A model study of cellular short-term memory produced by slowly inactivating potassium conductances

Abstract. We analyzed the cellular short-term memory effects induced by a slowly inactivating potassium (Ks) conductance using a biophysical model of a neuron. We first described latency-to-first-spike and temporal changes in firing frequency as a function of parameters of the model, injected current and prior history of the neuron (deinactivation level) under current clamp. This provided a complete set of properties describing the Ks conductance in a neuron. We then showed that the action of the Ks conductance is not generally appropriate for controlling latency-to-first-spike under random synaptic stimulation. However, reliable latencies were found when neuronal population computation was used. Ks inactivation was found to control the rate of convergence to steady-state discharge behavior and to allow frequency to increase at variable rates in sets of synaptically connected neurons. These results suggest that inactivation of the Ks conductance can have a reliable influence on the behavior of neuronal populations under real physiological conditions

A model study of cellular short-term memory produced by slowly inactivating potassium conductances

Abstract. We analyzed the cellular short-term memory effects induced by a slowly inactivating potassium (Ks) conductance using a biophysical model of a neuron. We first described latency-to-first-spike and temporal changes in firing frequency as a function of parameters of the model, injected current and prior history of the neuron (deinactivation level) under current clamp. This provided a complete set of properties describing the Ks conductance in a neuron. We then showed that the action of the Ks conductance is not generally appropriate for controlling latency-to-first-spike under random synaptic stimulation. However, reliable latencies were found when neuronal population computation was used. Ks inactivation was found to control the rate of convergence to steady-state discharge behavior and to allow frequency to increase at variable rates in sets of synaptically connected neurons. These results suggest that inactivation of the Ks conductance can have a reliable influence on the behavior of neuronal populations under real physiological conditions

Learning intrinsic excitability in medium spiny neurons

We present an unsupervised, local activation-dependent learning rule for intrinsic plasticity (IP) which affects the composition of ion channel conductances for single neurons in a use-dependent way. We use a single-compartment conductance-based model for medium spiny striatal neurons in order to show the effects of parametrization of individual ion channels on the neuronal activation function. We show that parameter changes within the physiological ranges are sufficient to create an ensemble of neurons with significantly different activation functions. We emphasize that the effects of intrinsic neuronal variability on spiking behavior require a distributed mode of synaptic input and can be eliminated by strongly correlated input. We show how variability and adaptivity in ion channel conductances can be utilized to store patterns without an additional contribution by synaptic plasticity (SP). The adaptation of the spike response may result in either "positive" or "negative" pattern learning. However, read-out of stored information depends on a distributed pattern of synaptic activity to let intrinsic variability determine spike response. We briefly discuss the implications of this conditional memory on learning and addiction.Comment: 20 pages, 8 figure

Parameter Optimization for Excitable Cell Models

The electrophysiology of nodose ganglia neurons is of great interest in the analysis of cell membrane currents and action potential behavior. This behavior was initially outlined in the Hodgkin-Huxley conductance model [1] using a system of nonlinear differential equations. Later, Schild et al. [2] developed an extension of the Hodgkin-Huxley model to provide a more exhaustive description of ion channels involved in nodose neuronal action potential activity. We consider a variety of methods to fit the parameters of both the Hodgkin-Huxley and Schild et al. models to an empirical stimulus response dataset. Our methods were validated using synthetic datasets, as well as voltage-clamp data for nodose neurons. The fitting procedure that we implemented demonstrates the predictive efficacy of the Schild et al. model as well as its ability to provide a superior characterization of electrical signatures of nodose neurons

Mechanisms of the Coregulation of Multiple Ionic Currents for the Control of Neuronal Activity

An open question in contemporary neuroscience is how neuromodulators coregulate multiple conductances to maintain functional neuronal activity. Neuromodulators enact changes to properties of biophysical characteristics, such as the maximal conductance or voltage of half-activation of an ionic current, which determine the type and properties of neuronal activity. We apply dynamical systems theory to study the changes to neuronal activity that arise from neuromodulation. Neuromulators can act on multiple targets within a cell. The coregulation of mulitple ionic currents extends the scope of dynamic control on neuronal activity. Different aspects of neuronal activity can be independently controlled by different currents. The coregulation of multiple ionic currents provides precise control over the temporal characteristics of neuronal activity. Compensatory changes in multiple ionic currents could be used to avoid dangerous dynamics or maintain some aspect of neuronal activity. The coregulation of multiple ionic currents can be used as bifurcation control to ensure robust dynamics or expand the range of coexisting regimes. Multiple ionic currents could be involved in increasing the range of dynamic control over neuronal activity. The coregulation of multiple ionic currents in neuromodulation expands the range over which biophysical parameters support functional activity

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

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

Modulation of cardiac Kv currents by Kvbeta2 and pyridine nucleotides.

Myocardial voltage-gated potassium (Kv) channels regulate the resting membrane potential and the repolarization phase of the action potential. Members of the Kv1 and Kv4 family associate with ancillary subunits, such as the Kvβ proteins, that modify channel kinetics, gating and trafficking. Previous investigation into the function of cardiac β subunits demonstrated that Kvβ1 regulates Ito and IK,slow currents in the heart, but the role of Kvβ2 in the myocardium remains unknown. In heterologous expression systems, Kvβ2 increases surface expression of Kv1 channels, shifts the activation potential of Kv1 channels to more polarized voltages, and increases the inactivation of Kv1 channels. Accordingly, the electrophysiological phenotype in Kvβ2-/- mice was examined to uncover its role. To investigate the effects of the loss of Kvβ2 on cardiac repolarization, we performed whole-cell electrophysiology on primary cardiac myocytes. We found Kv current density was reduced and action potential duration prolonged in myocytes lacking Kvβ2. To isolate the molecular interactions by which Kvβ2 was affecting Kv currents, we show that Kvβ2 co-immunoprecipitates with Kv1.4 and Kv1.5 in heart lysates. To measure if surface expression of these Kv channels was reduced with the loss of Kvβ2, we performed immunofluorescent confocal microscopy of isolated cardiac myocytes. We found that the surface expression of Kv1.5 was reduced in Kvβ2-/- myocytes. We also performed a membrane fractionation technique to demonstrate that the proportion of total cellular Kv1.5 at the membrane was reduced in Kvβ2-/-. Together, these findings support our hypothesis that Kvβ2 plays a role in the generation of functional Kv currents in the myocardium by interacting with members of the Kv family. The pyridine nucleotides, NAD[P](H), are ubiquitous cofactors utilized as electron donors and acceptors by over 250 cellular oxidoreductases. Work out of our laboratory has shown that the Kvβ proteins are functional enzymes of the aldo-keto reductase family, that utilize NAD[P]H to catalyze the reduction of substrates. Furthermore, follow up work has shown that the redox status of bound pyridine nucleotide (PN) modifies the gating of Kvα-Kvβ channel complexes in heterologous expression systems. To examine a physiological role for PN in cardiac repolarization, whole-cell and single channel cardiac myocyte currents were recorded under the exposure to various PN redox states. We found that the inactivation rates and open probabilities of Kv currents in isolated myocytes are sensitive to the redox status of PN, and that surface action potentials in an isolated heart model are prolonged by treatment with factors that increase intracellular NADH concentration