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.

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.

Instability of signaling resolution models of parent–offspring conflict

Recent signaling resolution models of parent–offspring conflict have provided an important framework for theoretical and empirical studies of communication and parental care. According to these models, signaling of need is stabilized by its cost. However, our computer simulations of the evolutionary dynamics of chick begging and parental investment show that in Godfray’s model the signaling equilibrium is evolutionarily unstable: populations that start at the signaling equilibrium quickly depart from it. Furthermore, the signaling and nonsignaling equilibria are linked by a continuum of equilibria where chicks above a certain condition do not signal and we show that, contrary to intuition, fitness increases monotonically as the proportion of young that signal decreases. This result forces us to reconsider much of the current literature on signaling of need and highlights the need to investigate the evolutionary stability of signaling equilibria based on the handicap principle.

An optimal Mg2+ concentration for kinetic folding of the Tetrahymena ribozyme

Divalent metal ions, such as Mg2+, are generally required for tertiary structure formation in RNA. Although the role of Mg2+ binding in RNA-folding equilibria has been studied extensively, little is known about the role of Mg2+ in RNA-folding kinetics. In this paper, we explore the effect of Mg2+ on the rate-limiting step in the kinetic folding pathway of the Tetrahymena ribozyme. Analysis of these data reveals the presence of a Mg2+-stabilized kinetic trap that slows folding at higher Mg2+ concentrations. Thus, the Tetrahymena ribozyme folds with an optimal rate at 2 mM Mg2+, just above the concentration required for stable structure formation. These results suggest that thermodynamic and kinetic folding of RNA are cooptimized at a Mg2+ concentration that is sufficient to stabilize the folded form but low enough to avoid kinetic traps and misfolding.

Analysis of linear trade models and relation to scale economies

We discuss linear Ricardo models with a range of parameters. We show that the exact boundary of the region of equilibria of these models is obtained by solving a simple integer programming problem. We show that there is also an exact correspondence between many of the equilibria resulting from families of linear models and the multiple equilibria of economies of scale models.

An α-Tubulin Mutant Destabilizes the Heterodimer: Phenotypic Consequences and Interactions with Tubulin-binding Proteins

Many effectors of microtubule assembly in vitro enhance the polymerization of subunits. However, several Saccharomyces cerevisiae genes that affect cellular microtubule-dependent processes appear to act at other steps in assembly and to affect polymerization only indirectly. Here we use a mutant α-tubulin to probe cellular regulation of microtubule assembly. tub1-724 mutant cells arrest at low temperature with no assembled microtubules. The results of several assays reported here demonstrate that the heterodimer formed between Tub1-724p and β-tubulin is less stable than wild-type heterodimer. The unstable heterodimer explains several conditional phenotypes conferred by the mutation. These include the lethality of tub1-724 haploid cells when the β-tubulin–binding protein Rbl2p is either overexpressed or absent. It also explains why the TUB1/tub1-724 heterozygotes are cold sensitive for growth and why overexpression of Rbl2p rescues that conditional lethality. Both haploid and heterozygous tub1-724 cells are inviable when another microtubule effector, PAC2, is overexpressed. These effects are explained by the ability of Pac2p to bind α-tubulin, a complex we demonstrate directly. The results suggest that tubulin-binding proteins can participate in equilibria between the heterodimer and its components.

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.

A quantitative method for evaluating the stabilities of nucleic acids

We report a general method for screening, in solution, the impact of deviations from canonical Watson-Crick composition on the thermodynamic stability of nucleic acid duplexes. We demonstrate how fluorescence resonance energy transfer (FRET) can be used to detect directly free energy differences between an initially formed “reference” duplex (usually a Watson-Crick duplex) and a related “test” duplex containing a lesion/alteration of interest (e.g., a mismatch, a modified, a deleted, or a bulged base, etc.). In one application, one titrates into a solution containing a fluorescently labeled, FRET-active, reference duplex, an unlabeled, single-stranded nucleic acid (test strand), which may or may not compete successfully to form a new duplex. When a new duplex forms by strand displacement, it will not exhibit FRET. The resultant titration curve (normalized fluorescence intensity vs. logarithm of test strand concentration) yields a value for the difference in stability (free energy) between the newly formed, test strand-containing duplex and the initial reference duplex. The use of competitive equilibria in this assay allows the measurement of equilibrium association constants that far exceed the magnitudes accessible by conventional titrimetric techniques. Additionally, because of the sensitivity of fluorescence, the method requires several orders of magnitude less material than most other solution methods. We discuss the advantages of this method for detecting and characterizing any modification that alters duplex stability, including, but not limited to, mutagenic lesions. We underscore the wide range of accessible free energy values that can be defined by this method, the applicability of the method in probing for a myriad of nucleic acid variations, such as single nucleotide polymorphisms, and the potential of the method for high throughput screening.

Conversion of a maltose receptor into a zinc biosensor by computational design

We have demonstrated that it is possible to radically change the specificity of maltose binding protein by converting it into a zinc sensor using a rational design approach. In this new molecular sensor, zinc binding is transduced into a readily detected fluorescence signal by use of an engineered conformational coupling mechanism linking ligand binding to reporter group response. An iterative progressive design strategy led to the construction of variants with increased zinc affinity by combining binding sites, optimizing the primary coordination sphere, and exploiting conformational equilibria. Intermediates in the design series show that the adaptive process involves both introduction and optimization of new functions and removal of adverse vestigial interactions. The latter demonstrates the importance of the rational design approach in uncovering cryptic phenomena in protein function, which cannot be revealed by the study of naturally evolved systems.

Potential effects of gas hydrate on human welfare

For almost 30 years. serious interest has been directed toward natural gas hydrate, a crystalline solid composed of water and methane, as a potential (i) energy resource, (ii) factor in global climate change, and (iii) submarine geohazard. Although each of these issues can affect human welfare, only (iii) is considered to be of immediate importance. Assessments of gas hydrate as an energy resource have often been overly optimistic, based in part on its very high methane content and on its worldwide occurrence in continental margins. Although these attributes are attractive, geologic settings, reservoir properties, and phase-equilibria considerations diminish the energy resource potential of natural gas hydrate. The possible role of gas hydrate in global climate change has been often overstated. Although methane is a “greenhouse” gas in the atmosphere, much methane from dissociated gas hydrate may never reach the atmosphere, but rather may be converted to carbon dioxide and sequestered by the hydrosphere/biosphere before reaching the atmosphere. Thus, methane from gas hydrate may have little opportunity to affect global climate change. However, submarine geohazards (such as sediment instabilities and slope failures on local and regional scales, leading to debris flows, slumps, slides, and possible tsunamis) caused by gas-hydrate dissociation are of immediate and increasing importance as humankind moves to exploit seabed resources in ever-deepening waters of coastal oceans. The vulnerability of gas hydrate to temperature and sea level changes enhances the instability of deep-water oceanic sediments, and thus human activities and installations in this setting can be affected.

Regulation of Actin Tension in Plant Cells by Kinases and Phosphatases1

Changes in the organization and mechanical properties of the actin network within plant and animal cells are primary responses to cell signaling. These changes are suggested to be mediated through the regulation of G/F-actin equilibria, alterations in the amount and/or type of actin-binding proteins, the binding of myosin to F-actin, and the formation of myosin filaments associated with F-actin. In the present communication, the cell optical displacement assay was used to investigate the role of phosphatases and kinases in modifying the tension and organization within the actin network of soybean cells. The results from these biophysical measurements suggest that: (a) calcium-regulated kinases and phosphatases are involved in the regulation of tension, (b) calcium transients induce changes in the tension and organization of the actin network through the stimulation of proteins containing calmodulin-like domains or calcium/calmodulin-dependent regulatory proteins, (c) myosin and/or actin cross-linking proteins may be the principal regulator(s) of tension within the actin network, and (d) these actin cross-linking proteins may be the principal targets of calcium-regulated kinases and phosphatases.

An information theory model of hydrophobic interactions.

A molecular model of poorly understood hydrophobic effects is heuristically developed using the methods of information theory. Because primitive hydrophobic effects can be tied to the probability of observing a molecular-sized cavity in the solvent, the probability distribution of the number of solvent centers in a cavity volume is modeled on the basis of the two moments available from the density and radial distribution of oxygen atoms in liquid water. The modeled distribution then yields the probability that no solvent centers are found in the cavity volume. This model is shown to account quantitatively for the central hydrophobic phenomena of cavity formation and association of inert gas solutes. The connection of information theory to statistical thermodynamics provides a basis for clarification of hydrophobic effects. The simplicity and flexibility of the approach suggest that it should permit applications to conformational equilibria of nonpolar solutes and hydrophobic residues in biopolymers.

Gas-phase nitronium ion affinities.

Evaluation of nitronium ion-transfer equilibria, L1NO2+ + L2 = L2NO2+ + L1 (where L1 and L2 are ligands 1 and 2, respectively) by Fourier-transform ion cyclotron resonance mass spectrometry and application of the kinetic method, based on the metastable fragmentation of L1(NO2+)L2 nitronium ion-bound dimers led to a scale of relative gas-phase nitronium ion affinities. This scale, calibrated to a recent literature value for the NO2+ affinity of water, led for 18 ligands, including methanol, ammonia, representative ketones, nitriles, and nitroalkanes, to absolute NO2+ affinities, that fit a reasonably linear general correlation when plotted vs. the corresponding proton affinities (PAs). The slope of the plot depends to a certain extent on the specific nature of the ligands and, hence, the correlations between the NO2+ affinities, and the PAs of a given class of compounds display a better linearity than the general correlation and may afford a useful tool for predicting the NO2+ affinity of a molecule based on its PA. The NO2+ binding energies are considerably lower than the corresponding PAs and well below the binding energies of related polyatomic cations, such as NO+, a trend consistent with the available theoretical results on the structure and the stability of simple NO2+ complexes. The present study reports an example of extension of the kinetic method to dimers, such as L1(NO2+)L2, bound by polyatomic ions, which may considerably widen its scope. Finally, measurement of the NO2+ affinity of ammonia allowed evaluation of the otherwise inaccessible PA of the amino group of nitramide and, hence, direct experimental verification of previous theoretical estimates.

Significant discrepancies between van't Hoff and calorimetric enthalpies.

In this paper we show that the usual assumption in studies of the temperature variation of equilibrium constants for equilibria of the form A+B <-->AB that a plot of ln K vs. 1/T (K = equilibrium constant, T = temperature in degrees kelvin) is a straight line with slope equal to -delta HvH/R (delta HvH = van't Hoff or apparent enthalpy, R = gas constant) is not valid in many cases. In all the cases considered here, delta HvH is temperature dependent and is significantly different from the true or calorimetrically measured enthalpy, and the respective values for delta Cp are also significantly different.