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1.  Impact of Fast Sodium Channel Inactivation on Spike Threshold Dynamics and Synaptic Integration 
PLoS Computational Biology  2011;7(5):e1001129.
Neurons spike when their membrane potential exceeds a threshold value. In central neurons, the spike threshold is not constant but depends on the stimulation. Thus, input-output properties of neurons depend both on the effect of presynaptic spikes on the membrane potential and on the dynamics of the spike threshold. Among the possible mechanisms that may modulate the threshold, one strong candidate is Na channel inactivation, because it specifically impacts spike initiation without affecting the membrane potential. We collected voltage-clamp data from the literature and we found, based on a theoretical criterion, that the properties of Na inactivation could indeed cause substantial threshold variability by itself. By analyzing simple neuron models with fast Na inactivation (one channel subtype), we found that the spike threshold is correlated with the mean membrane potential and negatively correlated with the preceding depolarization slope, consistent with experiments. We then analyzed the impact of threshold dynamics on synaptic integration. The difference between the postsynaptic potential (PSP) and the dynamic threshold in response to a presynaptic spike defines an effective PSP. When the neuron is sufficiently depolarized, this effective PSP is briefer than the PSP. This mechanism regulates the temporal window of synaptic integration in an adaptive way. Finally, we discuss the role of other potential mechanisms. Distal spike initiation, channel noise and Na activation dynamics cannot account for the observed negative slope-threshold relationship, while adaptive conductances (e.g. K+) and Na inactivation can. We conclude that Na inactivation is a metabolically efficient mechanism to control the temporal resolution of synaptic integration.
Author Summary
Neurons spike when their combined inputs exceed a threshold value, but recent experimental findings have shown that this value also depends on the inputs. Thus, to understand how neurons respond to input spikes, it is important to know how inputs modify the spike threshold. Spikes are generated by sodium channels, which inactivate when the neuron is depolarized, raising the threshold for spike initiation. We found that inactivation properties of sodium channels could indeed cause substantial threshold variability in central neurons. We then analyzed in models the implications of this form of threshold modulation on neuronal function. We found that this mechanism makes neurons more sensitive to coincident spikes and provides them with an energetically efficient form of gain control.
doi:10.1371/journal.pcbi.1001129
PMCID: PMC3088652  PMID: 21573200
2.  Input-dependent subcellular localization of spike initiation between soma and axon at cortical pyramidal neurons 
Molecular Brain  2014;7:26.
Background
Action potentials can be initiated at various subcellular compartments, such as axonal hillock, soma and dendrite. Mechanisms and physiological impacts for this relocation remain elusive, which may rely on input signal patterns and intrinsic properties in these subcellular compartments. We examined this hypothesis at the soma and axon of cortical pyramidal neurons by analyzing their spike capability and voltage-gated sodium channel dynamics in response to different input signals.
Results
Electrophysiological recordings were simultaneously conducted at the somata and axons of identical pyramidal neurons in the cortical slices. The somata dominantly produced sequential spikes in response to long-time steady depolarization pulse, and the axons produced more spikes in response to fluctuated pulse. Compared with the axons, the somata possessed lower spike threshold and shorter refractory periods in response to long-time steady depolarization, and somatic voltage-gated sodium channels demonstrated less inactivation and easier reactivation in response to steady depolarization. Based on local VGSC dynamics, computational simulated spike initiation locations were consistent with those from the experiments. In terms of physiological impact, this input-dependent plasticity of spike initiation location made neuronal encoding to be efficient.
Conclusions
Long-time steady depolarization primarily induces somatic spikes and short-time pulses induce axonal spikes. The input signal patterns influence spike initiations at the axon or soma of cortical pyramidal neurons through modulating local voltage-gated sodium channel dynamics.
doi:10.1186/1756-6606-7-26
PMCID: PMC4022375  PMID: 24708847
Action potential; Soma; Axon; Neuron and sodium channel
3.  Metabolic efficiency with fast spiking in the squid axon 
Fundamentally, action potentials in the squid axon are consequence of the entrance of sodium ions during the depolarization of the rising phase of the spike mediated by the outflow of potassium ions during the hyperpolarization of the falling phase. Perfect metabolic efficiency with a minimum charge needed for the change in voltage during the action potential would confine sodium entry to the rising phase and potassium efflux to the falling phase. However, because sodium channels remain open to a significant extent during the falling phase, a certain overlap of inward and outward currents is observed. In this work we investigate the impact of ion overlap on the number of the adenosine triphosphate (ATP) molecules and energy cost required per action potential as a function of the temperature in a Hodgkin–Huxley model. Based on a recent approach to computing the energy cost of neuronal action potential generation not based on ion counting, we show that increased firing frequencies induced by higher temperatures imply more efficient use of sodium entry, and then a decrease in the metabolic energy cost required to restore the concentration gradients after an action potential. Also, we determine values of sodium conductance at which the hydrolysis efficiency presents a clear minimum.
doi:10.3389/fncom.2012.00095
PMCID: PMC3498622  PMID: 23162461
Hodgkin–Huxley model; action potential; neuron metabolic energy; sodium entry; overlap load; regular-spiking cells
4.  Enhancement of Asynchronous Release from Fast-Spiking Interneuron in Human and Rat Epileptic Neocortex 
PLoS Biology  2012;10(5):e1001324.
Asynchronous GABA release occurs at output synapses of fast-spiking interneurons in human and rat neocortex and is elevated in epileptic tissues from both species.
Down-regulation of GABAergic inhibition may result in the generation of epileptiform activities. Besides spike-triggered synchronous GABA release, changes in asynchronous release (AR) following high-frequency discharges may further regulate epileptiform activities. In brain slices obtained from surgically removed human neocortical tissues of patients with intractable epilepsy and brain tumor, we found that AR occurred at GABAergic output synapses of fast-spiking (FS) neurons and its strength depended on the type of connections, with FS autapses showing the strongest AR. In addition, we found that AR depended on residual Ca2+ at presynaptic terminals but was independent of postsynaptic firing. Furthermore, AR at FS autapses was markedly elevated in human epileptic tissue as compared to non-epileptic tissue. In a rat model of epilepsy, we found similar elevation of AR at both FS autapses and synapses onto excitatory neurons. Further experiments and analysis showed that AR elevation in epileptic tissue may result from an increase in action potential amplitude in the FS neurons and elevation of residual Ca2+ concentration. Together, these results revealed that GABAergic AR occurred at both human and rat neocortex, and its elevation in epileptic tissue may contribute to the regulation of epileptiform activities.
Author Summary
The balance between excitation and inhibition in the cerebral cortex is important for multiple brain functions. Down-regulation of GABA-induced inhibition disrupts this balance and may lead to epileptic seizures. Asynchronous release of GABA is known to occur at certain GABAergic synapses and represents release of inhibitory neurotransmitter that is not precisely timed to presynaptic action potentials. Whether asynchronous release is subject to change after the induction of epilepsy remains unclear. In this study, using simultaneous recordings from inhibitory fast-spiking neurons and excitatory pyramidal cells, we found that asynchronous release occurred at the output synapses of fast-spiking neurons in both human and rat neocortex. The occurrence of asynchronous release depended on the level of residual calcium at the presynaptic terminals but not on postsynaptic spiking. Further experiments using cortical tissue derived from human patients with intractable epilepsy and from a rat model of the disorder revealed an elevation of asynchronous release in epileptic cortex, possibly resulting from an increase in action potential amplitude of fast-spiking neurons and changes in calcium dynamics in their axon terminals. Taken together, these results demonstrate that asynchronous release is a fundamental property shared by neocortical fast-spiking neurons regardless of species, and the enhancement of asynchronous release in epileptic tissue suggests a role for it in regulating epileptic activities.
doi:10.1371/journal.pbio.1001324
PMCID: PMC3348166  PMID: 22589699
5.  Temporal Coding at the Immature Depolarizing GABAergic Synapse 
In the developing hippocampus, GABA exerts depolarizing and excitatory actions and contributes to the generation of neuronal network driven giant depolarizing potentials (GDPs). Here, we studied spike time coding at immature GABAergic synapses and its impact on synchronization of the neuronal network during GDPs in the neonatal (postnatal days P2–6) rat hippocampal slices. Using extracellular recordings, we found that the delays of action potentials (APs) evoked by synaptic activation of GABA(A) receptors are long (mean, 65 ms) and variable (within a time window of 10–200 ms). During patch-clamp recordings, depolarizing GABAergic responses were mainly subthreshold and their amplification by persistent sodium conductance was required to trigger APs. AP delays at GABAergic synapses shortened and their variability reduced with an increase in intracellular chloride concentration during whole-cell recordings. Negative shift of the GABA reversal potential (EGABA) with low concentrations of bumetanide, or potentiation of GABA(A) receptors with diazepam reduced GDPs amplitude, desynchronized neuronal firing during GDPs and slowed down GDPs propagation. Partial blockade of GABA(A) receptors with bicuculline increased neuronal synchronization and accelerated GDPs propagation. We propose that spike timing at depolarizing GABA synapses is determined by intracellular chloride concentration. At physiological levels of intracellular chloride GABAergic depolarization does not reach the action potential threshold and amplification of GABAergic responses by non-inactivating sodium conductance is required for postsynaptic AP initiation. Slow and variable excitation at GABAergic synapse determines the level of neuronal synchrony and the rate of GDPs propagation in the developing hippocampus.
doi:10.3389/fncel.2010.00017
PMCID: PMC2914581  PMID: 20725525
gamma aminobutyric acid; development; neonatal; hippocampus
6.  Dendritic Properties of Turtle Pyramidal Neurons 
Journal of neurophysiology  2007;99(2):683-694.
The six-layered mammalian neocortex evolved from the three-layered paleocortex, which is retained in present-day reptiles such as the turtle. Thus the turtle offers an opportunity to examine which cellular and circuit properties are fundamental to cortical function. We characterized the dendritic properties of pyramidal neurons in different cortical regions of mature turtles, Pseudemys scripta elegans, using whole cell recordings and calcium imaging from the axon, soma, and dendrites in a slice preparation. The firing properties, in response to intrasomatic depolarization, resembled those previously recorded with sharp electrodes in this preparation. Somatic spikes led to active backpropagating high-amplitude dendritic action potentials and intracellular calcium ion concentration ([Ca2+]i) changes at all dendritic locations, suggesting that both backpropagation and dendritic voltage-gated Ca2+ channels are primitive traits. We found no indication that Ca2+ spikes could be evoked in the dendrites, but fast Na+ spikes could be initiated there following intradendritic stimulation. Several lines of evidence indicate that fast, smaller-amplitude somatic spikes (“prepotentials”) that are easily recorded in this preparation are generated in the axon. Most synaptically activated [Ca2+]i changes resulted from Ca2+ entry through voltage-gated channels. In some cells synaptic stimulation evoked a delayed Ca2+ wave due to release from internal stores following activation of metabotropic glutamate receptors. With some small differences these properties resemble those of pyramidal neurons in mammalian species. We conclude that spike backpropagation, dendritic Ca2+ channels, and synaptically activated Ca2+ release are primitive and conserved features of cortical pyramidal cells, and therefore likely fundamental to cortical function.
doi:10.1152/jn.01076.2007
PMCID: PMC3106292  PMID: 18045998
7.  Transient sodium current at subthreshold voltages: activation by EPSP waveforms 
Neuron  2012;75(6):1081-1093.
Summary
Tetrodotoxin (TTX)-sensitive sodium channels carry large transient currents during action potentials and also “persistent” sodium current, a non-inactivating TTX-sensitive current present at subthreshold voltages. We examined gating of subthreshold sodium current in dissociated cerebellar Purkinje neurons and hippocampal CA1 neurons, studied at 37 °C with near-physiological ionic conditions. Unexpectedly, in both cell types small voltage steps at subthreshold voltages activated a substantial component of transient sodium current as well as persistent current. Subthreshold EPSP-like waveforms also activated a large component of transient sodium current, but IPSP-like waveforms engaged primarily persistent sodium current with only a small additional transient component. Activation of transient as well as persistent sodium current at subthreshold voltages produces amplification of EPSPs that is sensitive to the rate of depolarization and can help account for the dependence of spike threshold on depolarization rate, as previously observed in vivo.
doi:10.1016/j.neuron.2012.08.033
PMCID: PMC3460524  PMID: 22998875
CA1 pyramidal neuron; Purkinje neuron; persistent sodium current; IPSP; sodium channel
8.  Desynchronization of Neocortical Networks by Asynchronous Release of GABA at Autaptic and Synaptic Contacts from Fast-Spiking Interneurons 
PLoS Biology  2010;8(9):e1000492.
An activity-dependent long-lasting asynchronous release of GABA from identified fast-spiking inhibitory neurons in the neocortex can impair the reliability and temporal precision of activity in a cortical network.
Networks of specific inhibitory interneurons regulate principal cell firing in several forms of neocortical activity. Fast-spiking (FS) interneurons are potently self-inhibited by GABAergic autaptic transmission, allowing them to precisely control their own firing dynamics and timing. Here we show that in FS interneurons, high-frequency trains of action potentials can generate a delayed and prolonged GABAergic self-inhibition due to sustained asynchronous release at FS-cell autapses. Asynchronous release of GABA is simultaneously recorded in connected pyramidal (P) neurons. Asynchronous and synchronous autaptic release show differential presynaptic Ca2+ sensitivity, suggesting that they rely on different Ca2+ sensors and/or involve distinct pools of vesicles. In addition, asynchronous release is modulated by the endogenous Ca2+ buffer parvalbumin. Functionally, asynchronous release decreases FS-cell spike reliability and reduces the ability of P neurons to integrate incoming stimuli into precise firing. Since each FS cell contacts many P neurons, asynchronous release from a single interneuron may desynchronize a large portion of the local network and disrupt cortical information processing.
Author Summary
In the cerebral cortex (neocortex) of the brain, fast-spiking (FS) inhibitory cells contact many principal pyramidal (P) neurons on their cell bodies, which allows the FS cells to control the generation of action potentials (neuronal output). FS-cell-mediated rhythmic and synchronous inhibition drives coherent network oscillations of large ensembles of P neurons, indicating that FS interneurons are needed for the precise timing of cortical circuits. Interestingly, FS cells are self-innervated by GABAergic autaptic contacts, whose synchronous activation regulates FS-cell precise firing. Here we report that high-frequency firing in FS interneurons results in a massive (>10-fold), delayed, and prolonged (for seconds) increase in inhibitory events, occurring at both autaptic (FS–FS) and synaptic (FS–P) sites. This increased inhibition is due to asynchronous release of GABA from presynaptic FS cells. Delayed and disorganized asynchronous inhibitory responses significantly affected the input–output properties of both FS and P neurons, suggesting that asynchronous release of GABA might promote network desynchronization. FS interneurons can fire at high frequency (>100 Hz) in vitro and in vivo, and are known for their reliable and precise signaling. Our results show an unprecedented action of these cells, by which their tight temporal control of cortical circuits can be broken when they are driven to fire above certain frequencies.
doi:10.1371/journal.pbio.1000492
PMCID: PMC2946936  PMID: 20927409
9.  MATURATION OF FIRING PATTERN IN CHICK VESTIBULAR NUCLEUS NEURONS 
Neuroscience  2006;141(2):711-726.
The principal cells of the chick tangential nucleus are vestibular nucleus neurons participating in the vestibuloocular and vestibulocollic reflexes. In birds and mammals, spontaneous and stimulus-evoked firing of action potentials is essential for vestibular nucleus neurons to generate mature vestibular reflex activity. The emergence of spike-firing pattern and the underlying ion channels were studied in morphologically-identified principal cells using whole-cell patch-clamp recordings from brain slices of late-term embryos (embryonic day 16) and hatchling chickens (hatching day 1 and hatching day 5). Spontaneous spike activity emerged around the perinatal period, since at embryonic day 16 none of the principal cells generated spontaneous action potentials. However, at hatching day 1, 50% of the cells fired spontaneously (range, 3 to 32 spikes/s), which depended on synaptic transmission in most cells. By hatching day 5, 80% of the principal cells could fire action potentials spontaneously (range, 5 to 80 spikes/s), and this activity was independent of synaptic transmission and showed faster kinetics than at hatching day 1. Repetitive firing in response to depolarizing pulses appeared in the principal cells starting around embryonic day 16, when < 20% of the neurons fired repetitively. However, almost 90% of the principal cells exhibited repetitive firing on depolarization at hatching day 1, and 100% by hatching day 5. From embryonic day 16 to hatching day 5, the gain for evoked spike firing increased almost 10-fold. At hatching day 5, a persistent sodium channel was essential for the generation of spontaneous spike activity, while a small conductance, calcium-dependent potassium current modulated both the spontaneous and evoked spike firing activity. Altogether, these in vitro studies showed that during the perinatal period, the principal cells switched from displaying no spontaneous spike activity at resting membrane potential and generating one spike on depolarization to the tonic firing of spontaneous and evoked action potentials.
doi:10.1016/j.neuroscience.2006.03.061
PMCID: PMC1899235  PMID: 16690214
intrinsic membrane properties; spike activity; brain slice
10.  Ionic Mechanism Underlying Optimal Stimuli for Neuronal Excitation: Role of Na+ Channel Inactivation 
PLoS ONE  2012;7(9):e45983.
The ionic mechanism underlying optimal stimulus shapes that induce a neuron to fire an action potential, or spike, is relevant to understanding optimal information transmission and therapeutic stimulation in the nervous system. Here we analyze for the first time the ionic basis for stimulus optimality in the Hodgkin and Huxley model and for eliciting a spike in squid giant axons, the preparation for which the model was devised. The experimentally determined stimulus is a smoothly varying biphasic current waveform having a relatively long and shallow hyperpolarizing phase followed by a depolarizing phase of briefer duration. The hyperpolarizing phase removes a small degree of the resting level of Na+ channel inactivation. This result together with the subsequent depolarizing phase provides a signal that is energetically more efficient for eliciting spikes than rectangular current pulses. Sodium channel inactivation is the only variable that is changed during the stimulus waveform, other than the membrane potential, V. The activation variables for Na+ and K+ channels are unchanged throughout the stimulus. This result demonstrates how an optimal stimulus waveform relates to ionic dynamics and may have implications for energy efficiency of neural excitation in many systems including the mammalian brain.
doi:10.1371/journal.pone.0045983
PMCID: PMC3458826  PMID: 23049913
11.  Complex Intrinsic Membrane Properties and Dopamine Shape Spiking Activity in a Motor Axon 
We studied the peripheral motor axons of the two pyloric dilator (PD) neurons of the stomatogastric ganglion in the lobster, Homarus americanus. Intracellular recordings from the motor nerve showed both fast and slow voltage- and activity-dependent dynamics. During rhythmic bursts, the PD axons displayed changes in spike amplitude and duration. Pharmacological experiments and the voltage-dependence of these phenomena suggest that inactivation of sodium and A-type potassium channels are responsible. In addition, the “resting” membrane potential was dependent on ongoing spike or burst activity, with more hyperpolarized values when activity was strong. Nerve stimulations, pharmacological block and current clamp experiments suggest that this is due to a functional antagonism between a slow after-hyperpolarization (sAHP) and inward rectification through hyperpolarization-activated current (IH). Dopamine application resulted in modest depolarization and “ectopic” peripheral spike initiation in the absence of centrally generated activity. This effect was blocked by CsCl and ZD7288, consistent with a role of IH. High frequency nerve stimulation inhibited peripheral spike initiation for several seconds, presumably due to the sAHP. Both during normal bursting activity and antidromic nerve stimulation, the conduction delay over the length of the peripheral nerve changed in a complex manner. This suggests that axonal membrane dynamics can have a substantial effect on the temporal fidelity of spike patterns propagated from a spike initiation site to a synaptic target, and that neuromodulators can influence the extent to which spike patterns are modified.
doi:10.1523/JNEUROSCI.0716-09.2009
PMCID: PMC2743087  PMID: 19386902
Central Pattern Generator; Neuromodulation; Crustacean; Neurohormones; Sag Potential; Spike Frequency Adaptation
12.  Local Control of Postinhibitory Rebound Spiking in CA1 Pyramidal Neuron Dendrites 
The Journal of Neuroscience  2010;30(18):6434-6442.
Postinhibitory rebound spiking is characteristic of several neuron types and brain regions, where it sustains spontaneous activity and central pattern generation. However, rebound spikes are rarely observed in the principal cells of the hippocampus under physiological conditions. We report that CA1 pyramidal neurons support rebound spikes mediated by hyperpolarization-activated inward current (Ih), and normally masked by A-type potassium channels (KA). In both experiments and computational models, KA blockage or reduction consistently resulted in a somatic action potential upon release from hyperpolarizing injections in the soma or main apical dendrite. Rebound spiking was systematically abolished by the additional blockage or reduction of Ih. Since the density of both KA and Ih increases in these cells with the distance from the soma, such “latent” mechanism may be most effective in the distal dendrites, which are targeted by a variety of GABAergic interneurons. Detailed computer simulations, validated against the experimental data, demonstrate that rebound spiking can result from activation of distal inhibitory synapses. In particular, partial KA reduction confined to one or few branches of the apical tuft may be sufficient to elicit a local spike following a train of synaptic inhibition. Moreover, the spatial extent and amount of KA reduction determines whether the dendritic spike propagates to the soma. These data suggest that the plastic regulation of KA can provide a dynamic switch to unmask postinhibitory spiking in CA1 pyramidal neurons. This newly discovered local modulation of postinhibitory spiking further increases the signal processing power of the CA1 synaptic microcircuitry.
doi:10.1523/JNEUROSCI.4066-09.2010
PMCID: PMC3319664  PMID: 20445069
13.  Intrinsic and integrative properties of substantia nigra pars reticulata neurons 
Neuroscience  2011;198:69-94.
The GABA projection neurons of the substantia nigra pars reticulata (SNr) are output neurons for the basal ganglia and thus critical for movement control. Their most striking neurophysiological feature is sustained, spontaneous high frequency spike firing. A fundamental question is: what are the key ion channels supporting the remarkable firing capability in these neurons? Recent studies indicate that these neurons express tonically active TRPC3 channels that conduct a Na-dependent inward current even at hyperpolarized membrane potentials. When the membrane potential reaches −60 mV, a voltage-gated persistent sodium current (INaP) starts to activate, further depolarizing the membrane potential. At or slightly below −50 mV, the large transient voltage-activated sodium current (INaT) starts to activate and eventually triggers the rapid rising phase of action potentials. SNr GABA neurons have a higher density of (INaT), contributing to the faster rise and larger amplitude of action potentials, compared with the slow-spiking dopamine neurons. INaT also recovers from inactivation more quickly in SNr GABA neurons than in nigral dopamine neurons. In SNr GABA neurons, the rising phase of the action potential triggers the activation of high-threshold, inactivation-resistant Kv3-like channels that can rapidly repolarize the membrane. These intrinsic ion channels provide SNr GABA neurons with the ability to fire spontaneous and sustained high frequency spikes. Additionally, robust GABA inputs from direct pathway medium spiny neurons in the striatum and GABA neurons in the globus pallidus may inhibit and silence SNr GABA neurons, whereas glutamate synaptic input from the subthalamic nucleus may induce burst firing in SNr GABA neurons. Thus, afferent GABA and glutamate synaptic inputs sculpt the tonic high frequency firing of SNr GABA neurons and the consequent inhibition of their targets into an integrated motor control signal that is further fine-tuned by neuromodulators including dopamine, serotonin, endocannabinoids, and H2O2.
doi:10.1016/j.neuroscience.2011.07.061
PMCID: PMC3221915  PMID: 21839148
action potential; basal ganglia; ion channel; Parkinson’s disease; substantia nigra; synapse
14.  Axons Amplify Somatic Incomplete Spikes into Uniform Amplitudes in Mouse Cortical Pyramidal Neurons 
PLoS ONE  2010;5(7):e11868.
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.
doi:10.1371/journal.pone.0011868
PMCID: PMC2912328  PMID: 20686619
15.  Biophysical Basis for Three Distinct Dynamical Mechanisms of Action Potential Initiation 
PLoS Computational Biology  2008;4(10):e1000198.
Transduction of graded synaptic input into trains of all-or-none action potentials (spikes) is a crucial step in neural coding. Hodgkin identified three classes of neurons with qualitatively different analog-to-digital transduction properties. Despite widespread use of this classification scheme, a generalizable explanation of its biophysical basis has not been described. We recorded from spinal sensory neurons representing each class and reproduced their transduction properties in a minimal model. With phase plane and bifurcation analysis, each class of excitability was shown to derive from distinct spike initiating dynamics. Excitability could be converted between all three classes by varying single parameters; moreover, several parameters, when varied one at a time, had functionally equivalent effects on excitability. From this, we conclude that the spike-initiating dynamics associated with each of Hodgkin's classes represent different outcomes in a nonlinear competition between oppositely directed, kinetically mismatched currents. Class 1 excitability occurs through a saddle node on invariant circle bifurcation when net current at perithreshold potentials is inward (depolarizing) at steady state. Class 2 excitability occurs through a Hopf bifurcation when, despite net current being outward (hyperpolarizing) at steady state, spike initiation occurs because inward current activates faster than outward current. Class 3 excitability occurs through a quasi-separatrix crossing when fast-activating inward current overpowers slow-activating outward current during a stimulus transient, although slow-activating outward current dominates during constant stimulation. Experiments confirmed that different classes of spinal lamina I neurons express the subthreshold currents predicted by our simulations and, further, that those currents are necessary for the excitability in each cell class. Thus, our results demonstrate that all three classes of excitability arise from a continuum in the direction and magnitude of subthreshold currents. Through detailed analysis of the spike-initiating process, we have explained a fundamental link between biophysical properties and qualitative differences in how neurons encode sensory input.
Author Summary
Information is transmitted through the nervous system in the form of action potentials or spikes. Contrary to popular belief, a spike is not generated instantaneously when membrane potential crosses some preordained threshold. In fact, different neurons employ different rules to determine when and why they spike. These different rules translate into diverse spiking patterns that have been observed experimentally and replicated time and again in computational models. In this study, our aim was not simply to replicate different spiking patterns; instead, we sought to provide deeper insight into the connection between biophysics and neural coding by relating each to the process of spike initiation. We show that Hodgkin's three classes of excitability result from a nonlinear competition between oppositely directed, kinetically mismatched currents; the outcome of that competition is manifested as dynamically distinct spike-initiating mechanisms. Our results highlight the benefits of forward engineering minimal models capable of reproducing phenomena of interest and then dissecting those models in order to identify general explanations of how those phenomena arise. Furthermore, understanding nonlinear dynamical processes such as spike initiation is crucial for definitively explaining how biophysical properties impact neural coding.
doi:10.1371/journal.pcbi.1000198
PMCID: PMC2551735  PMID: 18846205
16.  Essential role of axonal VGSC inactivation in time-dependent deceleration and unreliability of spike propagation at cerebellar Purkinje cells 
Molecular Brain  2014;7:1.
Background
The output of the neuronal digital spikes is fulfilled by axonal propagation and synaptic transmission to influence postsynaptic cells. Similar to synaptic transmission, spike propagation on the axon is not secure, especially in cerebellar Purkinje cells whose spiking rate is high. The characteristics, mechanisms and physiological impacts of propagation deceleration and infidelity remain elusive. The spike propagation is presumably initiated by local currents that raise membrane potential to the threshold of activating voltage-gated sodium channels (VGSC).
Results
We have investigated the natures of spike propagation and the role of VGSCs in this process by recording spikes simultaneously on the somata and axonal terminals of Purkinje cells in cerebellar slices. The velocity and fidelity of spike propagation decreased during long-lasting spikes, to which the velocity change was more sensitive than fidelity change. These time-dependent deceleration and infidelity of spike propagation were improved by facilitating axonal VGSC reactivation, and worsen by intensifying VGSC inactivation.
Conclusion
Our studies indicate that the functional status of axonal VGSCs is essential to influencing the velocity and fidelity of spike propagation.
doi:10.1186/1756-6606-7-1
PMCID: PMC3880351  PMID: 24382121
Axon; Neuron; Action potential; Spike propagation; Purkinje cell; Cerebellum
17.  Sodium Along With Low-Threshold Potassium Currents Enhance Coincidence Detection of Subthreshold Noisy Signals in MSO Neurons 
Journal of neurophysiology  2004;91(6):2465-2473.
Voltage-dependent membrane conductances support specific neurophysiological properties. To investigate the mechanisms of coincidence detection, we activated gerbil medial superior olivary (MSO) neurons with dynamic current-clamp stimuli in vitro. Spike-triggered reverse-correlation analysis for injected current was used to evaluate the integration of subthreshold noisy signals. Consistent with previous reports, the partial blockade of low-threshold potassium channels (IKLT) reduced coincidence detection by slowing the rise of current needed on average to evoke a spike. However, two factors point toward the involvement of a second mechanism. First, the reverse correlation currents revealed that spike generation was associated with a preceding hyperpolarization. Second, rebound action potentials are 45% larger compared to depolarization-evoked spikes in the presence of an IKLT antagonist. These observations suggest that the sodium current (INa) was substantially inactivated at rest. To test this idea, INa was enhanced by increasing extracellular sodium concentration. This manipulation reduced coincidence detection, as reflected by slower spike-triggering current, and diminished the hyperpolarization phase in the reverse-correlation currents. As expected, a small outward bias current decreased the pre-spike hyperpolarization phase, and TTX blockade of INa nearly eliminated the hyperpolarization phase in the reverse correlation current. A computer model including Hodgkin-Huxley type conductances for spike generation and for IKLT showed reduction in coincidence detection when IKLT was reduced or when INa was increased. We hypothesize that desirable synaptic signals first remove some inactivation of INa and reduce activation of IKLT to create a brief temporal window for coincidence detection of subthreshold noisy signals.
doi:10.1152/jn.00717.2003
PMCID: PMC3683536  PMID: 14749317
18.  LTS and FS Inhibitory Interneurons, Short-Term Synaptic Plasticity, and Cortical Circuit Dynamics 
PLoS Computational Biology  2011;7(10):e1002248.
Somatostatin-expressing, low threshold-spiking (LTS) cells and fast-spiking (FS) cells are two common subtypes of inhibitory neocortical interneuron. Excitatory synapses from regular-spiking (RS) pyramidal neurons to LTS cells strongly facilitate when activated repetitively, whereas RS-to-FS synapses depress. This suggests that LTS neurons may be especially relevant at high rate regimes and protect cortical circuits against over-excitation and seizures. However, the inhibitory synapses from LTS cells usually depress, which may reduce their effectiveness at high rates. We ask: by which mechanisms and at what firing rates do LTS neurons control the activity of cortical circuits responding to thalamic input, and how is control by LTS neurons different from that of FS neurons? We study rate models of circuits that include RS cells and LTS and FS inhibitory cells with short-term synaptic plasticity. LTS neurons shift the RS firing-rate vs. current curve to the right at high rates and reduce its slope at low rates; the LTS effect is delayed and prolonged. FS neurons always shift the curve to the right and affect RS firing transiently. In an RS-LTS-FS network, FS neurons reach a quiescent state if they receive weak input, LTS neurons are quiescent if RS neurons receive weak input, and both FS and RS populations are active if they both receive large inputs. In general, FS neurons tend to follow the spiking of RS neurons much more closely than LTS neurons. A novel type of facilitation-induced slow oscillations is observed above the LTS firing threshold with a frequency determined by the time scale of recovery from facilitation. To conclude, contrary to earlier proposals, LTS neurons affect the transient and steady state responses of cortical circuits over a range of firing rates, not only during the high rate regime; LTS neurons protect against over-activation about as well as FS neurons.
Author Summary
The brain consists of circuits of neurons that signal to one another via synapses. There are two classes of neurons: excitatory cells, which cause other neurons to become more active, and inhibitory neurons, which cause other neurons to become less active. It is thought that the activity of excitatory neurons is kept in check largely by inhibitory neurons; when such an inhibitory “brake” fails, a seizure can result. Inhibitory neurons of the low-threshold spiking (LTS) subtype can potentially fulfill this braking, or anticonvulsant, role because the synaptic input to these neurons facilitates, i.e., those neurons are active when excitatory neurons are strongly active. Using a computational model we show that, because the synaptic output of LTS neurons onto excitatory neurons depresses (decreases with activity), the ability of LTS neurons to prevent strong cortical activity and seizures is not qualitatively larger than that of inhibitory neurons of another subtype, the fast-spiking (FS) cells. Furthermore, short-term (∼one second) changes in the strength of synapses to and from LTS interneurons allow them to shape the behavior of cortical circuits even at modest rates of activity, and an RS-LTS-FS circuit is capable of producing slow oscillations, on the time scale of these short-term changes.
doi:10.1371/journal.pcbi.1002248
PMCID: PMC3203067  PMID: 22046121
19.  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.
doi:10.1523/JNEUROSCI.0771-12.2013
PMCID: PMC3964617  PMID: 23392659
20.  How Modeling Can Reconcile Apparently Discrepant Experimental Results: The Case of Pacemaking in Dopaminergic Neurons 
PLoS Computational Biology  2011;7(5):e1002050.
Midbrain dopaminergic neurons are endowed with endogenous slow pacemaking properties. In recent years, many different groups have studied the basis for this phenomenon, often with conflicting conclusions. In particular, the role of a slowly-inactivating L-type calcium channel in the depolarizing phase between spikes is controversial, and the analysis of slow oscillatory potential (SOP) recordings during the blockade of sodium channels has led to conflicting conclusions. Based on a minimal model of a dopaminergic neuron, our analysis suggests that the same experimental protocol may lead to drastically different observations in almost identical neurons. For example, complete L-type calcium channel blockade eliminates spontaneous firing or has almost no effect in two neurons differing by less than 1% in their maximal sodium conductance. The same prediction can be reproduced in a state of the art detailed model of a dopaminergic neuron. Some of these predictions are confirmed experimentally using single-cell recordings in brain slices. Our minimal model exhibits SOPs when sodium channels are blocked, these SOPs being uncorrelated with the spiking activity, as has been shown experimentally. We also show that block of a specific conductance (in this case, the SK conductance) can have a different effect on these two oscillatory behaviors (pacemaking and SOPs), despite the fact that they have the same initiating mechanism. These results highlight the fact that computational approaches, besides their well known confirmatory and predictive interests in neurophysiology, may also be useful to resolve apparent discrepancies between experimental results.
Author Summary
Dopamine is a neurotransmitter which plays important roles in the control of voluntary movement, motivation and reward, attention, and learning. Dysfunction of midbrain dopaminergic systems is involved in various diseases such as Parkinson's disease, schizophrenia and drug abuse. This underlines the importance of a tight regulation of dopamine levels in the brain. At the cellular level, the release of dopamine is directly correlated to the type of electrical activity (the firing pattern) of nerve cells that produce it, the so-called “dopaminergic neurons”. Therefore, an in depth understanding of the mechanisms underlying the electrical behavior of dopaminergic neurons is of critical importance to find new strategies for the treatment of diseases that result from dysfunction of this system.
doi:10.1371/journal.pcbi.1002050
PMCID: PMC3102759  PMID: 21637742
21.  Complex Events Initiated by Individual Spikes in the Human Cerebral Cortex  
PLoS Biology  2008;6(9):e222.
Synaptic interactions between neurons of the human cerebral cortex were not directly studied to date. We recorded the first dataset, to our knowledge, on the synaptic effect of identified human pyramidal cells on various types of postsynaptic neurons and reveal complex events triggered by individual action potentials in the human neocortical network. Brain slices were prepared from nonpathological samples of cortex that had to be removed for the surgical treatment of brain areas beneath association cortices of 58 patients aged 18 to 73 y. Simultaneous triple and quadruple whole-cell patch clamp recordings were performed testing mono- and polysynaptic potentials in target neurons following a single action potential fired by layer 2/3 pyramidal cells, and the temporal structure of events and underlying mechanisms were analyzed. In addition to monosynaptic postsynaptic potentials, individual action potentials in presynaptic pyramidal cells initiated long-lasting (37 ± 17 ms) sequences of events in the network lasting an order of magnitude longer than detected previously in other species. These event series were composed of specifically alternating glutamatergic and GABAergic postsynaptic potentials and required selective spike-to-spike coupling from pyramidal cells to GABAergic interneurons producing concomitant inhibitory as well as excitatory feed-forward action of GABA. Single action potentials of human neurons are sufficient to recruit Hebbian-like neuronal assemblies that are proposed to participate in cognitive processes.
Author Summary
We recorded the first connections, to our knowledge, between human nerve cells and reveal that a subset of interactions is so strong that some presynaptic cells are capable of eliciting action potentials in the postsynaptic target neurons. Interestingly, these strong connections selectively link pyramidal cells using the neurotransmitter glutamate to neurons releasing gamma aminobutyric acid (GABA). Moreover, the GABAergic neurons receiving the strong connections include different types: basket cells, which inhibit several target cell populations, and another type called the chandelier cells, which can be excitatory and target pyramidal cells only. Thus, the activation originating from a single pyramidal cell propagates to synchronously working inhibitory and excitatory GABAergic neurons. Inhibition then arrives to various neuron classes, but excitation finds only pyramidal cells, which in turn, can propagate excitation even further in the network of neurons. This chain of events revealed here leads to network activation approximately an order of magnitude longer than detected previously in response to a single action potential in a single neuron. Individual-neuron–activated groups of neurons resemble the so-called functional assemblies that were proposed as building blocks of higher order cognitive representations.
A novel study on connections between human neurons reveals that single spikes in pyramidal cells can activate synchronously timed assemblies through strong connections linking pyramidal cells with inhibitory and excitatory GABAergic neurons.
doi:10.1371/journal.pbio.0060222
PMCID: PMC2528052  PMID: 18767905
22.  Membrane Potential-Dependent Modulation of Recurrent Inhibition in Rat Neocortex 
PLoS Biology  2011;9(3):e1001032.
Dynamic balance of excitation and inhibition is crucial for network stability and cortical processing, but it is unclear how this balance is achieved at different membrane potentials (Vm) of cortical neurons, as found during persistent activity or slow Vm oscillation. Here we report that a Vm-dependent modulation of recurrent inhibition between pyramidal cells (PCs) contributes to the excitation-inhibition balance. Whole-cell recording from paired layer-5 PCs in rat somatosensory cortical slices revealed that both the slow and the fast disynaptic IPSPs, presumably mediated by low-threshold spiking and fast spiking interneurons, respectively, were modulated by changes in presynaptic Vm. Somatic depolarization (>5 mV) of the presynaptic PC substantially increased the amplitude and shortened the onset latency of the slow disynaptic IPSPs in neighboring PCs, leading to a narrowed time window for EPSP integration. A similar increase in the amplitude of the fast disynaptic IPSPs in response to presynaptic depolarization was also observed. Further paired recording from PCs and interneurons revealed that PC depolarization increases EPSP amplitude and thus elevates interneuronal firing and inhibition of neighboring PCs, a reflection of the analog mode of excitatory synaptic transmission between PCs and interneurons. Together, these results revealed an immediate Vm-dependent modulation of cortical inhibition, a key strategy through which the cortex dynamically maintains the balance of excitation and inhibition at different states of cortical activity.
Author Summary
Proper functioning of the neocortex requires a balance between excitation and inhibition. This balance can be achieved through the operation of cortical microcircuits interweaved by excitatory and inhibitory neurons. Since the membrane potentials (Vm) of cortical neurons fluctuate at different levels during cortical activities, it is important to know how the balance of excitation and inhibition is dynamically maintained at different Vm. Recurrent inhibition between excitatory pyramidal cells is mediated by two distinct types of inhibitory interneurons. Here, we show that the amount of recurrent inhibition depends on the Vm levels of presynaptic pyramidal cells. Modest depolarization of a pyramidal cell substantially increases, and sometimes turns on, disynaptic inhibition on its neighboring pyramidal cells. We find that this effect is due to an increase in the strength of synaptic connections from the pyramidal cell to inhibitory interneurons and a consequent elevation of interneuronal firing. The depolarization-induced increase in synaptic strength from the pyramidal cell therefore reflects “analog-mode” signaling in cortical excitatory synapses. We thus reveal a profound impact of analog-mode signaling on the operation of cortical microcircuits and provide a new mechanism for dynamic control of the balance of cortical excitation and inhibition.
doi:10.1371/journal.pbio.1001032
PMCID: PMC3062529  PMID: 21445327
23.  Purkinje neuron synchrony elicits time-locked spiking in the cerebellar nuclei 
Nature  2011;481(7382):502-505.
An unusual feature of the cerebellar cortex is that its output neurons, Purkinje cells, are GABAergic. Their high intrinsic firing rates1 (50 Hz) and extensive convergence2,3 predict that that target neurons in the cerebellar nuclei would be largely inhibited unless Purkinje cells pause their spiking, yet Purkinje and nuclear neuron firing rates do not always vary inversely4. A potential clue to how these synapses transmit information is that populations of Purkinje neurons synchronize their spikes during cerebellar behaviors5–11. If nuclear neurons respond to Purkinje synchrony, they may encode signals from subsets of inhibitory inputs7,12–14. Here we show in weanling and adult mice that nuclear neurons transmit the timing of synchronous Purkinje afferent spikes, owing to modest Purkinje-to-nuclear convergence ratios (~40:1), fast IPSC kinetics (τdecay=2.5 ms), and high intrinsic firing rates (~90 Hz). In vitro, dynamically clamped asynchronous IPSPs mimicking Purkinje afferents suppress nuclear cell spiking, whereas synchronous IPSPs entrain nuclear cell spiking. With partial synchrony, nuclear neurons time-lock their spikes to the synchronous subpopulation of inputs, even when only 2 of 40 afferents synchronize. In vivo, nuclear neurons reliably phase-lock to regular trains of molecular layer stimulation. Thus, cerebellar nuclear neurons can preferentially relay the spike timing of synchronized Purkinje cells to downstream premotor areas.
doi:10.1038/nature10732
PMCID: PMC3268051  PMID: 22198670
24.  Cannabinoids attenuate hippocampal gamma oscillations by suppressing excitatory synaptic input onto CA3 pyramidal neurons and fast spiking basket cells 
The Journal of Physiology  2011;589(20):4921-4934.
Non-Technical Summary
Administration of cannabinoids can impair several cognitive functions, including memory by altering synchronous activities in cortical networks. We show that the gamma frequency (40 Hz) oscillations in hippocampal slices, that are prominent oscillations in electroencephalogram during awake states in vivo, are reduced by cannabinoids. This effect can be explained by the suppression of the excitatory synaptic transmission onto fast spiking basket cells, GABAergic cells that are key players in oscillogenesis. The reduced excitatory drive onto these interneurons leads to a reduction in neuronal firing frequency and precision, and thus to smaller field potentials. Our data further our understanding of the synaptic mechanisms of how cannabinoids alter neuronal operation.
Abstract
CB1 cannabinoid receptor (CB1R) activation by exogenous ligands can impair memory processes, which critically depend on synchronous neuronal activities that are temporarily structured by oscillations. In this study, we aimed to reveal the mechanisms underlying the cannabinoid-induced decrease in gamma oscillations. We first verified that cannabinoids (CP55,940 and WIN55,212-2) readily suppressed carbachol-induced gamma oscillations in the CA3 region of hippocampal slices via activation of CB1Rs. The cannabinoid-induced decrease in the peak power of oscillations was accompanied by reduced and less precise firing activity in CA3 pyramidal cells and fast spiking basket cells. By examining the cannabinoid sensitivity of synaptic inputs we found that the amplitude of evoked excitatory postsynaptic currents was significantly suppressed upon CB1R activation in both CA3 pyramidal cells and fast spiking basket cells. In contrast, evoked inhibitory postsynaptic currents in CA3 pyramidal cells were unaltered. Furthermore, we observed that a CB1R agonist-induced decrease in the oscillation power at the beginning of the drug application was accompanied primarily by the reduced discharge of fast spiking basket cells, while pyramidal cell firing was unaltered. This result implies that the dampening of cholinergically induced gamma oscillations in the hippocampus by cannabinoids can be explained by a reduced excitatory input predominantly onto fast spiking basket cells, which leads to a reduction in neuronal firing frequency and precision, and thus to smaller field potentials. In addition, we uncovered that the spontaneously occurring sharp wave-ripple activities in hippocampal slices could also be suppressed by CB1R activation suggesting that cannabinoids profoundly reduce the intrinsically generated oscillatory activities at distinct frequencies in CA3 networks by reducing synaptic neurotransmission.
doi:10.1113/jphysiol.2011.216259
PMCID: PMC3224883  PMID: 21859823
25.  Cannabinoids attenuate hippocampal gamma oscillations by suppressing excitatory synaptic input onto CA3 pyramidal neurons and fast spiking basket cells 
The Journal of Physiology  2011;589(Pt 20):4921-4934.
Non-technical summary
Administration of cannabinoids can impair several cognitive functions, including memory by altering synchronous activities in cortical networks. We show that the gamma frequency (40 Hz) oscillations in hippocampal slices, that are prominent oscillations in electroencephalogram during awake states in vivo, are reduced by cannabinoids. This effect can be explained by the suppression of the excitatory synaptic transmission onto fast spiking basket cells, GABAergic cells that are key players in oscillogenesis. The reduced excitatory drive onto these interneurons leads to a reduction in neuronal firing frequency and precision, and thus to smaller field potentials. Our data further our understanding of the synaptic mechanisms of how cannabinoids alter neuronal operation.
Abstract
CB1 cannabinoid receptor (CB1R) activation by exogenous ligands can impair memory processes, which critically depend on synchronous neuronal activities that are temporarily structured by oscillations. In this study, we aimed to reveal the mechanisms underlying the cannabinoid-induced decrease in gamma oscillations. We first verified that cannabinoids (CP55,940 and WIN55,212-2) readily suppressed carbachol-induced gamma oscillations in the CA3 region of hippocampal slices via activation of CB1Rs. The cannabinoid-induced decrease in the peak power of oscillations was accompanied by reduced and less precise firing activity in CA3 pyramidal cells and fast spiking basket cells. By examining the cannabinoid sensitivity of synaptic inputs we found that the amplitude of evoked excitatory postsynaptic currents was significantly suppressed upon CB1R activation in both CA3 pyramidal cells and fast spiking basket cells. In contrast, evoked inhibitory postsynaptic currents in CA3 pyramidal cells were unaltered. Furthermore, we observed that a CB1R agonist-induced decrease in the oscillation power at the beginning of the drug application was accompanied primarily by the reduced discharge of fast spiking basket cells, while pyramidal cell firing was unaltered. This result implies that the dampening of cholinergically induced gamma oscillations in the hippocampus by cannabinoids can be explained by a reduced excitatory input predominantly onto fast spiking basket cells, which leads to a reduction in neuronal firing frequency and precision, and thus to smaller field potentials. In addition, we uncovered that the spontaneously occurring sharp wave-ripple activities in hippocampal slices could also be suppressed by CB1R activation suggesting that cannabinoids profoundly reduce the intrinsically generated oscillatory activities at distinct frequencies in CA3 networks by reducing synaptic neurotransmission.
doi:10.1113/jphysiol.2011.216259
PMCID: PMC3224883  PMID: 21859823

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