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

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

Learning of Precise Spike Times with Homeostatic Membrane Potential Dependent Synaptic Plasticity

Precise spatio-temporal patterns of neuronal action potentials underly e.g. sensory representations and control of muscle activities. However, it is not known how the synaptic efficacies in the neuronal networks of the brain adapt such that they can reliably generate spikes at specific points in time. Existing activity-dependent plasticity rules like Spike-Timing-Dependent Plasticity are agnostic to the goal of learning spike times. On the other hand, the existing formal and supervised learning algorithms perform a temporally precise comparison of projected activity with the target, but there is no known biologically plausible implementation of this comparison. Here, we propose a simple and local unsupervised synaptic plasticity mechanism that is derived from the requirement of a balanced membrane potential. Since the relevant signal for synaptic change is the postsynaptic voltage rather than spike times, we call the plasticity rule Membrane Potential Dependent Plasticity (MPDP). Combining our plasticity mechanism with spike after-hyperpolarization causes a sensitivity of synaptic change to pre- and postsynaptic spike times which can reproduce Hebbian spike timing dependent plasticity for inhibitory synapses as was found in experiments. In addition, the sensitivity of MPDP to the time course of the voltage when generating a spike allows MPDP to distinguish between weak (spurious) and strong (teacher) spikes, which therefore provides a neuronal basis for the comparison of actual and target activity. For spatio-temporal input spike patterns our conceptually simple plasticity rule achieves a surprisingly high storage capacity for spike associations. The sensitivity of the MPDP to the subthreshold membrane potential during training allows robust memory retrieval after learning even in the presence of activity corrupted by noise. We propose that MPDP represents a biophysically plausible mechanism to learn temporal target activity patterns.     

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.     

Regulation of spike timing in visual cortical circuits

A train of action potentials (a spike train) can carry information in both the average firing rate and the pattern of spikes in the train. But can such a spike-pattern code be supported by cortical circuits? Neurons in vitro produce a spike pattern in response to the injection of a fluctuating current. However, cortical neurons in vivo are modulated by local oscillatory neuronal activity and by top-down inputs. In a cortical circuit, precise spike patterns thus reflect the interaction between internally generated activity and sensory information encoded by input spike trains. We review the evidence for precise and reliable spike timing in the cortex and discuss its computational role.     

Pre & postsynaptic tuning of action potential timing by spontaneous GABAergic activity

Frequency and timing of action potential discharge are key elements for coding and transfer of information between neurons. The nature and location of the synaptic contacts, the biophysical parameters of the receptor-operated channels and their kinetics of activation are major determinants of the firing behaviour of each individual neuron. Ultimately the intrinsic excitability of each neuron determines the input-output function. Here we evaluate the influence of spontaneous GABAergic synaptic activity on the timing of action potentials in Layer 2/3 pyramidal neurones in acute brain slices from the somatosensory cortex of young rats. Somatic dynamic current injection to mimic synaptic input events was employed, together with a simple computational model that reproduce subthreshold membrane properties. Besides the well-documented control of neuronal excitability, spontaneous background GABAergic activity has a major detrimental effect on spike timing. In fact, GABA(A) receptors tune the relationship between the excitability and fidelity of pyramidal neurons via a postsynaptic (the reversal potential for GABA(A) activity) and a presynaptic (the frequency of spontaneous activity) mechanism. GABAergic activity can decrease or increase the excitability of pyramidal neurones, depending on the difference between the reversal potential for GABA(A) receptors and the threshold for action potential. In contrast, spike time jitter can only be increased proportionally to the difference between these two membrane potentials. Changes in excitability by background GABAergic activity can therefore only be associated with deterioration of the reliability of spike timing.     

A computational framework for cortical learning

Recent physiological findings have revealed that long-term adaptation of the synaptic strengths between cortical pyramidal neurons depends on the temporal order of presynaptic and postsynaptic spikes, which is called spike-timing-dependent plasticity (STDP) or temporally asymmetric Hebbian (TAH) learning. Here I prove by analytical means that a physiologically plausible variant of STDP adapts synaptic strengths such that the presynaptic spikes predict the postsynaptic spikes with minimal error. This prediction error model of STDP implies a mechanism for cortical memory: cortical tissue learns temporal spike patterns if these spike patterns are repeatedly elicited in a set of pyramidal neurons. The trained network finishes these patterns if their beginnings are presented, thereby recalling the memory. Implementations of the proposed algorithms may be useful for applications in voice recognition and computer vision.     

Studying spike trains using a van Rossum metric with a synapse-like filter

Spike trains are unreliable. For example, in the primary sensory areas, spike patterns and precise spike times will vary between responses to the same stimulus. Nonetheless, information about sensory inputs is communicated in the form of spike trains. A challenge in understanding spike trains is to assess the significance of individual spikes in encoding information. One approach is to define a spike train metric, allowing a distance to be calculated between pairs of spike trains. In a good metric, this distance will depend on the information the spike trains encode. This method has been used previously to calculate the timescale over which the precision of spike times is significant. Here, a new metric is constructed based on a simple model of synaptic conductances which includes binding site depletion. Including binding site depletion in the metric means that a given individual spike has a smaller effect on the distance if it occurs soon after other spikes. The metric proves effective at classifying neuronal responses by stimuli in the sample data set of electro-physiological recordings from the primary auditory area of the zebra finch fore-brain. This shows that this is an effective metric for these spike trains suggesting that in these spike trains the significance of a spike is modulated by its proximity to previous spikes. This modulation is a putative information-coding property of spike trains.     

Consequences of Converting Graded to Action Potentials upon Neural Information Coding and Energy Efficiency

Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na⁺ and K⁺ channels, with generator potential and graded potential models lacking voltage-gated Na⁺ channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na⁺ channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a ‘footprint’ in the generator potential that obscures incoming signals. These three processes reduce information rates by ∼50% in generator potentials, to ∼3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation.     

Direction of action potential propagation influences calcium increases in distal dendrites of the cricket giant interneurons

To understand the relationship between the propagation direction of action potentials and dendritic Ca(2+) elevation, simultaneous measurements of intracellular Ca(2+) concentration ([Ca(2+)](i)) and intradendritic membrane potential were performed in the wind-sensitive giant interneurons of the cricket. The dendritic Ca(2+) transients induced by synaptically-evoked action potentials had larger amplitudes than those induced by backpropagating spikes evoked by antidromic stimulation. The amplitude of the [Ca(2+)](i) changes induced by antidromic stimuli combined with subthreshold synaptic stimulation was not different from that of the Ca(2+) increases evoked by the backpropagating spikes alone. This result means that the synaptically activated Ca(2+) release from intracellular stores does not contribute to enhancement of Ca(2+) elevation induced by backpropagating spikes. On the other hand, the synaptically evoked action potentials were also increased at distal dendrites in which the Ca(2+) elevation was enhanced. When the dendritic and axonal spikes were simultaneously recorded, the delay between dendritic spike and ascending axonal spike depended upon which side of the cercal nerves was stimulated. Further, dual intracellular recording at different dendritic branches illustrated that the dendritic spike at the branch arborizing on the stimulated side preceded the spike recorded at the other side of the dendrite. These results suggest that the spike-initiation site shifts depending on the location of the activated postsynaptic site. It is proposed that the difference of spike propagation manner could change the action potential waveform at the distal dendrite, and could produce synaptic activity-dependent Ca(2+) dynamics in the giant interneurons.     

Network variability limits stimulus-evoked spike timing precision in retinal ganglion cells

Visual, auditory, somatosensory, and olfactory stimuli generate temporally precise patterns of action potentials (spikes). It is unclear, however, how the precision of spike generation relates to the pattern and variability of synaptic input elicited by physiological stimuli. We determined how synaptic conductances evoked by light stimuli that activate the rod bipolar pathway control spike generation in three identified types of mouse retinal ganglion cells (RGCs). The relative amplitude, timing, and impact of excitatory and inhibitory input differed dramatically between On and Off RGCs. Spikes evoked by repeated somatic injection of identical light-evoked synaptic conductances were more temporally precise than those evoked by light. However, the precision of spikes evoked by conductances that varied from trial to trial was similar to that of light-evoked spikes. Thus, the rod bipolar pathway modulates different RGCs via unique combinations of synaptic input, and RGC temporal variability reflects variability in the input this circuit provides.     

神经元放电阈值的可变性及其意义

神经元能够将不同时空模式的突触输入转化为时序精确的动作电位输出，这种灵活、可靠的信息编码方式是神经集群在动态环境或特定任务下产生所需活动模式的重要基础。动作电位的产生遵循全或无规律，只有当细胞膜电压达到放电阈值时，神经元才产生动作电位。放电阈值在细胞内和细胞间具有高度可变性，具体动态依赖于刺激输入和放电历史。特别是，放电阈值对动作电位起始前的膜电压变化十分敏感，这种状态依赖性产生的生物物理根源包括Na⁺失活和K⁺激活。在绝大多数神经元中，动作电位的触发位置是轴突起始端，这个位置处的阈值可变性是决定神经元对时空输入转化规律的关键因素。但是，电生理实验中动作电位的记录位置却通常是胞体或近端树突，此处的阈值可变性高于轴突起始端，而其产生的重要根源是轴突动作电位的反向传播。基于胞体测量的相关研究显示，放电阈值动态能够增强神经元的时间编码、特征选择、增益调控和同时侦测能力。本文首先介绍放电阈值的概念及量化方法，然后详细梳理近年来国内外关于放电阈值可变性及产生根源的研究进展，在此基础上归纳总结放电阈值可变性对神经元编码的重要性，最后对未来放电阈值的研究方向进行展望。     

Intracellular electrophysiology of mammalian peptidergic neurons in rat hypothalamic slices

The magnocellular neuropeptidergic cells (MNCs) of the paraventricular and supraoptic nuclei have been a model for biochemical and physiological studies of peptidergic neurons in the mammalian brain, but nearly all the electrophysiological studies of these vasopressinergic and oxytocinergic neuroendocrine cells are based on extracellular recordings. This paper reviews recent literature on electrophysiological properties of neurons in the magnocellular nuclei in which the rat in vitro slice preparation and intracellular recording were used. Spontaneously occurring action potentials and synaptic potentials (excitatory and inhibitory) have been observed in hypothalamic slices. The spike patterns have included slow and irregular firing, short rapid bursts of inactivating spikes, and slow phasic discharge with prolonged active and silent periods. Some studies have shown that increased osmolality causes neuronal firing, but this area is controversial. Intracellular injections of lucifer yellow have shown that some MNCs are dye-coupled and electron microscopic observations with the freeze-fracture technique have revealed occasional gap junctions, thus suggesting that some MNCs are electrotonically coupled. Both excitatory and inhibitory postsynaptic potentials have been evoked with extracellular stimulation. Therefore, action potentials, synaptic potentials, burst discharges, and probably electrotonic coupling have been found with intracellular recording in mammalian neuroendocrine cells. Future studies with intracellular recording and staining followed by immunohistochemical identification of cells should provide significant new information on the membrane physiology and synaptic pharmacology of vasopressinergic and oxytocinergic cells.     

The impact of short term synaptic depression and stochastic vesicle dynamics on neuronal variability

Neuronal variability plays a central role in neural coding and impacts the dynamics of neuronal networks. Unreliability of synaptic transmission is a major source of neural variability: synaptic neurotransmitter vesicles are released probabilistically in response to presynaptic action potentials and are recovered stochastically in time. The dynamics of this process of vesicle release and recovery interacts with variability in the arrival times of presynaptic spikes to shape the variability of the postsynaptic response. We use continuous time Markov chain methods to analyze a model of short term synaptic depression with stochastic vesicle dynamics coupled with three different models of presynaptic spiking: one model in which the timing of presynaptic action potentials are modeled as a Poisson process, one in which action potentials occur more regularly than a Poisson process (sub-Poisson) and one in which action potentials occur more irregularly (super-Poisson). We use this analysis to investigate how variability in a presynaptic spike train is transformed by short term depression and stochastic vesicle dynamics to determine the variability of the postsynaptic response. We find that sub-Poisson presynaptic spiking increases the average rate at which vesicles are released, that the number of vesicles released over a time window is more variable for smaller time windows than larger time windows and that fast presynaptic spiking gives rise to Poisson-like variability of the postsynaptic response even when presynaptic spike times are non-Poisson. Our results complement and extend previously reported theoretical results and provide possible explanations for some trends observed in recorded data.     

Balanced Excitatory and Inhibitory Synaptic Currents Promote Efficient Coding and Metabolic Efficiency

A balance between excitatory and inhibitory synaptic currents is thought to be important for several aspects of information processing in cortical neurons in vivo, including gain control, bandwidth and receptive field structure. These factors will affect the firing rate of cortical neurons and their reliability, with consequences for their information coding and energy consumption. Yet how balanced synaptic currents contribute to the coding efficiency and energy efficiency of cortical neurons remains unclear. We used single compartment computational models with stochastic voltage-gated ion channels to determine whether synaptic regimes that produce balanced excitatory and inhibitory currents have specific advantages over other input regimes. Specifically, we compared models with only excitatory synaptic inputs to those with equal excitatory and inhibitory conductances, and stronger inhibitory than excitatory conductances (i.e. approximately balanced synaptic currents). Using these models, we show that balanced synaptic currents evoke fewer spikes per second than excitatory inputs alone or equal excitatory and inhibitory conductances. However, spikes evoked by balanced synaptic inputs are more informative (bits/spike), so that spike trains evoked by all three regimes have similar information rates (bits/s). Consequently, because spikes dominate the energy consumption of our computational models, approximately balanced synaptic currents are also more energy efficient than other synaptic regimes. Thus, by producing fewer, more informative spikes approximately balanced synaptic currents in cortical neurons can promote both coding efficiency and energy efficiency.     

Integrative Synaptic Mechanisms in the Caudal Ganglion of the Crayfish

A study of activity recorded with intracellular micropipettes was undertaken in the caudal abdominal ganglion of the crayfish in order to gain information about central fiber to fiber synaptic mechanisms. This synaptic system has well developed integrative properties. Excitatory post-synaptic potentials can be graded, and synaptic potentials from different inputs can sum to initiate spike discharge. In most impaled units, the spike discharge fails to destroy the synaptic potential, thereby allowing sustained depolarization and multiple spike discharge following single pulse stimulation to an afferent input. Some units had characteristics which suggest a graded threshold for spike generation along the post-synaptic fiber membrane. Other impaled units responded to afferent stimulation with spike discharges of two distinct amplitudes. The smaller or "abortive" spikes in such units may represent non-invading activity in branches of the post-synaptic axon. On a few occasions one afferent input was shown to inhibit the spike discharge initiated by another presynaptic input.     

Axons Amplify Somatic Incomplete Spikes into Uniform Amplitudes in Mouse Cortical Pyramidal Neurons

Background

Action potentials are the essential unit of neuronal encoding. Somatic sequential spikes in the central nervous system appear various in amplitudes. To be effective neuronal codes, these spikes should be propagated to axonal terminals where they activate the synapses and drive postsynaptic neurons. It remains unclear whether these effective neuronal codes are based on spike timing orders and/or amplitudes.

Methodology/Principal Findings

We investigated this fundamental issue by simultaneously recording the axon versus soma of identical neurons and presynaptic vs. postsynaptic neurons in the cortical slices. The axons enable somatic spikes in low amplitude be enlarged, which activate synaptic transmission in consistent patterns. This facilitation in the propagation of sequential spikes through the axons is mechanistically founded by the short refractory periods, large currents and high opening probability of axonal voltage-gated sodium channels.

Conclusion/Significance

An amplification of somatic incomplete spikes into axonal complete ones makes sequential spikes to activate consistent synaptic transmission. Therefore, neuronal encoding is likely based on spike timing order, instead of graded analogues.     

Inhibitory postsynaptic potentials carry synchronized frequency information in active cortical networks

Temporal precision in spike timing is important in cortical function, interactions, and plasticity. We found that, during periods of recurrent network activity (UP states), cortical pyramidal cells in vivo and in vitro receive strong barrages of both excitatory and inhibitory postsynaptic potentials, with the inhibitory potentials showing much higher power at all frequencies above approximately 10 Hz and more synchrony between nearby neurons. Fast-spiking inhibitory interneurons discharged strongly in relation to higher-frequency oscillations in the field potential in vivo and possess membrane, synaptic, and action potential properties that are advantageous for transmission of higher-frequency activity. Intracellular injection of synaptic conductances having the characteristics of the recorded EPSPs and IPSPs reveal that IPSPs are important in controlling the timing and probability of action potential generation in pyramidal cells. Our results support the hypothesis that inhibitory networks are largely responsible for the dissemination of higher-frequency activity in cortex.     

Action potential generation by turtle cortical neurons. Dendritic and somatic spikes

Action potentials of neurons of the turtle general cortex and the pattern of their generation were studied by an intracellular recording method. Besides the complete action potential, the cells also generate partial spikes of varied amplitude which compose the complete action potential. The threshold of generation and the discrete amplitude of each partial spike are not strictly constant but they fluctuate gradually and spontaneously within certain limits without any change in membrane potential of the cell. Somatic and dendritic spikes are distinguished. The trigger zones of the latter are located at various distances from the soma. During orthodromic activation of cortical neurons dendritic spikes are generated consecutively and spread to the some electrotonically with a decrement. They are the immediate cause of generation of the somatic spike.M. V. Lomonovsov Moscow State University. Translated from Neirofiziologiya, Vol. 8, No. 3, pp. 237–242, May–June, 1976.     

Spike-timing dependent synaptic plasticity: a phenomenological framework

 In this paper a phenomenological model of spike-timing dependent synaptic plasticity (STDP) is developed that is based on a Volterra series-like expansion. Synaptic weight changes as a function of the relative timing of pre- and postsynaptic spikes are described by integral kernels that can easily be inferred from experimental data. The resulting weight dynamics can be stated in terms of statistical properties of pre- and postsynaptic spike trains. Generalizations to neurons that fire two different types of action potentials, such as cerebellar Purkinje cells where synaptic plasticity depends on correlations in two distinct presynaptic fibers, are discussed. We show that synaptic plasticity, together with strictly local bounds for the weights, can result in synaptic competition that is required for any form of pattern formation. This is illustrated by a concrete example where a single neuron equipped with STDP can selectively strengthen those synapses with presynaptic neurons that reliably deliver precisely timed spikes at the expense of other synapses which transmit spikes with a broad temporal distribution. Such a mechanism may be of vital importance for any neuronal system where information is coded in the timing of individual action potentials. Received: 23 January 2002 / Accepted: 28 March 2002 Correspondence to: W.M. Kistler (e-mail: kistler@anat.fgg.eur.nl Fax: +31 10 408 5459)     

三叉神经中脑核神经元膜的电学特性

用大鼠脑干脑片,给三叉神经中脑核79个神经元作了细胞内记录,测算了20个神经元膜的电学特性:静息电位-60.3±5.6mV;输入阻抗为10.5±5.4MΩ;时间常数1.3±0.5ms。电刺激可诱发动作电位,测算32个神经元的有关参数:阈电位-50—-55mV;波幅69.5±6.1mV;超射11.9±3.6mV;波宽0.8±0.2ms。TTX(0.3μmol/L)或无钠使之消失。通以长时程矩形波电流可引起200—250Hz的2—15个重复放电,但在通电停止前终止,TEA或4-AP可延长放电。膜电位-60—-55mV时在动作电位之后可看到阈下电位波动,它不受TTX的影响,无钙时消失,TEA或4-AP使波幅增大。静息电位去极化可使45个神经元中的40个发生外向整流作用,并被TEA,4-AP或无钙抑制,超极化则发生内向整流作用,Cs或无钠抑制之。灌流液中加入各种钾通道阻断药时神经元的稳态I-V曲线发生相应变化,提示I_(DR),l_A,I_(K(Ca))及I_Q可能都与静息时的膜电导有关。