The "30-nm" chromatin fibers, as observed in eukaryotic nuclei, are considered a discrete level in a hierarchy of DNA folding. At present, there is considerable debate as to how the nudeosomes and linker DNA are organized within chromatin fibers, and a number of models have been proposed, many of which are based on helical symmetry and imply specific contacts between nucleosomes. However, when observed in nuclei or after isolation, chromatin fibers show considerable structural irregularity. In the present study, chromatin folding is considered solely in terms of the known properties of the nudeosome-linker unit, taking into account the relative rotation between consecutive nucleosomes that results from the helical twist of DNA. Model building based on this premise, and with a constant length of linker DNA between consecutive nucleosomes, results in a family of fiber-and ribbon-like structure. When the linker length between nucleosomes is aflowed to vary, as occurs in nature, fibers showing the types of irregulaity observed in nuclei and in isolated chromatin are created. The potential application of the model in determining the three-dimensional organization of chromatin in which nucleosome positions are known is discussed.The genome of most eukaryotes is complexed with proteins to form chromatin (1). Under low salt conditions in vitro, the complex assumes its simplest conformation and is seen as a beaded chain of 11-nm (diameter) nucleosomes (e.g., ref.2). As the ionic strength of the medium is raised, the nucleosomal chain condenses, eventually forming a compact fiber 30-40 nm in diameter (1-3). These compact fibers observed in isolated chromatin in vitro are presumed to be related to similar structures seen in thin sections of certain types of nuclei such as nucleated erythrocytes (e.g., refs. 4 and 5). X-ray scattering studies of whole cells and nuclei often show 30-to 45-nm reflections that have been interpreted as arising from the center-to-center spacing of compact chromatin fibers (6). These results suggest that the compact chromatin fiber constitutes a distinct level of chromatin organization, especially for transcriptionally inactive chromatin. In this context, the architecture of the fiber would implicitly define the substrate for the regulatory events that lead to chromatin unfolding, a prerequisite for transcription.Attempts to deduce the structure of compact chromatin fibers have resulted in a number of proposals that include both symmetrical and nonsymmetrical arrangements of nucleosomes (reviewed in ref. 7). There is evidence suggesting some degree of symmetry in fiber structure: an intermediate conformation between the nucleosome chain and the compact chromatin fiber is a "zig-zag ribbon" (2) that can display considerable regularity (8), and isolated fibers prepared for electron microscopy contain regions with a limited amount of internal order (2, 3, 9-11). All proposed model structuresThe publication costs of this article were defrayed in part by page charge payment. This article must ...

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In the present work, we focus on the cases of twosite (dimer) and three-site (trimer) configurations, i.e. oligomers, respecting the parity-time (PT ) symmetry, i.e. with a spatially odd gain-loss profile. We examine different types of solutions of such configurations with linear and nonlinear gain/loss profiles. Solutions beyond the linear PT -symmetry critical point as well as solutions with asymmetric linearization eigenvalues are found in both the nonlinear dimer and trimer. The latter feature is absent in linear PT -symmetric trimers, while both of them are absent in linear PT -symmetric dimers. Furthermore, nonlinear gain/loss terms enable the existence of both symmetric and asymmetric solution profiles (and of bifurcations between them), while only symmetric solutions are present in the linear PT -symmetric dimers and trimers. The linear stability analysis around the obtained solutions is discussed and their dynamical evolution is explored by means of direct numerical simulations. Finally, a brief discussion is also given of recent progress in the context of PT -symmetric quadrimers.

Abstract. Foundation species are basal species that play an important role in determining community composition by physically structuring ecosystems and modulating ecosystem processes. Foundation species largely operate via non-trophic interactions, presenting a challenge to incorporating them into food web models. Here, we used non-linear, bioenergetic predator-prey models to explore the role of foundation species and their non-trophic effects. We explored four types of models in which the foundation species reduced the metabolic rates of species in a specific trophic position. We examined the outcomes of each of these models for six metabolic rate ''treatments'' in which the foundation species altered the metabolic rates of associated species by one-tenth to ten times their allometric baseline metabolic rates. For each model simulation, we looked at how foundation species influenced food web structure during community assembly and the subsequent change in food web structure when the foundation species was removed. When a foundation species lowered the metabolic rate of only basal species, the resultant webs were complex, species-rich, and robust to foundation species removals. On the other hand, when a foundation species lowered the metabolic rate of only consumer species, all species, or no species, the resultant webs were species-poor and the subsequent removal of the foundation species resulted in the further loss of species and complexity. This suggests that in nature we should look for foundation species to predominantly facilitate basal species.