Bayesian Inference in Stochastic Biological Systems

by Sascha Lambert
Doctoral thesis
Date of Examination:2025-02-20
Date of issue:2025-06-26
Advisor:Prof. Dr. Stefan Klumpp
Referee:Prof. Dr. Florentin Wörgötter
Persistent Address: http://dx.doi.org/10.53846/goediss-11359

 

 

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Abstract

English

Many biological systems, especially microscopic ones, are highly complex and chaotic, consisting of vast amounts and types of particles interacting via a wide variety of forces. This complexity renders an atomistic description of these sys- tems infeasible, and one has to resort to coarse-grained models that abstract away details and are easier to deal with. A primary abstraction is the introduction of randomness into the models to represent effectively unpredictable behavior. In this thesis, we explore several such biological systems whose dynamics are ex- plained by stochastics. The primary question we ask is how to gather insight into the systems and their parameters by carefully observing and analyzing experi- mentally accessible dynamic properties. We will utilize a Bayesian approach to this learning endeavor. The thesis is divided into three parts. In the first part, we will review the essentials of Bayesian inference and important practical considerations. We will primarily use Markov-Chain Monte-Carlo methods to carry out the inference numerically. In the second part, we will analyze the stochastic bonding behavior of Vimentin intermediate filaments with microtubules. This is a stochastically forming connection between the two protein polymers and is described without memory, allowing us to explore the Bayesian method without much technical complexity. In the third part, we will work with Active Brownian Particles, a prototypical model of microbial motility. In particular, we will look at systems where the par- ticle interacts with obstacles. This state-space model exhibits a high-dimensional configuration space that poses difficult numerical challenges. We will deal with this using two different approaches. The first is to use strong linearizations that simplify the model, making it numerically tractable. For the second approach, we introduce a Brownian Bridge that functions as a guide to the particle movement and improves the sampling efficiency of the inference inside the large search space.
Keywords: Bayesian Inference; Microbiology; Machine Learning; Markov-Chain Monte-Carlo; Particle Filters
 
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