Dynamical Eigenmodes of Star and Tadpole Polymers

The dynamics of phantom bead-spring chains with the topology of a symmetric star with $f$ arms and tadpoles ($f=3$, a special case) is studied, in the overdamped limit. In the simplified case where the hydrodynamic radius of the central monomer is $f$ times as heavy as the other beads, we determine their dynamical eigenmodes exactly, along the lines of the Rouse modes for linear bead-spring chains. These eigenmodes allow full analytical calculations of virtually any dynamical quantity. As examples we determine the radius of gyration, the mean square displacement of a tagged monomer, and, for star polymers, the autocorrelation function of the vector that spans from the center of the star to a bead on one of the arms.Comment: 21 pages in double spacing preprint format, 5 figures, minor changes in the "Discussion" section, to appear in JSTA

Dynamical Eigenmodes of a Polymerized Membrane

We study the bead-spring model for a polymerized phantom membrane in the overdamped limit, which is the two-dimensional generalization of the well-known Rouse model for polymers. We derive the {\it exact} eigenmodes of the membrane dynamics (the "Rouse modes"). This allows us to obtain exact analytical expressions for virtually any equilibrium or dynamical quantity for the membrane. As examples we determine the radius of gyration, the mean square displacement of a tagged bead, and the autocorrelation function of the difference vector between two tagged beads. Interestingly, even in the presence of tensile forces of any magnitude the Rouse modes remain the exact eigenmodes for the membrane. With stronger forces the membrane becomes essentially flat, and does not get the opportunity to intersect itself; in such a situation our analysis provides a useful and exactly soluble approach to the dynamics for a realistic model flat membrane under tension.Comment: 17 pages, 4 figures, minor changes, references updated, to appear in JSTA

Linear model for fast background subtraction in oligonucleotide microarrays

One important preprocessing step in the analysis of microarray data is background subtraction. In high-density oligonucleotide arrays this is recognized as a crucial step for the global performance of the data analysis from raw intensities to expression values. We propose here an algorithm for background estimation based on a model in which the cost function is quadratic in a set of fitting parameters such that minimization can be performed through linear algebra. The model incorporates two effects: 1) Correlated intensities between neighboring features in the chip and 2) sequence-dependent affinities for non-specific hybridization fitted by an extended nearest-neighbor model. The algorithm has been tested on 360 GeneChips from publicly available data of recent expression experiments. The algorithm is fast and accurate. Strong correlations between the fitted values for different experiments as well as between the free-energy parameters and their counterparts in aqueous solution indicate that the model captures a significant part of the underlying physical chemistry.Comment: 21 pages, 5 figure

Through the Eye of the Needle: Recent Advances in Understanding Biopolymer Translocation

In recent years polymer translocation, i.e., transport of polymeric molecules through nanometer-sized pores and channels embedded in membranes, has witnessed strong advances. It is now possible to observe single-molecule polymer dynamics during the motion through channels with unprecedented spatial and temporal resolution. These striking experimental studies have stimulated many theoretical developments. In this short theory-experiment review, we discuss recent progress in this field with a strong focus on non-equilibrium aspects of polymer dynamics during the translocation process.Comment: 29 pages, 6 figures, 3 tables, to appear in J. Phys.: Condens. Matter as a Topical Revie

Probing the Shape of a Graphene Nanobubble

Gas molecules trapped between graphene and various substrates in the form of bubbles are observed experimentally. The study of these bubbles is useful in determining the elastic and mechanical properties of graphene, adhesion energy between graphene and substrate, and manipulating the electronic properties via strain engineering. In our numerical simulations, we use a simple description of elastic potential and adhesion energy to show that for small gas bubbles ($\sim 10$ nm) the van der Waals pressure is in the order of 1 GPa. These bubbles show universal shape behavior irrespective of their size, as observed in recent experiments. With our results the shape and volume of the trapped gas can be determined via the vibrational density of states (VDOS) using experimental techniques such as inelastic tunneling and inelastic neutron scattering. The elastic energy distribution in the graphene layer which traps the nanobubble is homogeneous apart from its edge, but the strain depends on the bubble size thus variation in bubble size allows control of the electronic and optical properties.Comment: 5 Figures (Supplementary: 1 Figure), Accepted for publication in PCC

A model for the dynamics of extensible semiflexible polymers

We present a model for semiflexible polymers in Hamiltonian formulation which interpolates between a Rouse chain and worm-like chain. Both models are realized as limits for the parameters. The model parameters can also be chosen to match the experimental force-extension curve for double-stranded DNA. Near the ground state of the Hamiltonian, the eigenvalues for the longitudinal (stretching) and the transversal (bending) modes of a chain with N springs, indexed by p, scale as lambda_lp ~ (p/N)^2 and lambda_tp ~ p^2(p-1)^2/N^4 respectively for small p. We also show that the associated decay times tau_p ~ (N/p)^4 will not be observed if they exceed the orientational time scale tau_r ~ N^3 for an equally-long rigid rod, as the driven decay is then washed out by diffusive motion.Comment: 28 pages, 2 figure

Dynamic Sampling from a Discrete Probability Distribution with a Known Distribution of Rates

In this paper, we consider a number of efficient data structures for the problem of sampling from a dynamically changing discrete probability distribution, where some prior information is known on the distribution of the rates, in particular the maximum and minimum rate, and where the number of possible outcomes N is large. We consider three basic data structures, the Acceptance-Rejection method, the Complete Binary Tree and the Alias Method. These can be used as building blocks in a multi-level data structure, where at each of the levels, one of the basic data structures can be used. Depending on assumptions on the distribution of the rates of outcomes, different combinations of the basic structures can be used. We prove that for particular data structures the expected time of sampling and update is constant, when the rates follow a non-decreasing distribution, log-uniform distribution or an inverse polynomial distribution, and show that for any distribution, an expected time of sampling and update of $O\left(\log\log{r_{max}}/{r_{min}}\right)$ is possible, where $r_{max}$ is the maximum rate and $r_{min}$ the minimum rate. We also present an experimental verification, highlighting the limits given by the constraints of a real-life setting