Simultaneous Bayesian parameter estimation and particle-tracking including calculation of mis-linking probabilities
Abstract: Since 1994 super-resolution microscopes enable us to visualize processes in the nanome- ter regime where bio-molecules work. Consequently, there is a great need for methods analyzing the generated data to transfer the motion of molecules, seen as white dots, into trajectories. Important steps in understanding bio-molecular behavior are first the detection of those and then generating trajectories based on a physical model. Many particle-tracking methods have been reviewed and it was concluded that it is advisable when linking dots into trajectories to know the particle dynamics [Chenouard et al., “Objective comparison of particle tracking methods” in Nature methods 16.5 2019, pp. 387-395]. However, this leads to a so-called catch-22 dilemma as the physical model describing the particles’ motion is parameter dependent and so is the physical model- based linking process. To solve this dilemma we implement a Bayesian framework providing the best-fitting parameters and proposing trajectories in one go. This method does not require any prior information and is based on a parameter-dependent Brown- ian motion model with drift. In addition, we are the first to give mis-linking probabilities for each proposed step. Our proposed method recovers trajectories well and estimates the diffusion constant and drift velocity of simulated data successfully. The calculation of mis-linking proba- bilities in unconstrained Brownian motion agrees with the ground truth recovery rate of the molecules’ steps. We note that our methodology works especially well with low particle densities. If the particle density is high we recover less of the ground truth tra- jectories. In the case of constrained one-dimensional Brownian motion, where particles are trapped in nano-channels, we estimate the designated parameters well but under- estimate the mis-linking probability. Lastly, we successfully apply our methodology to experimental data of that specific case. When dealing with experimental data we do not cover particle disappearance or ’extra’ particles due to overlapping, moving out of the focal plane, or limited fluoresc- ing abilities. This can lead to incomplete trajectories, worse parameter estimation, and wrong calculations of mis-linking probabilities.
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