Seminar on the Theory of Complex Systems  Summer Term 2014

Cytokinesis is the process of physical cleavage at the end of cell division; it proceeds by ingression of an actomyosin furrow at the equator of the cell. Its failure leads to multinucleated cells and is a possible cause of tumorigenesis. Here, we calculate the full dynamics of furrow ingression and predict cytokinesis completion above a well-defined threshold of equatorial contractility. The cortical actomyosin is identified as the main source of mechanical dissipation and active forces. Thereupon, we propose a viscous active non-linear membrane theory of the cortex that explicitly includes actin turnover and where the active RhoA signal leads to an equatorial band of myosin overactivity. The resulting cortex deformation is calculated numerically and reproduces well the features of cytokinesis such as cell shape and cortical flows toward the equator. Our theory gives a physical explanation of the independence of cytokinesis duration on cell size in embryos. It also predicts a critical role of turnover on the rate and success of furrow constriction. Scaling arguments allow for a simple interpretation of the numerical results and unveil the key mechanism that generates the threshold for cytokinesis completion: cytoplasmic incompressibility results in a competition between the furrow line tension and the cell poles surface tension.

Polymeric semiconductors present a prominent example of complex hierarchical structuring of material. Features of the morphology are coupled across multiple length scales, and mesoscale ordering is affected by fine details of molecular architecture and interactions.
In this talk, we would like to discuss perspectives of describing such mesoscopic morphologies with models using a combined particle-based coarse-graining method. We impose some aspects of thermodynamics of the system in a top-down approach [1,2,3], i.e. a simple equation of state and liquid-crystalline biaxial-nematic ordering, in order to reproduce main features of the real material structure and symmetry. Simultaneously, we model chain connectivity with coarse-grained bonded potentials which were derived in a bottom-up approach from the underlying atomistic degrees of freedom.[4]
In the first part of the talk, we will consider as a case study the modeling of poly(3-alkylthiophene) and how the model can reproduce basic physical properties of the real material.[3] In the second part, we will focus on the estimation of Frank elastic constants for nematic, polymeric systems [5] in a more generic framework, presenting how such simple, soft coarse-grained models can help to study mesoscale features and possibly link to field-based simulation techniques. As an outlook, we will briefly mention the extension of the modeling for describing polymer-fullerene blends and the study of phase segregation in such systems, as well as some aspects of how the microscopic features of the material can be reintroduced at a later stage of simulation (back-mapping).
[1] Daoulas et al., J. Phys.: Condens. Matter 24, 284121 (2012); [2] Müller, J. Stat. Phys. 145, 967 (2011); [3] Gemünden et al., Macromolecules, 46, 5762 (2013); [4] Peter & Kremer, Soft Matter 5, 4357 (2009); [5] Le Doussal & Nelson, Europhys. Lett. 15, 161 (1991);

Recurrent processes are a general feature of living systems, from the cell cycle to circadian rhythms to hibernation cycles. During development and life, numerous recurrent processes are controlled by genetic oscillators, a specific class of genetic regulatory networks characterized by oscillations in the level of gene expression products. A prominent example for such a process takes place during the embryonic development of vertebrates: the precursors of the vertebrae are formed through the rhythmic and sequential segmentation of the elongating body axis. In this talk, I will first give a brief introduction to genetic oscillators and their role in pattern formation during vertebrate segmentation. I will then present new results from a combined theoretical and experimental approach, showing that the timing of segmentation is regulated through the complex interplay of different time and length scales in a hitherto unanticipated way.

Glasses, spin-glasses and many other disordered systems show critical slowing down as some critical temperature T_c is approached. Below this temperature criticality persists and in addition aging phenomena show up. As prototype for this behavior a mean field model, the spherical spin-glass with p-spin interactions, is investigated. Above T_c it is equivalent to mode coupling theory near the ideal glass transition. Below T_c the dynamics is ruled by several fixed points and crossover scaling. This is in close analogy to multicritical phenomena near phase transition, e.g. an anisotropic magnet. The critical exponents are, however, not universal. In the aging regime the existence of time-reparamertization-invariant solutions has been postulated. This puzzle is discussed and hopefully clarified.