Diffusion Processes with Hidden States from ... - FU Berlin, FB MI

molecules from bovine retinal rod cells. In these experiments the individual transducin positionson the disc membrane were tracked in time and corresponding two-dimensional trajectories havebeen collected. The challenge addressed in the present work is to derive a computational methodwhich can detect the hidden states 1−3 from the data and estimate the local diffusion laws in eachstate.In order to model this hidden states sequences, the mathematical concept of Hidden Markov modelsis used. Within this thesis a Markov chain with three states is assumed for modeling the threemolecular states given above. These states interconvert with fixed rate constants or switchingprobability, modeling the binding/unbinding of transducin to/from the membrane and rhodopsin.Within the states, a local Langevin equation is active which governs the diffusion behavior at thetime. Methods to estimate the most likely Hidden Markov model under the given observation arepresented.The procedure proposed here is demonstrated to work reliably on model data. The available experimentaldata was found to be insufficient in order to parametrize state 3. For state 1 and 2,diffusion models could be obtained from the particle tracking trajectories with diffusivities thatagreed to complementary experimental data.VI