Seminar on the Theory of Complex Systems  Winter Term 2012/13

For simulations of proteins there are essentially two approaches, namely the atomistically detailed molecular dynamics for individual proteins, and the colloidal-scale Brownian dynamics for many-particle simulations of crudely simplified proteins. To fill this gap in resolution and time-scales, a number of so-called "coarse-grained" models have been developed recently, most of which start from the atomistic side and increase efficiency by grouping atoms together. Here I present a different, "fine-graining" approach which is based on the implicit solvent concept of Brownian dynamics. A flexible particle setup together with some recent methodological advances then allowed us to set up a hierarchical model of the protein backbone that has a near-atomistic resolution on the residue scale, while the overall numerical costs are still comparable to a macroscopic bead-spring model. I will also show that hydrodynamic interactions are very important when flexible protein models are simulated and how these many-body correlations can be efficiently approximated. The current state of our protein backbone model with its simplified sidechains already allows to study the dynamics and agglomeration of intrinsically unstructured proteins, while a straightforward addition of more detailed sidechains will then allow to simulate also the folding of globular proteins.

More information can be found here. Note that the workshop takes place in the Speyerer Str. 6

We propose a theory for gating (the opening and closing) of voltage gated biological ion channels, that follow the basic architecture of KCsA. To this end we study the interaction of the voltage sensor domains of the channel, that have been studied before as partial model, and the hydrophobic gating region. The voltage sensors of the channel can move in the electric field of the membrane potential and thereby sterically restrict the shape of the gating region. The interplay between the gate and the voltage sensor allow us to predict realistic characteristic behavior of the channel as a function of the membrane potential, such as the conductance. Our model might be in general useful to study gating of ion channels, even if other gating mechanisms are at work.

The role of microscopic chaos in the observable behavior of many-particles systems remains a controversial topic since the inception of statistical physics at the turn of the twentieth century. I will describe our ongoing efforts to investigate chaotic properties of quantum and classical many-spin systems. The talk is to be organized into three parts: (1) manifestations of chaos in the observable relaxation measured by nuclear magnetic resonance; (2) properties of chaotic Lyapunov instabilities in classical spin systems; and (3) signatures of chaos in the time series generated by spin systems.

Periodic stripe patterns are ubiquitous in living organisms. In many cases, however, the underlying developmental processes are complex and difficult to disentangle. In a novel synthetic biology approach we have implemented a genetic circuit that couples cell density and motility into the bacterium E. coli. This system enabled the programmed cells to form periodic stripes of high- and low- cell densities sequentially and autonomously. To study theoretically the origin and mechanism of this process we have developed a kinetic model that includes growth and density-suppressed motility of the cells. In this model we analyze the onset of pattern formation by calculating the front profile of a region of immotile cells that spreads into an initially cell-free region. From the calculated front profile we provide an analytic ansatz to determine the phase boundary between the stripe and the no-stripe phases. The influence of various parameters on the phase boundary is discussed.

Intrinsically disordered proteins (IDPs) form a unique protein category characterized by the absence of a well-defined structure and by remarkable conformational flexibility. Electron paramagnetic resonance (EPR) spectroscopy has witnessed tremendous methodological and instrumental developments during the last two decades. These new methods have strong impact on various areas of chemistry, materials science, physics, and especially biophysical chemistry. With the advent of site-directed spin-labeling (SDSL) of proteins and DNA or RNA, EPR spectroscopy thus became a valuable technique for obtaining information on structure and dynamics of biomacromolecules. SDSL EPR is amongst the most suitable methods to unravel structure and dynamics of IDPs. This contribution summarizes methodological developments in the area of SDSL EPR including in-cell EPR. Recent results on the intrinsically disordered Parkinson's disease protein Synuclein illustrate that the method gains increasing attention in IDP research.

The accessibility of genetic information in eukaryotes is dictated by the positioning of histone protein complexes along the DNA, the so-called nucleosomes. To regulate this pattern, cells express chromatin remodeling enzymes that can translocate nucleosomes in an energy-dependent manner to new positions. Thus, these enzymes are key regulators for chromatin structure and gene activity. Here, a model for the function and search mechanism of chromatin remodelers is proposed based on mobility measurements conducted in living cells. Remodelers seem to identify their target sites in a diffusion-driven process and actively translocate only a small subset of nucleosomes in steady-state, arguing for a rather stationary nucleosome distribution and gene expression pattern.

Magnetic Soft Matter encompasses such fascinating materials as ferrofluids, magnetorheological fluids, magnetic colloids, ferrogels, magnetic foams and rubber. All systems belong to the broad and interesting class of complex fluids or soft matter which have strong magnetic (dipolar) interactions. Depending on the properties of the embedding matrix they respond in various ways to internal and external magnetic fields, i.e. one can observe chain formation in magnetorheological fluids, the buckling of ferrogels, cluster formations of magnetic colloids, or the deformation of magnetic rubber. In this talk we will discuss two distinct classes of magnetic soft matter: In the first part we will present a recent study of magnetic gels, so-called ferrogels, that consist of a polymer network, into which magnetic nanoparticles are embedded. The interesting properties of ferrogels originate from a complex interplay of the mechanical properties of the polymers with the magnetic interactions of the embedded nanoparticles. The ability to control the system by an external magnetic field may give rise to applications in medicine and engineering. We present results [1] of two microscopical simulation models for a 2D ferrogel which are suited to explain two distinct mechanisms of deformation in such a system. The first model focusses on a deformation of the gel due to the dipole-dipole interaction between the magnetic nanoparticles. In an external magnetic field, a gel of this kind elongates in the direction parallel to the field and shrinks in the perpendicular direction. The second model deals with a distortion of the polymer matrix due to the transmission of torques from the magnetic nanoparticles to the polymer network. Here we observe an isotropic shrinking of the gel in an external magnetic field.
The second part of the talk deals with a non-standard magnetic colloidal system that we have termed shifted dipols [2,3]. They possess very unusual magnetic properties, that can, for example, be used for reversible self-assembly processes.

1. R. Weeber, S.S. Kantorovich, C. Holm, Deformation mechanisms in 2D magnetic gels studied by computer simulations. Soft Matter 8, 9923 (2012).
2. S. S. Kantorovich, R. Weeber, J.J. Cerda, C. Holm, Ferrofluids with shifted dipoles: ground state structures, Soft Matter 7, 5217 (2011).
3. M. Klingikt, R. Weeber, S.S. Kantorovich, C. Holm, Cluster Formation in Systems of Shifted-Dipole Particles, Soft Matter, in press, (2013).

In this talk I describe recent analytical progress in understanding clustering and collision processes of inertial particles suspended in smooth random flows. Three results are summarised. First, I discuss mechanisms leading to clustering of inertial particles in mixing flows (preferential concentration and multiplicative amplification). I demonstrate under which circumstances one or the other mechanism dominates, and when both are important. Second, I summarise new results concerning the rate-of-caustic formation for inertial particles in random flows. Third, these results determine the distribution of collision velocities. I describe the known properties of this distribution. I address to which extent these results describe the dynamics of inertial particles suspended in multi-scale turbulent flows, and conclude with a number of open questions. The talk is based on results obtained together with my main collaborators M. Wilkinson and K. Gustavsson.