{"id":{"repo_id":"freiburg-diss","oai_identifier":"oai:freidok.uni-freiburg.de:1842"},"canonical_url":"https://search.dev.ndltd.org/etd/freiburg-diss/oai:freidok.uni-freiburg.de:1842","repository":{"repo_id":"freiburg-diss","name":"University of Freiburg","base_url":"https://freidok.uni-freiburg.de/oai/oai2.php"},"display":{"title":"Analysis of ion channels with hidden Markov models : parameter identifiability and the problem of time interval omission","abstract":"This thesis deals with a certain class of stochastic processes, namely the hidden Markov models. Hidden Markov models have proved to be an appropriate description for the ionic current through specialised proteins situated in the cell membrane. These ion channels open and close randomly and control the flux of ions into and out of the cell. With the study of the current through individual ion channels it is possible to deepen the understanding of the structure of the protein. <br>In addition, the theoretical investigation of hidden Markov models itself provides interesting results. A Markov chain governs the dynamics of the process. The observation occurs indirectly and different states of the Markov chain can lead to the same measured output. Therefore, inference of hidden Markov models is an important task which is studied in the present work.<br>Moreover, a major part of this thesis covers the problem that, in practice, current records of single <br>channel measurements show a limited time resolution, i.e. brief openings and closings are not detected.<br>Exact solutions that take these \"missed events\" and the sampling into account are calculated analytically. Furthermore an approximate solution for the problem is derived. <br>Another major chapter of the thesis is addressed to the analysis of Na-channel data. For this study data of five different mutants and of the wild-type channel have been investigated. A biologically plausible model is developed that is compatible to the data of all mutants and that gives experimental evidence for hypothetical molecular mechanisms discussed in the literature.","abstract_html":"This thesis deals with a certain class of stochastic processes, namely the hidden Markov models. Hidden Markov models have proved to be an appropriate description for the ionic current through specialised proteins situated in the cell membrane. These ion channels open and close randomly and control the flux of ions into and out of the cell. With the study of the current through individual ion channels it is possible to deepen the understanding of the structure of the protein. &lt;br&gt;In addition, the theoretical investigation of hidden Markov models itself provides interesting results. A Markov chain governs the dynamics of the process. The observation occurs indirectly and different states of the Markov chain can lead to the same measured output. Therefore, inference of hidden Markov models is an important task which is studied in the present work.&lt;br&gt;Moreover, a major part of this thesis covers the problem that, in practice, current records of single &lt;br&gt;channel measurements show a limited time resolution, i.e. brief openings and closings are not detected.&lt;br&gt;Exact solutions that take these &quot;missed events&quot; and the sampling into account are calculated analytically. Furthermore an approximate solution for the problem is derived. &lt;br&gt;Another major chapter of the thesis is addressed to the analysis of Na-channel data. For this study data of five different mutants and of the wild-type channel have been investigated. A biologically plausible model is developed that is compatible to the data of all mutants and that gives experimental evidence for hypothetical molecular mechanisms discussed in the literature.","abstract_has_math":false,"creators":["The, Yu-Kai"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Timmer, Jens"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T02:22:28Z","subjects":["hidden Markov model, parameter estimation","ion channel"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://freidok.uni-freiburg.de/data/1842","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Timmer, Jens"]},{"key":"dc:creator","label":"Author","values":["The, Yu-Kai"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["DoctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["hidden Markov model, parameter estimation","ion channel"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis deals with a certain class of stochastic processes, namely the hidden Markov models. Hidden Markov models have proved to be an appropriate description for the ionic current through specialised proteins situated in the cell membrane. These ion channels open and close randomly and control the flux of ions into and out of the cell. With the study of the current through individual ion channels it is possible to deepen the understanding of the structure of the protein. <br>In addition, the theoretical investigation of hidden Markov models itself provides interesting results. A Markov chain governs the dynamics of the process. The observation occurs indirectly and different states of the Markov chain can lead to the same measured output. Therefore, inference of hidden Markov models is an important task which is studied in the present work.<br>Moreover, a major part of this thesis covers the problem that, in practice, current records of single <br>channel measurements show a limited time resolution, i.e. brief openings and closings are not detected.<br>Exact solutions that take these \"missed events\" and the sampling into account are calculated analytically. Furthermore an approximate solution for the problem is derived. <br>Another major chapter of the thesis is addressed to the analysis of Na-channel data. For this study data of five different mutants and of the wild-type channel have been investigated. A biologically plausible model is developed that is compatible to the data of all mutants and that gives experimental evidence for hypothetical molecular mechanisms discussed in the literature.","Die vorliegende Arbeit behandelt eine spezielle Klasse von stochastischen Prozessen, die Hidden Markov Modelle. Diese Modellklasse hat sich als nützlich erwiesen, um Ionenströme durch spezielle Membranproteine zu beschreiben. Diese sogenannten Ionenkanäle öffnen und schließen zufällig and kontrollieren den Ionenfluß in die Zelle. Mit der Untersuchung von Einzelkanalströmen ist es möglich, das Verständnis der Struktur dieser Proteine zu erweitern. <br> <br>Ferner liefert die theoretische Untersuchung von Hidden Markov Modellen selbst für interessante Ergebnisse. Eine Markovkette ist für die Dynamik des Prozesses verantwortlich. Die Beobachtung erfolgt indirekt, und verschiedene Zustände der Markovkette können zu derselben gemessenen Ausgabe führen. Deshalb stellt die Identifizierbarkeit eine wichtige Aufgabe dar, die in dieser Arbeit untersucht wird. <br> <br>Weiterhin wird in der Dissertation das Problem behandelt, daß die Zeitauflösung von Einzelkanalaufnahmen begrenzt ist, d.h. kurze Öffnungen oder Schließungen werden nicht detektiert. Exakte Lösungen, die diese \"missed events\" und Sampling der Daten berücksichtigen, werden analytisch berechnet. Ferner wird eine approximative Lösung hergeleitet. <br> <br>Ein weiteres umfangreiches Kapitel der Arbeit beschäftigt sich mit der Analyse von Na-Kanaldaten. Es wurden fünf verschiedene Mutanten und der Wildtyp Kanal untersucht. Ein biologisch plausibles Modell wurde entwickelt, welches die Daten aller Mutanten adäquat beschreibt und welches experimentelle Evidenz von hypothetischen molekularen Mechanismen gibt, die in der Literatur diskutiert werden."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Analysis of ion channels with hidden Markov models : parameter identifiability and the problem of time interval omission","Analyse von Ionenkanälen mit Hidden Markov Modellen"]}]}],"canonical_facts":{"dc:contributor":["Timmer, Jens"],"dc:creator":["The, Yu-Kai"],"dc:description.abstract":["This thesis deals with a certain class of stochastic processes, namely the hidden Markov models. Hidden Markov models have proved to be an appropriate description for the ionic current through specialised proteins situated in the cell membrane. These ion channels open and close randomly and control the flux of ions into and out of the cell. With the study of the current through individual ion channels it is possible to deepen the understanding of the structure of the protein. <br>In addition, the theoretical investigation of hidden Markov models itself provides interesting results. A Markov chain governs the dynamics of the process. The observation occurs indirectly and different states of the Markov chain can lead to the same measured output. Therefore, inference of hidden Markov models is an important task which is studied in the present work.<br>Moreover, a major part of this thesis covers the problem that, in practice, current records of single <br>channel measurements show a limited time resolution, i.e. brief openings and closings are not detected.<br>Exact solutions that take these \"missed events\" and the sampling into account are calculated analytically. Furthermore an approximate solution for the problem is derived. <br>Another major chapter of the thesis is addressed to the analysis of Na-channel data. For this study data of five different mutants and of the wild-type channel have been investigated. A biologically plausible model is developed that is compatible to the data of all mutants and that gives experimental evidence for hypothetical molecular mechanisms discussed in the literature.","Die vorliegende Arbeit behandelt eine spezielle Klasse von stochastischen Prozessen, die Hidden Markov Modelle. Diese Modellklasse hat sich als nützlich erwiesen, um Ionenströme durch spezielle Membranproteine zu beschreiben. Diese sogenannten Ionenkanäle öffnen und schließen zufällig and kontrollieren den Ionenfluß in die Zelle. Mit der Untersuchung von Einzelkanalströmen ist es möglich, das Verständnis der Struktur dieser Proteine zu erweitern. <br> <br>Ferner liefert die theoretische Untersuchung von Hidden Markov Modellen selbst für interessante Ergebnisse. Eine Markovkette ist für die Dynamik des Prozesses verantwortlich. Die Beobachtung erfolgt indirekt, und verschiedene Zustände der Markovkette können zu derselben gemessenen Ausgabe führen. Deshalb stellt die Identifizierbarkeit eine wichtige Aufgabe dar, die in dieser Arbeit untersucht wird. <br> <br>Weiterhin wird in der Dissertation das Problem behandelt, daß die Zeitauflösung von Einzelkanalaufnahmen begrenzt ist, d.h. kurze Öffnungen oder Schließungen werden nicht detektiert. Exakte Lösungen, die diese \"missed events\" und Sampling der Daten berücksichtigen, werden analytisch berechnet. Ferner wird eine approximative Lösung hergeleitet. <br> <br>Ein weiteres umfangreiches Kapitel der Arbeit beschäftigt sich mit der Analyse von Na-Kanaldaten. Es wurden fünf verschiedene Mutanten und der Wildtyp Kanal untersucht. Ein biologisch plausibles Modell wurde entwickelt, welches die Daten aller Mutanten adäquat beschreibt und welches experimentelle Evidenz von hypothetischen molekularen Mechanismen gibt, die in der Literatur diskutiert werden."],"dc:format.medium":["application/pdf"],"dc:subject":["hidden Markov model, parameter estimation","ion channel"],"dc:title":["Analysis of ion channels with hidden Markov models : parameter identifiability and the problem of time interval omission","Analyse von Ionenkanälen mit Hidden Markov Modellen"],"dc:type":["DoctoralThesis"]},"updated_at":"2026-07-24T02:22:28Z"}