Cochlear implants (CIs) are prosthetic devices used to partially restore hearing for profound and severely deaf individuals. CIs convert sounds into electrical pulses which stimulate the auditory nerve fibers. An accurate model of auditory nerve fibers (ANFs) would help in improving the functionality of CIs. Previous studies have shown that the original Hodgkin-Huxley (1952) model (with kinetics adjusted for mammalian body temperature) may be better at describing nodes of Ranvier in ANFs than models for other mammalian axon types. However, the Hodgkin-Huxley model is still unable to explain a number of phenomena observed in auditory nerve responses to CI stimulation, such as short-term and long-term adaptation, the time-course of relative refractoriness, and stimulus-dependent random fluctuations in membrane threshold. Recent physiological investigations of spiral ganglion cells have shown the presence of a number of ion channel types not considered in the previous modelling studies, including low-threshold potassium (𝐼^KLT) channels and hyperpolarization-activated cation (𝐼^h) channels. In this thesis, inclusion of these ion channel types in a stochastic Hodgkin-Huxley model is investigated. Four versions of the model are formed and compared: that is, the standard Hodgkin-Huxley model, the standard model with /h only added, the standard model with 𝐼^KLT only added, and finally, the standard model with both h and 𝐼^KLT added. Two group of responses are explored: i) single-pulse responses and ii) pules-train responses. For the single pulse responses, a charge-balanced biphasic stimulus pulse is used. The effect of varying the pulse-width and the interphase gap is investigated for both leading phase polarities. Results are compared to responses for single monophasic stimulus pulses in some cases. Pulse-train responses are investigated for charge-balanced depolarizing-phase leading biphasic pulses at rates of 200, 800, and 2000 pulse/s. Results from single-pulse responses show an increase in spike threshold when one or both of these channel types are included. The addition of 𝐼^KLT increases random threshold fluctuations in the stochastic model, particularly for longer pulse widths. For pulse-train responses, rapid adaptation in spike rate may be resulting from 𝐼^KLT whereas 𝐼^h produces slower "short-term" adaptation. Thus, the simulation results suggest that including 𝐼^KLT and/or 𝐼^h in a Hodgkin-Huxley model improves the accuracy of the model in describing auditory nerve fiber responses during cochlear implant stimulation. / Thesis / Master of Applied Science (MASc)

No description available.

A Hodgkin-Huxley style system of ODEs was developed to model the ion channel activity of A. punctulata sperm flagellum during exposure to resact during chemotaxis. Empirical data was used in conjunction with parameter estimation methods in an attempt for the model to reproduce realistic Voltage potentials and ion concentrations. The change in calcium concentration is of particular interest, as it is essential in the waveform of the flagellum during chemotaxis.

Abstract The activity of neurons is critically dependent upon the suite of voltage-dependent ion channels expressed in their membranes. In particular, voltage-gated K+ channels are extremely diverse in their function, contributing to the regulation of distinct aspects of neuronal activity by shaping the voltage responses. In this study the role of K+ channels in neural coding is investigated in Drosophila photoreceptors by using biophysical models with parameters derived from the electrophysiological experiments. Due to their biophysical properties, the Shaker channels attenuate the fast transients and amplify the slower signal components, enabling photoreceptors to use their voltage range more effectively. Slow delayed rectifier channels, shown to be encoded by the Shab gene, activate at high light intensities, thereby attenuating the light-induced depolarization and preventing response saturation. Activation of Shab channels also reduces the membrane time constant making it possible to encode faster events. Interactions between the voltage-gated K+ channels and the currents generated by the light induced conductance (LIC) were investigated during naturalistic stimulation in wild type and Shaker mutant photoreceptors. It is shown that in addition to eliminating the Shaker current, the mutation increased the Shab current and affected the current flowing through the LIC. Part of these changes could be attributed to direct feedback from the Shaker channels via the membrane potential. However, it is suggested that also other changes may occur in the LIC due to mutation in K+ channels, possibly during photoreceptor development. Comparison of the Shaker and Shab mutant photoreceptors with the wild type revealed that a concurrent decrease in the steady-state input resistance followed from deletion of the voltage-gated K+ channels. This allowed partial compensation of the compression and saturation caused by the loss of Shaker channels and it maintained the characteristics of the light-voltage relationship in Shab mutant photoreceptors. However, wild type properties were not fully restored in either mutant. Indeed, decreased input resistance results in reduced efficiency of neural processing, assessed by the metabolic cost of information. Results of this study demonstrate the importance of the voltage-gated K+ channels for neural coding precision and highlight the robustness of neuronal information processing gained through regulation of the electrical properties.

Neural oscillations, including rhythms in the beta1 band (12-20 Hz), are important in various cognitive functions. Often brain networks receive rhythmic input at frequencies different than their natural frequency, so understanding how neural networks process rhythmic input is important for understanding their function in the brain. In the current thesis we study a beta1 rhythm that appears in the parietal cortex, focusing on the way it interacts with other incoming rhythms, and the implications of this interaction for cognition. The main part of the thesis consists of two stand-alone chapters, both using as a basis a biophysical neural network model that has been previously proposed to model the parietal beta1 rhythm and validated with in vitro experiments. In the first chapter we use a reduced version of this model, in order to study its dynamics, applying both analytic and numerical methods from dynamical systems. We show that a cell can respond at the same time to two periodic stimuli of unrelated frequencies, firing in phase with one, but with a mean firing rate equal to the other, a consequence of general properties of the dynamics of the network. We next show numerically that the behavior of a different cell, which is modeled as a high-dimensional dynamical system, can be described in a surprisingly simple way, owing to a reset that occurs in the state space when the cell fires. The interaction of the two cells leads to novel combinations of properties for neural dynamics, such as mode-locking to an input without phase-locking to it. In the second chapter, we study the ability of the beta1 model to support memory functions, in particular working memory. Working memory is a highly distributed component of the brain's memory systems, partially based in the parietal cortex. We show numerically that the parietal beta1 rhythm can provide an anatomical substrate for an episodic buffer of working memory. Specifically, it can support flexible and updatable representations of sensory input which are sensitive to distractors, allow for a read-out mechanism, and can be modulated or terminated by executive input.

Neste trabalho as equações fenomenológicas (tetra-dimensionais) de Hodgkin-Huxley [5], para a membrana da fibra do neurônio, são estudadas mediante transformações não-lineares de variáveis. As transformações de variáveis visam estabelecer um processo controlado de redução de variáveis até chegar a um modelo bidimensional com o menor prejuízo quantitativo possível. O objetivo primordial é aprofundar o entendimento da aparente relação das equações de Hodgkin-Huxley com uma versão da equação de 2ª ordem de van der Pol, conhecida na literatura pelos nomes de equação de FitzHugh-Nagumo [83], equação de Nagumo [84] ou equação Bonhoeffer-van der Pol [7]. É proposta também uma nova formulação matemática para o modelo da corrente de potássio. Estas modificações possibilitam a elaboração de uma remodelagem do aspecto e funcionamento interno do circuito equivalente da membrana. Este circuito, além de facilitar as simplificações para comparar as novas equações em relação ao modelo tipo van der pol, apresenta também potencial teórico mais desenvolvido do que o circuito equivalente original de Hodgkin-Huxley, já que ao contrário deste os elementos do novo circuito podem ser mais facilmente reconhecidos e manipulados dentro da teoria usual de circuitos elétricos. Uma primeira conseqüência da concepção do novo circuito, aqui explorada, é a formulação do modelo da membrana na linguagem da mecânica analítica. / The phenomenological four-variable equations of Hodgkin and Huxley [5] for the neuron fiber membrane are studied by means of nonlinear transformations of variables . The purpose is gradually reduce the number of variables to a three and then to a two-dimensional model, with smallest possible deviations from the quantitative properties of the original model. The primary aim is to get better insights into the apparent connect ion between the Hodgkin-Huxley equations and a version of the second order equation of van der Pol, usually called FitzHugh-Nagumo equation [83], or Nagumo equation [84], or Bonhoeffer- van der Pol equation [7]. An alternative formulation for the potassium current is also proposed. The above modifications lead to an alternative circuit model for the nerve membrane. Such circuit helps the comparison with the van der Pol-type model. It exhibits also better theoretical appeal than the original circuit of Hodgkin and Huxley in the sense that the circuit elements are now properly defined in terms of usual electrical circuit theory. An application of the proposed equivalent circuit i s a description of the Hodgkin-Huxley membrane model according to the formalism of analytical mechanics.

Neste trabalho as equações fenomenológicas (tetra-dimensionais) de Hodgkin-Huxley [5], para a membrana da fibra do neurônio, são estudadas mediante transformações não-lineares de variáveis. As transformações de variáveis visam estabelecer um processo controlado de redução de variáveis até chegar a um modelo bidimensional com o menor prejuízo quantitativo possível. O objetivo primordial é aprofundar o entendimento da aparente relação das equações de Hodgkin-Huxley com uma versão da equação de 2ª ordem de van der Pol, conhecida na literatura pelos nomes de equação de FitzHugh-Nagumo [83], equação de Nagumo [84] ou equação Bonhoeffer-van der Pol [7]. É proposta também uma nova formulação matemática para o modelo da corrente de potássio. Estas modificações possibilitam a elaboração de uma remodelagem do aspecto e funcionamento interno do circuito equivalente da membrana. Este circuito, além de facilitar as simplificações para comparar as novas equações em relação ao modelo tipo van der pol, apresenta também potencial teórico mais desenvolvido do que o circuito equivalente original de Hodgkin-Huxley, já que ao contrário deste os elementos do novo circuito podem ser mais facilmente reconhecidos e manipulados dentro da teoria usual de circuitos elétricos. Uma primeira conseqüência da concepção do novo circuito, aqui explorada, é a formulação do modelo da membrana na linguagem da mecânica analítica. / The phenomenological four-variable equations of Hodgkin and Huxley [5] for the neuron fiber membrane are studied by means of nonlinear transformations of variables . The purpose is gradually reduce the number of variables to a three and then to a two-dimensional model, with smallest possible deviations from the quantitative properties of the original model. The primary aim is to get better insights into the apparent connect ion between the Hodgkin-Huxley equations and a version of the second order equation of van der Pol, usually called FitzHugh-Nagumo equation [83], or Nagumo equation [84], or Bonhoeffer- van der Pol equation [7]. An alternative formulation for the potassium current is also proposed. The above modifications lead to an alternative circuit model for the nerve membrane. Such circuit helps the comparison with the van der Pol-type model. It exhibits also better theoretical appeal than the original circuit of Hodgkin and Huxley in the sense that the circuit elements are now properly defined in terms of usual electrical circuit theory. An application of the proposed equivalent circuit i s a description of the Hodgkin-Huxley membrane model according to the formalism of analytical mechanics.

Thesis (MSc (Biochemistry))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: The Hodgkin-Huxley model, created in 1952, was one of the first models in computational neuroscience and remains the best studied neuronal model to date. Although many other models have a more detailed system description than the Hodgkin-Huxley model, it nonetheless gives an accurate account of various high-level neuronal behaviours. The fields of computational neuroscience and Systems Biology have developed as separate disciplines for a long time and only fairly recently has the neurosciences started to incorporate methods from Systems Biology. Metabolic Control Analysis (MCA), a Systems Biology tool, has not been used in the neurosciences. This study aims to further bring these two fields together, by testing the feasibility of an MCA approach to analyse the Hodgkin-Huxley model. In MCA it is not the parameters of the system that are perturbed, as in the more traditional sensitivity analysis, but the system processes, allowing the formulation of summation and connectivity theorems. In order to determine if MCA can be performed on the Hodgkin-Huxley model, we identified all the discernable model processes of the neuronal system. We performed MCA and quantified the control of the model processes on various high-level time invariant system observables, e.g. the action potential (AP) peak, firing threshold, propagation speed and firing frequency. From this analysis we identified patterns in process control, e.g. the processes that would cause an increase in sodium current, would also cause the AP threshold to lower (decrease its negative value) and the AP peak, propagation speed and firing frequency to increase. Using experimental inhibitor titrations from literature we calculated the control of the sodium channel on AP characteristics and compared it with control coefficients derived from our model simulation. Additionally, we performed MCA on the model’s time-dependent state variables during an AP. This revealed an intricate linking of the system variables via the membrane potential. We developed a method to quantify the contribution of the individual feedback loops in the system. We could thus calculate the percentage contribution of the sodium, potassium and leak currents leading to the observed global change after a system perturbation. Lastly, we compared ion channel mutations to our model simulations and showed how MCA can be useful in identifying targets to counter the effect of these mutations. In this thesis we extended the framework of MCA to neuronal systems and have successfully applied the analysis framework to quantify the contribution of the system processes to the model behaviour. / AFRIKAANSE OPSOMMINMG: Die Hodgkin-Huxley-model, wat in 1952 ontwikkel is, was een van die eerste modelle in rekenaarmagtige neurowetenskap en is vandag steeds een van die bes-bestudeerde neuronmodelle. Hoewel daar vele modelle bestaan met ’n meer uitvoerige sisteembeskrywing as die Hodgkin-Huxley-model gee dié model nietemin ’n akkurate beskrywing van verskeie hoëvlak-sisteemverskynsels. Die twee velde van sisteembiologie en neurowetenskap het lank as onafhanklike dissiplines ontwikkel en slegs betreklik onlangs het die veld van neurowetenskap begin om metodes van sisteembiologie te benut. ’n Sisteembiologiemetode genaamd metaboliese kontrole-analise (MKA) is tot dusver nog nie in die neurowetenskap gebruik nie. Hierdie studie het gepoog om die twee velde nader aan mekaar te bring deurdat die toepasbaarheid van die MKA-raamwerk op die Hodgkin-Huxley-model getoets word. In MKA is dit nie die parameters van die sisteem wat geperturbeer word soos in die meer tradisionele sensitiwiteitsanalise nie, maar die sisteemprosesse. Dit laat die formulering van sommasie- en konnektiwiteitsteoremas toe. Om die toepasbaarheid van die MKA-raamwerk op die Hodgkin-Huxleymodel te toets, is al die onderskeibare modelprosesse van die neurale sisteem geïdentifiseer. Ons het MKA toegepas en die kontrole van die model-prosesse op verskeie hoëvlak, tydsonafhanklike waarneembare sisteemvlak-eienskappe, soos die aksiepotensiaal-kruin, aksiepotensiaal-drempel, voortplantingspoed en aksiepotensiaal-frekwensie, gekwantifiseer. Vanuit hierdie analise kon daar patrone in die proseskontrole geïdentifiseer word, naamlik dat die prosesse wat ’n toename in die natriumstroom veroorsaak, ook sal lei tot ’n afname in die aksiepotensiaal-drempel (die negatiewe waarde verminder) en tot ’n toename in die aksiepotensiaal-kruin, voortplantingspoed en aksiepotensiaalfrekwensie. Deur gebruik te maak van eksperimentele stremmer-titrasies vanuit die literatuur kon die kontrole van die natriumkanaal op die aksiepotensiaaleienskappe bereken en vergelyk word met die kontrole-koëffisiënte vanuit die modelsimulasie. Ons het ook MKA op die model se tydsafhanklike veranderlikes deur die verloop van die aksiepotensiaal uitgevoer. Die analise het getoon dat die sisteemveranderlikes ingewikkeld verbind is via die membraanpotensiaal. Ons het ’n metode ontwikkel om die bydrae van die individuele terugvoerlusse in die sisteem te kwantifiseer. Die persentasie-bydrae van die natrium-, kalium- en lekstrome wat tot die waarneembare globale verandering ná ’n sisteemperturbasie lei, kon dus bepaal word. Laastens het ons ioonkanaalmutasies met ons modelsimulasies vergelyk en getoon hoe MKA nuttig kan wees in die identifisering van teikens om die effek van hierdie mutasies teen te werk. In hierdie tesis het ons die raamwerk van MKA uitgebrei na neurale sisteme en die analise-raamwerk suksesvol toegepas om die bydrae van die sisteemprosesse tot die modelgedrag te kwantifiseer.

Noise-like activity (NLA) refers to spontaneous subthreshold fluctuations in membrane potential. In this thesis, we examine the role that synaptic channel fluctuations play in contributing to NLA by comparing a detailed biophysical model to experimental data from whole-intact hippocampal interneurons. To represent the contribution from synaptic channel fluctuations, we switch the synapses in the model from traditional to Markovian formalisms and demonstrate statistically relevant increases the standard deviation; power-law scaling exponent; and power spectral density in the 5-100 Hz and 1-5 kHz ranges. However, while synaptic channel fluctuations have a definite effect, we found that they were significantly more subtle than the synaptic response to network activity. This indicates that synaptic channel fluctuations do indeed play a significant role in subthreshold noise, but, overall, synaptic NLA is dominated by the synaptic response to presynaptic network activity.

Noise-like activity (NLA) refers to spontaneous subthreshold fluctuations in membrane potential. In this thesis, we examine the role that synaptic channel fluctuations play in contributing to NLA by comparing a detailed biophysical model to experimental data from whole-intact hippocampal interneurons. To represent the contribution from synaptic channel fluctuations, we switch the synapses in the model from traditional to Markovian formalisms and demonstrate statistically relevant increases the standard deviation; power-law scaling exponent; and power spectral density in the 5-100 Hz and 1-5 kHz ranges. However, while synaptic channel fluctuations have a definite effect, we found that they were significantly more subtle than the synaptic response to network activity. This indicates that synaptic channel fluctuations do indeed play a significant role in subthreshold noise, but, overall, synaptic NLA is dominated by the synaptic response to presynaptic network activity.