Topological interactions between ring polymers: Implications for chromatin loops

Chromatin looping is a major epigenetic regulatory mechanism in higher eukaryotes. Besides its role in transcriptional regulation, chromatin loops have been proposed to play a pivotal role in the segregation of entire chromosomes. The detailed topological and entropic forces between loops still remain elusive. Here, we quantitatively determine the potential of mean force between the centers of mass of two ring polymers, i.e. loops. We find that the transition from a linear to a ring polymer induces a strong increase in the entropic repulsion between these two polymers. On top, topological interactions such as the non-catenation constraint further reduce the number of accessible conformations of close-by ring polymers by about 50%, resulting in an additional effective repulsion. Furthermore, the transition from linear to ring polymers displays changes in the conformational and structural properties of the system. In fact, ring polymers adopt a markedly more ordered and aligned state than linear ones. The forces and accompanying changes in shape and alignment between ring polymers suggest an important regulatory function of such a topology in biopolymers. We conjecture that dynamic loop formation in chromatin might act as a versatile control mechanism regulating and maintaining different local states of compaction and order.Comment: 12 pages, 11 figures. The article has been accepted by The Journal Of Chemical Physics. After it is published, it will be found at http://jcp.aip.or

Moving precision agriculture to a new dimension: the ARS/CSU precision farming project at Wiggins, Colorado

Presented at the Central Plains irrigation short course and exposition on February 17-18, 1998 at the Camino Inn in North Platte, Nebraska.Includes bibliographical references.As more producers become aware of precision farming technology they are asking how it can improve productivity and profitability. There is a vast array of claims, beliefs, and testimony, yet little quantitative data to answer this question. Multi-disciplinary field scale research is needed in precision farming to answer the questions of productivity and profitability. The Agricultural Research Service and Colorado State University have begun a multi-disciplinary research program that focuses on developing a clearer scientific understanding of the causes of yield variability. We intend to develop decision support systems for site specific management. A team of 15 scientists covering the areas of soil fertility, crop production, weed science, entomology, plant pathology, system engineering, remote sensing, GIS, irrigation engineering, agricultural economics and statistics has started a project to develop a better understanding of precision agriculture in Colorado. They are collecting and analyzing data from 2 center pivot irrigated fields Cooperating farmers manage all the crop production operations and provide yield maps of the corn grown on the fields (175 and 130 ac.). The important variables for crop production have been sampled at several different intervals. Both fields have been sampled at a grid spacing of 250 feet. More intensive sampling has been done by various disciplines in smaller areas at a variety of scales down to 50 feet. Concurrent work, in cooperation with industry, is developing center pivot and linear move irrigation systems to apply variable site specific rates of chemicals and water. We will discuss the project and the various data layers being collected

Approaching equilibrium and the distribution of clusters

We investigate the approach to stable and metastable equilibrium in Ising models using a cluster representation. The distribution of nucleation times is determined using the Metropolis algorithm and the corresponding $\phi^{4}$ model using Langevin dynamics. We find that the nucleation rate is suppressed at early times even after global variables such as the magnetization and energy have apparently reached their time independent values. The mean number of clusters whose size is comparable to the size of the nucleating droplet becomes time independent at about the same time that the nucleation rate reaches its constant value. We also find subtle structural differences between the nucleating droplets formed before and after apparent metastable equilibrium has been established.Comment: 22 pages, 16 figure

Conformational properties of compact polymers

Monte Carlo simulations of coarse-grained polymers provide a useful tool to deepen the understanding of conformational and statistical properties of polymers both in physical as well as in biological systems. In this study we sample compact conformations on a cubic LxLxL lattice with different occupancy fractions by modifying a recently proposed algorithm. The system sizes studied extend up to N=256000 monomers, going well beyond the limits of older publications on compact polymers. We analyze several conformational properties of these polymers, including segment correlations and screening of excluded volume. Most importantly we propose a scaling law for the end-to-end distance distribution and analyze the moments of this distribution. It shows universality with respect to different occupancy fractions, i.e. system densities. We further analyze the distance distribution between intrachain segments, which turns out to be of great importance for biological experiments. We apply these new findings to the problem of chromatin folding inside interphase nuclei and show that -- although chromatin is in a compacted state -- the classical theory of compact polymers does not explain recent experimental results

The Impact of Entropy on the Spatial Organization of Synaptonemal Complexes within the Cell Nucleus

We employ 4Pi-microscopy to study SC organization in mouse spermatocyte nuclei allowing for the three-dimensional reconstruction of the SC's backbone arrangement. Additionally, we model the SCs in the cell nucleus by confined, self-avoiding polymers, whose chain ends are attached to the envelope of the confining cavity and diffuse along it. This work helps to elucidate the role of entropy in shaping pachytene SC organization. The framework provided by the complex interplay between SC polymer rigidity, tethering and confinement is able to qualitatively explain features of SC organization, such as mean squared end-to-end distances, mean squared center-of-mass distances, or SC density distributions. However, it fails in correctly assessing SC entanglement within the nucleus. In fact, our analysis of the 4Pi-microscopy images reveals a higher ordering of SCs within the nuclear volume than what is expected by our numerical model. This suggests that while effects of entropy impact SC organization, the dedicated action of proteins or actin cables is required to fine-tune the spatial ordering of SCs within the cell nucleus

Zeros of the Partition Function and Pseudospinodals in Long-Range Ising Models

The relation between the zeros of the partition function and spinodal critical points in Ising models with long-range interactions is investigated. We find the spinodal is associated with the zeros of the partition function in four-dimensional complex temperature/magnetic field space. The zeros approach the real temperature/magnetic field plane as the range of interaction increases.Comment: 20 pages, 9 figures, accepted to PR

Phase Transitions in a Two-Component Site-Bond Percolation Model

A method to treat a N-component percolation model as effective one component model is presented by introducing a scaled control variable $p_{+}$. In Monte Carlo simulations on $16^{3}$, $32^{3}$, $64^{3}$ and $128^{3}$ simple cubic lattices the percolation threshold in terms of $p_{+}$ is determined for N=2. Phase transitions are reported in two limits for the bond existence probabilities $p_{=}$ and $p_{\neq}$. In the same limits, empirical formulas for the percolation threshold $p_{+}^{c}$ as function of one component-concentration, $f_{b}$, are proposed. In the limit $p_{=} = 0$ a new site percolation threshold, $f_{b}^{c} \simeq 0.145$, is reported.Comment: RevTeX, 5 pages, 5 eps-figure

Nucleation in Systems with Elastic Forces

Systems with long-range interactions when quenced into a metastable state near the pseudo-spinodal exhibit nucleation processes that are quite different from the classical nucleation seen near the coexistence curve. In systems with long-range elastic forces the description of the nucleation process can be quite subtle due to the presence of bulk/interface elastic compatibility constraints. We analyze the nucleation process in a simple 2d model with elastic forces and show that the nucleation process generates critical droplets with a different structure than the stable phase. This has implications for nucleation in many crystal-crystal transitions and the structure of the final state