Seminar on the Theory of Complex Systems  Winter Term 2011/2012

I will present a closed, time-independent Hamiltonian, which could be realized experimentally without great difficulty. The system has only two degrees of freedom, but it nonetheless seems to behave very much like a heat engine. One degree of freedom is fast, while the other is slow, but their highly nonlinear coupling allows resonant exchange of energy when the slow particle moves at a critical speed. Insofar as heat may be defined within mechanics as the energy carried by fast degrees of freedom, therefore, this system can exhibit the conversion of heat into work. Remarkably, moreover, the resonant energy transfer at the critical speed can be self-stabilizing, so that a large amount of work is quite unambiguously done on the slow particle. The result is that the system exhibits two dramatically different adiabatic regimes. The non-adiabatic switching between the two regimes appears furthermore to be chaotic.
 
I will discuss the classical dynamics of this simple but surprising system in detail, and then present some initial results for the corresponding quantum system. I will state no strong conclusions, but the system I analyze will incorporate multiple time scales, dynamical chaos, quantum mechanics, and work. Hence although it is quite unclear whether or not the model truly incorporates heat, it may at least tell us something about heat, as a phenomenon within Hamiltonian mechanics.

The cytoskeleton is constituted of rigid filaments, actin and microtubules, that interact with molecular motors introducing filament sliding and active reorganization. Experimentally it has been shown that reconstituted cytoskeleton solutions are able to self-organize into many different filament patterns like asters, vortices, bundles, etc. I will discuss recent modelings of this structure formation process involving filaments, motors and passive crosslinks. In the second part I will present a simple model describing how cells (or simpler cell fragments) can use active processes, namely active polymerization and motor-induced contraction, to move on a substrate. This model consists of a simplified version of the orientational filament dynamics, coupled to a phase-field description of the cell membrane. This model successfully reproduces the primary phenomenology of cell motility: discontinuous onset of motion, diversity of cell shapes and shape oscillations.

1. D. Smith, F. Ziebert et al. Molecular motor-induced instabilities and crosslinkers determine biopolymer organization, Biophys. J. 93, 4445 (2007).
2. F. Ziebert, I.S. Aranson and L. S. Tsimring Effects of crosslinks on filament-motor organization, New J. Phys. 9, 421 (2007).
3. F. Ziebert, S. Swaminathan and I. S. Aranson, 'Model for self-polarization and motility of keratocyte fragments', J. R. Soc. Interface, published online (2011).

Interphase chromosomes are organized into discrete chromosome territories (CTs) that may occupy preferred sub-nuclear positions. While chromosome size and gene density appear to influence positioning, the biophysical mechanisms behind CT localization, especially the relationship between morphology and positioning, remain obscure. One reason for this has been the difficulty in imaging, segmenting, and analyzing structures with variable or imprecise boundaries. Back in 2007, this prompted us to develop a novel approach, based on the 2D Wavelet-Transform-Modulus-Maxima (WTMM) method, adapted to perform objective and rigorous CT segmentation from nuclear background. The wavelet-transform acts as a mathematical microscope to characterize spatial image information over a continuous range of size scales. This space-scale nature, combined with full objectivity of the formalism, makes it more accurate than intensity-based segmentation algorithms. Using the WTMM method in combination with numerical simulation models, we had shown that CTs have a highly non-spherical 3D morphology, that CT positioning is non-random, and favors heterologous CT groupings and that translocation rates are strongly correlated with chromosome proximity.
As we now move to the large-scale, 3D analysis of vast quantities of CT images in collaboration with several international labs, new questions may be answered and novel modeling ideas must be implemented. One of these ideas is to develop a “top-down” CT model approach, where the CTs are modeled as physical, malleable objects, as they grow from the condensed metaphase state to the decondensed interphase state.

We discuss properties of a spin-polarized dipolar interacting ultracold Bose atom cloud confined in a harmonic trap. On the basis of an analytical treatment of the dipole-dipole interaction between the atoms, using results of 19th century potential theory and the Josephson equations of macroscopic quantum physics, we then present a study of low lying collective modes of density oscillations around the ellipsoidal shaped ground-state of the cold atom cloud for various harmonic traps with spherical, uni-axial and tri-axial symmetry.