In this project, we want to explore the capability of neural networks to infer kinetics of electrophysiological time series with Markov models. Patch-Clamp recordings of single ion channels provide a wealth of information on the functional properties of proteins that by far outperform macroscopic measurements. However, modelling of single-channel data is still a major challenge not only because it is very time-consuming. Likely, the most sophisticated way to relate kinetics and protein function is to utilize hidden Markov models (Huth et al., 2008). Scientists have developed several different methods for this purpose (Sakmann and Neher, 1995). All these methods share at least some of the following disadvantages. They require specific assumptions, specific corrections dependent on the time series, are sensitive to noise (Huth et al., 2006), are limited to the bandwidth of the recording system (Huth et al., 2006; Qin, 2014) or do not provide statistics to estimate how well they have approximated the data.
We have developed a 2D-Fit algorithm with simulations and have improved it over the years (Huth et al., 2006). The algorithm is based on the idealization of time series and the generation of two-dimensional-dwell-time-distribution from neighboring events. To a certain extent, it does not share afore mentioned limitations and it has some unique features that makes it superior to other tools. It does capture gating kinetics with a high background of noise and can extract rate constants even beyond the recording bandwidth. That could make the 2D-Fit exceptional valuable for relating electrophysiology kinetics with data from simulations of single protein molecules. In addition, 2D-distributions preserve the coherency of connected states. Thereby the algorithm can extract the full complexity of underlying models and distinguish different Markov models. However, the computational requirements are enormous, repeatedly for each time series that is analyzed. Neural networks have the reverse approach. Once datasets are generated and the networks are trained, time series could be analyzed in real time during experiments. It has to be determined whether deep networks are capable of outperforming the powerful simulation approach.
The basic aim of this thesis is to analyze two-dimensional-dwell-time-histograms with neuronal networks, a task of image analysis, to extract the underlying kinetics of Markov models. In parallel, another master student will explore the direct analysis of time series. Both approaches have to our knowledge not yet been investigated for Patch-Clamp data. It will be very interesting to compare the results of both approaches.
In the first part of the project, the objective is to generate training datasets with the 2D-Fit algorithm (already implemented) and to deploy networks capable to analyze simple Markov models (preliminary results are available for a 3-state model). The master student will evaluate the capabilities of the networks related to bandwidth and noise of time series. The next step will be to find strategies to increase the number of states of the underlying models that the network is able to distinguish. Finally, and not directly related, the capabilities of networks to distinguish different Markov models will be explored. We expect that networks could really excel in this task of pattern recognition.
Huth T, Schmidtmayer J, Alzheimer C, Hansen UP (2008) Four-mode gating model of fast inactivation of sodium channel Nav1.2a. Pflugers Archiv European Journal of Physiology 457:103–119.
Huth T, Schroeder I, Hansen U-P (2006) The power of two-dimensional dwell-time analysis for model discrimination, temporal resolution, multichannel analysis and level detection. Journal of Membrane Biology 214:19–32.
Qin F (2014) Principles of single-channel kinetic analysis. Methods in Molecular Biology 1183:371–399.
Sakmann B, Neher E (1995) Single-Channel Recordings (Sakmann B, Neher E, eds)., 2nd ed. New York and Lodon: Plenum Press.