Analysis of ion channels with hidden Markov models : parameter identifiability and the problem of time interval omission

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.

Author dc:creator

• The, Yu-Kai

Contributors dc:contributor

• Timmer, Jens

• hidden Markov model, parameter estimation
• ion channel

Repository record source_url

https://freidok.uni-freiburg.de/data/1842

OAI identifier oai:identifier

oai:freidok.uni-freiburg.de:1842