Ligand concentrations

The plot of AEi/2 as a function of the log of the ligand concentration is shown in Figure 11.43. Finear regression gives the equation for the straight line as... 

Scheme VIII has the form of Scheme II, so the relaxation time is given by Eq. (4-15)—appjirently. However, there is a difference between these two schemes in that L in Scheme VIII is also a participant in an acid-base equilibrium. The proton transfer is much more rapid than is the complex formation, so the acid-base system is considered to be at equilibrium throughout the complex formation. The experiment can be carried out by setting the total ligand concentration comparable to the total metal ion concentration, so that the solution is not buffered. As the base form L of the ligand undergoes coordination, the acid-base equilibrium shifts, thus changing the pH. This pH shift is detected by incorporating an acid-base indicator in the solution.

In view of the magnitude of crystal-field effects it is not surprising that the spectra of actinide ions are sensitive to the latter s environment and, in contrast to the lanthanides, may change drastically from one compound to another. Unfortunately, because of the complexity of the spectra and the low symmetry of many of the complexes, spectra are not easily used as a means of deducing stereochemistry except when used as fingerprints for comparison with spectra of previously characterized compounds. However, the dependence on ligand concentration of the positions and intensities, especially of the charge-transfer bands, can profitably be used to estimate stability constants. 

The rates of reaction of 1 are dependent on both metal ion and ligand concentrations... 

However, the results shown in Table 6 indicate that the k values calculated by using the ligand concentration ([ligand]T) instead of the complex concentration ([C]0) are much smaller than the kc value in the case of 29c-Zn2+. The [C]0 = 1.6 x 10-6 M for the 29-Zn2 + complex can be calculated based on K = 1.7 x 10-5 M 2 (Table 5), but it is difficult to calculate corrected ka values based on the equations in footnote (c) in Table 6, because the B values are close to [ligand]T = 1x10-4 M and much larger than [C]0, due to the acylation of almost all ligands. 

As noted previously, in all cases these various functions describe an inverse sigmoidal curve between the displacing ligand and the signal. Therefore, the mechanism of interaction cannot be determined from a single displacement curve. However, observation of a pattern of such curves obtained at different tracer ligand concentrations (range of [A ] values) may indicate whether the displacements are due to a competitive, noncompetitive, or allosteric mechanism. 

By using Hill s coefficient, it is possible to draw a conclusion about the character of the process and to determine ligand concentration in one cooperative unit. 

Because of the relationship between compounds in the adjacent oxidation states +2 and +3, they are grouped together here the section is subdivided by ligand, concentrating on some classes of complex important in their diversity and in current research interest. 

A Scatchard plot is a plot of B/x against B (where B is the amount of bound ligand and x is the ligand concentration), which is used to estimate the maximal binding, Bmax as well as the binding affinity (K). 

Organic complexes with ligands and free ligand concentration... 

Limitations. Of the three methods, polarization has the lowest signal-to-noise ratio, and is most limited in its ligand concentration range. It works best when a significant fraction of the ligand is bound to the receptor. For FLPEP and cells the practical range is 0.5 to 3 njy (X L R). This method works best when free L is substantially depleted by the binding process. 

Waldmann-Meyer, HK, Protein Ion Equilibria, Total Evaluation of Binding Parameters and Net Charge from the Electrophoretic Mobility as a Function of Ligand Concentration. In Recent Developments in Chromatography and Electrophoresis Frigerio, A McCamish, M, eds. Elsevier Scientific Amsterdam, 1980 Vol. 10, p 125. 

Thus, the decomposition of Ni(COD)2 by dihydrogen in the presence of HDA yields nanoparticles, the aspect ratio of which depends upon the ligand concentration. Thus for one or less equivalent HDA, the reaction produces isotropic Ni particles whereas using ten equivalent HDA, nanorods, monodis-perse in diameter, are obtained [74]. The formation of nanowires can also be promoted by a rapid decomposition process. This is illustrated by the decom-... 

In the same context, Kang et al. have examined several bidentate thiol derivatives as ligands in the same reaction to that described above. A nickel complex derived from the p-amino thiol depicted in Scheme 2.31 catalysed the reaction in a useful asymmetric level of 74% ee, whereas the use of the thiol phosphine ligand depicted in Scheme 2.31 gave a lower enantioselectivity of 27% ee. In this study, the authors found that the enantioselectivity was strongly dependent on the ligand concentration and on the nickel-to-ligand ratio. 

The effect of Rh concentration on the selectivity was negligible. The ligand concentration, on the other hand, is expected to have a considerable effect on the selectivity thus experiments were carried out with different ligand concentrations. A higher ligand concentration retards the overall rate, but increases the selectivity to pentanal. At the lowest L/Rh ratio (10), the ratio pentanal-to-2-methylbutanal was about 3.4, while it became about 5 for the highest L/Rh ratio (10). 

The Relationship between Ligand Concentration and Receptor Occupancy... 

This is the important Hill-Langmuir equation. A. V. Hill was the first (in 1909) to apply the law of mass action to the relationship between ligand concentration and receptor occupancy at equilibrium and to the rate at which this equilibrium is approached. The physical chemist I. Langmuir showed a few years later that a similar equation (the Langmuir adsorption isotherm) applies to the adsorption of gases at a surface (e g., of a metal or of charcoal). 

FIGURE 1.1 The relationship between binding-site occupancy and ligand concentration ([A] linear scale, left log scale, right), as predicted by the Hill-Langmuir equation. KA has been taken to be 1 pM for both curves. 

One way to reduce the risk of confusion is to express ligand concentrations in terms of KA. This normalized concentration is defined as [A IKA and will be denoted here by the symbol eA. We can therefore write the Hill-Langmuir equation in three different though equivalent ways ... 

The occupancy at each subunit is p= [L]/Kd + [L], where [L] is the ligand concentration. If activation of the subunits is independent, as assumed, the number of activated subunits at the receptor complex will follow a binomial distribution that is, the likelihood for activation of n subunits is K4 /F "(1 - p)n. The current will be proportional to ... 

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