Dynamics of polymers: classic results and recent developments

In this chapter we review concepts and theories of polymer dynamics. We think of it as an introduction to the topic for scientists specializing in other subfields of statistical mechanics and condensed matter theory, so, for the readers reference, we start with a short review of the equilibrium static properties of polymer systems. Most attention is paid to the dynamics of unentangled polymer systems, where apart from classical Rouse and Zimm models we review some recent scaling and analytical generalizations. The dynamics of systems with entanglements is also briefly reviewed. Special attention is paid to the discussion of comparatively weakly understood topological states of polymer systems and possible approaches to the description of their dynamics

Towards a robust algorithm to determine topological domains from colocalization data

One of the most important tasks in understanding the complex spatial organization of the genome consists in extracting information about this spatial organization, the function and structure of chromatin topological domains from existing experimental data, in particular, from genome colocalization (Hi-C) matrices. Here we present an algorithm allowing to reveal the underlying hierarchical domain structure of a polymer conformation from analyzing the modularity of colocalization matrices. We also test this algorithm on several model polymer structures: equilibrium globules, random fractal globules and regular fractal (Peano) conformations. We define what we call a spectrum of cluster borders, and show that these spectra behave strikingly differently for equilibrium and fractal conformations, allowing us to suggest an additional criterion to identify fractal polymer conformations

Topological transition in disordered planar matching: combinatorial arcs expansion

In this paper, we investigate analytically the properties of the disordered Bernoulli model of planar matching. This model is characterized by a topological phase transition, yielding complete planar matching solutions only above a critical density threshold. We develop a combinatorial procedure of arcs expansion that explicitly takes into account the contribution of short arcs, and allows to obtain an accurate analytical estimation of the critical value by reducing the global constrained problem to a set of local ones. As an application to a toy representation of the RNA secondary structures, we suggest generalized models that incorporate a one-to-one correspondence between the contact matrix and the RNA-type sequence, thus giving sense to the notion of effective non-integer alphabets.Comment: 28 pages, 6 figures, published versio

Number of Common Sites Visited by N Random Walkers

We compute analytically the mean number of common sites, W_N(t), visited by N independent random walkers each of length t and all starting at the origin at t=0 in d dimensions. We show that in the (N-d) plane, there are three distinct regimes for the asymptotic large t growth of W_N(t). These three regimes are separated by two critical lines d=2 and d=d_c(N)=2N/(N-1) in the (N-d) plane. For d<2, W_N(t)\sim t^{d/2} for large t (the N dependence is only in the prefactor). For 2<d<d_c(N), W_N(t)\sim t^{\nu} where the exponent \nu= N-d(N-1)/2 varies with N and d. For d>d_c(N), W_N(t) approaches a constant as t\to \infty. Exactly at the critical dimensions there are logaritmic corrections: for d=2, we get W_N(t)\sim t/[\ln t]^N, while for d=d_c(N), W_N(t)\sim \ln t for large t. Our analytical predictions are verified in numerical simulations.Comment: 5 pages, 3 .eps figures include

Beringian Standstill and Spread of Native American Founders

Native Americans derive from a small number of Asian founders who likely arrived to the Americas via Beringia. However, additional details about the intial colonization of the Americas remain unclear. To investigate the pioneering phase in the Americas we analyzed a total of 623 complete mtDNAs from the Americas and Asia, including 20 new complete mtDNAs from the Americas and seven from Asia. This sequence data was used to direct high-resolution genotyping from 20 American and 26 Asian populations. Here we describe more genetic diversity within the founder population than was previously reported. The newly resolved phylogenetic structure suggests that ancestors of Native Americans paused when they reached Beringia, during which time New World founder lineages differentiated from their Asian sister-clades. This pause in movement was followed by a swift migration southward that distributed the founder types all the way to South America. The data also suggest more recent bi-directional gene flow between Siberia and the North American Arctic

Origin and spread of human mitochondrial DNA haplogroup U7

Human mitochondrial DNA haplogroup U is among the initial maternal founders in Southwest Asia and Europe and one that best indicates matrilineal genetic continuity between late Pleistocene hunter-gatherer groups and present-day populations of Europe. While most haplogroup U subclades are older than 30 thousand years, the comparatively recent coalescence time of the extant variation of haplogroup U7 (~16–19 thousand years ago) suggests that its current distribution is the consequence of more recent dispersal events, despite its wide geographical range across Europe, the Near East and South Asia. Here we report 267 new U7 mitogenomes that – analysed alongside 100 published ones – enable us to discern at least two distinct temporal phases of dispersal, both of which most likely emanated from the Near East. The earlier one began prior to the Holocene (~11.5 thousand years ago) towards South Asia, while the later dispersal took place more recently towards Mediterranean Europe during the Neolithic (~8 thousand years ago). These findings imply that the carriers of haplogroup U7 spread to South Asia and Europe before the suggested Bronze Age expansion of Indo-European languages from the Pontic-Caspian Steppe region

The Changing Landscape for Stroke\ua0Prevention in AF: Findings From the GLORIA-AF Registry Phase 2

Background GLORIA-AF (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients with Atrial Fibrillation) is a prospective, global registry program describing antithrombotic treatment patterns in patients with newly diagnosed nonvalvular atrial fibrillation at risk of stroke. Phase 2 began when dabigatran, the first non\u2013vitamin K antagonist oral anticoagulant (NOAC), became available. Objectives This study sought to describe phase 2 baseline data and compare these with the pre-NOAC era collected during phase&nbsp;1. Methods During phase 2, 15,641 consenting patients were enrolled (November 2011 to December 2014); 15,092 were eligible. This pre-specified cross-sectional analysis describes eligible patients\u2019 baseline characteristics. Atrial fibrillation&nbsp;disease characteristics, medical outcomes, and concomitant diseases and medications were collected. Data were analyzed using descriptive statistics. Results Of the total patients, 45.5% were female; median age was 71 (interquartile range: 64, 78) years. Patients were from Europe (47.1%), North America (22.5%), Asia (20.3%), Latin America (6.0%), and the Middle East/Africa (4.0%). Most had high stroke risk (CHA2DS2-VASc [Congestive heart failure, Hypertension, Age&nbsp; 6575 years, Diabetes mellitus, previous Stroke, Vascular disease, Age 65 to 74 years, Sex category] score&nbsp; 652; 86.1%); 13.9% had moderate risk (CHA2DS2-VASc&nbsp;= 1). Overall, 79.9% received oral anticoagulants, of whom 47.6% received NOAC and 32.3% vitamin K antagonists (VKA); 12.1% received antiplatelet agents; 7.8% received no antithrombotic treatment. For comparison, the proportion of phase 1 patients (of N&nbsp;= 1,063 all eligible) prescribed VKA was 32.8%, acetylsalicylic acid 41.7%, and no therapy 20.2%. In Europe in phase 2, treatment with NOAC was more common than VKA (52.3% and 37.8%, respectively); 6.0% of patients received antiplatelet treatment; and 3.8% received no antithrombotic treatment. In North America, 52.1%, 26.2%, and 14.0% of patients received NOAC, VKA, and antiplatelet drugs, respectively; 7.5% received no antithrombotic treatment. NOAC use was less common in Asia (27.7%), where 27.5% of patients received VKA, 25.0% antiplatelet drugs, and 19.8% no antithrombotic treatment. Conclusions The baseline data from GLORIA-AF phase 2 demonstrate that in newly diagnosed nonvalvular atrial fibrillation patients, NOAC have been highly adopted into practice, becoming more frequently prescribed than VKA in&nbsp;Europe and North America. Worldwide, however, a large proportion of patients remain undertreated, particularly in&nbsp;Asia&nbsp;and North America. (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients With Atrial Fibrillation [GLORIA-AF]; NCT01468701