I will present several bridging algorithms which are suitable for simulation of globular phases of single polymers [1]. In this context, the determination of knots provides a measure for entanglement which allows us to gauge the efficiency of the move sets. The algorithm is applied to study semi-flexible polymers in spherical confinement as a model system for DNA in viral capsids and to random copolymers in globular states to study aspects of protein-like systems. In the second part of my talk I will give a short overview of knots in proteins with a focus on structures discovered in the past three years [2].
[1] D. Reith, P. Virnau, Comput Phys Commun 181, 800 (2010)
[2] D. Bölinger, J. Sulkowska, H.-P. Hsu et al, PLoS Comp Biol 6, e1000731 (2010)

Ageing phenomena are known from glassy systems, but it has been realised that ageing can also occur in systems which can be either unfrustrated or without disorder. In general, ageing can be characterised by the following properties: (i) slow, non-exponential relaxation, (ii) absence of time-translation-invariance and (iii) dynamical scaling. Here, we shall show that ageing can also occur in non-equilibrium whose dynamics does not satisfy detailed balance such that the stationary states are not equilibrium states. We shall illustrate this by analysing two-time correlation and response functions in several simple reaction-diffusion systems. Directed percolation will serve as a paradigmatic example. Particular attention will be given to a precise description of the fluctuation-dissipation relationship and to numerical tests of theoretical predictions on the form of the non-trivial scaling functions.
M. Henkel and M. Pleimling, Non-equilibrium phase transitions, vol. 2: ageing and dynamical scaling far from equilibrium, Springer (Heidelberg 2010).

Sensitivity to noise makes most of the current quantum computing schemes prone to error and nonscalable, allowing only for very small proof of principle devices. In topological quantum error correction decoherence effects are prevented by encoding logical qubits in nonlocal degrees of freedom, while actively correcting for errors that occur locally in the system. We study the effects of different error sources to topological error correction codes by mapping the quantum problem onto a classical disordered statistical-mechanical model. The quantum error tolerance then corresponds to the point in the disorder-temperature phase diagram where the ferromagnetic phase of the classical model is lost. In order to compute this figure of merit, large-scale Monte Carlo simulations are needed.

tba

Models of biochemical pathways often comprise of hundreds of parameters. Since in many cases the available data is limited many parameter values are unknown. Moreover, this data is hampered by noise, scaling and offset parameters which reduce the inferential power of the data. As a consequence, the modeller is left with a parameter estimation problem, where multiple parameter sets can adequately describe the acquired data to an acceptable degree [1,2]. In recent years, several new methods to deal with inferential problems have been developed, both from the Bayesian as well as the frequentist side. Our work identifies opportunities to combine different approaches into a consistent strategy for uncertainty analysis. Methods The inferential methods we employ include Multiple Minimisation approaches, Profile Likelihood analysis [2] and Hessian-based Markov Chain Monte Carlo [1]. These methods were subsequently used to parameterise a 7 parameter mass action model of the JAK-STAT pathway [2]. Results Results indicate that combining several approaches leads to insights into model behaviour and avoids potential pitfalls of each individual method. Depending on the data used for parameterisation some parameters can be quite constrained by data, while others are not. In such cases, assuming that the model can be described by a single parameter set can lead to overconfident conclusions. Exploring the effects of uncertainty on model predictions to be able to assess whether the predictions of interest can truly be used to falsify a given hypothesis is therefore important. Furthermore, it appeared that model parameters and parameters involved in scaling the data were strongly related to kinetic model parameters and can hamper model analysis. Our results provide suggestions for dealing with such situations.
[1] R. N. Gutenkunst et al. “Universally Sloppy Parameter Sensitivities in Systems Biology Models”, PLoS Comput Biol, Vol. 3 (2007).
[2] A. Raue et al. “Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood”, Bioinformatics, Vol. 25 (2008)

Molecular assembly is a promising strategy for creating device-oriented or functional structures for bio/nanotechnology related applications. Typically these structures present several mesoscopic spatial and temporal scales, therefore their theoretical description relies on efficient simulation techniques based on a coarse-grained representation of the considered systems. In this scope we will present the concept of density-functional-theory-based Monte Carlo (DFT-MC) approaches suitable for describing the assembly of complex fluids. Some of their advantages include: a) the ability to describe multicomponent systems, with complex molecular architecture and boundary conditions b) the straightforward parameterization of the model and c) the ability to establish a quantitative relation to field-theoretic approaches (e.g. SCF theory). After discussing some general technical aspects of the DFT-MC simulations we will illustrate their implementation to the study of amphiphilic membranes in the framework of a DFT-based solvent-free model. The chain architecture is captured via a generic, bead-spring model while the density functional of the non-bonded interactions has the form of a third-order expansion with respect to the local densities of the hydrophilic and hydrophobic beads. The model can be combined with a novel thermodynamic integration (TDI) scheme to compute the free energies of mesoscopic structures in membranes. As an example, we consider the thermodynamic stability of the stalk structure (i.e. a hourglass connection between apposing membranes). The TDI method is based on reversibly transforming a morphology of two apposed bilayers into the structure of interest (e.g. the stalk) using an external field which allows the calculation of a free energy per molecule with an accuracy of 10^3 kT. To illustrate the connection of the DFT-MC simulations with field-theoretical approaches we present a three-dimensional, real-space SCF theory based on the continuum limit of the same model, i.e., a Gaussian thread representation of the chain architecture and strictly local interactions. The predictions of the SCF theory regarding representative membrane properties are compared with the results of the particle-based simulations. The free energy of the stalk morphology is obtained within the SCF theory calculations and the predictions of the mean-field theory regarding its thermodynamic stability are similar to those of the TDI approach.

Empirically observed patterns of genetic variation are shaped by the genetic history of the population in question which in turn is determined by geographical, historical, and ecological factors. Together with mutations and linkage disequilibrium, these factors give rise to the observed patterns. The patterns are today routinely interpreted in terms of stochastic gene-genealogical models. I briefly describe the standard model (Kingman's coalescent model) and summarise how it is simulated on a computer. By way of example I briefly describe two questions we have addressed using this approach: the effect of selective seeps on linkage-disequilibrium patterns, and genealogies of a spatially fragmented population (using the sea snail L. saxatilis as an example).
[1] An accurate model for genetic hitch-hiking A. Eriksson, P. Fernstrom, B. Mehlig, and S. Sagitov, Genetics 178 (2008) 439
[2] Multiple paternity: determining the minimum number of sires of a large brood, A. Eriksson, B. Mehlig, M. Panova, C. Andre, and K. Johannesson, Mol. Ecol. Res 10 (2010) 282

A linear DNA molecule which is confined to a narrow channel will be stretched along the channel direction. The amount of stretching is well established theoretically in the limit of very narrow (the Odijk regime) and very wide channels (the de Gennes regime). We investigate the validity of these theories by Monte Carlo simulation of a model system. Apart from the two limiting cases, we are particularly interested in the intermediate regime, which is most relevant experimentally. Finally, we investigate the behaviour of circular DNA molecules confined to narrow channels, also by means of Monte Carlo simulations.

In this talk we show that a trivial implementation of the "checkerboard algorithm" that is often used for parallelizing off-lattice Monte-Carlo simulations yields a non-physical ensemble. Furthermore, we point to a parallel Monte-Carlo algorithm that does not have these problems, and we explain how the algorithm can be healed by means of some more bookkeeping.

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated with graphs that can be decomposable or non-decomposable. We extend our sampling algorithms to a novel class of conditionally autoregressive models for sparse estimation in multivariate lattice data, with a special emphasis on the analysis of spatial data. These models embed a great deal of flexibility in estimating both the correlation structure across outcomes and the spatial correlation structure, thereby allowing for adaptive smoothing and spatial autocorrelation parameters. Our methods are illustrated using simulated and real-world examples, including an application to cancer mortality surveillance.

The poster discusses several bridging algorithms which are suitable for simulation of globular phases of single polymers [1]. In this context, the determination of knots provides a measure for entanglement which allows us to gauge the efficiency of the move sets. The second part of the poster provides a short overview on the occurrence of knots in globular phases.
[1] D. Reith, P. Virnau, Comput Phys Commun 181, 800 (2010)