Self-organization in heterogeneous biological systems

Würthner, Laeschkir Lukman (2022): Self-organization in heterogeneous biological systems: how geometric and biochemical cues control pattern formation. Dissertation, LMU München: Fakultät für Physik

Abstract

Self-organization is an ubiquitous and fundamental process that underlies all living systems. In cellular organisms, many vital processes, such as cell division and growth, are spatially and temporally regulated by proteins -- the building blocks of life. To achieve this, proteins self-organize and form spatiotemporal patterns. In general, protein patterns respond to a variety of internal and external stimuli, such as cell shape or inhomogeneities in protein activity. As a result, the dynamics of intracellular pattern formation generally span multiple spatial and temporal scales. This thesis addresses the underlying mechanisms that lead to the formation of heterogeneous patterns. The main themes of this work are organized into three parts, which are summarized below. The first part deals with the general problem of mass-conserving reaction-diffusion dynamics in spatially non-uniform systems. In section 1 of chapter II, we study the dynamics of the E. coli Min protein system -- a paradigmatic model for pattern formation. More specifically, we consider a setup with a fixed spatial heterogeneity in a control parameter, and show that this leads to complex multiscale pattern formation. We develop a coarse-graining approach that enables us to explain and reduce the dynamics to the "hydrodynamic variables'' at large length and time scales. In another project, we consider a system where spatial heterogeneities are not imposed externally, but self-generated by the dynamics via a mechanochemical feedback loop between geometry and reaction-diffusion system (section 2 of chapter II). We show that the resulting dynamics can be explained from the phase-space geometry of the reaction-diffusion system. The second part focuses on how patterns in realistic cell geometries are controlled by shape and biochemical cues. We examine axis selection of PAR polarity patterns in C. elegans, where we show that spatial variations in the bulk-surface ratio and a tendency of the system to minimize the pattern interface yield robust long-axis polarization of PAR protein patterns (section 1 of chapter III). In a second project, we develop a theoretical model that explains the localization of the B. subtilis Min protein system (section 2 of chapter 3). We show that a biochemical cue -- which acts as a template for pattern formation -- guides and stabilizes Min patterns. In the third part, we study the coupling between lipid membranes and curvature-generating proteins. We demonstrate that myosin-VI motor proteins cooperatively bind to saddle-shaped regions of lipid membranes, and thereby induce large-scale membrane remodeling (section 1 of chapter IV). To understand the dynamics, we develop a coarse-grained geometric model and show that the emergence of regular spatial structures can be explained by a "push-pull'' mechanism: protein binding destabilizes the membrane shape at all length scales, and this is counteracted by line tension. Inspired by this system, we then investigate a general model for the dynamics of growing protein-lipid interfaces (section 2 of chapter IV). A key feature of the model is that the protein binding kinetics is explicitly coupled to the morphology of the interface. We show that such a coupling leads to turbulent dynamics and a roughening transition of the interface that is characterized by universal scaling behaviour.

• Dokumententyp: Dissertationen (Dissertation, LMU München)
• Keywords: Self-organization, protein patterns, cell geometry, heterogeneous systems, guiding cues
• Themengebiete: 500 Naturwissenschaften und Mathematik ; 500 Naturwissenschaften und Mathematik > 530 Physik
• Fakultäten: Fakultät für Physik
• Sprache der Hochschulschrift: Englisch
• Datum der mündlichen Prüfung: 17. Oktober 2022
• 1. Bericht­erstatter:in: Frey, Erwin