Nonatomic games on Loeb spaces

In the setting of noncooperative game theory, strategic negligibility of individual agents, or diffuseness of information, has been modeled as a nonatomic measure space, typically the unit interval endowed with Lebesgue measure. However, recent work has shown that with uncountable action sets, for example the unit interval, there do not exist pure-strategy Nash equilibria in such nonatomic games. In this brief announcement, we show that there is a perfectly satisfactory existence theory for nonatomic games provided this nonatomicity is formulated on the basis of a particular class of measure spaces, hyperfinite Loeb spaces. We also emphasize other desirable properties of games on hyperfinite Loeb spaces, and present a synthetic treatment, embracing both large games as well as those with incomplete information.

Evidence for protein X binding to a discontinuous epitope on the cellular prion protein during scrapie prion propagation

Studies on the transmission of human (Hu) prions to transgenic (Tg) mice suggested that another molecule provisionally designated protein X participates in the formation of nascent scrapie isoform of prion protein (PrPSc). We report the identification of the site at which protein X binds to the cellular isoform of PrP (PrPC) using scrapie-infected mouse (Mo) neuroblastoma cells transfected with chimeric Hu/MoPrP genes even though protein X has not yet been isolated. Substitution of a Hu residue at position 214 or 218 prevented PrPSc formation. The side chains of these residues protrude from the same surface of the C-terminal α-helix and form a discontinuous epitope with residues 167 and 171 in an adjacent loop. Substitution of a basic residue at positions 167, 171, or 218 also prevented PrPSc formation: at a mechanistic level, these mutant PrPs appear to act as “dominant negatives” by binding protein X and rendering it unavailable for prion propagation. Our findings seem to explain the protective effects of basic polymorphic residues in PrP of humans and sheep and suggest therapeutic and prophylactic approaches to prion diseases.

The heme oxygenase gene (pbsA) in the red alga Rhodella violacea is discontinuous and transcriptionally activated during iron limitation

Heme oxygenase (HO) catalyzes the opening of the heme ring with the release of iron in both plants and animals. In cyanobacteria, red algae, and cryptophyceae, HO is a key enzyme in the synthesis of the chromophoric part of the photosynthetic antennae. In an attempt to study the regulation of this key metabolic step, we cloned and sequenced the pbsA gene encoding this enzyme from the red alga Rhodella violacea. The gene is located on the chloroplast genome, split into three distant exons, and is presumably expressed by a trans-splicing mechanism. The deduced polypeptide sequence is homologous to other reported HOs from organisms containing phycobilisomes (Porphyra purpurea and Synechocystis sp. strain PCC 6803) and, to a lesser extent, to vertebrate enzymes. The expression is transcriptionally activated under iron deprivation, a stress condition frequently encountered by algae, suggesting a second role for HO as an iron-mobilizing agent in photosynthetic organisms.

Game theory and reciprocity in some extensive form experimental games

We examine decision making in two-person extensive form game trees using nine treatments that vary matching protocol, payoffs, and payoff information. Our objective is to establish replicable principles of cooperative versus noncooperative behavior that involve the use of signaling, reciprocity, and backward induction strategies, depending on the availability of dominated direct punishing strategies and the probability of repeated interaction with the same partner. Contrary to the predictions of game theory, we find substantial support for cooperation under complete information even in various single-play treatments.

Nas–Walras equilibria of a large economy

Individuals exchange contracts for the delivery of commodities in competitive markets and, simultaneously, act strategically; actions affect utilities across individuals directly or through the payoffs of contracts. This encompasses economies with asymmetric information. Nash–Walras equilibria exist for large economies, even if utility functions are not quasi-concave and choice sets are not convex, which is the case in standard settings; the separation of the purchase from the sale of contracts and the pooling of the deliveries on contracts guarantee that the markets for commodities clear.

OliI, a unique restriction endonuclease that recognizes the discontinuous sequence 5′-CACNN↓NNGTG-3′

A new type II restriction endonuclease designated OliI has been partially purified from the halophilic bacterium Oceanospirillum linum 4-5D. OliI recognizes the interrupted hexanucleotide palindrome 5′-CACNN↓NNGTG-3′ and cleaves it in the center generating blunt-ended DNA fragments.

Evaluation of the role of heterogeneous nuclear ribonucleoprotein A1 as a host factor in murine coronavirus discontinuous transcription and genome replication

Viruses with RNA genomes often capture and redirect host cell components to assist in mechanisms particular to RNA-dependent RNA synthesis. The nidoviruses are an order of positive-stranded RNA viruses, comprising coronaviruses and arteriviruses, that employ a unique strategy of discontinuous transcription, producing a series of subgenomic mRNAs linking a 5′ leader to distal portions of the genome. For the prototype coronavirus mouse hepatitis virus (MHV), heterogeneous nuclear ribonucleoprotein (hnRNP) A1 has been shown to be able to bind in vitro to the negative strand of the intergenic sequence, a cis-acting element found in the leader RNA and preceding each downstream ORF in the genome. hnRNP A1 thus has been proposed as a host factor in MHV transcription. To test this hypothesis genetically, we initially constructed MHV mutants with a very high-affinity hnRNP A1 binding site inserted in place of, or adjacent to, an intergenic sequence in the MHV genome. This inserted hnRNP A1 binding site was not able to functionally replace, or enhance transcription from, the intergenic sequence. This finding led us to test more directly the role of hnRNP A1 by analysis of MHV replication and RNA synthesis in a murine cell line that does not express this protein. The cellular absence of hnRNP A1 had no detectable effect on the production of infectious virus, the synthesis of genomic RNA, or the quantity or quality of subgenomic mRNAs. These results strongly suggest that hnRNP A1 is not a required host factor for MHV discontinuous transcription or genome replication.

Stochastic game theory: For playing games, not just for doing theory

Recent theoretical advances have dramatically increased the relevance of game theory for predicting human behavior in interactive situations. By relaxing the classical assumptions of perfect rationality and perfect foresight, we obtain much improved explanations of initial decisions, dynamic patterns of learning and adjustment, and equilibrium steady-state distributions.

Observation via one-dimensional 13Calpha NMR of local conformational substates in thermal unfolding equilibria of a synthetic analog of the GCN4 leucine zipper.

Synthesis of a 33-residue, capped leucine zipper analogous to that in GCN4 is reported. Histidine and arginine residues are mutated to lysine to reduce the unfolding temperature. CD and ultracentrifugation studies indicate that the molecule is a two-stranded coiled coil under benign conditions. Versions of the same peptide are made with 99% 13Calpha at selected sites. One-dimensional 13C NMR spectra are assigned by inspection and used to study thermal unfolding equilibria over the entire transition from 8 to 73 degrees C. Spectra at the temperature extremes establish the approximate chemical shifts for folded and unfolded forms at each labeled site. Resonances for each amino acid appear at both locations at intermediate T, indicating that folded and unfolded forms interconvert slowly (> >2 ms) on the NMR time scale. Moreover, near room temperature, the structured form's resonance is double at several, but not all, sites, indicating at least two slowly interconverting, structured, local conformational substates. Analysis of the dynamics is possible. For example, near room temperature at the Val-9, Ala-24, and Gly-31 positions, the equilibrium constant for interconversion of the two structured forms is near unity and the time scale is > or= 10-20 ms.

Discontinuous epitopes of hepatitis B surface antigen derived from a filamentous phage peptide library.

The structure of the small hepatitis B virus surface antigen (HBsAg) was investigated by epitope mapping of four anti-HBsAg monoclonal antibodies (mAbs). Amino acid sequences of epitopes were derived from affinity-enrichment experiments (biopanning) using a filamentous phage peptide library. The library consists of 10(9) different clones bearing a 30-residue peptide fused to gene III. Sequence homologies between peptides obtained from panning the library against the antibodies and the native HBsAg sequence allowed for precise description of the binding regions. Three of four mAbs were found to bind to distinct discontinuous epitopes between amino acid residues 101 and 207 of HBsAg. The fourth mAb was demonstrated to bind to residues 121-124. The sequence data are supported by ELISA assays demonstrating the binding of the HBsAg-specific peptides on filamentous phage to mAbs. The sequence data were used to map the surface of HBsAg and to derive a topological model for the alpha-carbon trace of the 101-207 region of HBsAg. The approach should be useful for other proteins for which the crystal structure is not available but a representative set of mAbs can be obtained.