Hybrid Equilibrium Research Articles

Stochastic mathematical programs with hybrid equilibrium constraints

This paper considers a stochastic mathematical program with hybrid equilibrium constraints (SMPHEC), which includes either “here-and-now” or “wait-and-see” type complementarity constraints. An example is given to describe the necessity to study SMPHEC. In order to solve the problem, the sampling average approximation techniques are employed to approximate the expectations and smoothing and penalty techniques are used to deal with the complementarity constraints. Limiting behaviors of the proposed approach are discussed. Preliminary numerical experiments show that the proposed approach is applicable.

Effect of Surface Binding on Heterogeneous DNA Melting Equilibria: A Monte Carlo Simulation Study

Deoxyribonucleic acid (DNA) microarrays are constructed with a surface-immobilized single-stranded probe sequence that hydrogen bonds with its complementary target strand from solution and is subsequently detected, making their hybridization equilibrium of central importance. Unexpectedly, the effect of surface immobilization is that if the sequences of probe and target are exchanged, the hybridization equilibrium shifts. Here, configurational-bias Monte Carlo simulations using a coarse-grained model for DNA were carried out for an undecamer double helix both in solution and bound to a surface to determine dissociation equilibria. Four possible surface binding orientations were independently investigated. Analysis shows that the effect of surface binding is to destabilize hydrogen-bonding interactions of bases proximal to the binding site and enhance those of distal bases due to the double helix lying flat on the surface. Results have implications for predicting surface-bound DNA hybridization equilibria.

The bargaining set in strategic market games

This paper presents a hybrid equilibrium notion that blends together the ‘cooperative’ and the ‘noncooperative’ theories of competition. In particular, the Mas-Colell bargaining set has been modified in order to accommodate the features of strategic market games. In other words, allocations, objections and counter objections of the standard bargaining set theory are described for an economy, where trades among groups of individuals are conducted via the Shapley–Shubik mechanism. In the main part of the paper, it is proved that in atomless economies the allocations resulting from this equilibrium notion are competitive.

Useful pharmacological parameters for G-protein-coupled receptor homodimers obtained from competition experiments. Agonist–antagonist binding modulation

Many G-protein-coupled receptors (GPCRs) are expressed on the plasma membrane as dimers. Since drug binding data are currently fitted using equations developed for monomeric receptors, the interpretation of the pharmacological data are equivocal in many cases. As reported here, GPCR dimer models account for changes in competition curve shape as a function of the radioligand concentration used, something that cannot be explained by monomeric receptor models. Macroscopic equilibrium dissociation constants for the agonist and homotropic cooperativity index reflecting the intramolecular communication within the dopamine D 1 or adenosine A 2A receptor homodimer as well as hybrid equilibrium dissociation constant, which reflects the antagonist/agonist modulation may be calculated by fitting binding data from antagonist/agonist competition experiments to equations developed from dimer receptor models. Comparing fitting the data by assuming a classical monomeric receptor model or a dimer model, it is shown that dimer receptor models provide more clues useful in drug discovery than monomer-based models.

Different Strategies of Covalent Attachment of Oligonucleotide Probe onto Glass Beads and the Hybridization Properties

The glass bead is a new biochip support material for immobilization biomolecules, due to its independence and convenient rearrangement. In order to optimize the immobilization efficiency of oligonucleotides onto glass beads and obtain the highest hybridization efficiency, three commonly used coupling strategies have been studied for covalently attaching oligonucleotides onto large glass beads. Glass beads with 250 microm diameter were amino-silaned with 2% 3-aminopropyltrimethoxysilane (APTMS) and then reacted separately with glutaraldehyde, succinic anhydride and 1,4-phenylene diisothiocyanate (PDITC) to derive CHO beads, COOH beads and isothiocyanate-modified beads (NCS-Beads) accordingly. Afterwards, amino-terminal oligonucleotides were covalently attached onto the surface of beads achieved by three strategies mentioned above. The immobilization efficiency were studied to compare the three strategies, which turned out 2.55 x 10(13) probes/cm2 for CHO-Beads, 3.21 x 10(13) probes/cm2 for COOH beads and 6.68 x 10(13) probes/cm2 for NCS beads. It meant that the immobilization efficiency based on NCS beads was most acceptable. And the method, developed by attaching amino-terminal oligonucleotides onto these cyanate active beads, could be regarded as an efficient one for immobilizing oligonucleotides onto a solid surface. Moreover, in this paper, the hybridization properties of NCS bead-based oligonucleotides have been studied by employing Cy5-tagged complementary oligonucleotides. It was found that the high probe density NCS beads led to low hybridization efficiency possibly due to the existence of steric crowding. In addition, the equilibrium binding constant KA was determined by employing Langmuir isotherm model, which was 7.0 x 10(6) M(-1) for NCS beads with the density of 6.7 x 10(13) probes/cm2. Furthermore, it only took 60 min to reach hybridization equilibrium. These large microspheres (>100 microm) can be employed in the mesofluidic systems for automated heterogeneous assays.

On-Chip Hybridization Kinetics for Optimization of Gene Expression Experiments

DNA microarray technology is a powerful tool for getting an overview of gene expression in biological samples. Although the successful use of microarray-based expression analysis was demonstrated in a number of applications, the main problem with this approach is the fact that expression levels deduced from hybridization experiments do not necessarily correlate with RNA concentrations. Moreover oligonucleotide probes corresponding to the same gene can give different hybridization signals. Apart from cross-hybridizations and differential splicing, this could be due to secondary structures of probes or targets. In addition, for low-copy genes, hybridization equilibrium may be reached after hybridization times much longer than the one commonly used (overnight, i.e., 15 h). Thus, hybridization signals could depend on kinetic properties of the probe, which may vary between different oligonucleotide probes immobilized on the same microarray. To validate this hypothesis, on-chip hybridization kinetics and duplex thermostability analysis were performed using oligonucleotide microarrays containing 50-mer probes corresponding to 10 mouse genes. We demonstrate that differences in hybridization kinetics between the probes exist and can influence the interpretation of expression data. In addition, we show that using on-chip hybridization kinetics, quantification of targets is feasible using calibration curves.

Hybrid equilibrium hexahedral elements and super‐elements

AbstractEquilibrated solutions, locally satisfying all the equilibrium conditions, may be obtained by using a special case of the hybrid finite element formulation. Unlike simplicial super‐elements in 2D and 3D, which are free from spurious kinematic modes, and the quadrilateral super‐element with diagonal subdivision, which has exactly one internal spurious kinematic mode, no hexahedral super‐element free of external spurious kinematic modes is yet known as far as the author is aware. Copyright © 2006 John Wiley & Sons, Ltd.

Sub-modelling and boundary conditions with [formula omitted]-type hybrid-equilibrium plate-membrane elements

The main topics of this paper, sub-modelling and associated boundary conditions, are presented in two parts. The first part details a general method for evaluating consistent displacement or traction modes for hybrid equilibrium plate models to represent arbitrarily specified boundary conditions. The inheritance of boundary conditions in a process of uniform h-type refinement is considered as a particular case. The second part investigates the methodology and performance of a sub-modelling technique involving equilibrium elements, which has the aim of recovering a local quantity of interest with greater accuracy than that directly obtained from the original global or parent equilibrium model. A crucial step in this technique is the transfer of appropriate boundary tractions from the parent model to the sub-model (child). The sub-modelling technique is presented initially based on the extraction of a single element for h- and/or p-type refinement into sub-models. A more general form of sub-modelling is then presented in which the boundary of the sub-model does not coincide with that of an element, or patch of elements, in the parent model. This requires the evaluation of modes of traction around an arbitrary region, and a scheme to achieve this is presented and demonstrated using, as an example, a geometric perturbation of a single element extraction. The performances of sub-models are compared using both complete sets of traction modes and reduced, or basic, sets.

The forgotten variables of DNA array hybridization

The reproducibility and reliability of DNA array measurements have been repeatedly questioned during the years. A reassessment of fundamental variables of nucleic acid hybridization might help to solve some of these problems. The hybridization equilibrium, t(1/2), is 41 days for a target human genome. Similar hybridization t(1/2) are expected for whole-transcriptome chips hybridized with tissue cDNA. This implies that most studies on mammalian cells have not been performed under equilibrium conditions. Non-equilibrium binding introduces a stochastic factor into hybridization dynamics; in other words, hybridization will prevail at different spots in different experiments, everything else being equal. A careful re-evaluation of results obtained under non-equilibrium conditions might prove fruitful and help to explain instances where findings conflict.

Hybrid singular elements in fracture mechanics

A method using the concept of singular hybrid finite element for the determination of the stress intensity factor and the T stress of cracked panels submitted to plane stress and plane strain states is presented. A complete formulation of a hybrid equilibrium singular superelement is presented. This superelement includes linear, bilinear, and quadratic shape functions, allowing its use with linear, bilinear, and quadratic displacementbased conventional finite elements. The method is applied to various typical configurations of cracked rectangular plates, including stiffened panels. The results obtained are discussed and compared with previous available data.

Hybrid singular elements in fracture mechanics

A method using the concept of singular hybrid finite element for the determination of the stress intensity factor and the T stress of cracked panels submitted to plane stress and plane strain states is presented. A complete formulation of a hybrid equilibrium singular superelement is presented. This superelement includes linear, bilinear, and quadratic shape functions, allowing its use with linear, bilinear, and quadratic displacementbased conventional finite elements. The method is applied to various typical configurations of cracked rectangular plates, including stiffened panels. The results obtained are discussed and compared with previous available data.

A triangular hybrid equilibrium plate element of general degree

Hybrid stress-based finite elements with side displacement fields have been used to generate equilibrium models having the property of equilibrium in a strong form. This paper establishes the static and kinematic characteristics of a flat triangular hybrid equilibrium element with both membrane and plate bending actions of general polynomial degree p. The principal characteristics concern the existence of hyperstatic stress fields and spurious kinematic modes. The former are shown to exist for p>3, and their significance to finite element analysis is reviewed. Knowledge of the latter is crucial to the determination of the stability of a mesh of triangular elements, and to the choice of procedure adopted for the solution of the system of equations. Both types of characteristic are dependent on p, and are established as regards their numbers and general algebraic forms. Graphical illustrations of these forms are included in the paper. Copyright © 2005 John Wiley & Sons, Ltd.

Hybridization isotherms of DNA microarrays and the quantification of mutation studies.

Diagnostic DNA arrays for detection of point mutations as markers for cancer usually function in the presence of a large excess of wild-type DNA. This excess can give rise to false positives as a result of competitive hybridization of the wild-type target at the mutation spot. Analysis of the DNA array data is typically qualitative, aimed at establishing the presence or absence of a particular point mutation. Our theoretical approach yields methods for quantifying the analysis to obtain the ratio of concentrations of mutated and wild-type DNA. The theory is formulated in terms of the hybridization isotherms relating the hybridization fraction at the spot to the composition of the sample solutions at thermodynamic equilibrium. It focuses on samples containing an excess of single-stranded DNA and on DNA arrays with a low surface density of probes. The hybridization equilibrium constants can be obtained by the nearest-neighbor method. Two approaches allow acquisition of quantitative results from the DNA array data. In one, the signal of the mutation spot is compared with that of the wild-type spot. The implementation requires knowledge of the saturation intensity of the two spots. The second approach requires comparison of the intensity of the mutation spot at two different temperatures. In this case, knowledge of the saturation signal is not always necessary. DNA arrays can be used to obtain quantitative results on the concentration ratio of mutated DNA to wild-type DNA in studies of somatic point mutations.

Hybrid Equilibrium Finite Elements for Wave Diffraction Problems

Hybrid equilibrium finite elements based on the direct approximation of the domain stress and boundary displacement fields are presented. The structure is divided into a far field, which is considered as an infinite super element, and a near field, which is in turn discretized into finite elements. The displacements in the domains of typical finite elements are obtained from the assumed domain stress field by using the dynamic equilibrium equations. The Helmholtz equation is satisfied in the domain of the infinite super element, and the domain stress fields are associated with elastic and compatible displacements. The resulting governing system is symmetric, sparse, and, if well done, positive. Numerical applications are presented to illustrate the performance of the formulation.

Use of hybridization kinetics for differentiating specific from non-specific binding to oligonucleotide microarrays.

Hybridization kinetics were found to be significantly different for specific and non-specific binding of labeled cRNA to surface-bound oligonucleotides on microarrays. We show direct evidence that in a complex sample specific binding takes longer to reach hybridization equilibrium than the non- specific binding. We find that this property can be used to estimate and to correct for the hybridization contributed by non-specific binding. Useful applications are illustrated including the selection of superior oligonucleotides, and the reduction of false positives in exon identification.

The Chemical Transformations of Chromium in Natural Waters – A Model Study

A hybrid chemical kinetic and equilibrium model has been developed to quantitatively assess the dynamic oxidation-reduction (redox) transformations of chromium in natural waters. Simulations are conducted to examine the effects of 11 chemical and environmental parameters on the redox cycle between trivalent [Cr(III)] and hexavalent [Cr(VI)] chromium. Based on the model results, it is found that natural water serves as a reductive environment for chromium under typical conditions, since the common oxidants of Cr(III) (e.g., hydroxyl radical and manganese) do not convert chromium to Cr(VI) at significant rates because of their extremely low levels or slow oxidation kinetics. At low pH ( 6.0), ferrous iron [Fe(II)] becomes the predominant reductant. However, at pH greater than 8.0 and in the presence of dissolved oxygen (DO), Cr(VI) reduction by Fe(II) is greatly suppressed due to the rapid oxidation of Fe(II) by DO. Other reactive species such as hydroperoxyl radical (HO2•/O2•-) and hydrogen peroxide (H2O2) present in sunlit waters can indirectly affect the chromium redox cycle through their reactions with iron and S(IV). pH appears to be an important parameter, as it affects both chemical speciation and reaction kinetics. Chelating agents in natural waters should not significantly affect chromium redox transformations due to their usually low concentrations and generally weak interactions with Fe(II).

Existence of Hybrid Equilibrium in a Differential Game

The paper formalizes and investigates a concept of new solving the differential positional linear-quadratic non-cooperative four-person game under uncertainty. The given solution unites the well-known concepts of optimality of non-cooperative games theory (Nash equilibrium and equilibrium of threats and counterthreats). The account of uncertain factors is made by means of "analog of a vector saddle point". The existence conditions are established and the explicit form of such solution is found.

Hybridization of single-stranded DNA targets to immobilized complementary DNA probes: comparison of hairpin versus linear capture probes.

A microtiter-based assay system is described in which DNA hairpin probes with dangling ends and single-stranded, linear DNA probes were immobilized and compared based on their ability to capture single-strand target DNA. Hairpin probes consisted of a 16 bp duplex stem, linked by a T(2)-biotin.dT-T(2) loop. The third base was a biotinylated uracil (U(B)) necessary for coupling to avidin coated microtiter wells. The capture region of the hairpin was a 3' dangling end composed of either 16 or 32 bases. Fundamental parameters of the system, such as probe density and avidin adsorption capacity of the plates were characterized. The target DNA consisted of 65 bases whose 3' end was complementary to the dangling end of the hairpin or to the linear probe sequence. The assay system was employed to measure the time dependence and thermodynamic stability of target hybridization with hairpin and linear probes. Target molecules were labeled with either a 5'-FITC, or radiolabeled with [gamma-(33)P]ATP and captured by either linear or hairpin probes affixed to the solid support. Over the range of target concentrations from 10 to 640 pmol hybridization rates increased with increasing target concentration, but varied for the different probes examined. Hairpin probes displayed higher rates of hybridization and larger equilibrium amounts of captured targets than linear probes. At 25 and 45 degrees C, rates of hybridization were better than twice as great for the hairpin compared with the linear capture probes. Hairpin-target complexes were also more thermodynamically stable. Binding free energies were evaluated from the observed equilibrium constants for complex formation. Results showed the order of stability of the probes to be: hairpins with 32 base dangling ends > hairpin probes with l6 base dangling ends > 16 base linear probes > 32 base linear probes. The physical characteristics of hairpins could offer substantial advantages as nucleic acid capture moieties in solid support based hybridization systems.

Between Search and Walras

This paper presents a framework that nests search and Walrasian-type models to study the evolution of stationary equilibria in the region between the two approaches. In our model unemployed workers can simultaneously approach n firms every period. We regard n as a proxy for information completeness: the more firms a worker samples, the better informed he is about the labor market conditions. Low n's yield wage dispersion below the marginal product of labor, as in typical search models. As n increases the equilibrium wage structure transforms to the Walrasian-type. Subjected to random shocks, the equilibrium results in of wage rigidity. We study the evolution of stationary equilibria in a framework that nests search and Walrasian-type models. In our model unemployed workers simultaneously approach n firms every period. Low n yields wage dispersion below the MPL, which is typical for search models. Interestingly, the Walrasian-type equilibrium obtains for relatively small values of n: all firms offer wage equal to MPL, yet unemployment persists. A hybrid equilibrium type prevails for intermediate values of n. Subjected to random shocks, the equilibrium yields wage rigidity. The model yields empirical predictions on unemployment.

A hybrid equilibrium in segmented markets: the three-firm case

In this paper, we characterize two hybrid equilibria for the three-firm case in segmented markets in which consumers not only value the product itself but also the environment within which the consumption takes place. In equilibrium, the firm with the larger population of loyal consumers chooses the monopoly price while the remaining two firms play a mixed strategy. In the duopoly case, the unique equilibrium is in mixed strategies and no firm focuses only on its loyal consumers.