Emergence of robust nucleosome patterns from an interplay of positioning mechanisms

Proper positioning of nucleosomes in eukaryotic cells is determined by a complex interplay of factors, including nucleosome-nucleosome interactions, DNA sequence, and active chromatin remodeling. Yet, characteristic features of nucleosome positioning, such as geneaveraged nucleosome patterns, are surprisingly robust across perturbations, conditions, and species. Here, we explore how this robustness arises despite the underlying complexity. We leverage mathematical models to show that a large class of positioning mechanisms merely affects the quantitative characteristics of qualitatively robust positioning patterns. We demonstrate how statistical positioning emerges as an effective description from the complex interplay of different positioning mechanisms, which ultimately only renormalize the model parameter quantifying the effective softness of nucleosomes. This renormalization can be species-specific, rationalizing a puzzling discrepancy between the effective nucleosome softness of S. pombe and S. cerevisiae. More generally, we establish a quantitative framework for dissecting the interplay of different nucleosome positioning determinants

Color Screening and the Suppression of the Charmonium State Yield in Nuclear Reactions

We discuss the new data for the production of the $\psi'$ meson in pA collisions at 450 GeV at CERN-SPS (of the NA50-collaboration) [1]. We extract from the CERN data $\sigma(\psi' N)\approx 8$ mb under the assumption that the $\psi'$ is produced as a result of the space-time evolution of a point-like $c\bar c$ pair which expands with time to the full size of the charmonium state. In the analysis we assume the existence of a relationship between the distribution of color in a hadron and the cross section of its interaction with a nucleon. However, our result is rather sensitive to the pattern of the expansion of the wave packet and significantly larger values of $\sigma(\psi' N)$ are not ruled out by the data. We show that recent CERN data confirm the suggestion of [2] that color fluctuations of the strengths in charmonium-nucleon interaction are the major source of suppression of the $J/\psi$ yield as observed at CERN in both pA and AA collisions.Comment: 10 pages, 5 figures (one with color

J/\Psi production, χ\chi polarization and Color Fluctuations

The hard contributions to the heavy quarkonium-nucleon cross sections are calculated based on the QCD factorization theorem and the nonrelativistic quarkonium model. We evaluate the nonperturbative part of these cross sections which dominates at $\sqrt{s_{NN}}\approx 20$ GeV at the Cern Super Proton Synchrotron (SPS) and becomes a correction at $\sqrt{s_{NN}}\approx 6$ TeV at the CERN Large Hadron Collider (LHC). \J production at the CERN SPS is well described by hard QCD, when the larger absorption cross sections of the $\chi$ states predicted by QCD are taken into account. We predict an $A$-dependent polarization of the $\chi$ states. The expansion of small wave packets is discussed.Comment: 13 pages REVTEX, 1 table, 2 PostScript, corrected some typo

Directed motion emerging from two coupled random processes: Translocation of a chain through a membrane nanopore driven by binding proteins

We investigate the translocation of a stiff polymer consisting of M monomers through a nanopore in a membrane, in the presence of binding particles (chaperones) that bind onto the polymer, and partially prevent backsliding of the polymer through the pore. The process is characterized by the rates: k for the polymer to make a diffusive jump through the pore, q for unbinding of a chaperone, and the rate q kappa for binding (with a binding strength kappa); except for the case of no binding kappa=0 the presence of the chaperones give rise to an effective force that drives the translocation process. Based on a (2+1) variate master equation, we study in detail the coupled dynamics of diffusive translocation and (partial) rectification by the binding proteins. In particular, we calculate the mean translocation time as a function of the various physical parameters.Comment: 22 pages, 5 figures, IOP styl

Nonequilibrium Steady States and Fano-Kondo Resonances in an AB Ring with a Quantum Dot

Electron transport through a strongly correlated quantum dot (QD) embedded in an Aharonov-Bohm (AB) ring is investigated with the aid of the finite-U slave-boson mean-field (SBMF) approach extended to nonequilibrium regime. A nonequilibrium steady state (NESS) of the mean-field Hamiltonian is constructed with the aid of the C*-algebraic approach for studying infinitely extended systems. In the linear response regime, the Fano-Kondo resonances and AB oscillations of the conductance obtained from the SBMF approach are in good agreement with those from the numerical renormalization group technique (NRG) by Hofstetter et al. by using twice larger Coulomb interaction. At zero temperature and finite bias voltage, the resonance peaks of the differential conductance tend to split into two. At low bias voltage, the split of the asymmetric resonance can be observed as an increase of the conductance plateau. We also found that the differential conductance has zero-bias maximum or minimum depending on the background transmission via direct tunneling between the electrodes.Comment: 24 pages,17 figure

Kondo Correlations and the Fano Effect in Closed AB-Interferometers

We study the Fano-Kondo effect in a closed Aharonov-Bohm (AB) interferometer which contains a single-level quantum dot and predict a frequency doubling of the AB oscillations as a signature of Kondo-correlated states. Using Keldysh formalism, Friedel sum rule and Numerical Renormalization Group, we calculate the exact zero-temperature linear conductance $G$ as a function of AB phase $\phi$ and level position $\epsilon$. In the unitary limit, $G(\phi)$ reaches its maximum $2e^2/h$ at $\phi=\pi/2$. We find a Fano-suppressed Kondo plateau for $G(\epsilon)$ similar to recent experiments.Comment: 4 pages, 4 eps figure

MCMC for Bayesian uncertainty quantification from time-series data

In computational neuroscience, Neural Population Models (NPMs) are mechanistic models that describe brain physiology in a range of different states. Within computational neuroscience there is growing interest in the inverse problem of inferring NPM parameters from recordings such as the EEG (Electroencephalogram). Uncertainty quantification is essential in this application area in order to infer the mechanistic effect of interventions such as anaesthesia. This paper presents Open image in new window software for Bayesian uncertainty quantification in the parameters of NPMs from approximately stationary data using Markov Chain Monte Carlo (MCMC). Modern MCMC methods require first order (and in some cases higher order) derivatives of the posterior density. The software presented offers two distinct methods of evaluating derivatives: finite differences and exact derivatives obtained through Algorithmic Differentiation (AD). For AD, two different implementations are used: the open source Stan Math Library and the commercially licenced Open image in new window tool distributed by NAG (Numerical Algorithms Group). The use of derivative information in MCMC sampling is demonstrated through a simple example, the noise-driven harmonic oscillator. And different methods for computing derivatives are compared. The software is written in a modular object-oriented way such that it can be extended to derivative based MCMC for other scientific domains

Spin Effects and Transport in Quantum Dots with overlapping Resonances

The role of spin is investigated in the transport through a quantum dot with two overlapping resonances (one having a width larger than the level separation and the other very narrow, cf. Silvestrov and Imry, Phys. Rev. Lett. {\bf 85}, 2565 (2000)). For a series of consecutive charging resonances, one electron from the leads populates one and the same broad level in the dot. Moreover, there is the tendency to occupy the same level also by the second electron within the same resonance. This second electron is taken from the narrow levels in the dot. The narrow levels are populated (and broad level is depopulated) via sharp rearrangements of the electronic configuration in the Coulomb blockade valleys. Possible experimental manifestations of this scenario are considered. Among these there are sharp features in the valleys and in the Mixed Valence regime and an unusual Kondo effect.Comment: 7 pages, 3 figures, just a published versio

Open charm and charmonium production at relativistic energies

We calculate open charm and charmonium production in $Au+Au$ reactions at $\sqrt{s}$ = 200 GeV within the hadron-string dynamics (HSD) transport approach employing open charm cross sections from $pN$ and $\pi N$ reactions that are fitted to results from PYTHIA and scaled in magnitude to the available experimental data. Charmonium dissociation with nucleons and formed mesons to open charm ($D+\bar{D}$ pairs) is included dynamically. The 'comover' dissociation cross sections are described by a simple phase-space model including a single free parameter, i.e. an interaction strength $M_0^2$, that is fitted to the $J/\Psi$ suppression data for $Pb+Pb$ collisions at SPS energies. As a novel feature we implement the backward channels for charmonium reproduction by $D \bar{D}$ channels employing detailed balance. From our dynamical calculations we find that the charmonium recreation is comparable to the dissociation by 'comoving' mesons. This leads to the final result that the total $J/\Psi$ suppression at $\sqrt{s}$ = 200 GeV as a function of centrality is slightly less than the suppression seen at SPS energies by the NA50 Collaboration, where the 'comover' dissociation is substantial and the backward channels play no role. Furthermore, even in case that all directly produced $J/\Psi$ mesons dissociate immediately (or are not formed as a mesonic state), a sizeable amount of charmonia is found asymptotically due to the $D+\bar{D} \to J/\Psi$ + meson channels in central collisions of $Au+Au$ at $\sqrt{s}$ = 200 GeV which, however, is lower than the $J/\Psi$ yield expected from binary scaling of $pp$ collisions.Comment: 42 pages, including 14 eps figures, discussions extended and references added, to be published in Phys. Rev.

Aharonov-Bohm interferometry with quantum dots: scattering approach versus tunneling picture

We address the question of how to model electron transport through closed Aharonov-Bohm interferometers which contain quantum dots. By explicitly studying interferometers with one and two quantum dots, we establish the connection between a tunneling-Hamiltonian formulation on the one hand and a scattering-matrix approach on the other hand. We prove that, under certain circumstances, both approaches are equivalent, i.e., both types of models can describe the same experimental setups. Furthermore, we analyze how the interplay of the Aharonov-Bohm phase and the orbital phase associated with the lengths of the interferometers' arms affect transport properties.Comment: 8 pages, 8 figures, published versio