The determinants of the onset dynamics of action potentials in a computational model

New methods for quantifying rapidity of action potential onset differentiate neuron types

Two new methods for quantifying the rapidity of action potential onset have lower relative standard deviations and better distinguish neuron cell types than current methods. Action potentials (APs) in most central mammalian neurons exhibit sharp onset dynamics. The main views explaining such an abrupt onset differ. Some studies suggest sharp onsets reflect cooperative sodium channels activation, while others suggest they reflect AP backpropagation from the axon initial segment. However, AP onset rapidity is defined subjectively in these studies, often using the slope at an arbitrary value on the phase plot. Thus, we proposed more systematic methods using the membrane potential's second-time derivative ([Formula: see text]) peak width. Here, the AP rapidity was measured for four different cortical and hippocampal neuron types using four quantification methods: the inverse of full-width at the half maximum of the [Formula: see text] peak (IFWd2), the inverse of half-width at the half maximum of the [Formula: see text] peak (IHWd2), the phase plot slope, and the error ratio method. The IFWd2 and IHWd2 methods show the smallest variation among neurons of the same type. Furthermore, the AP rapidity, using the [Formula: see text] peak width methods, significantly differentiates between different types of neurons, indicating that AP rapidity can be used to classify neuron types. The AP rapidity measured using the IFWd2 method was able to differentiate between all four neuron types analyzed. Therefore, the [Formula: see text] peak width methods provide another sensitive tool to investigate the mechanisms impacting the AP onset dynamics.

Brief Sensory Deprivation Triggers Cell Type-Specific Structural and Functional Plasticity in Olfactory Bulb Neurons

Can alterations in experience trigger different plastic modifications in neuronal structure and function, and if so, how do they integrate at the cellular level? To address this question, we interrogated circuitry in the mouse olfactory bulb responsible for the earliest steps in odor processing. We induced experience-dependent plasticity in mice of either sex by blocking one nostril for one day, a minimally invasive manipulation that leaves the sensory organ undamaged and is akin to the natural transient blockage suffered during common mild rhinal infections. We found that such brief sensory deprivation produced structural and functional plasticity in one highly specialized bulbar cell type: axon-bearing dopaminergic neurons in the glomerular layer. After 24 h naris occlusion, the axon initial segment (AIS) in bulbar dopaminergic neurons became significantly shorter, a structural modification that was also associated with a decrease in intrinsic excitability. These effects were specific to the AIS-positive dopaminergic subpopulation because no experience-dependent alterations in intrinsic excitability were observed in AIS-negative dopaminergic cells. Moreover, 24 h naris occlusion produced no structural changes at the AIS of bulbar excitatory neurons, mitral/tufted and external tufted cells, nor did it alter their intrinsic excitability. By targeting excitability in one specialized dopaminergic subpopulation, experience-dependent plasticity in early olfactory networks might act to fine-tune sensory processing in the face of continually fluctuating inputs.SIGNIFICANCE STATEMENT Sensory networks need to be plastic so they can adapt to changes in incoming stimuli. To see how cells in mouse olfactory circuits can change in response to sensory challenges, we blocked a nostril for just one day, a naturally relevant manipulation akin to the deprivation that occurs with a mild cold. We found that this brief deprivation induces forms of axonal and intrinsic functional plasticity in one specific olfactory bulb cell subtype: axon-bearing dopaminergic interneurons. In contrast, intrinsic properties of axon-lacking bulbar dopaminergic neurons and neighboring excitatory neurons remained unchanged. Within the same sensory circuits, specific cell types can therefore make distinct plastic changes in response to an ever-changing external landscape.

Distinct Heterosynaptic Plasticity in Fast Spiking and Non-Fast-Spiking Inhibitory Neurons in Rat Visual Cortex

Inhibition in neuronal networks of the neocortex serves a multitude of functions, such as balancing excitation and structuring neuronal activity in space and time. Plasticity of inhibition is mediated by changes at both inhibitory synapses, as well as excitatory synapses on inhibitory neurons. Using slices from visual cortex of young male rats, we describe a novel form of plasticity of excitatory synapses on inhibitory neurons, weight-dependent heterosynaptic plasticity. Recordings from connected pyramid-to-interneuron pairs confirm that postsynaptic activity alone can induce long-term changes at synapses that were not presynaptically active during the induction, i.e., heterosynaptic plasticity. Moreover, heterosynaptic changes can accompany homosynaptic plasticity induced in inhibitory neurons by conventional spike-timing-dependent plasticity protocols. In both fast-spiking (FS) and non-FS neurons, heterosynaptic changes were weight-dependent, because they correlated with initial paired-pulse ratio (PPR), indicative of initial strength of a synapse. Synapses with initially high PPR, indicative of low release probability ("weak" synapses), had the tendency to be potentiated, while synapses with low initial PPR ("strong" synapses) tended to depress or did not change. Interestingly, the net outcome of heterosynaptic changes was different in FS and non-FS neurons. FS neurons expressed balanced changes, with gross average (n = 142) not different from control. Non-FS neurons (n = 66) exhibited net potentiation. This difference could be because of higher initial PPR in the non-FS neurons. We propose that weight-dependent heterosynaptic plasticity may counteract runaway dynamics of excitatory inputs imposed by Hebbian-type learning rules and contribute to fine-tuning of distinct aspects of inhibitory function mediated by FS and non-FS neurons in neocortical networks.SIGNIFICANCE STATEMENT Dynamic balance of excitation and inhibition is fundamental for operation of neuronal networks. Fine-tuning of such balance requires synaptic plasticity. Knowledge about diverse forms of plasticity operating in excitatory and inhibitory neurons is necessary for understanding normal function and causes of dysfunction of the nervous system. Here we show that excitatory inputs to major archetypal classes of neocortical inhibitory neurons, fast-spiking (FS) and non-fast-spiking (non-FS), express a novel type of plasticity, weight-dependent heterosynaptic plasticity, which accompanies the induction of Hebbian-type changes. This novel form of plasticity may counteract runaway dynamics at excitatory synapses to inhibitory neurons imposed by Hebbian-type learning rules and contribute to fine-tuning of diverse aspects of inhibitory function mediated by FS and non-FS neurons in neocortical networks.

Embryonic and postnatal neurogenesis produce functionally distinct subclasses of dopaminergic neuron

Most neurogenesis in the mammalian brain is completed embryonically, but in certain areas the production of neurons continues throughout postnatal life. The functional properties of mature postnatally generated neurons often match those of their embryonically produced counterparts. However, we show here that in the olfactory bulb (OB), embryonic and postnatal neurogenesis produce functionally distinct subpopulations of dopaminergic (DA) neurons. We define two subclasses of OB DA neuron by the presence or absence of a key subcellular specialisation: the axon initial segment (AIS). Large AIS-positive axon-bearing DA neurons are exclusively produced during early embryonic stages, leaving small anaxonic AIS-negative cells as the only DA subtype generated via adult neurogenesis. These populations are functionally distinct: large DA cells are more excitable, yet display weaker and - for certain long-latency or inhibitory events - more broadly tuned responses to odorant stimuli. Embryonic and postnatal neurogenesis can therefore generate distinct neuronal subclasses, placing important constraints on the functional roles of adult-born neurons in sensory processing.

The basis of sharp spike onset in standard biophysical models

In most vertebrate neurons, spikes initiate in the axonal initial segment (AIS). When recorded in the soma, they have a surprisingly sharp onset, as if sodium (Na) channels opened abruptly. The main view stipulates that spikes initiate in a conventional manner at the distal end of the AIS, then progressively sharpen as they backpropagate to the soma. We examined the biophysical models used to substantiate this view, and we found that spikes do not initiate through a local axonal current loop that propagates along the axon, but through a global current loop encompassing the AIS and soma, which forms an electrical dipole. Therefore, the phenomenon is not adequately modeled as the backpropagation of an electrical wave along the axon, since the wavelength would be as large as the entire system. Instead, in these models, we found that spike initiation rather follows the critical resistive coupling model proposed recently, where the Na current entering the AIS is matched by the axial resistive current flowing to the soma. Besides demonstrating it by examining the balance of currents at spike initiation, we show that the observed increase in spike sharpness along the axon is artifactual and disappears when an appropriate measure of rapidness is used; instead, somatic onset rapidness can be predicted from spike shape at initiation site. Finally, we reproduce the phenomenon in a two-compartment model, showing that it does not rely on propagation. In these models, the sharp onset of somatic spikes is therefore not an artifact of observing spikes at the incorrect location, but rather the signature that spikes are initiated through a global soma-AIS current loop forming an electrical dipole.

Spike-Threshold Variability Originated from Separatrix-Crossing in Neuronal Dynamics

The threshold voltage for action potential generation is a key regulator of neuronal signal processing, yet the mechanism of its dynamic variation is still not well described. In this paper, we propose that threshold phenomena can be classified as parameter thresholds and state thresholds. Voltage thresholds which belong to the state threshold are determined by the 'general separatrix' in state space. We demonstrate that the separatrix generally exists in the state space of neuron models. The general form of separatrix was assumed as the function of both states and stimuli and the previously assumed threshold evolving equation versus time is naturally deduced from the separatrix. In terms of neuronal dynamics, the threshold voltage variation, which is affected by different stimuli, is determined by crossing the separatrix at different points in state space. We suggest that the separatrix-crossing mechanism in state space is the intrinsic dynamic mechanism for threshold voltages and post-stimulus threshold phenomena. These proposals are also systematically verified in example models, three of which have analytic separatrices and one is the classic Hodgkin-Huxley model. The separatrix-crossing framework provides an overview of the neuronal threshold and will facilitate understanding of the nature of threshold variability.

Modeling neural activity with cumulative damage distributions

Neurons transmit information as action potentials or spikes. Due to the inherent randomness of the inter-spike intervals (ISIs), probabilistic models are often used for their description. Cumulative damage (CD) distributions are a family of probabilistic models that has been widely considered for describing time-related cumulative processes. This family allows us to consider certain deterministic principles for modeling ISIs from a probabilistic viewpoint and to link its parameters to values with biological interpretation. The CD family includes the Birnbaum-Saunders and inverse Gaussian distributions, which possess distinctive properties and theoretical arguments useful for ISI description. We expand the use of CD distributions to the modeling of neural spiking behavior, mainly by testing the suitability of the Birnbaum-Saunders distribution, which has not been studied in the setting of neural activity. We validate this expansion with original experimental and simulated electrophysiological data.

Action potential initiation in a multi-compartmental model with cooperatively gating Na channels in the axon initial segment

Somatic action potentials (AP) of cortical pyramidal neurons have characteristically high onset-rapidness. The onset of the AP waveform is an indirect measure for the ability of a neuron to respond to temporally fast-changing stimuli. Theoretical studies on the pyramidal neuron response usually involves a canonical Hodgkin-Huxley (HH) type ion channel gating model, which assumes statistically independent gating of each individual channel. However, cooperative activity of ion channels are observed for various cell types, meaning that the activity (e.g. opening) of one channel triggers the activity (e.g. opening) of a certain fraction of its neighbors and hence, these groups of channels behave as a unit. In this study, we describe a multi-compartmental conductance-based model with cooperatively gating voltage-gated Na channels in the axon initial segment. Our model successfully reproduced the somatic sharp AP onsets of cortical pyramidal neurons. The onset latencies from the initiation site to the soma and the conduction velocities were also in agreement with the previous experimental studies.

Cortical Specializations Underlying Fast Computations

The time course of behaviorally relevant environmental events sets temporal constraints on neuronal processing. How does the mammalian brain make use of the increasingly complex networks of the neocortex, while making decisions and executing behavioral reactions within a reasonable time? The key parameter determining the speed of computations in neuronal networks is a time interval that neuronal ensembles need to process changes at their input and communicate results of this processing to downstream neurons. Theoretical analysis identified basic requirements for fast processing: use of neuronal populations for encoding, background activity, and fast onset dynamics of action potentials in neurons. Experimental evidence shows that populations of neocortical neurons fulfil these requirements. Indeed, they can change firing rate in response to input perturbations very quickly, within 1 to 3 ms, and encode high-frequency components of the input by phase-locking their spiking to frequencies up to 300 to 1000 Hz. This implies that time unit of computations by cortical ensembles is only few, 1 to 3 ms, which is considerably faster than the membrane time constant of individual neurons. The ability of cortical neuronal ensembles to communicate on a millisecond time scale allows for complex, multiple-step processing and precise coordination of neuronal activity in parallel processing streams, while keeping the speed of behavioral reactions within environmentally set temporal constraints.

Injection of fully-defined signal mixtures: a novel high-throughput tool to study neuronal encoding and computations

Understanding of how neurons transform fluctuations of membrane potential, reflecting input activity, into spike responses, which communicate the ultimate results of single-neuron computation, is one of the central challenges for cellular and computational neuroscience. To study this transformation under controlled conditions, previous work has used a signal immersed in noise paradigm where neurons are injected with a current consisting of fluctuating noise that mimics on-going synaptic activity and a systematic signal whose transmission is studied. One limitation of this established paradigm is that it is designed to examine the encoding of only one signal under a specific, repeated condition. As a result, characterizing how encoding depends on neuronal properties, signal parameters, and the interaction of multiple inputs is cumbersome. Here we introduce a novel fully-defined signal mixture paradigm, which allows us to overcome these problems. In this paradigm, current for injection is synthetized as a sum of artificial postsynaptic currents (PSCs) resulting from the activity of a large population of model presynaptic neurons. PSCs from any presynaptic neuron(s) can be now considered as "signal", while the sum of all other inputs is considered as "noise". This allows us to study the encoding of a large number of different signals in a single experiment, thus dramatically increasing the throughput of data acquisition. Using this novel paradigm, we characterize the detection of excitatory and inhibitory PSCs from neuronal spike responses over a wide range of amplitudes and firing-rates. We show, that for moderately-sized neuronal populations the detectability of individual inputs is higher for excitatory than for inhibitory inputs during the 2-5 ms following PSC onset, but becomes comparable after 7-8 ms. This transient imbalance of sensitivity in favor of excitation may enhance propagation of balanced signals through neuronal networks. Finally, we discuss several open questions that this novel high-throughput paradigm may address.

Sharpness of spike initiation in neurons explained by compartmentalization

In cortical neurons, spikes are initiated in the axon initial segment. Seen at the soma, they appear surprisingly sharp. A standard explanation is that the current coming from the axon becomes sharp as the spike is actively backpropagated to the soma. However, sharp initiation of spikes is also seen in the input–output properties of neurons, and not only in the somatic shape of spikes; for example, cortical neurons can transmit high frequency signals. An alternative hypothesis is that Na channels cooperate, but it is not currently supported by direct experimental evidence. I propose a simple explanation based on the compartmentalization of spike initiation. When Na channels are placed in the axon, the soma acts as a current sink for the Na current. I show that there is a critical distance to the soma above which an instability occurs, so that Na channels open abruptly rather than gradually as a function of somatic voltage.

Spike initiation determines how the combined inputs to a neuron are converted to an output. Since the pioneering work of Hodgkin and Huxley, it is known that spikes are generated by the opening of sodium channels with depolarization. According to this standard theory, these channels should open gradually when the membrane potential increases, but spikes measured at the soma appear to suddenly rise from rest. This apparent contradiction has triggered a controversy about the origin of spike “sharpness.” This study shows with biophysical modelling that if sodium channels are placed in the axon rather than in the soma, they open all at once when the somatic membrane potential exceeds a critical value. This work explains the sharpness of spike initiation and provides another demonstration that morphology plays a critical role in neural function.

Fast computations in cortical ensembles require rapid initiation of action potentials

The abilities of neuronal populations to encode rapidly varying stimuli and respond quickly to abrupt input changes are crucial for basic neuronal computations, such as coincidence detection, grouping by synchrony, and spike-timing-dependent plasticity, as well as for the processing speed of neuronal networks. Theoretical analyses have linked these abilities to the fast-onset dynamics of action potentials (APs). Using a combination of whole-cell recordings from rat neocortical neurons and computer simulations, we provide the first experimental evidence for this conjecture and prove its validity for the case of distal AP initiation in the axon initial segment (AIS), typical for cortical neurons. Neocortical neurons with fast-onset APs in the soma can phase-lock their population firing to signal frequencies up to ∼300-400 Hz and respond within 1-2 ms to subtle changes of input current. The ability to encode high frequencies and response speed were dramatically reduced when AP onset was slowed by experimental manipulations or was intrinsically slow due to immature AP generation mechanisms. Multicompartment conductance-based models reproducing the initiation of spikes in the AIS could encode high frequencies only if AP onset was fast at the initiation site (e.g., attributable to cooperative gating of a fraction of sodium channels) but not when fast onset of somatic AP was produced solely by backpropagation. We conclude that fast-onset dynamics is a genuine property of cortical AP generators. It enables fast computations in cortical circuits that are rich in recurrent connections both within each region and across the hierarchy of areas.

A small fraction of strongly cooperative sodium channels boosts neuronal encoding of high frequencies

Generation of action potentials (APs) is a crucial step in neuronal information processing. Existing biophysical models for AP generation almost universally assume that individual voltage-gated sodium channels operate statistically independently, and their avalanche-like opening that underlies AP generation is coordinated only through the transmembrane potential. However, biological ion channels of various types can exhibit strongly cooperative gating when clustered. Cooperative gating of sodium channels has been suggested to explain rapid onset dynamics and large threshold variability of APs in cortical neurons. It remains however unknown whether these characteristic properties of cortical APs can be reproduced if only a fraction of channels express cooperativity, and whether the presence of cooperative channels has an impact on encoding properties of neuronal populations. To address these questions we have constructed a conductance-based neuron model in which we continuously varied the size of a fraction [Formula: see text] of sodium channels expressing cooperativity and the strength of coupling between cooperative channels [Formula: see text]. We show that starting at a critical value of the coupling strength [Formula: see text], the activation curve of sodium channels develops a discontinuity at which opening of all coupled channels becomes an all-or-none event, leading to very rapid AP onsets. Models with a small fraction, [Formula: see text], of strongly cooperative channels generate APs with the most rapid onset dynamics. In this regime APs are triggered by simultaneous opening of the cooperative channel fraction and exhibit a pronounced biphasic waveform often observed in cortical neurons. We further show that presence of a small fraction of cooperative Na+ channels significantly improves the ability of neuronal populations to phase-lock their firing to high frequency input fluctuation. We conclude that presence of a small fraction of strongly coupled sodium channels can explain characteristic features of cortical APs and has a functional impact of enhancing the spike encoding of rapidly varying signals.

Dynamics of action potential initiation in the GABAergic thalamic reticular nucleus in vivo

Understanding the neural mechanisms of action potential generation is critical to establish the way neural circuits generate and coordinate activity. Accordingly, we investigated the dynamics of action potential initiation in the GABAergic thalamic reticular nucleus (TRN) using in vivo intracellular recordings in cats in order to preserve anatomically-intact axo-dendritic distributions and naturally-occurring spatiotemporal patterns of synaptic activity in this structure that regulates the thalamic relay to neocortex. We found a wide operational range of voltage thresholds for action potentials, mostly due to intrinsic voltage-gated conductances and not synaptic activity driven by network oscillations. Varying levels of synchronous synaptic inputs produced fast rates of membrane potential depolarization preceding the action potential onset that were associated with lower thresholds and increased excitability, consistent with TRN neurons performing as coincidence detectors. On the other hand the presence of action potentials preceding any given spike was associated with more depolarized thresholds. The phase-plane trajectory of the action potential showed somato-dendritic propagation, but no obvious axon initial segment component, prominent in other neuronal classes and allegedly responsible for the high onset speed. Overall, our results suggest that TRN neurons could flexibly integrate synaptic inputs to discharge action potentials over wide voltage ranges, and perform as coincidence detectors and temporal integrators, supported by a dynamic action potential threshold.