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.

abstract: It is increasingly common to see machine learning techniques applied in conjunction with computational modeling for data-driven research in neuroscience. Such applications include using machine learning for model development, particularly for optimization of parameters based on electrophysiological constraints. Alternatively, machine learning can be used to validate and enhance techniques for experimental data analysis or to analyze model simulation data in large-scale modeling studies, which is the approach I apply here. I use simulations of biophysically-realistic cortical neuron models to supplement a common feature-based technique for analysis of electrophysiological signals. I leverage these simulated electrophysiological signals to perform feature selection that provides an improved method for neuron-type classification. Additionally, I validate an unsupervised approach that extends this improved feature selection to discover signatures associated with neuron morphologies - performing in vivo histology in effect. The result is a simulation-based discovery of the underlying synaptic conditions responsible for patterns of extracellular signatures that can be applied to understand both simulation and experimental data. I also use unsupervised learning techniques to identify common channel mechanisms underlying electrophysiological behaviors of cortical neuron models. This work relies on an open-source database containing a large number of computational models for cortical neurons. I perform a quantitative data-driven analysis of these previously published ion channel and neuron models that uses information shared across models as opposed to information limited to individual models. The result is simulation-based discovery of model sub-types at two spatial scales which map functional relationships between activation/inactivation properties of channel family model sub-types to electrophysiological properties of cortical neuron model sub-types. Further, the combination of unsupervised learning techniques and parameter visualizations serve to integrate characterizations of model electrophysiological behavior across scales. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2020

Ziel dieser Arbeit ist es eine Beziehung zwischen den biophysikalischen Eigenschaften der Nervenmembran, und den ausgeführten Berechnungen und Filtereigenschaften eines tonisch feuernden Neurons, unter Einbeziehen intrinsischer Fluktuationen, herzustellen. Zu diesem Zweck werden zu erst die mikroskopischen Fluktuationen, die durch das stochastische Öffnen und Schließen der Ionenkanäle verursacht werden, zu makroskopischer Varibilität in den Zeitpunkten des Auftretens der Aktionspotentiale übersetzt, denn es sind diese Spikezeiten die in vielen sensorischen Systemen informationstragenden sind. Die Methode erlaubt es das stochastischer Verhalten komplizierter Ionenkanalstrukturen mit einer großen Zahl an Untereinheiten, in Spikezeitenvariabilität zu übersetzen. Als weiteres werden die Filtereigenschaften der Nervenzellen in der überschwelligen Dynamik, also bei Existenz eines stabilen Grenzzyklus, aus ihren Phasenantwortkurven (PAK), einer Eigenschaft des linearisierten adjungierten Flusses auf dem Grenzzyklus, in einem stöhrungstheoretischen Ansatz berechnet. Es ergibt sich, dass Charakteristika des Filter, wie beispielsweise die DC Komponente und die Eigenschaften des Filters um die Fundamentalfrequenz und ihrer Harmonien, von den Fourierkomponenten der PAK abhängen. Unter Verwendung der hergeleiteten Filter und weiterer Annahmen ist es möglich das frequenzabhängige Signal-zu-Rauschen Verhältnis zu berechnen, und damit eine untere Schranke für die Informationstransferrate eines Leitfähigkeitsmodells zu berechnen. Unter Zuhilfenahme der numerischen Kontinuierungsmethode ist es möglich die Veränderungen in der Spikevariabilität und den Filtern für jeden biophysikalischen Parameter des System zu verfolgen. Weiterhin wurde die verwendete Phasenreduktion durch eine Korrektur ergänzt, die die Radialdynamik einbezieht. Es zeigt sich, dass die Krümmung der Isochronen einen Einfluss darauf hat ob das Rauschen einen positiven oder negativen Frequenzschift hervorruft. / The goal of the thesis is to establish quantitative, analytical relations between the biophysical properties of nerve membranes and the performed neuronal computations for neurons in a tonically spiking regime and in the presence of intrinsic noise. For this purpose, two major lines of investigation are followed. Firstly, microscopic noise caused by the stochastic opening and closing of ion channels is mapped to the macroscopic spike jitter that affects neural coding. The method is generic enough to allow one to treat Markov channel models with complicated, high-dimensional state spaces and calculate from them the noise in the coding variable, i.e., the spike time. Secondly, the suprathreshold filtering properties of neurons are derived, based on the phase response curves (PRCs) by perturbing the associated Fokker-Planck equations. It turns out that key characteristics of the filter, such as the DC component of the gain and the behaviour near the fundamental frequency and its harmonics are related to the particular Fourier components of the PRC and hence the bifurcation type of the neuron. With the help of the derived filter and further approximations one is able to calculate the frequency resolved signal-to-noise ration and finally the total information transmission rate of a conductance based model. Using the method of numerical continuation it is possible to calculate the change in spike time noise level as well as the filtering properties for arbitrary changes in biophysical parameter such as varying channel densities or mean input to the cell. We extend the phase reduction to include correction terms from the amplitude dynamics that are related to the curvature of the isochrons and provide a method to identify the required amplitude sensitivities numerically. It can be shown that the curvature of the isochron has a direct consequence for the noise induced frequency shift.