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

5.5 Estimation of the Noise Intensities for Single Trajectoriesy-component:D (1) = 3.1 µm2 ,sD (2) = 0.01 µm2 .sAs we can see the estimated diffusion coefficients for the first state D (1) are also in good agreementto our chosen range for transducin diffusion coefficients, but we did not receive better results forthe second state.Due to this observation we can conclude that an estimation of the single x- and y-components isnot really recommended in order to achieve a better estimation results, compared to the estimationon the joint data set. This is an obvious result by the fact that we have not a sufficient amountof data, and a further division of this data in two distinct sets do not achieve a refinement of theestimation results.5.5 Estimation of the Noise Intensities for Single TrajectoriesHere we present the results of the estimation procedure on single trajectories. In the sections 5.2to 5.4 the estimation was applied to the whole data.Single trajectories were stored in separate files in order to ensure separate estimation on the singletrajectories. Afterwards we took the estimated covariance matrices for each of these trajectories,calculated the variances respectively the noise intensities σ for each of these trajectories, andplotted the results separately for the x- and the y-components of the single trajectories (see Figure5.4 (a) and (b)).The average value (mean) of the noise intensity σ m for both components is−35 J · Kgσ m = 0.35 · 10 .sThus the obtained average diffusion coefficient for both components isD m = 4.5 µm2 ,swhich is actually lying also in the chosen transducin diffusion coefficient rangeRegarding Figure 5.4 (a) and (b) a certain tendency of different states can be observed, especiallyon Figure 5.4 (a), which is showing the noise intensity σ y for the different trajectories. Thereare some narrow peaks which result in noise intensities between 1.0 J·Kgsand 1.7 J·Kgs, leadingto diffusion coefficients between 1.0 µm2sto 1.6 µm2s. This circumstance actually reproduces theexpectation that transducin diffusion coefficients are lying in a wide range, fluctuating around themean value D m . We considered and justified this circumstance in section 4.6 on page 71, withrecent works on the topic as background.Especially Saxton and Owicki ([31]) presented a first work on the concentration dependency ofthe diffusion coefficients. Due to this our results are successful, although they are because of the83