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.

Popular Abstract

Nowadays experimentalists can visualize objects smaller than the wavelength of light, such as molecules and other nano-particles. Instead of receiving reflected light one uses directly emitted light of fluorescing molecules and can shift resolution possibilities of optical systems, which can monitor those molecules as shining dots. Working with flu- orescent molecules a microscope combined with a camera can record stacks of images that can be rendered to videos. Then we can see molecules working in their environ- ment and fulfilling their purpose which allows us to live as we do.
Following a molecule’s path, we have to choose a parameter-depending model which potentially describes the motion we see under the microscope in the best way possible. Imagine being a shorter ’novisch’ student going to your first party with thousand of people in a cramped room. You are being pushed and kicked by other bigger students and can barely hold your position. Now it happens to be that you usually drink a lot and you are chaotically dancing and jumping around. Next, your best friend wants to discuss something very important and is pulling you, but you do not want to leave and stop dancing, so you are drifting unsteadily and uncontrolled towards the exit. In our case, we can characterize this motion through a so-called biased Brownian motion model with two parameters: the diffusion constant and drift velocity, which are the two motion properties we like to estimate when tracking the path a particle takes.
Videos of fluorescent labeled diffusive particles are simply a lot of images in a very short time. In-between those images, the particle jumps and we only observe fluores- cent dots where a particle is resting shortly. Therefore it is hard to assign consecutive positions into whole trajectories from a certain particle especially when trying to follow a lot of molecules. We have to test all possible paths we see in-between two images, as a particle could potentially take all of these steps, which is not computationally feasible. In this thesis, we tackle the problem of generating trajectories by running an assignment algorithm and acquiring a global solution, evaluated through our chosen model. Simul- taneously, we estimate the drift velocity and diffusion constant. In addition, we are the first to estimate how well we can recover the particles’ most likely path.
Ideally, we hope that we can set the base to find a way to quantify particle-tracking including parameter estimation. Potentially our thesis has to be extended towards more complex models to be tested and various parameters to be estimated improving the accuracy of the recovered trajectories.

• author: Golks, Lennart
• supervisor: Tobias Ambjörnsson
• organization: Department of Astronomy and Theoretical Physics - Has been reorganised
• course: FYTM04 20212
• year: 2021
• type: H1 - Master's Degree (One Year)
• subject: Physics and Astronomy
• language: English
• additional info: Department affilation moved from 011040003 (Department of Theoretical Physics) to v1000642 (Department of Astronomy and Theoretical Physics) on 2022-08-19 15:58:22.
• id: 9068274
• date added to LUP: 2022-01-26 09:51:16
• date last changed: 2022-08-19 15:58:22