Nucleosomes form the basic unit of compaction within eukaryotic genomes, and their locations represent an important, yet poorly understood, mechanism of genetic regulation. Quantifying the strength of interactions within the nucleosome is a central problem in biophysics and is critical to understanding how nucleosome positions influence gene expression. By comparing to single-molecule experiments, we demonstrate that a coarse-grained molecular model of the nucleosome can reproduce key aspects of nucleosome unwrapping. Using detailed simulations of DNA and histone proteins, we calculate the tension-dependent free energy surface corresponding to the unwrapping process. The model reproduces quantitatively the forces required to unwrap the nucleosome and reveals the role played by electrostatic interactions during this process. We then demonstrate that histone modifications and DNA sequence can have significant effects on the energies of nucleosome formation. Most notably, we show that histone tails contribute asymmetrically to the stability of the outer and inner turn of nucleosomal DNA and that depending on which histone tails are modified, the tension-dependent response is modulated differently.

The dynamic modulus G(*) of a viscoelastic medium is often measured by following the trajectory of a small bead subject to Brownian motion in a method called "passive microbead rheology." This equivalence between the positional autocorrelation function of the tracer bead and G(*) is assumed via the generalized Stokes-Einstein relation (GSER). However, inertia of both bead and medium are neglected in the GSER so that the analysis based on the GSER is not valid at high frequency where inertia is important. In this paper we show how to treat both contributions to inertia properly in one-bead passive microrheological analysis. A Maxwell fluid is studied as the simplest example of a viscoelastic fluid to resolve some apparent paradoxes of eliminating inertia. In the original GSER, the mean-square displacement (MSD) of the tracer bead does not satisfy the correct initial condition. If bead inertia is considered, the proper initial condition is realized, thereby indicating an importance of including inertia, but the MSD oscillates at a time regime smaller than the relaxation time of the fluid. This behavior is rather different from the original result of the GSER and what is observed. What is more, the discrepancy from the GSER result becomes worse with decreasing bead mass, and there is an anomalous gap between the MSD derived by naïvely taking the zero-mass limit in the equation of motion and the MSD for finite bead mass as indicated by McKinley et al. [J. Rheol. 53, 1487 (2009)]. In this paper we show what is necessary to take the zero-mass limit of the bead safely and correctly without causing either the inertial oscillation or the anomalous gap, while obtaining the proper initial condition. The presence of a very small purely viscous element can be used to eliminate bead inertia safely once included in the GSER. We also show that if the medium contains relaxation times outside the window where the single-mode Maxwell behavior is observed, the oscillation can be attenuated inside the window. This attenuation is realized even in the absence of a purely viscous element. Finally, fluid inertia also affects the bead autocorrelation through the Basset force and the fluid dragged around with the bead. We show that the Basset force plays the same role as the purely viscous element in high-frequency regime, and the oscillation of MSD is suppressed if fluid density and bead density are comparable.

A central question in epigenetics is how histone modifications influence the 3D structure of eukaryotic genomes and, ultimately, how this 3D structure is manifested in gene expression. The wide range of length scales that influence the 3D genome structure presents important challenges; epigenetic modifications to histones occur on scales of angstroms, yet the resulting effects of these modifications on genome structure can span micrometers. There is a scarcity of computational tools capable of providing a mechanistic picture of how molecular information from individual histones is propagated up to large regions of the genome. In this work, a new molecular model of chromatin is presented that provides such a picture. This new model, referred to as 1CPN, is structured around a rigorous multiscale approach, whereby free energies from an established and extensively validated model of the nucleosome are mapped onto a reduced coarse-grained topology. As such, 1CPN incorporates detailed physics from the nucleosome, such as histone modifications and DNA sequence, while maintaining the computational efficiency that is required to permit kilobase-scale simulations of genomic DNA. The 1CPN model reproduces the free energies and dynamics of both single nucleosomes and short chromatin fibers, and it is shown to be compatible with recently developed models of the linker histone. It is applied here to examine the effects of the linker DNA on the free energies of chromatin assembly and to demonstrate that these free energies are strongly dependent on the linker DNA length, pitch, and even DNA sequence. The 1CPN model is implemented in the LAMMPS simulation package and is distributed freely for public use.

A sequence of physical processes determined and quantified in LAOS: An instantaneous local 2D/3D approach J. Rheol. 56, 1129Rheol. 56, (2012 The rheological characterization of algae suspensions for the production of biofuels J. Rheol. 56, 925 (2012) A sequence of physical processes determined and quantified in large-amplitude oscillatory shear (LAOS): Application to theoretical nonlinear models J. Rheol. 56, 1 (2012) Analysis of medium amplitude oscillatory shear data of entangled linear and model comb polymers SynopsisViscoelastic properties of condensed soft matter can be estimated by following the trajectory of an embedded micron-sized particle in a method called passive microbead rheology. Data analysis of passive microbead rheology is usually based on formulas that relate bead displacement statistics to the dynamic modulus of the material in the frequency-domain. Therefore, methods of analysis require conversion of the data to the frequency-domain using numerical Fourier transform routines. These methods are known to introduce errors associated with frequency discretization and finite window size. Time-domain data analysis methods based on a single bead trajectory were introduced by Fricks et al. [SIAM J. Appl. Math. 69, 1277-1308 as an alternative to the frequency-domain formulas. We have expanded these ideas with the aim of performing Monte Carlo simulations on synthetic data to evaluate and compare analysis algorithms for systems in which particles are trapped in linear or nonlinear traps. Brownian dynamics simulations were used to generate trajectories of beads embedded in viscoelastic materials having a discrete relaxation spectrum, with multiple relaxation times. We show that by including a small purely dissipative element in the memory function of the generalized Langevin equation (GLE), we can eliminate inertia-related fast variables directly from the GLE to find an inertia-less GLE, avoiding the singularity reported by McKinley et al. [J. Rheol. 53, 1487-1506]. Using the inertia-less GLE, the computational cost of the simulations is reduced by nearly 5 orders of magnitude. We also show that, in real systems, this purely dissipative element can arise from fluid inertia, since for the bead the Basset force acts dissipative at high frequencies. V C 2012 The Society of Rheology.

We analyze the appropriate form for the generalized Stokes-Einstein relation (GSER) for viscoelastic solids and fluids when bead inertia and medium inertia are taken into account, which we call the inertial GSER. It was previously shown for Maxwell fluids that the Basset (or Boussinesq) force arising from medium inertia can act purely dissipatively at high frequencies, where elasticity of the medium is dominant. In order to elucidate the cause of this counterintuitive result, we consider Brownian motion in a purely elastic solid where ordinary Stokes-type dissipation is not possible. The fluctuation-dissipation theorem requires the presence of a dissipative mechanism for the particle to experience fluctuating Brownian forces in a purely elastic solid. We show that the mechanism for such dissipation arises from the radiation of elastic waves toward the system boundaries. The frictional force associated with this mechanism is the Basset force, and it exists only when medium inertia is taken into consideration in the analysis of such a system. We consider first a one-dimensional harmonic lattice where all terms in the generalized Langevin equation--i.e., the elastic term, the memory kernel, and Brownian forces-can be found analytically from projection-operator methods. We show that the dissipation is purely from radiation of elastic waves. A similar analysis is made on a particle in a continuum, three-dimensional purely elastic solid, where the memory kernel is determined from continuum mechanics. Again, dissipation arises only from radiation of elastic shear waves toward infinite boundaries when medium inertia is taken into account. If the medium is a viscoelastic solid, Stokes-type dissipation is possible in addition to radiational dissipation so that the wave decays at the penetration depth. Inertial motion of the bead couples with the elasticity of the viscoelastic material, resulting in a possible resonant oscillation of the mean-square displacement (MSD) of the bead. On the other hand, medium inertia (the Basset force) tends to attenuate the oscillations by the dissipation mechanism described above. Thus competition between bead inertia and medium inertia determines whether or not the MSD oscillates. We find that, if the medium density is larger than 4/7 of the bead density, the Basset damping will suppress oscillations in the MSD; this criterion is sufficient but not necessary to present oscillations.