arXiv subjects

B. Duenweg

Publications and source records attributed to B. Duenweg.

11 recordsLinked to original sources

arXiv2020

Computing 3D chromatin configurations from contact probability maps by Inverse Brownian Dynamics

The three-dimensional organization of chromatin, on the length scale of a few genes, is crucial in determining the functional state - accessibility and the amount of gene expression - of the chromatin. Recent advances in chromosome conformation capture experiments provide partial information on the chromatin organization in a cell population, namely the contact count between any segment pairs, but not on the interaction strength that leads to these contact counts. However, given the contact matrix, determining the complete 3D organization of the whole chromatin polymer is an inverse problem. In the present work, a novel Inverse Brownian Dynamics (IBD) method based on a coarse grained bead-spring chain model has been proposed to compute the optimal interaction strengths between different segments of chromatin such that the experimentally measured contact count probability constraints are satisfied. Applying this method to the α-globin gene locus in two different cell types, we predict the 3D organizations corresponding to active and repressed states of chromatin at the locus. We show that the average distance between any two segments of the region has a broad distribution and cannot be computed as a simple inverse relation based on the contact probability alone. The results presented for multiple normalization methods suggest that all measurable quantities may crucially depend on the nature of normalization. We argue that by experimentally measuring predicted quantities, one may infer the appropriate form of normalization.

cond-mat.soft↗

arXiv2019

Universality of the collapse transition of sticky polymers

The universality of the swelling of the radius of gyration of a homopolymer relative to its value in the $θ$ state, independent of polymer-solvent chemistry, in the crossover regime between $θ$ and athermal solvent conditions, is well known. Here we study, by Brownian dynamics, a polymer model where a subset of monomers is labelled as "stickers". The mutual interaction of the stickers is more attractive than those of the other ("backbone") monomers, and has the additional important characteristic of "functionality" $φ$, i.e., the maximum number of stickers that can locally bind to a given sticker. A saturated bond formed in this manner remains bound until it breaks due to thermal fluctuations, a requirement which can be viewed as an additional Boolean degree of freedom that describes the bonding. This, in turn, makes the question of the order of the collapse transition a non-trivial one. Nevertheless, for the parameters that we have studied (in particular, $φ=1$), we find a standard second-order $θ$ collapse, using a renormalised solvent quality parameter that takes into account the increased average attraction due to the presence of stickers. We examine the swelling of the radius of gyration of such a sticky polymer relative to its value in the altered $θ$ state, using a novel potential to model the various excluded volume interactions that occur between the monomers on the chain. We find that the swelling of such sticky polymers is identical to the universal swelling of homopolymers in the thermal crossover regime. Additionally, for our model, the Kuhn segment length under $θ$ conditions is found to be the same for chains with and without stickers.

cond-mat.soft↗

arXiv2018

Shear thinning in dilute and semidilute solutions of polystyrene and DNA

The viscosity of dilute and semidilute unentangled DNA solutions, in steady simple shear flow, has been measured across a range of temperatures and concentrations. For polystyrene solutions, measurements of viscosity have been carried out in the semidilute unentangled regime, while results of prior experimental measurements in the dilute regime have been used for the purpose of data analysis, and for comparison with the behaviour of DNA solutions. Interpretation of the shear rate dependence of viscosity in terms of suitably defined non-dimensional variables, is shown to lead to master plots, independent of temperature and concentration, in each of the two concentration regimes. In the case of semidilute unentangled solutions, defining the Weissenberg number in terms of a concentration dependent large scale relaxation time is found not to lead to data collapse across different concentrations. On the other hand, the use of an alternative relaxation time, with the concentration dependence of a single correlation blob, suggests the existence of universal shear thinning behaviour at large shear rates.

cond-mat.soft↗

arXiv2016

Equilibrium binding energies from fluctuation theorems and force spectroscopy simulations

Brownian dynamics simulations are used to study the detachment of a particle from a substrate. Although the model is simple and generic, we attempt to map its energy, length and time scales onto a specific experimental system, namely a bead that is weakly bound to a cell and then removed by an optical tweezer. The external driving force arises from the combined optical tweezer and substrate potentials, and thermal fluctuations are taken into account by a Brownian force. The Jarzynski equality and Crooks' fluctuation theorem are applied to obtain the equilibrium free energy difference between the final and initial states. To this end, we sample non--equilibrium work trajectories for various tweezer pulling rates. We argue that this methodology should also be feasible experimentally for the envisioned system. Furthermore, we outline how the measurement of a whole free energy profile would allow the experimentalist to retrieve the unknown substrate potential by means of a suitable deconvolution. The influence of the pulling rate on the accuracy of the results is investigated, and umbrella sampling is used to obtain the equilibrium probability of particle escape for a variety of trap potentials.

cond-mat.soft↗

arXiv2012

Dynamic crossover scaling in polymer solutions

The crossover region in the phase diagram of polymer solutions, in the regime above the overlap concentration, is explored by Brownian Dynamics simulations, to map out the universal crossover scaling functions for the gyration radius and the single-chain diffusion constant. Scaling considerations, our simulation results, and recently reported data on the polymer contribution to the viscosity obtained from rheological measurements on DNA systems, support the assumption that there are simple relations between these functions, such that they can be inferred from one another.

cond-mat.soft↗

arXiv2012

Numerical electrokinetics

A new lattice method is presented in order to efficiently solve the electrokinetic equations, which describe the structure and dynamics of the charge cloud and the flow field surrounding a single charged colloidal sphere, or a fixed array of such objects. We focus on calculating the electrophoretic mobility in the limit of small driving field, and systematically linearise the equations with respect to the latter. This gives rise to several subproblems, each of which is solved by a specialised numerical algorithm. For the total problem we combine these solvers in an iterative procedure. Applying this method, we study the effect of the screening mechanism (salt screening vs. counterion screening) on the electrophoretic mobility, and find a weak non-trivial dependence, as expected from scaling theory. Furthermore, we find that the orientation of the charge cloud (i. e. its dipole moment) depends on the value of the colloid charge, as a result of a competition between electrostatic and hydrodynamic effects.

cond-mat.soft↗

arXiv2011

Studying Flow Close to an Interface by Total Internal Reflection Fluorescence Cross Correlation Spectroscopy: Quantitative Data Analysis

Total Internal Reflection Fluorescence Cross Correlation Spectroscopy (TIR-FCCS) has recently (S. Yordanov et al., Optics Express 17, 21149 (2009)) been established as an experimental method to probe hydrodynamic flows near surfaces, on length scales of tens of nanometers. Its main advantage is that fluorescence only occurs for tracer particles close to the surface, thus resulting in high sensitivity. However, the measured correlation functions only provide rather indirect information about the flow parameters of interest, such as the shear rate and the slip length. In the present paper, we show how to combine detailed and fairly realistic theoretical modeling of the phenomena by Brownian Dynamics simulations with accurate measurements of the correlation functions, in order to establish a quantitative method to retrieve the flow properties from the experiments. Firstly, Brownian Dynamics is used to sample highly accurate correlation functions for a fixed set of model parameters. Secondly, these parameters are varied systematically by means of an importance-sampling Monte Carlo procedure in order to fit the experiments. This provides the optimum parameter values together with their statistical error bars. The approach is well suited for massively parallel computers, which allows us to do the data analysis within moderate computing times. The method is applied to flow near a hydrophilic surface, where the slip length is observed to be smaller than 10nm, and, within the limitations of the experiments and the model, indistinguishable from zero.

cond-mat.soft↗

arXiv2009

Simple and Robust Solver for the Poisson-Boltzmann Equation

A variational approach is used to develop a robust numerical procedure for solving the nonlinear Poisson-Boltzmann equation. Following Maggs et al., we construct an appropriate constrained free energy functional, such that its Euler-Lagrange equations are equivalent to the Poisson-Boltzmann equation. We then develop, implement, and test an algorithm for its numerical minimization, which is quite simple and unconditionally stable. The analytic solution for planar geometry is used for validation. Furthermore, some results are presented for a charged colloidal sphere surrounded by counterions.

cond-mat.soft↗

arXiv2008

Colloidal electrophoresis: Scaling analysis, Green-Kubo relation, and numerical results

We consider electrophoresis of a single charged colloidal particle in a finite box with periodic boundary conditions, where added counterions and salt ions ensure charge neutrality. A systematic rescaling of the electrokinetic equations allows us to identify a minimum set of suitable dimensionless parameters, which, within this theoretical framework, determine the reduced electrophoretic mobility. It turns out that the salt-free case can, on the Mean Field level, be described in terms of just three parameters. A fourth parameter, which had previously been identified on the basis of straightforward dimensional analysis, can only be important beyond Mean Field. More complicated behavior is expected to arise when further ionic species are added. However, for a certain parameter regime, we can demonstrate that the salt-free case can be mapped onto a corresponding system containing additional salt. The Green-Kubo formula for the electrophoretic mobility is derived, and its usefulness demonstrated by simulation data. Finally, we report on finite-element solutions of the electrokinetic equations, using the commercial software package COMSOL.

cond-mat.soft↗

arXiv1999

Optimized Constant Pressure Stochastic Dynamics

A recently proposed method for computer simulations in the isothermal-isobaric (NPT) ensemble, based on Langevin-type equations of motion for the particle coordinates and the ``piston'' degree of freedom, is re-derived by straightforward application of the standard Kramers-Moyal formalism. An integration scheme is developed which reduces to a time-reversible symplectic integrator in the limit of vanishing friction. This algorithm is hence expected to be quite stable for small friction, allowing for a large time step. We discuss the optimal choice of parameters, and present some numerical test results.

cond-mat.soft↗

arXiv1997

Molecular Dynamics Simulations of the Thermal Glass Transition in Polymer Melts: Alpha-Relaxation Behaviour

We present Molecular Dynamics simulations of the thermal glass transition in a dense model polymer liquid. We performed a comparative study of both constant volume and constant pressure cooling of the polymer melt. Great emphasis was laid on a careful equilibration of the dense polymer melt at all studied temperatures. Our model introduces competing length scales in the interaction to prevent any cristallisation tendency. In this first manuscript we we analyse the structural properties as a function of temperature and the long alpha-relaxation behaviour as observed in the dynamic structure factor and the self-diffusion of the polymer chains. The relaxation can be consistently analysed in terms of the mode coupling theory (MCT) of the glass transition. The mode coupling critical temperature and the exponent gamma, defining the power law divergence of the alpha-relaxation timescale both depend on the thermodynamic ensemble employed in the simulation.

cond-mat.stat-mech↗