Regular and stochastic dynamics in the real quadratic family

We prove the Regulat or Stochastic Conjecture for the real quadratic family which asserts that almost every real quadratic map Pc, c ∈ [−2, 1/4], has either an attracting cycle or an absolutely continuous invariant measure.

Tree rings, carbon dioxide, and climatic change

Tree rings have been used in various applications to reconstruct past climates as well as to assess the effects of recent climatic and environmental change on tree growth. In this paper we briefly review two ways that tree rings provide information about climate change and CO2: (i) in determining whether recent warming during the period of instrumental observations is unusual relative to prior centuries to millennia, and thus might be related to increasing greenhouse gases; and (ii) in evaluating whether enhanced radial growth has taken place in recent decades that appears to be unexplained by climate and might instead be due to increasing atmospheric CO2 or other nutrient fertilization. It is found that a number of tree-ring studies from temperature-sensitive settings indicate unusual recent warming, although there are also exceptions at certain sites. The present tree-ring evidence for a possible CO2 fertilization effect under natural environmental conditions appears to be very limited.

Chaperone rings in protein folding and degradation

Chaperone rings play a vital role in the opposing ATP-mediated processes of folding and degradation of many cellular proteins, but the mechanisms by which they assist these life and death actions are only beginning to be understood. Ring structures present an advantage to both processes, providing for compartmentalization of the substrate protein inside a central cavity in which multivalent, potentially cooperative interactions can take place between the substrate and a high local concentration of binding sites, while access of other proteins to the cavity is restricted sterically. Such restriction prevents outside interference that could lead to nonproductive fates of the substrate protein while it is present in non-native form, such as aggregation. At the step of recognition, chaperone rings recognize different motifs in their substrates, exposed hydrophobicity in the case of protein-folding chaperonins, and specific “tag” sequences in at least some cases of the proteolytic chaperones. For both folding and proteolytic complexes, ATP directs conformational changes in the chaperone rings that govern release of the bound polypeptide. In the case of chaperonins, ATP enables a released protein to pursue the native state in a sequestered hydrophilic folding chamber, and, in the case of the proteases, the released polypeptide is translocated into a degradation chamber. These divergent fates are at least partly governed by very different cooperating components that associate with the chaperone rings: that is, cochaperonin rings on one hand and proteolytic ring assemblies on the other. Here we review the structures and mechanisms of the two types of chaperone ring system.

Bacteriophage T7 helicase/primase proteins form rings around single-stranded DNA that suggest a general structure for hexameric helicases.

Most helicases studied to date have been characterized as oligomeric, but the relation between their structure and function has not been understood. The bacteriophage T7 gene 4 helicase/primase proteins act in T7 DNA replication. We have used electron microscopy, three-dimensional reconstruction, and protein crosslinking to demonstrate that both proteins form hexameric rings around single-stranded DNA. Each subunit has two lobes, so the hexamer appears to be two-tiered, with a small ring stacked on a large ring. The single-stranded DNA passes through the central hole of the hexamer, and the data exclude substantial wrapping of the DNA about or within the protein ring. Further, the hexamer binds DNA with a defined polarity as the smaller ring of the hexamer points toward the 5' end of the DNA. The similarity in three-dimensional structure of the T7 gene 4 proteins to that of the Escherichia coli RuvB helicase suggests that polar rings assembled around DNA may be a general feature of numerous hexameric helicases involved in DNA replication, transcription, recombination, and repair.