Self-organization in heterogeneous biological systems

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

Geometry-induced patterns through mechanochemical coupling

Intracellular protein patterns regulate a variety of vital cellular processes such as cell division and motility, which often involve dynamic changes of cell shape. These changes in cell shape may in turn affect the dynamics of pattern-forming proteins, hence leading to an intricate feedback loop between cell shape and chemical dynamics. While several computational studies have examined the resulting rich dynamics, the underlying mechanisms are not yet fully understood. To elucidate some of these mechanisms, we explore a conceptual model for cell polarity on a dynamic one-dimensional manifold. Using concepts from differential geometry, we derive the equations governing mass-conserving reaction-diffusion systems on time-evolving manifolds. Analyzing these equations mathematically, we show that dynamic shape changes of the membrane can induce pattern-forming instabilities in parts of the membrane, which we refer to as regional instabilities. Deformations of the local membrane geometry can also (regionally) suppress pattern formation and spatially shift already existing patterns. We explain our findings by applying and generalizing the local equilibria theory of mass-conserving reaction-diffusion systems. This allows us to determine a simple onset criterion for geometry-induced pattern-forming instabilities, which is linked to the phase-space structure of the reaction-diffusion system. The feedback loop between membrane shape deformations and reaction-diffusion dynamics then leads to a surprisingly rich phenomenology of patterns, including oscillations, traveling waves, and standing waves that do not occur in systems with a fixed membrane shape. Our work reveals that the local conformation of the membrane geometry acts as an important dynamical control parameter for pattern formation in mass-conserving reaction-diffusion systems

Geometric cues stabilise long-axis polarisation of PAR protein patterns in C. elegans

In the Caenorhabditis elegans zygote, PAR protein patterns, driven by mutual anatagonism, determine the anterior-posterior axis and facilitate the redistribution of proteins for the first cell division. Yet, the factors that determine the selection of the polarity axis remain unclear. We present a reaction-diffusion model in realistic cell geometry, based on biomolecular reactions and accounting for the coupling between membrane and cytosolic dynamics. We find that the kinetics of the phosphorylation-dephosphorylation cycle of PARs and the diffusive protein fluxes from the cytosol towards the membrane are crucial for the robust selection of the anterior-posterior axis for polarisation. The local ratio of membrane surface to cytosolic volume is the main geometric cue that initiates pattern formation, while the choice of the long-axis for polarisation is largely determined by the length of the aPAR-pPAR interface, and mediated by processes that minimise the diffusive fluxes of PAR proteins between cytosol and membrane

"Wind" (rlung) im Kontext der tibetischen Medizin

Die vorgelegte Diplomarbeit behandelt die Erklärung von rlung in den rGyud bzhi, dem Hauptwerk der tibetischen Wissenschaft des Heilens (gso ba rig pa). Darin wird rlung als das Wind- oder Luft-Element im menschlichen Körper verstanden. Es ist neben „Galle“ (mkhris pa) und „Schleim“ (bad kan) einer der drei nyes pa (u.a. übersetzt mit Körperflüssigkeit). Das Hauptaugenmerk dieser Arbeit liegt auf der Übersetzung aus dem Kapitel über das Heilen von rlung-Krankheiten (rlung nad gso ba), welches das zweite Kapitel der dritten Überlieferung (Man ngag rgyud) der rGyud bzhi ist. Nach einer allgemeinen Einführung in die Grundlagen der tibetischen Medizin und deren Entstehung folgt die Übersetzung der Primärquelle. Diese wird mit dem Pendant der Bon-Tradition, den ‘Bum bzhi, verglichen. Daher werden auch die Grundlagen dieses Werkes im Vergleich zu den rGyud bzhi kurz dargestellt, sowie Unterschiede, die sich im Zuge meiner Übersetzung herausgestellt haben. Ferner wird untersucht, in welchem Zusammenhang rlung und die Leitbahnen (rtsa), durch die es fließt, mit dem sogenannten „feinstofflichen Körper“ stehen. Die Untersuchung der Begriffe basiert auf tibetischer sowie westlicher Literatur und wird gegebenenfalls durch Interviews mit fachkundigen Informanten ergänzt.The present thesis deals with the explanation of rlung in the rGyud bzhi, the main work of the Tibetan science of healing (gso ba rig pa). There rlung is seen as the wind or air element in the human body. Along with “bile” (mkhris pa) and “phlegm” (bad kan) it is one of the three nyes pa (a.o. translated as humours). The main focus of this work lies in the translation from the chapter about the healing of rlung diseases (rlung nad gso ba), which is the second chapter of the third transmission (Man ngag rgyud) of the rGyud bzhi. A general introduction into the fundamentals of Tibetan medicine and its development is followed by the translation of the primary source. This will be compared with the counterpart of the Bon tradition, the ’Bum bzhi. Therefore a comparison between the fundamentals of this work and the rGyud bzhi will also be briefly presented, as well as the distinctions which emerged in the course of my translation. Furthermore, it will be examined how rlung and the channels (rtsa) where it is circulating are associated with the so-called ‘subtle body’. The examination of the terms is based on Tibetan as well as Western literature and is completed by interviews with competent informants where required

5-Bromo-17-nitro-26,28-prop-2-en­oxy-25,27-dipropoxycalix[4]arene

Mol­ecules of the title compound, C40H42BrNO6, are located on a crystallographic twofold rotation axis. As a result, the nitro group and bromine residue are mutually disordered with equal occupancies. The prop­oxy-substituted aromatic rings are close to parallel to each other [dihedral angle = 21.24 (1)°], whereas the propen­oxy-substituted rings enclose a dihedral angle of 70.44 (1)°. The dihedral angles between the methyl­ene C atoms and the aromatic rings shows that the propen­oxy substituted rings are bent away from the calixarene cavity [dihedral angle between the planes = 35.22 (8)°], whereas the prop­oxy-substituted rings are almost perpendicular [79.38 (10)°] to the plane of the methyl­ene C atoms

Computational and spectroscopic studies of organic mixed-valence compounds: where is the charge?

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.This article discusses recent progress by a combination of spectroscopy and quantum-chemical calculations in classifying and characterizing organic mixed-valence systems in terms of their localized vs.delocalized character. A recently developed quantum-chemical protocol based on non-standard hybrid functionals and continuum solvent models is evaluated for an extended set of mixed-valence bis-triarylamine radical cations, augmented by unsymmetrical neutral triarylamine-perchlorotriphenylmethyl radicals. It turns out that the protocol is able to provide a successful assignment to class II or class III Robin-Day behavior and gives quite accurate ground- and excited-state properties for the radical cations. The limits of the protocol are probed by the anthracene-bridged system8, where it is suspected that specific solute–solvent interactions are important and not covered by the continuum solvent model. Intervalence charge-transfer excitation energies for the neutral unsymmetrical radicals are systematically overestimated, but dipole moments and a number of other properties are obtained accurately by the protocol.DFG, GRK 1221, Steuerung elektronischer Eigenschaften von Aggregaten pi-konjugierter Molekül

Field-dependent exciton dissociation in organic heterojunction solar cells

In organic heterojunction solar cells, the generation of free charge carriers takes place in a multistep process which involves charge transfer (CT) states, that is, bound electron-hole pairs at the interface between donor and acceptor molecules. Past efforts to model the CT-state dissociation during solar cell operation were not able to consistently reproduce the experimentally observed field and temperature dependence. This discrepancy between model and experiment was partly due to the field-dependent free charge carrier collection process, which plays an important role in the widely used bulk heterojunction cell configuration and superimposes a possible field-dependent charge carrier generation process. In order to distinguish between generation and collection of free charge carriers, we propose the planar heterojunction cell configuration as a model system to study the field-dependent charge carrier generation process in organic heterojunction solar cells. We apply this model system to check current CT-state dissociation models against experimental data. Although the models can quantitatively account for the photocurrent's dependence on the applied voltage and the device thickness, they fail to account for the virtually negligible temperature dependence of the field-dependent charge-generation process. This discrepancy is traced back to a common feature of the models: an Arrhenius-like temperature dependence, distinctive of all processes involving a thermally activated jump over an energy barrier. As a solution to the problem, we introduce an exciton dissociation model based on a field-dependent tunnel process and demonstrate its consistency with the experimental observations. Our results indicate that the current microscopic picture of the charge-generation process in organic heterojunction solar cells being limited by the CT-state dissociation process needs to be reconsidered