, a less intense input was needed to initiate somatic spiking than with passive dendrites because a distal dendritic spike could easily propagate by means of longitudinal current spread to the soma. Once somatic spiking was initiated, though, spike rates tended to be lower with active than with passive dendrites because the soma recovered more slowly from its post-spike refractory period if it was also influenced by refractory periods in the dendrites. The experiment of comparing neurons with active and passive dendrites was repeated at a different, higher value of synaptic input. The same differences in transfer properties between the active and passive cases emerged as before. Spiking patterns in neurons with active dendrites were also affected by the time distribution of synaptic inputs. In a previous study, inputs had been random over both space and time, varying about a predetermined mean, whereas in the present study, inputs were random over space but uniform over time. When inputs were made uniform over time, spiking became more difficult to initiate and the transition from graded to bistable response became less sharp.     

Spike timing precision of neuronal circuits

Spike timing is believed to be a key factor in sensory information encoding and computations performed by the neurons and neuronal circuits. However, the considerable noise and variability, arising from the inherently stochastic mechanisms that exist in the neurons and the synapses, degrade spike timing precision. Computational modeling can help decipher the mechanisms utilized by the neuronal circuits in order to regulate timing precision. In this paper, we utilize semi-analytical techniques, which were adapted from previously developed methods for electronic circuits, for the stochastic characterization of neuronal circuits. These techniques, which are orders of magnitude faster than traditional Monte Carlo type simulations, can be used to directly compute the spike timing jitter variance, power spectral densities, correlation functions, and other stochastic characterizations of neuronal circuit operation. We consider three distinct neuronal circuit motifs: Feedback inhibition, synaptic integration, and synaptic coupling. First, we show that both the spike timing precision and the energy efficiency of a spiking neuron are improved with feedback inhibition. We unveil the underlying mechanism through which this is achieved. Then, we demonstrate that a neuron can improve on the timing precision of its synaptic inputs, coming from multiple sources, via synaptic integration: The phase of the output spikes of the integrator neuron has the same variance as that of the sample average of the phases of its inputs. Finally, we reveal that weak synaptic coupling among neurons, in a fully connected network, enables them to behave like a single neuron with a larger membrane area, resulting in an improvement in the timing precision through cooperation.     

Computational simulation of the input-output relationship in hippocampal pyramidal cells

The precise mapping of how complex patterns of synaptic inputs are integrated into specific patterns of spiking output is an essential step in the characterization of the cellular basis of network dynamics and function. Relative to other principal neurons of the hippocampus, the electrophysiology of CA1 pyramidal cells has been extensively investigated. Yet, the precise input-output relationship is to date unknown even for this neuronal class. CA1 pyramidal neurons receive laminated excitatory inputs from three distinct pathways: recurrent CA1 collaterals on basal dendrites, CA3 Schaffer collaterals, mostly on oblique and proximal apical dendrites, and entorhinal perforant pathway on distal apical dendrites. We implemented detailed computer simulations of pyramidal cell electrophysiology based on three-dimensional anatomical reconstructions and compartmental models of available biophysical properties from the experimental literature. To investigate the effect of synaptic input on axosomatic firing, we stochastically distributed a realistic number of excitatory synapses in each of the three dendritic layers. We then recorded the spiking response to different stimulation patterns. For all dendritic layers, synchronous stimuli resulted in trains of spiking output and a linear relationship between input and output firing frequencies. In contrast, asynchronous stimuli evoked non-bursting spike patterns and the corresponding firing frequency input-output function was logarithmic. The regular/irregular nature of the input synaptic intervals was only reflected in the regularity of output inter-burst intervals in response to synchronous stimulation, and never affected firing frequency. Synaptic stimulations in the basal and proximal apical trees across individual neuronal morphologies yielded remarkably similar input-output relationships. Results were also robust with respect to the detailed distributions of dendritic and synaptic conductances within a plausible range constrained by experimental evidence. In contrast, the input-output relationship in response to distal apical stimuli showed dramatic differences from the other dendritic locations as well as among neurons, and was more sensible to the exact channel densities. Action Editor: Alain Destexhe     

Activity-dependent regulation of receptive field properties of cat area 17 by supervised Hebbian learning.

Most algorithms currently used to model synaptic plasticity in self-organizing cortical networks suppose that the change in synaptic efficacy is governed by the same structuring factor, i.e., the temporal correlation of activity between pre- and postsynaptic neurons. Functional predictions generated by such algorithms have been tested electrophysiologically in the visual cortex of anesthetized and paralyzed cats. Supervised learning procedures were applied at the cellular level to change receptive field (RF) properties during the time of recording of an individual functionally identified cell. The protocols were devised as cellular analogs of the plasticity of RF properties, which is normally expressed during a critical period of postnatal development. We summarize here evidence demonstrating that changes in covariance between afferent input and postsynaptic response imposed during extracellular and intracellular conditioning can acutely induce selective long-lasting up- and down-regulations of visual responses. The functional properties that could be modified in 40% of cells submitted to differential pairing protocols include ocular dominance, orientation selectivity and orientation preference, interocular orientation disparity, and the relative dominance of ON and OFF responses. Since changes in RF properties can be induced in the adult as well, our findings also suggest that similar activity-dependent processes may occur during development and during active phases of learning under the supervision of behavioral attention or contextual signals. Such potential for plasticity in primary visual cortical neurons suggests the existence of a hidden connectivity expressing a wider functional competence than the one revealed at the spiking level. In particular, in the spatial domain the sensory synaptic integration field is larger than the classical discharge field. It can be shaped by supervised learning and its subthreshold extent can be unmasked by the pharmacological blockade of intracortical inhibition.     

The neurochemical basis of recurrent inhibition in the reflex arch of the defensive reaction]

Mechanisms of habituation in the network of identified neurones were investigated in isolated preparation of central nervous system in the snail Helix. It has been found that intracellularly induced spike discharge in premotor command neurones decreases synaptic responses to repeated nerve stimulation in all recorded command neurones. Application of the neuropeptide FMRFamide elicits similar changes in the network. Taking into account that the investigated command neurones contain FMRFamide, as was shown immunochemically, it is possible to assume the existence of recurrent inhibition in the network underlying avoidance reactions. This recurrent inhibition causes habituation of the network output in the cases when the repeated stimuli do not evoke sensitization via activation of serotonergic cells.     

Conflicting effects of excitatory synaptic and electric coupling on the dynamics of square-wave bursters

Using two-cell and 50-cell networks of square-wave bursters, we studied how excitatory coupling of individual neurons affects the bursting output of the network. Our results show that the effects of synaptic excitation vs. electrical coupling are distinct. Increasing excitatory synaptic coupling generally increases burst duration. Electrical coupling also increases burst duration for low to moderate values, but at sufficiently strong values promotes a switch to highly synchronous bursts where further increases in electrical or synaptic coupling have a minimal effect on burst duration. These effects are largely mediated by spike synchrony, which is determined by the stability of the in-phase spiking solution during the burst. Even when both coupling mechanisms are strong, one form (in-phase or anti-phase) of spike synchrony will determine the burst dynamics, resulting in a sharp boundary in the space of the coupling parameters. This boundary exists in both two cell and network simulations. We use these results to interpret the effects of gap-junction blockers on the neuronal circuitry that underlies respiration.     

Synaptic conditions for auto-associative memory storage and pattern completion in Jensen et al.’s model of hippocampal area CA3

Jensen et al. (Learn Memory 3(2–3):243–256, 1996b) proposed an auto-associative memory model using an integrated short-term memory (STM) and long-term memory (LTM) spiking neural network. Their model requires that distinct pyramidal cells encoding different STM patterns are fired in different high-frequency gamma subcycles within each low-frequency theta oscillation. Auto-associative LTM is formed by modifying the recurrent synaptic efficacy between pyramidal cells. In order to store auto-associative LTM correctly, the recurrent synaptic efficacy must be bounded. The synaptic efficacy must be upper bounded to prevent re-firing of pyramidal cells in subsequent gamma subcycles. If cells encoding one memory item were to re-fire synchronously with other cells encoding another item in subsequent gamma subcycle, LTM stored via modifiable recurrent synapses would be corrupted. The synaptic efficacy must also be lower bounded so that memory pattern completion can be performed correctly. This paper uses the original model by Jensen et al. as the basis to illustrate the following points. Firstly, the importance of coordinated long-term memory (LTM) synaptic modification. Secondly, the use of a generic mathematical formulation (spiking response model) that can theoretically extend the results to other spiking network utilizing threshold-fire spiking neuron model. Thirdly, the interaction of long-term and short-term memory networks that possibly explains the asymmetric distribution of spike density in theta cycle through the merger of STM patterns with interaction of LTM network.     

Preserved Excitatory-Inhibitory Balance of Cortical Synaptic Inputs following Deprived Eye Stimulation after a Saturating Period of Monocular Deprivation in Rats

Monocular deprivation (MD) during development leads to a dramatic loss of responsiveness through the deprived eye in primary visual cortical neurons, and to degraded spatial vision (amblyopia) in all species tested so far, including rodents. Such loss of responsiveness is accompanied since the beginning by a decreased excitatory drive from the thalamo-cortical inputs. However, in the thalamorecipient layer 4, inhibitory interneurons are initially unaffected by MD and their synapses onto pyramidal cells potentiate. It remains controversial whether ocular dominance plasticity similarly or differentially affects the excitatory and inhibitory synaptic conductances driven by visual stimulation of the deprived eye and impinging onto visual cortical pyramids, after a saturating period of MD. To address this issue, we isolated visually-driven excitatory and inhibitory conductances by in vivo whole-cell recordings from layer 4 regular-spiking neurons in the primary visual cortex (V1) of juvenile rats. We found that a saturating period of MD comparably reduced visually–driven excitatory and inhibitory conductances driven by visual stimulation of the deprived eye. Also, the excitatory and inhibitory conductances underlying the synaptic responses driven by the ipsilateral, left open eye were similarly potentiated compared to controls. Multiunit recordings in layer 4 followed by spike sorting indicated that the suprathreshold loss of responsiveness and the MD-driven ocular preference shifts were similar for narrow spiking, putative inhibitory neurons and broad spiking, putative excitatory neurons. Thus, by the time the plastic response has reached a plateau, inhibitory circuits adjust to preserve the normal balance between excitation and inhibition in the cortical network of the main thalamorecipient layer.     

Direction selectivity of excitation and inhibition in simple cells of the cat primary visual cortex

Direction selectivity in simple cells of primary visual cortex, defined from their spike responses, cannot be predicted using linear models. It has been suggested that the shunting inhibition evoked by visual stimulation is responsible for the nonlinear component of direction selectivity. Cortical inhibition would suppress a neuron's firing when stimuli move in the nonpreferred direction, but would allow responses to stimuli in the preferred direction. Models of direction selectivity based solely on input from the lateral geniculate nucleus, however, propose that the nonlinear response is caused by spike threshold. By extracting excitatory and inhibitory components of synaptic inputs from intracellular records obtained in vivo, we demonstrate that excitation and inhibition are tuned for the same direction, but differ in relative timing. Further, membrane potential responses combine in a linear fashion. Spike threshold, however, quantitatively accounts for the nonlinear component of direction selectivity, amplifying the direction selectivity of spike output relative to that of synaptic inputs.     

Auditory Nerve Spike Generator Modeled as a Variable Attenuator Based on a Saddle Node on Invariant Circle Bifurcation

Mammalian inner hair cells transduce the sound waves amplified by the cochlear amplifier (CA) into a graded neurotransmitter release that activates channels on auditory nerve fibers (ANF). These synaptic channels then charge its dendritic spike generator. While the outer hair cells of the CA employ positive feedback, poising on Andronov-Hopf type instabilities which make them extremely sensitive to faint sounds and make CA output strongly nonlinear, the ANF appears to be based on different principles and a different type of dynamical instability. Its spike generator “digitizes” CA output into trains of action potentials and behaves as a linear filter, rate-coding sound intensity across a wide dynamic range. Here we model the spike generator as a 3 dimensional version of a saddle node on invariant circle (SNIC) bifurcation. The generic 2d SNIC increases its spike rate as the square root of the input current above its spiking threshold. We add negative feedback in the form of a low voltage-threshold potassium conductance that slows down the generator’s rate of increase of its spike rate. A Poisson random source simulates an inner hair cell, outputting a series of noisy periodic current pulses to the model ANF whose spikes phase lock to these pulses and have a linear frequency to current relation with a wide dynamic range. Also, the spike generator compartment has a cholinergic feedback connection from the olive and experiments show that such feedback is able to alter the amount of H conductance inside the generator compartment. We show that an olive able to decrease H would be able to shift the spike generator’s dynamic range to higher sound intensities. In a quiet environment by increasing H the olive would be able to make spike trains similar to those caused by synaptic input.     

The chronotron: a neuron that learns to fire temporally precise spike patterns

In many cases, neurons process information carried by the precise timings of spikes. Here we show how neurons can learn to generate specific temporally precise output spikes in response to input patterns of spikes having precise timings, thus processing and memorizing information that is entirely temporally coded, both as input and as output. We introduce two new supervised learning rules for spiking neurons with temporal coding of information (chronotrons), one that provides high memory capacity (E-learning), and one that has a higher biological plausibility (I-learning). With I-learning, the neuron learns to fire the target spike trains through synaptic changes that are proportional to the synaptic currents at the timings of real and target output spikes. We study these learning rules in computer simulations where we train integrate-and-fire neurons. Both learning rules allow neurons to fire at the desired timings, with sub-millisecond precision. We show how chronotrons can learn to classify their inputs, by firing identical, temporally precise spike trains for different inputs belonging to the same class. When the input is noisy, the classification also leads to noise reduction. We compute lower bounds for the memory capacity of chronotrons and explore the influence of various parameters on chronotrons' performance. The chronotrons can model neurons that encode information in the time of the first spike relative to the onset of salient stimuli or neurons in oscillatory networks that encode information in the phases of spikes relative to the background oscillation. Our results show that firing one spike per cycle optimizes memory capacity in neurons encoding information in the phase of firing relative to a background rhythm.     

Broad inhibition sharpens orientation selectivity by expanding input dynamic range in mouse simple cells

Orientation selectivity (OS) is an emergent property in the primary visual cortex (V1). How OS arises from synaptic circuits remains unsolved. Here, in vivo whole-cell recordings in the mouse V1 revealed that simple cells received broadly tuned excitation and even more broadly tuned inhibition. Excitation and inhibition shared a similar orientation preference and temporally overlapped substantially. Neuron modeling and dynamic-clamp recording further revealed that excitatory inputs alone would result in membrane potential responses with significantly attenuated selectivity, due to a saturating input-output function of the membrane filtering. Inhibition ameliorated the attenuation of excitatory selectivity by expanding the input dynamic range and caused additional sharpening of output responses beyond unselectively suppressing responses at all orientations. This "blur-sharpening" effect allows selectivity conveyed by excitatory inputs to be better expressed, which may be a general mechanism underlying the generation of feature-selective responses in the face of strong excitatory inputs that are weakly biased.     

Spectral analysis of input spike trains by spike-timing-dependent plasticity

Spike-timing-dependent plasticity (STDP) has been observed in many brain areas such as sensory cortices, where it is hypothesized to structure synaptic connections between neurons. Previous studies have demonstrated how STDP can capture spiking information at short timescales using specific input configurations, such as coincident spiking, spike patterns and oscillatory spike trains. However, the corresponding computation in the case of arbitrary input signals is still unclear. This paper provides an overarching picture of the algorithm inherent to STDP, tying together many previous results for commonly used models of pairwise STDP. For a single neuron with plastic excitatory synapses, we show how STDP performs a spectral analysis on the temporal cross-correlograms between its afferent spike trains. The postsynaptic responses and STDP learning window determine kernel functions that specify how the neuron "sees" the input correlations. We thus denote this unsupervised learning scheme as 'kernel spectral component analysis' (kSCA). In particular, the whole input correlation structure must be considered since all plastic synapses compete with each other. We find that kSCA is enhanced when weight-dependent STDP induces gradual synaptic competition. For a spiking neuron with a "linear" response and pairwise STDP alone, we find that kSCA resembles principal component analysis (PCA). However, plain STDP does not isolate correlation sources in general, e.g., when they are mixed among the input spike trains. In other words, it does not perform independent component analysis (ICA). Tuning the neuron to a single correlation source can be achieved when STDP is paired with a homeostatic mechanism that reinforces the competition between synaptic inputs. Our results suggest that neuronal networks equipped with STDP can process signals encoded in the transient spiking activity at the timescales of tens of milliseconds for usual STDP.     

Enhancement of spike-timing precision by autaptic transmission in neocortical inhibitory interneurons

In vivo studies suggest that precise firing of neurons is important for correct sensory representation. Principal neocortical neurons fire imprecisely when repeatedly activated by fixed sensory stimuli or current depolarizations. Here we show that in contrast to pyramidal neurons, firing in neocortical GABAergic fast-spiking (FS) interneurons is quite precise. FS interneurons are self-innervated by powerful GABAergic autaptic connections reliably activated after each spike, suggesting that autapses strongly regulate FS-cell spike timing. Indeed, blockade of autaptic transmission degraded temporal precision in multiple ways. Under these conditions, realistic dynamic-clamp hyperpolarizing autapses restored precision of spike timing, even in the presence of synaptic noise. Furthermore, firing precision was increased in pyramidal neurons by artificial GABAergic autaptic conductances, suggesting that tightly coupled synaptic feedback inhibition regulates spike timing in principal cells. Thus, well-timed inhibition, whether autaptic or synaptic, facilitates precise spike timing and promotes synchronized cortical network oscillations relevant to several behaviors.