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A Cell-Level Neural Simulation Suite for the Analysis of Learning and Adaptive Behavior in the C Die approbierte Originalversion dieser Diplom-/ Masterarbeit ist in der Hauptbibliothek der Tech- nischen Universität Wien aufgestellt und zugänglich. http://www.ub.tuwien.ac.at The approved original version of this diploma or master thesis is available at the main library of the Vienna University of Technology. http://www.ub.tuwien.ac.at/eng A cell-level neural simulation suite for the analysis of learning and adaptive behavior in the C. elegans’ nervous system DIPLOMARBEIT zur Erlangung des akademischen Grades Diplom-Ingenieurin im Rahmen des Studiums Biomedical Engineering eingereicht von Magdalena Fuchs Matrikelnummer 00926092 an der Fakultät für Informatik der Technischen Universität Wien Betreuung: Prof. Radu Grosu Mitwirkung: Dott. Mag. Ramin Hasani Wien, 1. Mai 2018 Magdalena Fuchs Radu Grosu Technische Universität Wien A-1040 Wien Karlsplatz 13 Tel. +43-1-58801-0 www.tuwien.ac.at A Cell-level Neural Simulation Suite for the Analysis of Learning and Adaptive Behavior in the C. elegans’ Nervous System DIPLOMA THESIS submitted in partial fulfillment of the requirements for the degree of Diplom-Ingenieurin in Biomedical Engineering by Magdalena Fuchs Registration Number 00926092 to the Faculty of Informatics at the TU Wien Advisor: Prof. Radu Grosu Assistance: Dott. Mag. Ramin Hasani Vienna, 1st May, 2018 Magdalena Fuchs Radu Grosu Technische Universität Wien A-1040 Wien Karlsplatz 13 Tel. +43-1-58801-0 www.tuwien.ac.at Erklärung zur Verfassung der Arbeit Magdalena Fuchs Felbigergasse 108/12 Hiermit erkläre ich, dass ich diese Arbeit selbständig verfasst habe, dass ich die verwen- deten Quellen und Hilfsmittel vollständig angegeben habe und dass ich die Stellen der Arbeit – einschließlich Tabellen, Karten und Abbildungen –, die anderen Werken oder dem Internet im Wortlaut oder dem Sinn nach entnommen sind, auf jeden Fall unter Angabe der Quelle als Entlehnung kenntlich gemacht habe. Wien, 1. Mai 2018 Magdalena Fuchs v Acknowledgements I would like to thank my supervisors, Prof. Grosu and especially Dott. Mag. Ramin Hasani for their support, countless hours of discussion, ideas, and encouragement. This work was done in close collaboration with Ramin Hasani, to reflect this, the pronoun "we" is used throughout the thesis. Dr. Manuel Zimmer for insights into the nervous system dynamics of C. elegans , discussions and generously providing his data sets. Every one at the Cyber-Physical Systems Lab for discussions, lunch breaks and broadening my horizon by letting me be part of this group. I would like to thank my family and my friends for their never-ending support. vii Kurzfassung In dieser Arbeit wurde ein Setup zur Optimierung von realistischen Single-Compartment Neuronenmodellen implementiert. Diese Modelle können dafür genutzt werden Lern- mechanismen im Fadenwurm C. elegans zu beschreiben. Das gewählte Modell ist ein modifiziertes Hodgekin-Huxley Modell, bei dem auch das intrazelluläre Kalzium model- liert wird. Ein Modell der Synapse inkludiert die Dynamik der verschiedenen Schritte der Signalübertragung an der Synapse. Das Modell der Zelle ist modular veränderbar und wurde in MATLAB Simulink implementiert. Verschiedene Nervenzellen des Fadenwurms C. elegans zeigen unterschiedliches charakte- ristisches Verhalten. Dass das Modell dies reproduzieren kann, wurden die Parameter des Modells angepasst, um experimentelle Daten von Calcium Imaging Messungen zu reproduzieren. Die Suche nach geeigneten Parametern erfolgte durch händisches Aus- probieren und mit einem genetischen Algorithmus. Hierfür wird dem Neuronenmodell ein vordefinierter Input gegeben, der den Input des gesamten Netzwerkes approximiert. Die vom Modell produzierten Kalzium-Kurven sollen sich nun den am echten Wurm gemessenen Kurven so genau wie möglich annähern, während das Resultat gleichzeitig andere Anforderungen an die biologische Plausibilität erfüllen muss. Diese Optimierung führte zu Parameter-Sets, die die Kurven aus Experimenten gut reproduzieren konnten. Außerdem wurde im Neuronenmodell ein Mechanismus für Habituation, einen simplen nicht-assoziatives Lernprozess als Antwort auf sich wiederholende Stimuli, implemeniert. Habituation wurde anhand von zwei verschiedenen Prozessen in der Zelle und an der Synapse modelliert. In einem weiteren Versuch wurden Neuronale Netze mit Long Short Term Memory Units (LSTM) darauf trainiert, Kalziumkurven von C. elegans Interneuronen zu reproduzie- ren. Sowohl aktive Antworten auf Pulse, als auch Oszillationen als Antwort auf einen konstanten Input konnten reproduziert werden. Die Modelle könnten sowohl schnelle als auch langsame Prozesse in den Kalziumkurven reproduzieren. ix Abstract This thesis builds a simulation infrastructure for optimizing realistic single-compartmental neuron dynamics to model neural circuits and to investigate cell-level principles of learning and memory in the soil-worm, C. elegans . We design modified-Hodgkin-Huxley neuron models which incorporate kinetics of the intra- cellular calcium as a key-indicator of the cell-dynamics. We also include a biophysically- plausible synapse model which realizes multi-scale mechanisms underlying synaptic transmission between neurons. Models are modularly designed and implemented as MATLAB functions and Simulink models. Individual Neurons in nervous systems exploit various dynamics. To capture these dynamics for single neurons, we tune the parameters of the electrophysiological model of the nerve cells, to fit the experimental data obtained by calcium imaging. A search for the biophysical parameters of this model is performed by means of a genetic algorithm, where the model neuron is exposed to a predefined input current representing overall inputs from other parts of the nervous system. The algorithm is then constrained for keeping the ion-channel currents within reasonable ranges, while producing the best fit to a calcium imaging time series of interneurons in the “brain”’ of C. elegans . Our settings enable us to project a set of biophysical parameters to the the neuron kinetics observed in neuronal imaging. Moreover, we computationally discuss biophysical dynamics that induce a simple from of non-associative learning mechanism in C. elegans , when the worm is exposed to periodic touch/tap stimuli. We mathematically model this mechanosensory habituation in two paradigms of neuronal habituation and synaptic plasticity. We predict neuronal mechanisms that can presumably be the mathematical origin of habituation. Moreover, we analytically illustrate how synapses play a role in completion of habituation, dishabituation process and propagation of the neuronal habituation to the rest of a neural circuit. In a novel complementary study, we design and learn long short-term memory (LSTM) networks, gated recurrent neural networks, to model the dynamics of individual in- terneurons of the C. elegans ’ nervous system. A first-order gradient-based optimization algorithm known as Adam which is build out of estimates of lower-order moments, is used to train the LSTM networks. We show how complex dynamics of individual C. elegans cells such as: Stochastic oscillations, Active gating behavior, simultaneous fast and slow dynamics and electrotonic transmission can be effectively captured by the use of such phenomenological models. xi Contents Kurzfassung ix Abstract xi Contents xiii 1 Introduction 1 2 State of the Art 3 2.1 Fitting time-series data with Neural Networks . 8 3 Methods 11 3.1 Neuron Model . 11 3.2 Ion Channel Model . 12 3.3 Intracellular Calcium . 13 3.4 Synapse Model . 14 3.5 Model of Calcium Imaging . 14 3.6 Implementation: SIM-CE Platform [43] . 14 3.7 Optimizing to fit Real Neuron Traces . 15 3.8 Properties of Different Neurons . 18 3.9 Modeling Habituation in SIM-CE Platform . 20 3.10 Developing Phenomenological C. elegans Neuron Models by Recurrent Artificial Neural Networks . 23 4 Results 25 4.1 Single Neuron - Deterministic response . 25 4.2 Single Neuron- Stochastic response . 26 4.3 Reproducing Current-Voltage (IV) curves . 27 4.4 Individual Neuron Models . 27 4.5 Modeling Habituation . 40 4.6 Modeling Neuron responses by means of Neural Networks . 45 5 Discussion 49 xiii A Model Parameter values from literature 53 B Model Parameters 57 B.1 AVA..................................... 57 Bibliography 63 CHAPTER 1 Introduction With only 302 neurons the nematode C. elegans is able to perform complex tasks, such as locomotion [104, 13], searching for food [92] and avoidance of noxious stimuli [66]. Furthermore it is able to perform non-associative and even associative learning [4]. In contrast, artificial neural networks need hundreds of neurons to fulfill a single task [37]. Generating complex behavior with such a small number of neurons is possible, because in the nervous system of C. elegans , neurons perform more complex tasks than simple weighted additions. Each neuron has a specific role and exhibits individual dynamics, which arise from its different physical properties. When modeling the nervous system of C. elegans , these individual dynamics of each single neurons might need to be accounted for. The experimental data on the electrophysiological properties of single neurons is sparse [75, 53, 39], and electrophysiology measurements on the behaving worm cannot be feasibly conducted; therefore, most of the available data is from calcium imaging [56, 16, 97]. Thus, intracellular calcium has to be modeled instead of trans-membrane voltages. The model parameters, which describe intracellular calcium dynamics are hard to access in an experimental setup. Because
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