Ion Channel Density Regulates Switches between Regular and Fast Spiking in Soma but Not in Axons

The threshold firing frequency of a neuron is a characterizing feature of its dynamical behaviour, in turn determining its role in the oscillatory activity of the brain. Two main types of dynamics have been identified in brain neurons. Type 1 dynamics (regular spiking) shows a continuous relationship between frequency and stimulation current (f-Istim) and, thus, an arbitrarily low frequency at threshold current; Type 2 (fast spiking) shows a discontinuous f-Istim relationship and a minimum threshold frequency. In a previous study of a hippocampal neuron model, we demonstrated that its dynamics could be of both Type 1 and Type 2, depending on ion channel density. In the present study we analyse the effect of varying channel density on threshold firing frequency on two well-studied axon membranes, namely the frog myelinated axon and the squid giant axon. Moreover, we analyse the hippocampal neuron model in more detail. The models are all based on voltage-clamp studies, thus comprising experimentally measurable parameters. The choice of analysing effects of channel density modifications is due to their physiological and pharmacological relevance. We show, using bifurcation analysis, that both axon models display exclusively Type 2 dynamics, independently of ion channel density. Nevertheless, both models have a region in the channel-density plane characterized by an N-shaped steady-state current-voltage relationship (a prerequisite for Type 1 dynamics and associated with this type of dynamics in the hippocampal model). In summary, our results suggest that the hippocampal soma and the two axon membranes represent two distinct kinds of membranes; membranes with a channel-density dependent switching between Type 1 and 2 dynamics, and membranes with a channel-density independent dynamics. The difference between the two membrane types suggests functional differences, compatible with a more flexible role of the soma membrane than that of the axon membrane

Ion channel degeneracy enables robust and tunable neuronal firing rates.

Firing rate is an important means of encoding information in the nervous system. To reliably encode a wide range of signals, neurons need to achieve a broad range of firing frequencies and to move smoothly between low and high firing rates. This can be achieved with specific ionic currents, such as A-type potassium currents, which can linearize the frequency-input current curve. By applying recently developed mathematical tools to a number of biophysical neuron models, we show how currents that are classically thought to permit low firing rates can paradoxically cause a jump to a high minimum firing rate when expressed at higher levels. Consequently, achieving and maintaining a low firing rate is surprisingly difficult and fragile in a biological context. This difficulty can be overcome via interactions between multiple currents, implying a need for ion channel degeneracy in the tuning of neuronal properties.This is the author accepted manuscript. The final version is available from National Academy of Sciences via http://dx.doi.org/10.1073/pnas.1516400112

Electric and magnetic fields inside neurons and their impact upon the cytoskeletal microtubules

If we want to better understand how the microtubules can translate and input the information carried by the electrophysiologic impulses that enter the brain cortex, a detailed investigation of the local electromagnetic field structure is needed. In this paper are assessed the electric and the magnetic field strengths in different neuronal compartments. The calculated results are verified via experimental data comparison. It is shown that the magnetic field is too weak to input information to microtubules and no Hall effect, respectively QHE is realistic. Local magnetic flux density is less than 1/300 of the Earth’s magnetic field that’s why any magnetic signal will be suffocated by the surrounding noise. In contrast the electric field carries biologically important information and acts upon voltage-gated transmembrane ion channels that control the neuronal action potential. If mind is linked to subneuronal processing of information in the brain microtubules then microtubule interaction with the local electric field, as input source of information is crucial. The intensity of the electric field is estimated to be 10V/m inside the neuronal cytoplasm however the details of the tubulin-electric field interaction are still unknown. A novel hypothesis stressing on the tubulin C-termini intraneuronal function is presented replacing the current flawed models (Tuszynski 2003, Mershin 2003, Hameroff 2003, Porter 2003) presented at the Quantum Mind II Conference held at Tucson, Arizona, 15-19 March 2003, that are shown in this presentation to be biologically and physically inconsistent

Biophysics of Purkinje computation

Although others have reported and characterised different patterns of Purkinje firing (Womack and Khodakhah, 2002, 2003, 2004; McKay and Turner, 2005) this thesis is the first study that moves beyond their description and investigates the actual basis of their generation. Purkinje cells can intrinsically fire action potentials in a repeating trimodal or bimodal pattern. The trimodal pattern consists of tonic spiking, bursting and quiescence. The bimodal pattern consists of tonic spiking and quiescence. How these firing patterns are generated, and what ascertains which firing pattern is selected, has not been determined to date. We have constructed a detailed biophysical Purkinje cell model that can replicate these patterns and which shows that Na+/K+ pump activity sets the model’s operating mode. We propose that Na+/K+ pump modulation switches the Purkinje cell between different firing modes in a physiological setting and so innovatively hypothesise the Na+/K+ pump to be a computational element in Purkinje information coding. We present supporting in vitro Purkinje cell recordings in the presence of ouabain, which irreversibly blocks the Na+/K+ pump. Climbing fiber (CF) input has been shown experimentally to toggle a Purkinje cell between an up (firing) and down (quiescent) state and set the gain of its response to parallel fiber (PF) input (Mckay et al., 2007). Our Purkinje cell model captures these toggle and gain computations with a novel intracellular calcium computation that we hypothesise to be applicable in real Purkinje cells. So notably, our Purkinje cell model can compute, and importantly, relates biophysics to biological information processing. Our Purkinje cell model is biophysically detailed and as a result is very computationally intensive. This means that, whilst it is appropriate for studying properties of the 8 individual Purkinje cell (e.g. relating channel densities to firing properties), it is unsuitable for incorporation into network simulations. We have overcome this by deploying mathematical transforms to produce a simpler, surrogate version of our model that has the same electrical properties, but a lower computational overhead. Our hope is that this model, of intermediate biological fidelity and medium computational complexity, will be used in the future to bridge cellular and network studies and identify how distinctive Purkinje behaviours are important to network and system function

when channels cooperate or capacitance varies

Die elektrische Signalverarbeitung in Nervenzellen basiert auf deren erregbarer Zellmembran. Üblicherweise wird angenommen, dass die in der Membran eingebetteten leitfähigen Ionenkanäle nicht auf direkte Art gekoppelt sind und dass die Kapazität des von der Membran gebildeten Kondensators konstant ist. Allerdings scheinen diese Annahmen nicht für alle Nervenzellen zu gelten. Im Gegenteil, verschiedene Ionenkanäle “kooperieren” und auch die Vorstellung von einer konstanten spezifischen Membrankapazität wurde kürzlich in Frage gestellt. Die Auswirkungen dieser Abweichungen auf die elektrischen Eigenschaften von Nervenzellen ist das Thema der folgenden kumulativen Dissertationsschrift. Im ersten Projekt wird gezeigt, auf welche Weise stark kooperative spannungsabhängige Ionenkanäle eine Form von zellulärem Kurzzeitspeicher für elektrische Aktivität bilden könnten. Solche kooperativen Kanäle treten in der Membran häufig in kleinen räumlich getrennte Clustern auf. Basierend auf einem mathematischen Modell wird nachgewiesen, dass solche Kanalcluster als eine bistabile Leitfähigkeit agieren. Die dadurch entstehende große Speicherkapazität eines Ensembles dieser Kanalcluster könnte von Nervenzellen für stufenloses persistentes Feuern genutzt werden -- ein Feuerverhalten von Nutzen für das Kurzzeichgedächtnis. Im zweiten Projekt wird ein neues Dynamic Clamp Protokoll entwickelt, der Capacitance Clamp, das erlaubt, Änderungen der Membrankapazität in biologischen Nervenzellen zu emulieren. Eine solche experimentelle Möglichkeit, um systematisch die Rolle der Kapazität zu untersuchen, gab es bisher nicht. Nach einer Reihe von Tests in Simulationen und Experimenten wurde die Technik mit Körnerzellen des *Gyrus dentatus* genutzt, um den Einfluss von Kapazität auf deren Feuerverhalten zu studieren. Die Kombination beider Projekte zeigt die Relevanz dieser oft vernachlässigten Facetten von neuronalen Membranen für die Signalverarbeitung in Nervenzellen.Electrical signaling in neurons is shaped by their specialized excitable cell membranes. Commonly, it is assumed that the ion channels embedded in the membrane gate independently and that the electrical capacitance of neurons is constant. However, not all excitable membranes appear to adhere to these assumptions. On the contrary, ion channels are observed to gate cooperatively in several circumstances and also the notion of one fixed value for the specific membrane capacitance (per unit area) across neuronal membranes has been challenged recently. How these deviations from the original form of conductance-based neuron models affect their electrical properties has not been extensively explored and is the focus of this cumulative thesis. In the first project, strongly cooperative voltage-gated ion channels are proposed to provide a membrane potential-based mechanism for cellular short-term memory. Based on a mathematical model of cooperative gating, it is shown that coupled channels assembled into small clusters act as an ensemble of bistable conductances. The correspondingly large memory capacity of such an ensemble yields an alternative explanation for graded forms of cell-autonomous persistent firing – an observed firing mode implicated in working memory. In the second project, a novel dynamic clamp protocol -- the capacitance clamp -- is developed to artificially modify capacitance in biological neurons. Experimental means to systematically investigate capacitance, a basic parameter shared by all excitable cells, had previously been missing. The technique, thoroughly tested in simulations and experiments, is used to monitor how capacitance affects temporal integration and energetic costs of spiking in dentate gyrus granule cells. Combined, the projects identify computationally relevant consequences of these often neglected facets of neuronal membranes and extend the modeling and experimental techniques to further study them

Modeling the Influence of Ion Channels on Neuron Dynamics in Drosophila

abstract: Voltage gated ion channels play a major role in determining a neuron's firing behavior, resulting in the specific processing of synaptic input patterns. Drosophila and other invertebrates provide valuable model systems for investigating ion channel kinetics and their impact on firing properties. Despite the increasing importance of Drosophila as a model system, few computational models of its ion channel kinetics have been developed. In this study, experimentally observed biophysical properties of voltage gated ion channels from the fruitfly Drosophila melanogaster are used to develop a minimal, conductance based neuron model. We investigate the impact of the densities of these channels on the excitability of the model neuron. Changing the channel densities reproduces different in situ observed firing patterns and induces a switch from integrator to resonator properties. Further, we analyze the preference to input frequency and how it depends on the channel densities and the resulting bifurcation type the system undergoes. An extension to a three dimensional model demonstrates that the inactivation kinetics of the sodium channels play an important role, allowing for firing patterns with a delayed first spike and subsequent high frequency firing as often observed in invertebrates, without altering the kinetics of the delayed rectifier current.View the article as published at http://journal.frontiersin.org/article/10.3389/fncom.2015.00139/ful

Implications of stochastic ion channel gating and dendritic spine plasticity for neural information processing and storage

On short timescales, the brain represents, transmits, and processes information through the electrical activity of its neurons. On long timescales, the brain stores information in the strength of the synaptic connections between its neurons. This thesis examines the surprising implications of two separate, well documented microscopic processes — the stochastic gating of ion channels and the plasticity of dendritic spines — for neural information processing and storage. Electrical activity in neurons is mediated by many small membrane proteins called ion channels. Although single ion channels are known to open and close stochastically, the macroscopic behaviour of populations of ion channels are often approximated as deterministic. This is based on the assumption that the intrinsic noise introduced by stochastic ion channel gating is so weak as to be negligible. In this study we take advantage of newly developed efficient computer simulation methods to examine cases where this assumption breaks down. We find that ion channel noise can mediate spontaneous action potential firing in small nerve fibres, and explore its possible implications for neuropathic pain disorders of peripheral nerves. We then characterise the magnitude of ion channel noise for single neurons in the central nervous system, and demonstrate through simulation that channel noise is sufficient to corrupt synaptic integration, spike timing and spike reliability in dendritic neurons. The second topic concerns neural information storage. Learning and memory in the brain has long been believed to be mediated by changes in the strengths of synaptic connections between neurons — a phenomenon termed synaptic plasticity. Most excitatory synapses in the brain are hosted on small membrane structures called dendritic spines, and plasticity of these synapses is dependent on calcium concentration changes within the dendritic spine. In the last decade, it has become clear that spines are highly dynamic structures that appear and disappear, and can shrink and enlarge on rapid timescales. It is also clear that this spine structural plasticity is intimately linked to synaptic plasticity. Small spines host weak synapses, and large spines host strong synapses. Because spine size is one factor which determines synaptic calcium concentration, it is likely that spine structural plasticity influences the rules of synaptic plasticity. We theoretically study the consequences of this observation, and find that different spine-size to synaptic-strength relationships can lead to qualitative differences in long-term synaptic strength dynamics and information storage. This novel theory unifies much existing disparate data, including the unimodal distribution of synaptic strength, the saturation of synaptic plasticity, and the stability of strong synapses

Investigating the role of fast-spiking interneurons in neocortical dynamics

PhD ThesisFast-spiking interneurons are the largest interneuronal population in neocortex. It is well documented that this population is crucial in many functions of the neocortex by subserving all aspects of neural computation, like gain control, and by enabling dynamic phenomena, like the generation of high frequency oscillations. Fast-spiking interneurons, which represent mainly the parvalbumin-expressing, soma-targeting basket cells, are also implicated in pathological dynamics, like the propagation of seizures or the impaired coordination of activity in schizophrenia. In the present thesis, I investigate the role of fast-spiking interneurons in such dynamic phenomena by using computational and experimental techniques. First, I introduce a neural mass model of the neocortical microcircuit featuring divisive inhibition, a gain control mechanism, which is thought to be delivered mainly by the soma-targeting interneurons. Its dynamics were analysed at the onset of chaos and during the phenomena of entrainment and long-range synchronization. It is demonstrated that the mechanism of divisive inhibition reduces the sensitivity of the network to parameter changes and enhances the stability and exibility of oscillations. Next, in vitro electrophysiology was used to investigate the propagation of activity in the network of electrically coupled fast-spiking interneurons. Experimental evidence suggests that these interneurons and their gap junctions are involved in the propagation of seizures. Using multi-electrode array recordings and optogenetics, I investigated the possibility of such propagating activity under the conditions of raised extracellular K+ concentration which applies during seizures. Propagated activity was recorded and the involvement of gap junctions was con rmed by pharmacological manipulations. Finally, the interaction between two oscillations was investigated. Two oscillations with di erent frequencies were induced in cortical slices by directly activating the pyramidal cells using optogenetics. Their interaction suggested the possibility of a coincidence detection mechanism at the circuit level. Pharmacological manipulations were used to explore the role of the inhibitory interneurons during this phenomenon. The results, however, showed that the observed phenomenon was not a result of synaptic activity. Nevertheless, the experiments provided some insights about the excitability of the tissue through scattered light while using optogenetics. This investigation provides new insights into the role of fast-spiking interneurons in the neocortex. In particular, it is suggested that the gain control mechanism is important for the physiological oscillatory dynamics of the network and that the gap junctions between these interneurons can potentially contribute to the inhibitory restraint during a seizure.Wellcome Trust