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.

The orientation of the AP-1 heterodimer on DNA strongly affects transcriptional potency

Activation of gene transcription in eukaryotes requires the cooperative assembly of an initiation complex containing many protein subunits. The necessity that these components contact each other and the promoter/enhancer in defined ways suggests that their spatial arrangement might influence the activation response. Indeed, growing evidence indicates that DNA architecture can profoundly affect transcriptional potency. Much less is known about the influence of protein architecture on transcriptional activation. Here, we examine the architectural dependence of activator function through the analysis of matched pairs of AP-1•DNA complexes differing only in their orientation. Mutation of a critical Arg residue in the basic-leucine zipper domain of either Fos or Jun yielded single point-mutant heterodimers that bind DNA in a single defined orientation, as determined directly by native chemical ligation/affinity cleavage; by contrast, the corresponding wild-type protein binds DNA as a roughly equal mixture of two isomeric orientations, which are related by subunit interchange. The stereochemistry of the point-mutant heterodimers could be switched by inversion of a C•G base pair in the center of the AP-1 site, thus providing access to both fixed orientational isomers. Yeast reporter gene assays consistently revealed that one orientational isomer activates transcription at least 10-fold more strongly than the other. These results suggest that protein architecture, especially the spatial relationship of the activation domain to the promoter, can exert a powerful influence on activator potency.

Stochastic processes strongly influence HIV-1 evolution during suboptimal protease-inhibitor therapy

It has long been assumed that HIV-1 evolution is best described by deterministic evolutionary models because of the large population size. Recently, however, it was suggested that the effective population size (Ne) may be rather small, thereby allowing chance to influence evolution, a situation best described by a stochastic evolutionary model. To gain experimental evidence supporting one of the evolutionary models, we investigated whether the development of resistance to the protease inhibitor ritonavir affected the evolution of the env gene. Sequential serum samples from five patients treated with ritonavir were used for analysis of the protease gene and the V3 domain of the env gene. Multiple reverse transcription–PCR products were cloned, sequenced, and used to construct phylogenetic trees and to calculate the genetic variation and Ne. Genotypic resistance to ritonavir developed in all five patients, but each patient displayed a unique combination of mutations, indicating a stochastic element in the development of ritonavir resistance. Furthermore, development of resistance induced clear bottleneck effects in the env gene. The mean intrasample genetic variation, which ranged from 1.2% to 5.7% before treatment, decreased significantly (P < 0.025) during treatment. In agreement with these findings, Ne was estimated to be very small (500–15,000) compared with the total HIV-1 RNA copy number. This study combines three independent observations, strong population bottlenecking, small Ne, and selection of different combinations of protease-resistance mutations, all of which indicate that HIV-1 evolution is best described by a stochastic evolutionary model.

Phosphorylation of the Neurospora clock protein FREQUENCY determines its degradation rate and strongly influences the period length of the circadian clock

Under free running conditions, FREQUENCY (FRQ) protein, a central component of the Neurospora circadian clock, is progressively phosphorylated, becoming highly phosphorylated before its degradation late in the circadian day. To understand the biological function of FRQ phosphorylation, kinase inhibitors were used to block FRQ phosphorylation in vivo and the effects on FRQ and the clock observed. 6-dimethylaminopurine (a general kinase inhibitor) is able to block FRQ phosphorylation in vivo, reducing the rate of phosphorylation and the degradation of FRQ and lengthening the period of the clock in a dose-dependent manner. To confirm the role of FRQ phosphorylation in this clock effect, phosphorylation sites in FRQ were identified by systematic mutagenesis of the FRQ ORF. The mutation of one phosphorylation site at Ser-513 leads to a dramatic reduction of the rate of FRQ degradation and a very long period (>30 hr) of the clock. Taken together, these data strongly suggest that FRQ phosphorylation triggers its degradation, and the degradation rate of FRQ is a major determining factor for the period length of the Neurospora circadian clock.