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

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

Dendritic sodium spikes endow neurons with inverse firing rate response to correlated synaptic activity

Many neurons possess dendrites enriched with sodium channels and are capable of generating action potentials. However, the role of dendritic sodium spikes remain unclear. Here, we study computational models of neurons to investigate the functional effects of dendritic spikes. In agreement with previous studies, we found that point neurons or neurons with passive dendrites increase their somatic firing rate in response to the correlation of synaptic bombardment for a wide range of input conditions, i.e. input firing rates, synaptic conductances, or refractory periods. However, neurons with active dendrites show the opposite behavior: for a wide range of conditions the firing rate decreases as a function of correlation. We found this property in three types of models of dendritic excitability: a Hodgkin-Huxley model of dendritic spikes, a model with integrate and fire dendrites, and a discrete-state dendritic model. We conclude that fast dendritic spikes confer much broader computational properties to neurons, sometimes opposite to that of point neurons.     

Dendritic spikes and activity-dependent synaptic plasticity

Whereas the regenerative nature of action potential conduction in axons has been known since the late 1940s, neuronal dendrites have been considered as passive cables transferring incoming synaptic activity to the soma. The relatively recent discovery that neuronal dendrites contain active conductances has revolutionized our view of information processing in neurons. In many neuronal cell types, sodium action potentials initiated at the axon initial segment can back-propagate actively into the dendrite thereby serving, for the dendrite, as an indicator of the output activity of the neuron. In addition, the dendrites themselves can initiate action-potential-like regenerative responses, so-called dendritic spikes, that are mediated either by the activation of sodium, calcium, and/or N-methyl-D-aspartate receptor channels. Here, we review the recent experimental and theoretical evidence for a role of regenerative dendritic activity in information processing within neurons and, especially, in activity-dependent synaptic plasticity.     

Transmitter modulation of slow,activity-dependent alterations in sodium channel availability endows neurons with a novel form of cellular plasticity

Voltage-gated Na+ channels are major targets of G protein-coupled receptor (GPCR)-initiated signaling cascades. These cascades act principally through protein kinase-mediated phosphorylation of the channel alpha subunit. Phosphorylation reduces Na+ channel availability in most instances without producing major alterations of fast channel gating. The nature of this change in availability is poorly understood. The results described here show that both GPCR- and protein kinase-dependent reductions in Na+ channel availability are mediated by a slow, voltage-dependent process with striking similarity to slow inactivation, an intrinsic gating mechanism of Na+ channels. This process is strictly associated with neuronal activity and develops over seconds, endowing neurons with a novel form of cellular plasticity shaping synaptic integration, dendritic electrogenesis, and repetitive discharge.     

Synaptic integration in dendritic trees

Most neurons have elaborate dendritic trees that receive tens of thousands of synaptic inputs. Because postsynaptic responses to individual synaptic events are usually small and transient, the integration of many synaptic responses is needed to depolarize most neurons to action potential threshold. Over the past decade, advances in electrical and optical recording techniques have led to new insights into how synaptic responses propagate and interact within dendritic trees. In addition to their passive electrical and morphological properties, dendrites express active conductances that shape individual synaptic responses and influence synaptic integration locally within dendrites. Dendritic voltage-gated Na(+) and Ca(2+) channels support action potential backpropagation into the dendritic tree and local initiation of dendritic spikes, whereas K(+) conductances act to dampen dendritic excitability. While all dendrites investigated to date express active conductances, different neuronal types show specific patterns of dendritic channel expression leading to cell-specific differences in the way synaptic responses are integrated within dendritic trees. This review explores the way active and passive dendritic properties shape synaptic responses in the dendrites of central neurons, and emphasizes their role in synaptic integration.     

Plasticity of dendritic function

The various properties of neuronal dendrites--their morphology, active membrane and synaptic properties--all play important roles in determining the functional capabilities of central nervous system neurons. Because of their fundamental involvement in both synaptic integration and synaptic plasticity, the active dendritic properties are important for both neuronal information processing and storage. The active properties of dendrites are determined by the densities of voltage-gated ion channels located within the dendrites in addition to the biophysical characteristics of those channels. The real power of this system resides in the level of plasticity that is provided by the many forms of channel modulation known to exist in neurons. Indeed, voltage gated ion channel modulation shapes the active properties of neuronal dendrites to specific conditions, thus tailoring the functional role of the single neuron within its circuit.     

Stochastic differential equation model for cerebellar granule cell excitability

Neurons in the brain express intrinsic dynamic behavior which is known to be stochastic in nature. A crucial question in building models of neuronal excitability is how to be able to mimic the dynamic behavior of the biological counterpart accurately and how to perform simulations in the fastest possible way. The well-established Hodgkin-Huxley formalism has formed to a large extent the basis for building biophysically and anatomically detailed models of neurons. However, the deterministic Hodgkin-Huxley formalism does not take into account the stochastic behavior of voltage-dependent ion channels. Ion channel stochasticity is shown to be important in adjusting the transmembrane voltage dynamics at or close to the threshold of action potential firing, at the very least in small neurons. In order to achieve a better understanding of the dynamic behavior of a neuron, a new modeling and simulation approach based on stochastic differential equations and Brownian motion is developed. The basis of the work is a deterministic one-compartmental multi-conductance model of the cerebellar granule cell. This model includes six different types of voltage-dependent conductances described by Hodgkin-Huxley formalism and simple calcium dynamics. A new model for the granule cell is developed by incorporating stochasticity inherently present in the ion channel function into the gating variables of conductances. With the new stochastic model, the irregular electrophysiological activity of an in vitro granule cell is reproduced accurately, with the same parameter values for which the membrane potential of the original deterministic model exhibits regular behavior. The irregular electrophysiological activity includes experimentally observed random subthreshold oscillations, occasional spontaneous spikes, and clusters of action potentials. As a conclusion, the new stochastic differential equation model of the cerebellar granule cell excitability is found to expand the range of dynamics in comparison to the original deterministic model. Inclusion of stochastic elements in the operation of voltage-dependent conductances should thus be emphasized more in modeling the dynamic behavior of small neurons. Furthermore, the presented approach is valuable in providing faster computation times compared to the Markov chain type of modeling approaches and more sophisticated theoretical analysis tools compared to previously presented stochastic modeling approaches.     

Dendritic Nonlinearities Reduce Network Size Requirements and Mediate ON and OFF States of Persistent Activity in a PFC Microcircuit Model

Technological advances have unraveled the existence of small clusters of co-active neurons in the neocortex. The functional implications of these microcircuits are in large part unexplored. Using a heavily constrained biophysical model of a L5 PFC microcircuit, we recently showed that these structures act as tunable modules of persistent activity, the cellular correlate of working memory. Here, we investigate the mechanisms that underlie persistent activity emergence (ON) and termination (OFF) and search for the minimum network size required for expressing these states within physiological regimes. We show that (a) NMDA-mediated dendritic spikes gate the induction of persistent firing in the microcircuit. (b) The minimum network size required for persistent activity induction is inversely proportional to the synaptic drive of each excitatory neuron. (c) Relaxation of connectivity and synaptic delay constraints eliminates the gating effect of NMDA spikes, albeit at a cost of much larger networks. (d) Persistent activity termination by increased inhibition depends on the strength of the synaptic input and is negatively modulated by dADP. (e) Slow synaptic mechanisms and network activity contain predictive information regarding the ability of a given stimulus to turn ON and/or OFF persistent firing in the microcircuit model. Overall, this study zooms out from dendrites to cell assemblies and suggests a tight interaction between dendritic non-linearities and network properties (size/connectivity) that may facilitate the short-memory function of the PFC.     

Zinc effects on NMDA receptor gating kinetics

Zinc accumulates in the synaptic vesicles of certain glutamatergic forebrain neurons and modulates neuronal excitability and synaptic plasticity by multiple poorly understood mechanisms. Zinc directly inhibits NMDA-sensitive glutamate-gated channels by two separate mechanisms: high-affinity binding to N-terminal domains of GluN2A subunits reduces channel open probability, and low-affinity voltage-dependent binding to pore-lining residues blocks the channel. Insight into the high-affinity allosteric effect has been hampered by the receptor's complex gating; multiple, sometimes coupled, modulatory mechanisms; and practical difficulties in avoiding transient block by residual Mg²⁺. To sidestep these challenges, we examined how nanomolar zinc concentrations changed the gating kinetics of individual block-resistant receptors. We found that block-insensitive channels had lower intrinsic open probabilities but retained high sensitivity to zinc inhibition. Binding of zinc to these receptors resulted in longer closures and shorter openings within bursts of activity but had no effect on interburst intervals. Based on kinetic modeling of these data, we conclude that zinc-bound receptors have higher energy barriers to opening and less stable open states. We tested this model for its ability to predict zinc-dependent changes in macroscopic responses and to infer the impact of nanomolar zinc concentrations on synaptic currents mediated by 2A-type NMDA receptors.     

Dendritic spikes veto inhibition

How inhibition regulates dendritic excitability is critical to an understanding of the way neurons integrate the many thousands of synaptic inputs they receive. In this issue of Neuron, Müller et?al. (2012) show that inhibition blocks the generation of weak dendritic spikes, leaving strong dendritic spikes intact.     

Dendritic patch-clamp recording

The patch-clamp technique allows investigation of the electrical excitability of neurons and the functional properties and densities of ion channels. Most patch-clamp recordings from neurons have been made from the soma, the largest structure of individual neurons, while their dendrites, which form the majority of the surface area and receive most of the synaptic input, have been relatively neglected. This protocol describes techniques for recording from the dendrites of neurons in brain slices under direct visual control. Although the basic technique is similar to that used for somatic patching, we describe refinements and optimizations of slice quality, microscope optics, setup stability and electrode approach that are required for maximizing the success rate for dendritic recordings. Using this approach, all configurations of the patch-clamp technique (cell-attached, inside-out, whole-cell, outside-out and perforated patch) can be achieved, even for relatively distal dendrites, and simultaneous multiple-electrode dendritic recordings are also possible. The protocol--from the beginning of slice preparation to the end of the first successful recording--can be completed in 3 h.     

Dendritic Spikes Amplify the Synaptic Signal to Enhance Detection of Motion in a Simulation of the Direction-Selective Ganglion Cell

The On-Off direction-selective ganglion cell (DSGC) in mammalian retinas responds most strongly to a stimulus moving in a specific direction. The DSGC initiates spikes in its dendritic tree, which are thought to propagate to the soma with high probability. Both dendritic and somatic spikes in the DSGC display strong directional tuning, whereas somatic PSPs (postsynaptic potentials) are only weakly directional, indicating that spike generation includes marked enhancement of the directional signal. We used a realistic computational model based on anatomical and physiological measurements to determine the source of the enhancement. Our results indicate that the DSGC dendritic tree is partitioned into separate electrotonic regions, each summing its local excitatory and inhibitory synaptic inputs to initiate spikes. Within each local region the local spike threshold nonlinearly amplifies the preferred response over the null response on the basis of PSP amplitude. Using inhibitory conductances previously measured in DSGCs, the simulation results showed that inhibition is only sufficient to prevent spike initiation and cannot affect spike propagation. Therefore, inhibition will only act locally within the dendritic arbor. We identified the role of three mechanisms that generate directional selectivity (DS) in the local dendritic regions. First, a mechanism for DS intrinsic to the dendritic structure of the DSGC enhances DS on the null side of the cell''s dendritic tree and weakens it on the preferred side. Second, spatially offset postsynaptic inhibition generates robust DS in the isolated dendritic tips but weak DS near the soma. Third, presynaptic DS is apparently necessary because it is more robust across the dendritic tree. The pre- and postsynaptic mechanisms together can overcome the local intrinsic DS. These local dendritic mechanisms can perform independent nonlinear computations to make a decision, and there could be analogous mechanisms within cortical circuitry.     

The Role of Ongoing Dendritic Oscillations in Single-Neuron Dynamics

The dendritic tree contributes significantly to the elementary computations a neuron performs while converting its synaptic inputs into action potential output. Traditionally, these computations have been characterized as both temporally and spatially localized. Under this localist account, neurons compute near-instantaneous mappings from their current input to their current output, brought about by somatic summation of dendritic contributions that are generated in functionally segregated compartments. However, recent evidence about the presence of oscillations in dendrites suggests a qualitatively different mode of operation: the instantaneous phase of such oscillations can depend on a long history of inputs, and under appropriate conditions, even dendritic oscillators that are remote may interact through synchronization. Here, we develop a mathematical framework to analyze the interactions of local dendritic oscillations and the way these interactions influence single cell computations. Combining weakly coupled oscillator methods with cable theoretic arguments, we derive phase-locking states for multiple oscillating dendritic compartments. We characterize how the phase-locking properties depend on key parameters of the oscillating dendrite: the electrotonic properties of the (active) dendritic segment, and the intrinsic properties of the dendritic oscillators. As a direct consequence, we show how input to the dendrites can modulate phase-locking behavior and hence global dendritic coherence. In turn, dendritic coherence is able to gate the integration and propagation of synaptic signals to the soma, ultimately leading to an effective control of somatic spike generation. Our results suggest that dendritic oscillations enable the dendritic tree to operate on more global temporal and spatial scales than previously thought; notably that local dendritic activity may be a mechanism for generating on-going whole-cell voltage oscillations.     

The spikes trains probability distributions: A stochastic calculus approach

We discuss the statistics of spikes trains for different types of integrate-and-fire neurons and different types of synaptic noise models. In contrast with the usual approaches in neuroscience, mainly based on statistical physics methods such as the Fokker-Planck equation or the mean-field theory, we chose the point of the view of the stochastic calculus theory to characterize neurons in noisy environments. We present four stochastic calculus techniques that can be used to find the probability distributions attached to the spikes trains. We illustrate the power of these techniques for four types of widely used neuron models. Despite the fact that these techniques are mathematically intricate we believe that they can be useful for answering questions in neuroscience that naturally arise from the variability of neuronal activity. For each technique we indicate its range of applicability and its limitations.     

Inhibitory Control of Linear and Supralinear Dendritic Excitation in CA1 Pyramidal Neurons

The transformation of dendritic excitatory synaptic inputs to axonal action potential output is the fundamental computation performed by all principal neurons. We show that in the hippocampus this transformation is potently controlled by recurrent inhibitory microcircuits. However, excitatory input on highly excitable dendritic branches could resist inhibitory?control by generating strong dendritic spikes and?trigger precisely timed action potential output. Furthermore, we show that inhibition-sensitive branches can be transformed into inhibition-resistant, strongly spiking branches by intrinsic plasticity of branch excitability. In addition, we demonstrate that the inhibitory control of spatially defined dendritic excitation is strongly regulated by network activity patterns. Our findings suggest that dendritic spikes may serve to transform correlated branch input into reliable and temporally precise output even in the presence of inhibition.     

Neurotransmitter modulation of small-conductance Ca2+-activated K+ channels by regulation of Ca2+ gating

Small-conductance Ca2+-activated K+ (SK) channels are widely expressed in neuronal tissues where they underlie post-spike hyperpolarizations, regulate spike-frequency adaptation, and shape synaptic responses. SK channels constitutively interact with calmodulin (CaM), which serves as Ca2+ sensor, and with protein kinase CK2 and protein phosphatase 2A, which modulate their Ca2+ gating. By recording coupled activities of Ca2+ and SK2 channels, we showed that SK2 channels can be inhibited by neurotransmitters independently of changes in the activity of the priming Ca2+ channels. This inhibition involvesSK2-associated CK2 and results from a 3-fold reduction in the Ca2+ sensitivity of channel gating. CK2phosphorylated SK2-bound CaM but not KCNQ2-bound CaM, thereby selectively regulating SK2 channels. We extended these observations to sensory neurons by showing that noradrenaline inhibits SK current and increases neuronal excitability in aCK2-dependent fashion. Hence, neurotransmitter-initiated signaling cascades can dynamically regulate Ca2+ sensitivity of SK channels and directly influence somatic excitability.     

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.     

Identification and characterization of the slowly exchanging pH-dependent conformational rearrangement in KcsA

Gating of ion channels is strictly regulated by physiological conditions as well as intra/extracellular ligands. To understand the underlying structures mediating ion channel gating, we investigated the pH-dependent gating of the K(+) channel KcsA under near-physiological conditions, using solution-state NMR. In a series of (1)H(15)N-TROSY HSQC (transverse relaxation optimized spectroscopy-heteronuclear single quantum coherence) spectra measured at various pH values, significant chemical shift changes were detected between pH 3.9 and 5.2, reflecting a conformational rearrangement associated with the gating. The pH-dependent chemical shift changes were mainly observed for the resonances from the residues near the intracellular helix bundle, which has been considered to form the primary gate in the K(+) channel, as well as the intracellular extension of the inner helix. The substitution of His-25 by Ala abolished this pH-dependent conformational rearrangement, indicating that the residue serves as a "pH-sensor" for the channel. Although the electrophysiological open probability of KcsA is less than 10%, the conformations of the intracellular helix bundle between the acidic and neutral conditions seem to be remarkably different. This supports the recently proposed "dual gating" properties of the K(+) channel, in which the activation-coupled inactivation at the selectivity filter determines the channel open probability of the channel. Indeed, a pH-dependent chemical shift change was also observed for the signal from the Trp-67 indole, which is involved in a hydrogen bond network related to the activation-coupled inactivation. The slow kinetic parameter obtained for the intracellular bundle seems to fit better into the time scale for burst duration than very fast fluctuations within a burst period, indicating the existence of another gating element with faster kinetic properties.