Dissertations / Theses on the topic 'Hodgkin-Huxley model'

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.

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Para representar diferentes fenômenos e sistemas modelos matemáticos são largamente utilizados. Muitos deles são fundamentados em sistemas de equações diferenciais ordinárias (EDOs), isto é, baseiam-se em conjuntos de igualdades que envolvem variáveis dependentes, suas derivadas de primeira ordem e a variável independente. Neste trabalho, estudamos a modelagem da geração do potencial de ação em células excitáveis, como os neurônios. Existem dois modelos tradicionais e pioneiros que se destacam nessa área: Hodgkin-Huxley e FitzHugh-Nagumo. O objetivo desta dissertação é avaliar a possibilidade de modelar a geração do potencial de ação via uma única equação diferencial com atraso. Equações diferenciais com atraso são importantes por sua capacidade em reproduzir uma grande diversidade de fenômenos. Porém, seu uso na modelagem do potencial de ação de células excitáveis é ainda incipiente. Nesta dissertação, o método usado para alcançar este objetivo se baseou no desenvolvimento, inicialmente, de uma equação integro-diferencial que aproxima o sistema de EDOs. Em seguida, desenvolvemos uma aproximação para as integrais que usa termos tanto no instante atual quanto em instante anteriores, i.e., atrasados no tempo. Dessa forma, mostramos que é possível aproximar cada um dos sistemas de EDOS dos modelos de Hodgkin-Huxley e FitzHugh-Nagumo por uma única equação diferencial com atraso. Por fim, estes novos modelos são comparados com os originais, e são apontadas direções para a continuidade desta pesquisa.
To represent different phenomena and systems mathematical models are widely used. Many of them are based on systems of ordinary differential equations (ODEs), that is, they are based on sets of equalities involving dependent variables, their derivatives of first order and the independent variable. In this work, we study the modeling of action potential generation in excitable cells, such as neurons. There are two traditional and pioneering models that stand out in this area: Hodgkin-Huxley and FitzHugh-Nagumo. The objective of this dissertation is to evaluate the possibility of modeling the generation of the action potential via a single differential equation with delay. Differential equations with delay are important because of their capacity to reproduce a great diversity of phenomena. However, its use in modeling the action potential of excitable cells is still incipient. In this dissertation, the method used to achieve this goal was based on the development, initially, of an integral-differential equation that approximates the ODE system. Next, we develop an approximation for integrals that uses terms at both the current instant and the previous instant, i.e., time delayed. Thus, we show that it is possible to approximate each of the ODEs systems of the Hodgkin-Huxley and FitzHugh-Nagumo models by a single differential equation with delay. Finally, these new models are compared with the original ones, and directions are indicated for future works.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
In this thesis, it was investigated the influence of synaptic plasticity in the dynamics of neuronal networks. Specifically, we analyzed the effect on creation and suppression of synchronization spikes in networks composed of neurons with excitatory and inhibitory synapses. The spike timing-dependent plasticity (STDP) changes the strength of existing synapses in the neuronal network. To simulate the dynamics of each neuron, we considered the Hodgkin and Huxley model (HH), that is able to provide the main features of the temporal evolution of the membrane potential of each cell. The Kuramoto order parameter was utilized as synchronization diagnostic. First of all, we have studied the dynamics spikes in neuronal networks on a global and random topology with excitatory synapses with plasticity (STDP). It was observed that the STDP improves synchronization in a sufficiently dense neuronal networks. However, this effect is maximized by the insertion of an external perturbation of moderate intensity. Further, the system behavior was analyzed using the combination of inhibitory and excitatory synapses, both with spike timing-dependent plasticity. Our results indicated that the network becomes desynchronized when the intensity of inhibitory synapses is increased. Nevertheless, for small intensities of these synapses there was an increase in the values of the order parameter when the system with STDP was perturbed.
Nesta tese foi investigada a influência dos modelos de plasticidade sináptica na dinâmica de redes neuronais. Especificamente, foi analisado o efeito da plasticidade na criação e supressão da sincronização ao de disparos em redes compostas por neurônios com sinapses excitatórias e inibitórias. O modelo de plasticidade sináptica dependente do tempo entre disparos (do inglês: Spike-timing-dependent plasticity: STDP), modifica a intensidade das sinapses existentes na rede neuronal. Para simular a dinâmica de cada neurônio foi utilizado o modelo de Hodgkin e Huxley (HH), que ´e capaz de fornecer as principais características da evolução ao temporal do potencial de membrana de cada célula. Como diagnóstico de sincronização foi utilizado o parâmetro de ordem de Kuramoto. Primeiramente foi investigada a dinâmica de disparos em redes neuronais com topologia global e aleatória com sinapses excitatórias com plasticidade (STDP). Observou-se que a STDP contribui para a sincronização ao do sistema em redes neuronais suficientemente densas. No entanto, este efeito é maximizado com a inserção de uma perturbação o externa de intensidade moderada. Na sequência, foi analisado o comportamento do sistema com a combinação de sinapses excitatórias e inibitórias, ambas com STDP. Os resultados indicaram que a rede torna-se não sincronizada com o aumento da intensidade das sinapses inibitórias. Entretanto, para pequenas intensidades destas sinapses, observou-se um acréscimo nos valores do parâmetro de ordem quando o sistema com STDP foi perturbado.

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.

There have been many different studies performed in order to examine various properties of neurons. One of the most important properties of neurons is an ability to originate and propagate action potential. The action potential is a source of communication between different neural structures located in different anatomical regions. Many different studies use modeling to describe the action potential and its properties. These models mathematically describe physical properties of neurons and analyze and explain biological and electrochemical processes such as action potential initiation and propagation. Therefore, one of the most important functions of neurons is an ability to provide communication between different neural structures located in different anatomical regions. This is achieved by transmitting electrical signals from one part of the body to another. For example, neurons transmit signals from the brain to the motor neurons (efferent neurons) and from body tissues back to the brain (afferent neurons). This communication process is extremely important for a being to function properly. One of the most valuable studies in neuroscience was conducted by Alan Hodgkin and Andrew Huxley. In their work, Alan Hodgkin and Andrew Huxley used a giant squid axon to create a mathematical model which analyzes and explains the ionic mechanisms underlying the initiation and propagation of action potentials. They received the 1963 Nobel Prize in Physiology/Medicine for their valuable contribution to medical science. The Hodgkin and Huxley model is a mathematical model that describes how the action potential is initiated and how it propagates in a neuron. It is a set of nonlinear ordinary differential equations that approximates the electrical characteristics of excitable cells such as neurons and cardiomyocytes. This work focuses on modeling the Hodgkin and Huxley model using MATLAB extension - Simulink. This tool provides a graphical editor, customizable block libraries, and solvers for modeling and simulating dynamic systems. Simulink model is used to describe the mechanisms and underlying processes involved in action potential initiation and propagation.

Abstract Visual world is naturally correlated both spatially and temporally. The correlations are used in vision to enhance performance of neurons. For gaining maximal neural performance of the visual neurons, the experiments, from stimulus to the analysis, should be designed to take advantage of the correlations. In this thesis methods for generating and analyzing natural stimuli were examined by using computations and algorithms. For analyzing responses to natural stimuli in visual neurons, a method with only a few assumptions was developed for estimating information rate in long responses. The novel method gave a good agreement with Shannon information rate with linear system and Gaussian input but was able to handle also nonlinear processing and non-Gaussian data. Secondly, a computer controlled 3D virtual environment with a spherical screen was developed, with a large visual field. The image of the world was projected to the screen with a DLP projector, giving good enough temporal performance for insect vision research. A track-ball was used in closed loop experiments. Thirdly, properties of single photon (“bump”) information transfer at various light levels were investigated in cockroach photoreceptor with a coarse computational model. At dim light (< 10 ph/s), where single bump responses were visible, shot noise was dominant. At higher light levels latency distribution of the bump decreased the information rate, but amplitude distribution of bump did not have an effect. Fourthly, the contribution of K⁺ channels to information rate and energy consumption was investigated by creating a database of computation models with varying channel compositions. The information rate has a maximum as a function of mean conductance, which was a sum of the average K⁺ conductance and the leak conductance. This maximum was fine-tuned by the K⁺ channel composition, which had high so-called novel contribution and relatively low amount of other conductances.

Dans ces travaux de thèse, nous nous sommes intéressés à l'influence du bruit synaptique sur la plasticité synaptique dans un réseau de neurones biophysiquement réalistes. Le simulateur utilisé est un système électronique neuromorphique. Nous avons implanté un modèle de neurones à conductances basé sur le formalisme de Hodgkin et Huxley, et un modèle biophysique de plasticité. Ces travaux ont inclus la configuration du système, le développement d'outils pour l'exploiter, son utilisation ainsi que la mise en place d'une plateforme le rendant accessible à la communauté scientifique via Internet et l'utilisation de scripts PyNN (langage de description de simulations en neurosciences computationnelles)
In this work, we have investigated the effect of input noise patterns on synaptic plasticity applied to a neural network. The study was realised using a neuromorphic hardware simulation system. We have implemented a neural conductance model based on Hodgkin and Huxley formalism, and a biophysical model for plasticity. The tasks performed during this thesis project included the configuration of the system, the development of software tools, the analysis tools to explore experimental results, and the development of the software modules for the remote access to the system via Internet using PyNN scripts (PyNN is a neural network description language commonly used in computational neurosciences)

Electrical Engineering
M.S.E.E.
The aim of the research is to provide a computationally efficient neural network model for the study of deep brain stimulation efficacy in the treatment of Parkinson's disease. An Izhikevich neuron model was used to accomplish this task and four classes of neurons were modeled. The parameters of each class were estimated using a genetic algorithm with a fitness function based on spike frequency as a function of input current. After computing the optimal parameters the neurons were interconnected to form the network model. The estimated parameters were capable of replicating the normal firing characteristics for each type of neuron, but failed to replicate richer spiking characteristics such as post-inhibitory bursting and tonic firing. Without these characteristics, the network was unable to produce biologically feasible results. Findings indicate the Izhikevich model relies heavily on manual tuning and must be trained under an extensive set of conditions to allow for the majority of spiking characteristics to be learned. The use of the Izhikevich model in a network simulation will always be limited to the characteristics trained on a single neuron. When connected to the network the neuron may be exposed to a variety of unlearned conditions and therefore may not be capable of replicating biologically realistic behavior.
Temple University--Theses

Ces travaux ont été menés dans le cadre du projet européen FACETS-ITN. Nous avons contribué à la simulation de cellules corticales grâce à des données expérimentales d'électrophysiologie comme référence et d'un circuit intégré neuromorphique comme simulateur. Les propriétés intrinsèques temps réel de nos circuits neuromorphiques à base de modèles à conductance, autorisent une exploration détaillée des différents types de neurones. L'aspect analogique des circuits intégrés permet le développement d'un simulateur matériel temps réel à l'échelle du réseau. Le deuxième objectif de cette thèse est donc de contribuer au développement d'une plate-forme mixte - matérielle et logicielle - dédiée à la simulation de réseaux de neurones impulsionnels
This work has been supported by the European FACETS-ITN project. Within the frameworkof this project, we contribute to the simulation of cortical cell types (employingexperimental electrophysiological data of these cells as references), using a specific VLSIneural circuit to simulate, at the single cell level, the models studied as references in theFACETS project. The real-time intrinsic properties of the neuromorphic circuits, whichprecisely compute neuron conductance-based models, will allow a systematic and detailedexploration of the models, while the physical and analog aspect of the simulations, as opposedthe software simulation aspect, will provide inputs for the development of the neuralhardware at the network level. The second goal of this thesis is to contribute to the designof a mixed hardware-software platform (PAX), specifically designed to simulate spikingneural networks. The tasks performed during this thesis project included: 1) the methodsused to obtain the appropriate parameter sets of the cortical neuron models that can beimplemented in our analog neuromimetic chip (the parameter extraction steps was validatedusing a bifurcation analysis that shows that the simplified HH model implementedin our silicon neuron shares the dynamics of the HH model); 2) the fully customizablefitting method, in voltage-clamp mode, to tune our neuromimetic integrated circuits usinga metaheuristic algorithm; 3) the contribution to the development of the PAX systemin terms of software tools and a VHDL driver interface for neuron configuration in theplatform. Finally, it also addresses the issue of synaptic tuning for future SNN simulation

The purpose of this thesis work is to model the gate control theory, which explains the modulation of pain signals, with a motivation of finding new possible targets for pain treatment and to find novel control algorithms that can be used in engineering practice. The difference of the current study from the previous modeling trials is that morphologies of neurons that constitute gate control system are also included in the model by which structure-function relationship can be observed. Model of an excitable neuron is constructed and the response of the model for different perturbations are investigated. The simulation results of the excitable cell model is obtained and when compared with the experimental findings obtained by using crayfish, it is found that they are in good agreement. Model encodes stimulation intensity information as firing frequency and also it can add sub-threshold inputs and fire action potentials as real neurons. Moreover, model is able to predict depolarization block. Absolute refractory period of the single cell model is found as 3.7 ms. The developed model, produces no action potentials when the sodium channels are blocked by tetrodotoxin. Also, frequency and amplitudes of generated action potentials increase when the reversal potential of Na is increased. In addition, propagation of signals along myelinated and unmyelinated fibers is simulated and input current intensity-frequency relationships for both type of fibers are constructed. Myelinated fiber starts to conduct when current input is about 400 pA whereas this minimum threshold value for unmyelinated fiber is around 1100 pA. Propagation velocity in the 1 cm long unmyelinated fiber is found as 0.43 m/s whereas velocity along myelinated fiber with the same length is found to be 64.35 m/s. Developed synapse model exhibits the summation and tetanization properties of real synapses while simulating the time dependency of neurotransmitter concentration in the synaptic cleft. Morphometric analysis of neurons that constitute gate control system are done in order to find electrophysiological properties according to dimensions of the neurons. All of the individual parts of the gate control system are connected and the whole system is simulated. For different connection configurations, results of the simulations predict the observed phenomena for the suppression of pain. If the myelinated fiber is dissected, the projection neuron generates action potentials that would convey to brain and elicit pain. However, if the unmyelinated fiber is dissected, projection neuron remains silent. In this study all of the simulations are preformed using Simulink.

The work in this thesis concerns mechanisms of excitability of neurons. Specifically, it deals with how neurons respond to input, and how their response is controlled by ion channels and other active components of the neuron. I have studied excitability in two systems of the nervous system, the hippocampus which is responsible for memory and spatial navigation, and the peripheral C–fibre which is responsible for sensing and conducting sensory information to the spinal cord. Within the work, I have studied the role of excitability mechanisms in normal function and in pathological conditions. For hippocampus the normal function includes changes in excitability linked to learning and memory. However, it also is intimately linked to pathological increases in excitability observed in epilepsy. In C–fibres, excitability controls sensitivity to responses to stimuli. When this response becomes enhanced, this can lead to pain. I have used computational modelling as a tool for studying hyperexcitability in neurons in the central nervous system in order to address mechanisms of epileptogenesis. Epilepsy is a brain disorder in which a subject has repeated seizures (convulsions) over time. Seizures are characterized by increased and highly synchronized neural activity. Therefore, mechanisms that regulate synchronized neural activity are crucial for the understanding of epileptogenesis. Such mechanisms must differentiate between synchronized and semi synchronized synaptic input. The candidate I propose for such a mechanism is the fast outward current generated by the A-type potassium channel (KA). Additionally, I have studied the propagation of action potentials in peripheral axons, denoted C–fibres. These C–fibres mediate information about harmful peripheral stimuli from limbs and organs to the central nervous system and are thereby linked to pathological pain. If a C–fibre is activated repeatedly, the excitability is altered and the mechanisms for this alteration are unknown. By computational modelling, I have proposed mechanisms which can explain this alteration in excitability. In summary, in my work I have studied roles of particular ion channels in excitability related to functions in the nervous system. Using computational modelling, I have been able to relate specific properties of ion channels to functions of the nervous system such as sensing and learning, and in particular studied the implications of mechanisms of excitability changes in diseases.

QC 20102423

Modification of Hodgkin and Huxley’s experimentally derived set of nonlinear differential equations was implemented to accurately simulate the action potential of the Hirudo Medicinalis’s Retzius cell in MATLAB under analogous conditions to those found in the Retzius cell environment. The voltage-gated sodium and potassium channel responses to changes in membrane potential, as experimentally determined by Hodgkin and Huxley, were manipulated to suit simulation parameters established by electrophysiological Retzius cell recordings. Application of this methodology permitted additional accurate simulation of the Hirudo Medicinalis’s P cell under analogous conditions to those found in the P cell environment. Further refinement of this technique should allow for the voltage-gated behavioral based simulation of action potential waveforms found in variety of neurons under simulation conditions analogous to the nerve cell environment.

Thesis (Ph.D)--Algorithms, Combinatorics, and Optimization, Georgia Institute of Technology, 2010.
Committee Chair: Tovey, Craig; Committee Member: Butera, Rob; Committee Member: Nemirovski, Arkadi; Committee Member: Prinz, Astrid; Committee Member: Sokol, Joel. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Realizamos simulações computacionais de modelos da atividade elétrica de centros geradores de padrões para investigar o fato experimental de organismos vivos utilizarem neurônios caóticos para produzir padrões periódicos. Centros geradores de padrões biológicos produzem atividades motoras periódicas que devem ser robustas a pequenas flutuações das propriedades dos neurônios e sinapses, mas também flexíveis para permitir a neuromodulação do ritmo. Utilizamos principalmente dois modelos de atividade neural, um modelo fenomenológico do tipo Hindmarsh-Rose e um modelo baseado em condutâncias do tipo Hodgking-Huxley. Realizamos também experimentos com redes híbridas, conectando dois tipos de neurônios do gânglio estomatogástrico de crustáceos aos neurônios modelo, que confirmaram os resultados obtidos nas simulações. Observamos o comportamento das redes principalmente em função de dois parâmetros: um que controla a atividade intrínseca dos neurônios e outro que representa a condutância máxima das sinapses químicas usadas para formar a rede. As redes apresentam atividade robusta e flexível quando os neurônios que as compõem apresentam comportamento intrínseco entre rajadas e tônico. Esta é a região onde os neurônios modelo apresentam comportamento caótico, o que é uma evidência do motivo de se observar este tipo de comportamento em neurônios isolados do gânglio estomatogástrico dos crustáceos. Mostramos que o modelo tipo Hodgkin-Huxley, apesar de mais realista do ponto de vista eletrofisiológico, não apresenta um comportamento coletivo satisfatório em termos de flexibilidade e robustez. Os experimentos com redes híbridas evidenciaram como deveria ser modificado o modelo para que o comportamento coletivo fosse restaurado. Investigamos também outros aspectos da atividade neural: a obtenção de padrões oscilatórios com neurônios que não apresentam comportamento intrinsecamente oscilatório e a influência de perturbações causada por ruídos na atividade neural.
Realizamos simulações computacionais de modelos da atividade elétrica de centros geradores de padrões para investigar o fato experimental de organismos vivos utilizarem neurônios caóticos para produzir padrões periódicos. Centros geradores de padrões biológicos produzem atividades motoras periódicas que devem ser robustas a pequenas flutuações das propriedades dos neurônios e sinapses, mas também flexíveis para permitir a neuromodulação do ritmo. Utilizamos principalmente dois modelos de atividade neural, um modelo fenomenológico do tipo Hindmarsh-Rose e um modelo baseado em condutâncias do tipo Hodgking-Huxley. Realizamos também experimentos com redes híbridas, conectando dois tipos de neurônios do gânglio estomatogástrico de crustáceos aos neurônios modelo, que confirmaram os resultados obtidos nas simulações. Observamos o comportamento das redes principalmente em função de dois parâmetros: um que controla a atividade intrínseca dos neurônios e outro que representa a condutância máxima das sinapses químicas usadas para formar a rede. As redes apresentam atividade robusta e flexível quando os neurônios que as compõem apresentam comportamento intrínseco entre rajadas e tônico. Esta é a região onde os neurônios modelo apresentam comportamento caótico, o que é uma evidência do motivo de se observar este tipo de comportamento em neurônios isolados do gânglio estomatogástrico dos crustáceos. Mostramos que o modelo tipo Hodgkin-Huxley, apesar de mais realista do ponto de vista eletrofisiológico, não apresenta um comportamento coletivo satisfatório em termos de flexibilidade e robustez. Os experimentos com redes híbridas evidenciaram como deveria ser modificado o modelo para que o comportamento coletivo fosse restaurado. Investigamos também outros aspectos da atividade neural: a obtenção de padrões oscilatórios com neurônios que não apresentam comportamento intrinsecamente oscilatório e a influência de perturbações causada por ruídos na atividade neural. We have performed computational simulations of models of the neural electrical activity of central pattern generators in order to investigate the experimental fact that living organisms use chaotic neurons to produce periodic patterns. Biological central pattern generators produce periodic motor activity that must be robust to small fluctuacions in the neural and synaptic properties, but they must also be flexible to alow rhythm neuromodulation. We have used mainly two different models of neural activity, one phenomenological Hindmarsh-Rose type and another conductance based Hodgking-Huxley type. We have also performed experiments with hybrid networks, connecting two types crustacean stomatogastric ganglion neurons with the model neurons, which confirmed the results obtained with the simulations. We have simulated the network behavior as a function of two parameters: the maximal conductance of the chemical synapses by which neurons are connected and a parameter that controls the intrinsic behavior of the neurons. The networks present robust and flexible activity when the neurons have intrinsic beharior between bursting and tonic. This is the region in which model neurons present chaotic behavior, what is an evidence of why chaotic behavior takes place in isolated neurons from the stomatogastric ganglion (STG) of crustaceans. We have shown that the Hodgking-Huxley type model does not perform a satisfactory collective behavior in terms of flexibility and robustness, in spite of its electrophysiological realism. Experiments with hybrid networks showed how the model should be modified in order to restore the proper collective behavior. We have also investigated other aspects of the neural activity: the observation of oscillatory patterns in networks composed by neurons that are not endogenous bursters and the influence of perturbations in the neural activity caused by noize.

This work has been supported by the European FACETS-ITN project. Within the frameworkof this project, we contribute to the simulation of cortical cell types (employingexperimental electrophysiological data of these cells as references), using a specific VLSIneural circuit to simulate, at the single cell level, the models studied as references in theFACETS project. The real-time intrinsic properties of the neuromorphic circuits, whichprecisely compute neuron conductance-based models, will allow a systematic and detailedexploration of the models, while the physical and analog aspect of the simulations, as opposedthe software simulation aspect, will provide inputs for the development of the neuralhardware at the network level. The second goal of this thesis is to contribute to the designof a mixed hardware-software platform (PAX), specifically designed to simulate spikingneural networks. The tasks performed during this thesis project included: 1) the methodsused to obtain the appropriate parameter sets of the cortical neuron models that can beimplemented in our analog neuromimetic chip (the parameter extraction steps was validatedusing a bifurcation analysis that shows that the simplified HH model implementedin our silicon neuron shares the dynamics of the HH model); 2) the fully customizablefitting method, in voltage-clamp mode, to tune our neuromimetic integrated circuits usinga metaheuristic algorithm; 3) the contribution to the development of the PAX systemin terms of software tools and a VHDL driver interface for neuron configuration in theplatform. Finally, it also addresses the issue of synaptic tuning for future SNN simulation.

碩士
逢甲大學
應用數學所
94
Automatic neuron firing is an important and interesting research subject in neuroelectrophysiology. Through the original Hodgkin-Huxley model, we investigate its codimension 1 bifurcations along maximum conductance of sodium channel, maximum conductance of potassium channel, and extracellular potassium concentration. We find that increasing maximum conductance of sodium channel, or decreasing maximum conductance of potassium channel, or increasing extracellular potassium concentration will all cause spontaneous oscillation without any external stimulus current. The effect that increasing extracellular potassium concentration will cause repetitive neuron firing has been verified by experiments, but the effect of changing channel maximum conductance will cause automatic neuron firing is first analyzed in the current paper but not yet verified by experiments. We hope the experiment can be done in the future by using sodium channel activator and potassium channel blocker.

碩士
國立臺灣大學
應用數學科學研究所
107
This thesis presents a dynamic simulation of intracellular and extracellular ionic concentrations and electric potential, then create an action potential, which is generated by a difference of the electrochemical potential between two sides of a cell membrane. Ion species including Sodium, Potassium and Chlorine. This simulation would involve Poisson-Nernst-Planck (PNP) system and Hodgkin–Huxley (HH) model. The former gives a standard model for describing behaviors of ionic diffusion and electrophoresis. The latter gives a transformation between mechanism of ion channels and a circuit. We want to combine and compare the results of these two models, then try to verify that the PNP equations can reduce to the HH model. In this study, methodologies are based on finite volume method and pseudospectral method for space discretization. After changing the semi-discrete scheme to a system of ODE by method of lines(MOL), we use ode15s solver on MATLAB to handle for time integration.

Hodgkin-Huxley (HH) 模型對於電流生理學的發展有著深遠的影響。它能精確地模擬離子通道的變化。然而，隨著多年來的反覆驗證，研究人員發現HH模型亦有其局限性和不足之處。有見及此，本論文提出一個建基於變形動力學的模型，藉此以更深入的物理層面解釋Hodgkin與Huxley的實驗數據。新的模型為鉀與鈉離子通道建立了新的電導方程。在這模型的詮釋下，HH模型的鉀離子通道電導方程[附圖] 被[附圖]取代，而HH模型的鈉離子通道電導方程 [附圖] 則被 [附圖] 取而代之。縱使 n(t), m(t)和 h(t)在兩個模型中被授予不同的物理意義，但它們均是一階微分方程。此論文詳細闡述模型的建立過程及參數的推導，並論證它能準確地描繪Hodgkin與Huxley對於烏賊巨軸突的實驗數據。模型參數經由遺傳演算法優化後，新的模型不僅能夠準確描述離子通道的電導變化，還能闡述Cole-Moore shift現象。在相同強度的去極化刺激和溫度下，新的模型比HH模型能接近地模擬膜動作電位的實驗數據。
Hodgkin-Huxley (HH) model has a profound influence on the development of electrophysiology. It is capable of modeling the transient responses of voltage-gated ion channels precisely. Nevertheless, limitations and deficiencies of the model were found as researchers conducted subsequent experiments. In this regard, a new model based on deformation kinetic has been put forth to help explaining the HH experimental data with a deeper level of physical insight. Under the proposed model, the famous HH equation [with formula] for the description of potassium conductance was replaced by [with formula] and the HH sodium conductance equation [with formula] was substituted by [with formula]. Meanwhile, n(t), m(t) and h(t) are still first order differential equations as the HH case. This thesis contributes to illustrate the capability of the new model in approximating HH’s experimental data on squids’ giant axons. Detailed derivation of the new model and identification of the parametric functions are summarized in this report. A customized genetic algorithm was utilized to optimize the model parameters. After fine tuning the new model, we are able to describe the conductance behaviors of voltage-gated ion channels closely, and manage to account for the Cole-Moore shift phenomenon. Under identical initial depolarizing stimuli and temperature as stated in HH’s experiments, close approximations of membrane action potential can also be obtained by the new model.
Detailed summary in vernacular field only.
Yu, Cheuk Him Derek.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2012.
Includes bibliographical references (leaves 69-70).
Abstracts also in Chinese.
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Overview of Electrophysiological Models --- p.4
Chapter 1.2 --- The Hodgkin-Huxley Membrane Current Model --- p.4
Chapter 1.2.1 --- Hodgkin-Huxley Potassium Channel --- p.6
Chapter 1.2.2 --- Hodgkin-Huxley Sodium Channel --- p.8
Chapter 1.3 --- Proliferation of the Deformation Kinetic Based Model --- p.10
Chapter 1.4 --- Thesis Outline --- p.12
Chapter 2 --- The Deformation Kinetic Based Model --- p.13
Chapter 2.1 --- The Molecular Theory --- p.13
Chapter 2.1.1 --- Application of Deformation Kinetics --- p.13
Chapter 2.1.2 --- The Energy Function E{U+2093} (q) --- p.14
Chapter 2.1.3 --- The Population Distribution Function P{U+2093} (N,t) --- p.17
Chapter 2.1.4 --- Conductance Model for Voltage-gated Ion Channels --- p.18
Chapter 2.2 --- The Approximate Solutions --- p.19
Chapter 2.2.1 --- Approximation of the General Solution for G{U+2093} (N) --- p.19
Chapter 2.2.2 --- Approximation of the General Solution for P{U+2093} (N,t) --- p.19
Chapter 2.2.3 --- The Approximate Solution for Molecular g{U+2093} (t) --- p.23
Chapter 2.2.4 --- A Convenient Form of the Approximate Solutions --- p.24
Chapter 2.3 --- Chapter Summary --- p.25
Chapter 3 --- Voltage-gated Ion Channel Modeling --- p.27
Chapter 3.1 --- Voltage-gated Potassium Channel Modeling --- p.27
Chapter 3.2 --- Voltage-gated Sodium Channel Modeling --- p.29
Chapter 3.3 --- Chapter Summary --- p.31
Chapter 4 --- The Parametric Functions --- p.32
Chapter 4.1 --- The Curve Fitting References - HH Experimental Data --- p.32
Chapter 4.2 --- Curve Fitting through Genetic Algorithm --- p.34
Chapter 4.3 --- Functional Approximations w.r.t. HH Experimental Data --- p.37
Chapter 4.3.1 --- Parametric Functions for Voltage-gated Potassium Channel --- p.37
Chapter 4.3.2 --- Parametric Functions for Voltage-gated Sodium Channel --- p.39
Chapter 4.4 --- Chapter Summary --- p.46
Chapter 5 --- The Tracing Results --- p.47
Chapter 5.1 --- Voltage Clamp Tracings --- p.47
Chapter 5.1.1 --- Potassium Conductance Tracings --- p.48
Chapter 5.1.2 --- Sodium Conductance Tracings --- p.49
Chapter 5.2 --- Membrane Action Potential Tracings --- p.54
Chapter 5.3 --- Propagated Action Potential Tracings --- p.56
Chapter 5.4 --- Chapter Summary --- p.59
Chapter 6? --- The Cole-Moore Shift Phenomenon --- p.60
Chapter 6.1 --- Cole-Moore shift Phenomenon of Voltage-gated Potassium Channel --- p.61
Chapter 6.2 --- Cole-Moore Shift Phenomenon of Voltage-gated Sodium Channel --- p.62
Chapter 6.3 --- Chapter Summary --- p.64
Chapter 7 --- Discussions --- p.65
Conclusion --- p.67
Future Works --- p.68
References --- p.69
Chapter Appendix I --- Hodgkin-Huxley’s Analysis of Voltage-gated Channels’ Voltage Clamp Data
Chapter (a) --- HH’s Analysis of Potassium Conductance Change in Voltage Clamp Experiments --- p.71
Chapter (b) --- HH’s Analysis of Sodium Conductance Change in Voltage Clamp Experiments --- p.71
Chapter Appendix II --- Numerical Estimations of Hodgkin-Huxley’s Experimental Data
Chapter (a) --- Numerical Estimations of Podium Conductance Change in Voltage Clamp Experiments for HH axon 17 --- p.72
Chapter (b) --- Numerical Estimations of Sodium Conductance Change in Voltage Clamp Experiments for HH axon 17 --- p.73
Chapter (c) --- Numerical Estimations of Membrane Action Potential with Different Initial Depolarizations for HH axon 17 --- p.74
Chapter Appendix III --- Verification of the Replica of HH Model’s Simulations Results
Chapter (a) --- Comparison between HH Membrane Action Potential and Its Replica --- p.75
Chapter (b) --- Comparison between HH Propagated Action Potential and Its Replica --- p.76

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.

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.

Yes
This paper investigates the interaction phenomena of the coupled axons while the mutual coupling factor is presented as a pairwise description. Based on the Hodgkin-Huxley model and the coupling factor matrix, the membrane potentials of the coupled myelinated/unmyelinated axons are quantified which implies that the neural coupling can be characterised by the presented coupling factor. Meanwhile the equivalent electric circuit is supplied to illustrate the physical meaning of this extended model. In order to estimate the coupling factor, a data-based iterative learning identification algorithm is presented where the Rényi entropy of the estimation error has been minimised. The convergence of the presented algorithm is analysed and the learning rate is designed. To verified the presented model and the algorithm, the numerical simulation results indicate the correctness and the effectiveness. Furthermore, the statistical description of the neural coupling, the approximation using ordinary differential equation, the measurement and the conduction of the nerve signals are discussed respectively as advanced topics. The novelties can be summarised as follows: 1) the Hodgkin-Huxley model has been extended considering the mutual interaction between the neural axon membranes, 2) the iterative learning approach has been developed for factor identification using entropy criterion, and 3) the theoretical framework has been established for this class of system identification problems with convergence analysis.
This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 51807010, and in part by the Natural Science Foundation of Hunan under Grant 1541 and Grant 1734.
Research Development Fund Publication Prize Award winner, Nov 2020.