title: Pattern Formation and Dynamics in Bacterial Cells
title: Musterbildung und Dynamik in bakteriellen Zellen
titleType: AlternativeTitle
Creators: name: Subramanian, Srikanth
Publisher: name: Philipps-Universität Marburg
Year: 2023
Subjects: Non-Linear Dynamics
chromosome dynamics
partial differential equations
Biophysics
Reaction-diffusion systems
microsco
Turing Patterns
monte-carlo methods
polymer simulations
Statistical Mechanics
Pattern Formation
Pattern selection
Physics
Physik

description: Spatio-temporal organisation plays a critical role in all life. More specifically in biological cells, the spatial organisation of key proteins and the chromosome is essential for their function, segregation and faithful inheritance. Within bacterial cells pattern formation appears to play an essential role at different levels. Examples of pattern formation in proteins include pole-to-pole oscillations, self-positioning clusters and protein gradients. Chromosomes on the other hand display an ordered structure with individual domains exhibiting specific spatio-temporal organisation. This work examines the processes determining dynamics and organisation within bacterial cells by combining analytical, computational and experimental approaches. The thesis is split into two distinct parts, one providing new physical insights into pattern formation in general and the other detailing the dynamics of chromosomes. Reaction-diffusion systems are helpful models in order to study pattern formation in chemical, physical and biological systems. A pattern or Turing state emerges when the spatially homogeneous state becomes unstable to small perturbations. While initially intended for describing pattern formation in biological systems (for example embryogenesis, scale patterning etc.), their practical application has been notoriously difficult. The biggest challenge is our inability to predict in general the steady-state patterns obtained from a given set of parameters. While much is known near the onset (when the system is marginally unstable) of the spatial instability, the mechanisms underlying pattern selection and dynamics away from the onset are much less understood. In the first part of this thesis, we provide physical insight into the dynamics of these patterns and their selection at steady state. We find that peaks in a Turing pattern behave as point sinks, the dynamics of which are determined by the diffusive fluxes into them. As a result, peaks move toward a periodic steady-state configuration that minimizes the mass of the diffusive species. Importantly, we also show that the preferred number of peaks at the final steady state is such that this mass is minimized. Our work presents mass minimization as a general principle for understanding pattern formation in reaction-diffusion systems. In the second part, we discuss a more biological problem that involves the study of bacterial DNA loci dynamics at short time scales, where we perform polymer simulations, modelling and fluorescent tracking experiments in conjunction. Chromosomal loci in bacterial cells show a robust sub-diffusive scaling of the mean square displacement, $\textrm{MSD}(\tau) \sim \tau^{\alpha}$, with $\alpha &lt; 0.5$. This is in contrast to scaling predictions from simple polymer models ($\alpha \geq 0.5$). While the motion of the chromosome in a viscoelastic cytoplasm has been proposed as a possible explanation for the difference, recent experiments in compressed cells question this hypothesis. On the other hand, recent experiments have shown that DNA-bridging Nucleoid Associated Proteins (NAPs) play an important role in chromosome organisation and compaction. Here, using polymer simulations we investigate the role of DNA bridging in determining the dynamics of chromosomal loci. We find that bridging compacts the polymer and reproduces the sub-diffusive elastic dynamics of monomers at timescales shorter than the bridge lifetime. Consistent with this prediction, we measure a higher exponent in a NAP mutant ($\Delta$H-NS) compared to wild-type \textit{E. coli}. Furthermore, bridging can reproduce the rare but ubiquitous rapid movements of chromosomal loci that have been observed in experiments. In our model, the scaling exponent defines a relationship between the abundance of bridges and their lifetime. Using this and the observed mobility of chromosomal loci, we predict a lower bound on the average bridge lifetime of around $5$ seconds. We hope that this framework will help guide future model development and understanding of chromosome dynamics.