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

Stochastic Ion Channel Gating in Dendritic Neurons: Morphology Dependence and Probabilistic Synaptic Activation of Dendritic Spikes

Neuronal activity is mediated through changes in the probability of stochastic transitions between open and closed states of ion channels. While differences in morphology define neuronal cell types and may underlie neurological disorders, very little is known about influences of stochastic ion channel gating in neurons with complex morphology. We introduce and validate new computational tools that enable efficient generation and simulation of models containing stochastic ion channels distributed across dendritic and axonal membranes. Comparison of five morphologically distinct neuronal cell types reveals that when all simulated neurons contain identical densities of stochastic ion channels, the amplitude of stochastic membrane potential fluctuations differs between cell types and depends on sub-cellular location. For typical neurons, the amplitude of membrane potential fluctuations depends on channel kinetics as well as open probability. Using a detailed model of a hippocampal CA1 pyramidal neuron, we show that when intrinsic ion channels gate stochastically, the probability of initiation of dendritic or somatic spikes by dendritic synaptic input varies continuously between zero and one, whereas when ion channels gate deterministically, the probability is either zero or one. At physiological firing rates, stochastic gating of dendritic ion channels almost completely accounts for probabilistic somatic and dendritic spikes generated by the fully stochastic model. These results suggest that the consequences of stochastic ion channel gating differ globally between neuronal cell-types and locally between neuronal compartments. Whereas dendritic neurons are often assumed to behave deterministically, our simulations suggest that a direct consequence of stochastic gating of intrinsic ion channels is that spike output may instead be a probabilistic function of patterns of synaptic input to dendrites

Control of clustered action potential firing in a mathematical model of entorhinal cortex stellate cells.

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.The entorhinal cortex is a crucial component of our memory and spatial navigation systems and is one of the first areas to be affected in dementias featuring tau pathology, such as Alzheimer's disease and frontotemporal dementia. Electrophysiological recordings from principle cells of medial entorhinal cortex (layer II stellate cells, mEC-SCs) demonstrate a number of key identifying properties including subthreshold oscillations in the theta (4-12 Hz) range and clustered action potential firing. These single cell properties are correlated with network activity such as grid firing and coupling between theta and gamma rhythms, suggesting they are important for spatial memory. As such, experimental models of dementia have revealed disruption of organised dorsoventral gradients in clustered action potential firing. To better understand the mechanisms underpinning these different dynamics, we study a conductance based model of mEC-SCs. We demonstrate that the model, driven by extrinsic noise, can capture quantitative differences in clustered action potential firing patterns recorded from experimental models of tau pathology and healthy animals. The differential equation formulation of our model allows us to perform numerical bifurcation analyses in order to uncover the dynamic mechanisms underlying these patterns. We show that clustered dynamics can be understood as subcritical Hopf/homoclinic bursting in a fast-slow system where the slow sub-system is governed by activation of the persistent sodium current and inactivation of the slow A-type potassium current. In the full system, we demonstrate that clustered firing arises via flip bifurcations as conductance parameters are varied. Our model analyses confirm the experimentally suggested hypothesis that the breakdown of clustered dynamics in disease occurs via increases in AHP conductance.The contribution of MG, KTR and JB was generously supported by a Wellcome Trust Institutional Strategic Support Award (WT105618MA). MG and KT gratefully acknowledge the financial support of the EPSRC via grant EP/N014391/1. LT’s doctoral studentship is supported by the Alzheimer’s Society in partnership with the Garfield Weston Foundation (grant reference 231). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Population diversity and function of hyperpolarization-activated current in olfactory bulb mitral cells

Although neurons are known to exhibit a broad array of intrinsic properties that impact critically on the computations they perform, very few studies have quantified such biophysical diversity and its functional consequences. Using in vivo and in vitro whole-cell recordings here we show that mitral cells are extremely heterogeneous in their expression of a rebound depolarization (sag) at hyperpolarized potentials that is mediated by a ZD7288-sensitive current with properties typical of hyperpolarization-activated cyclic nucleotide gated (HCN) channels. The variability in sag expression reflects a functionally diverse population of mitral cells. For example, those cells with large amplitude sag exhibit more membrane noise, a lower rheobase and fire action potentials more regularly than cells where sag is absent. Thus, cell-to-cell variability in sag potential amplitude reflects diversity in the integrative properties of mitral cells that ensures a broad dynamic range for odor representation across these principal neurons

The Mechanism of Abrupt Transition between Theta and Hyper-Excitable Spiking Activity in Medial Entorhinal Cortex Layer II Stellate Cells

Recent studies have shown that stellate cells (SCs) of the medial entorhinal cortex become hyper-excitable in animal models of temporal lobe epilepsy. These studies have also demonstrated the existence of recurrent connections among SCs, reduced levels of recurrent inhibition in epileptic networks as compared to control ones, and comparable levels of recurrent excitation among SCs in both network types. In this work, we investigate the biophysical and dynamic mechanism of generation of the fast time scale corresponding to hyper-excitable firing and the transition between theta and fast firing frequency activity in SCs. We show that recurrently connected minimal networks of SCs exhibit abrupt, threshold-like transition between theta and hyper-excitable firing frequencies as the result of small changes in the maximal synaptic (AMPAergic) conductance. The threshold required for this transition is modulated by synaptic inhibition. Similar abrupt transition between firing frequency regimes can be observed in single, self-coupled SCs, which represent a network of recurrently coupled neurons synchronized in phase, but not in synaptically isolated SCs as the result of changes in the levels of the tonic drive. Using dynamical systems tools (phase-space analysis), we explain the dynamic mechanism underlying the genesis of the fast time scale and the abrupt transition between firing frequency regimes, their dependence on the intrinsic SC's currents and synaptic excitation. This abrupt transition is mechanistically different from others observed in similar networks with different cell types. Most notably, there is no bistability involved. ‘In vitro’ experiments using single SCs self-coupled with dynamic clamp show the abrupt transition between firing frequency regimes, and demonstrate that our theoretical predictions are not an artifact of the model. In addition, these experiments show that high-frequency firing is burst-like with a duration modulated by an M-current

Intrinsic electrophysiological properties of entorhinal cortex stellate cells and their contribution to grid cell firing fields

The medial entorhinal cortex (MEC) is an increasingly important focus for investigation of mechanisms for spatial representation. Grid cells found in layer II of the MEC are likely to be stellate cells, which form a major projection to the dentate gyrus. Entorhinal stellate cells are distinguished by distinct intrinsic electrophysiological properties, but how these properties contribute to representation of space is not yet clear. Here, we review the ionic conductances, synaptic, and excitable properties of stellate cells, and examine their implications for models of grid firing fields. We discuss why existing data are inconsistent with models of grid fields that require stellate cells to generate periodic oscillations. An alternative possibility is that the intrinsic electrophysiological properties of stellate cells are tuned specifically to control integration of synaptic input. We highlight recent evidence that the dorsal-ventral organization of synaptic integration by stellate cells, through differences in currents mediated by HCN and leak potassium channels, influences the corresponding organization of grid fields. Because accurate cellular data will be important for distinguishing mechanisms for generation of grid fields, we introduce new data comparing properties measured with whole-cell and perforated patch-clamp recordings. We find that clustered patterns of action potential firing and the action potential after-hyperpolarization (AHP) are particularly sensitive to recording condition. Nevertheless, with both methods, these properties, resting membrane properties and resonance follow a dorsal-ventral organization. Further investigation of the molecular basis for synaptic integration by stellate cells will be important for understanding mechanisms for generation of grid fields

Computational Properties of Cerebellar Nucleus Neurons: Effects of Stochastic Ion Channel Gating and Input Location

The function of the nervous system is shaped by the refined integration of synaptic inputs taking place at the single neuron level. Gain modulation is a computational principle that is widely used across the brain, in which the response of a neuronal unit to a set of inputs is affected in a multiplicative fashion by a second set of inputs, but without any effect on its selectivity. The arithmetic operations performed by pyramidal cells in cortical brain areas have been well characterised, along with the underlying mechanisms at the level of networks and cells, for instance background synaptic noise and dendritic saturation. However, in spite of the vast amount of research on the cerebellum and its function, little is known about neuronal computations carried out by its cellular components. A particular area of interest are the cerebellar nuclei, the main output gate of the cerebellum to the brain stem and cortical areas. The aim of this thesis is to contribute to an understanding of the arithmetic operations performed by neurons in the cerebellar nuclei. Focus is placed on two putative determinants, the location of the synaptic input and the presence of channel noise. To analyse the effect of channel noise, the known voltage-gated ion channels of a cerebellar nucleus neuron model are translated to stochastic Markov formalisms and their electrophysiologial behaviour is compared to their deterministic Hodgkin-Huxley counterparts. The findings demonstrate that in most cases, the behaviour of stochastic channels matches the reference deterministic models, with the notable exception of voltage-gated channels with fast kinetics. Two potential explanations are suggested for this discrepancy. Firstly, channels with fast kinetics are strongly affected by the artefactual loss of gating events in the simulation that is caused by the use of a finite-length time step. While this effect can be mitigated, in part, by using very small time steps, the second source of simulation artefacts is the rectification of the distribution of open channels, when channel kinetics characteristics allow the generation of a window current, with an temporal-averaged equilibrium close to zero. Further, stochastic gating is implemented in a realistic cerebellar nucleus neuronal model. The resulting stochastic model exhibits probabilistic spiking and a similar output rate as the corresponding deterministic cerebellar nucleus neuronal model. However, the outcomes of this thesis indicate the computational properties of the cerebellar nucleus neuronal model are independent of the presence of ion channel noise. The main result of this thesis is that the synaptic input location determines the single neuron computational properties, both in the cerebellar nucleus and layer Vb pyramidal neuronal models. The extent of multiplication increases systematically with the distance from the soma, for the cerebellar nucleus, but not for the layer Vb pyramidal neuron, where it is smaller than it would be expected for the distance from the soma. For both neurons, the underlying mechanism is related to the combined effect of nonlinearities introduced by dendritic saturation and the synaptic input noise. However, while excitatory inputs in the perisomatic areas in the cerebellar nucleus undergo additive operations and the distal areas multiplicative, in the layer Vb pyramidal neuron the integration of the excitatory driving input is always multiplicative. In addition, the change in gain is sensitive to the synchronicity of the excitatory synaptic input in the layer Vb pyramidal neuron, but not in the cerebellar nucleus neuron. These observations indicate that the same gain control mechanism might be utilized in distinct ways, in different computational contexts and across different areas, based on the neuronal type and its function

HCN4 subunit expression in fast-spiking interneurons of the rat spinal cord and hippocampus

Hyperpolarisation-activated (Ih) currents are considered important for dendritic integration, synaptic transmission, setting membrane potential and rhythmic action potential (AP) discharge in neurons of the central nervous system. Hyperpolarisation-activated cyclic nucleotide-gated (HCN) channels underlie these currents and are composed of homo- and hetero-tetramers of HCN channel subunits (HCN1–4), which confer distinct biophysical properties on the channel. Despite understanding the structure–function relationships of HCN channels with different subunit stoichiometry, our knowledge of their expression in defined neuronal populations remains limited. Recently, we have shownthat HCN subunit expression is a feature of a specific population of dorsal horn interneurons that exhibit high-frequency AP discharge. Here we expand on this observation and use neuroanatomical markers to first identify well-characterised neuronal populations in the lumbar spinal cord and hippocampus and subsequently determine whether HCN4 expression correlates with high-frequency AP discharge in these populations. In the spinal cord, HCN4 is expressed in several putative inhibitory interneuron populations including parvalbumin (PV)-expressing islet cells (84.1%; SD: ±2.87), in addition to all putative Renshaw cells and Ia inhibitory interneurons. Similarly, virtually all PVexpressing cells in the hippocampal CA1 subfield (93.5%;±3.40) and the dentate gyrus (90.9%; ±6.38) also express HCN4. This HCN4 expression profile in inhibitory interneurons mirrors both the prevalence of Ih sub-threshold currents and high-frequency AP discharge. Our findings indicate that HCN4 subunits are expressed in several populations of spinal and hippocampal interneurons, which are known to express both Ih sub-threshold currents and exhibit high-frequency AP discharge. As HCN channel function plays a critical role in pain perception, learning and memory,and sleep as well as the pathogenesis of several neurologicaldiseases, these findings provide important insights into the identity and neurochemical status of cells that could underlie such conditions

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review