Competitive equilibrium

If the antagonism is insurmountable, then there are a number of molecular mechanisms possible. The next question to ask is if the maximal response to the agonist can be completely depressed to basal levels. If this is not the case, then there could be partial allosteric alteration of the signaling properties of the receptor. Alternatively, this could be due to a hemi-equilibrium condition that produces a partial shortfall to true competitive equilibrium, leading to incomplete depression of the maximal response but also antagonist concentration-related dextral displacement of the concentration response curve to the agonist (see Figure 10.19a). The model (see Section 10.6.5) used to fit these data is discussed in Section 6.5 and shown in... 

Nelson et al(28) have developed an equation assuming competitive equilibrium between Pu(IV) and soluble complexing ligands and between Pu(IV) and a solid adsorber ... 

Figure 5 An example calibration curve. Absorbance is plotted against log (concentration of analyte). The competitive equilibrium binding process results in a sigmoidal curve that is fitted using a four-parameter fit. The IC50 is defined as the concentration of analyte that results in a 50% inhibition of the absorbance...

SCAM Simplified competitive equilibrium adsorption model... 

A number of attempts have been made to modify the IAS model (Eqs. 22-29) to improve its accuracy and reduce computational efforts. Using the IAS model, DiGiano et al. [80] derived a Simplified Competitive Equilibrium Adsorption Model (SCAM). This model, which is based on the Freundlich isotherm, assumes the single-solute isotherms of all the components are equal and it utilizes average isotherm constants when this assumption is not valid. The IAS model equations have been reduced to a single expression ... 

Antagonism Irreversible (non-equilibrium) competitive Equilibrium competitive Equilibrium competitive... 

The injection of a sample in a chromatographic column may result in more peaks than there are components in the mixture if the mobile phase contains one or several additives. These additional peaks result from the perturbation of the additive equilibrium between the two phases caused by the injection of a sample. It may be assumed that there is a competitive equilibrium of the sample and the modifier. Solutes enter the column, moving with the velocity of the mobile phase and not with the equilibrium velocities dictated by the equilibrium between mobile and stationary phases. System peaks are visualized with an appropriate detector, particularly a refractive index detector. This may cause trouble for the analyst, since the system peak may exhibit k values more than 1 (37). 

In order to determine the IC50, competition can be obtained by varying the nonlabeled ligand concentration to obtain a curve of competition equilibrium (Fig. 2B). 

For reverse-phase chromatography, the mobile phase is made by choosing one solvent in which the sample is very soluble and another solvent in which the sample is less soluble. One can then prepare a mobile phase by adjusting the amount of the strong and weak solvents to a ratio where the attraction of the solutes to the packing is in a competitive equilibrium with the attraction (solubility) of the solutes to the mobile phase. The equilibrium of the solutes in the mobile phase relative to the bonded phase determines the retention time and effects the separation. 

This value (K g) cannot be measimed directly, so we performed a competition experiment to obtain a competition equilibrium constant (K, as shown in Eq. (4). 

This competition equilibrium constant is inversely proportional... 

The explanation for the dependence of the kinetics on order of addition was that of competitive equilibrium in the formation of active centres from metal alkyl, TiCls and monomer. The build-up of polymerization is much faster than in those systems which rise to a steady rate, and the maximum rate is at least double the steady rate. The formation of the active but short-lived species in the example shown in Fig. 10a has not been associated with a large change in surface area since the steady rate is unchanged. However, more intensive grinding gives rise to a greater increase in the initial acceleration and to higher steady rates. 

The monopoly power deviation arises because the nature of economic man causes him or her to attempt to break out of a pure competitive equilibrium, or the equilibrating tatonnement process, and maximize his or her own economic situation relative to the rest of the world. The economic man will... 

According to traditional microeconomics, then, the natural economic process is one that proceeds from the natural state of pure competitive equilibrium, or from where the necessary conditions exist for the pure competitive tatonnement process to take place, to conditions of monopoly. 

Several heterogeneous electrochemical enzyme immunoassays have been demonstrated. These are based on the enzyme-linked immunosorbent assay (ELISA) technique in which antibody is immobilized on the walls of a small volume plastic vessel. The ELISA technique can follow either a competitive equilibrium or a sandwich format. Both formats have been used with electrochemical detection. The general protocol for these two formats is shown in Fig. 9. 

In the examples presented above, resource heterogeneity was not incorporated. Resources in nature are variable in regard to supply over both time and space, and this does much to explain the coexistence of competing species. Tilman represents this by projecting a 95% bivariate confidence interval, a circle, upon the resource space (Figure 11.9). In this case, the dynamics of the competitive interactions between the two species change depending upon the resource availability. In part of the confidence interval, a competitive equilibrium is possible. In other parts of the confidence interval, competitive displacement of species A is possible. 

Shifting of the confidence interval of resources. The addition of a toxicant that impacts organisms and that acts as a resource for other organisms can have dramatic effects without any direct impact upon the consumers. A shift in the resource region due to a shift in competitive interactions at other energetic levels can alter the competitive relationships of the consumers. The structure of the community is then altered even more dramatically. In this case, a situation with a general competitive equilibrium is shifted so that species A can be driven to extinction with the movement of the resource area. 

Many immunoassays require a separation step prior to quantitation, in order to separate the bound and free fractions of the labeled species. Consider an immunoassay in which a labeled ligand, Ag, competes with unlabeled analyte, Ag, for a limited quantity of antibody binding sites. This competitive equilibrium is represented by Eqs. 6.5 and 6.6,... 

This glucose sensor relies on macromolecules trapped at one terminus (the distal end) of an optical fiber for signal generation. The macromolecules, FITC-labeled dextran and rhodamine-labeled concanavalin A (Rh-ConA), are trapped by a hollow dialysis fiber that fits snugly over the end of the optical fiber, as shown in Figure 7.8(a). A competitive equilibrium is set up between glucose and FITC-dextran, both of which bind to Rh-ConA ... 

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