Free ligand concentrations

Organic complexes with ligands and free ligand concentration... 

Incubation is often performed in small plastic tubes, which can be centrifuged directly to form, within seconds, a cell or membrane pellet. The supernatant can then be either tipped off or removed by suction. The radioactivity of the supernatant can be measured to determine the free ligand concentration. Any supernatant remaining on the surface of the pellet or tube can be reduced by... 

A decrease in coordination number of Ln3+ complexes results, in general, in a decrease in lability. Solvent exchange rates measured on [Ln(TMU)e]3+ are much slower than corresponding values measured on [Ln(DMF)8]3+ (56,257-259) (Table XIX (56,257-259)). The exchange rates, measured in an inert diluent, were found to be independent of free ligand concentration, consistent with a d-activation mode. 

Exchange of complex cations. Complexation of transition metal cations with uncharged ligands such as with amines and with amino acids results in a selectivity enhancement compared to the selectivity of the aqueous metal cation (27, 65-72). Fig. 3 shows an example for the Cu(ethylenediamine) adsorption in montmorillonites of different charge density. Standard thermodynamic data for other cases are given in table IV. In all cases the free ligand concentration in equilibrium solution was... 

Clearly throughout the kinetic experiments the concentration of each of the components RL, R and L are changing but, if the initial ligand concentration [Lq] is very much greater than the total receptor concentration [Rq], the free ligand concentration will suffer little depletion as the association continues to equilibrium. This is referred to as pseudo first-order kinetics which are easier to analyse ... 

Such calculations can be done for a series of free ligand concentrations to generate a family of formation curves of concentration or mole fraction of metal complex species as a function of the concentration of the free ligand. Such curves are shown in Figs. 3.1 and 3.2. These calculations are particularly useful for trace level values of metal as they require only knowledge of the free ligand concentrations and the P . Values of stability constants can be found in Refs. [1,2]. 

The free ligand concentration, [A ], is an important parameter in the formation of metal complexes (see Chapter 3 and section 4.8). In a solvent extraction system with the volumes V and of the aqueous and organic phases, respectively, [A ] is calculated from the material balance ... 

In Eq. (4.91) x is usually the free ligand concentration [A ], or concentration [B] of the adduct former, while y is a simple function of the distribution... 

Industrial practice naturally requires the maximum use of the relatively expensive extractant, so that saturation of the extractant phase with reduction of the free ligand concentration to a minimum is the general rule. A model is thus needed to quantify the effect of a reduction in Dx as the concentration of the extracted species in the organic phase increases. 

In many extraction systems, Dx is proportional to [L]", where [L] is the free ligand concentration, and the exponent n is determined by the number of ligand molecules per molecule of extracted complex. In these systems, therefore, we may write ... 

The term in curved brackets on the right-hand side of the equation is the free ligand concentration. 

Where more than one component is extracted, then the free ligand concentration will be reduced by all components present in the organic phase. For example, consider the extraction of two components, A and B, that have similar chemistries of extraction. Assume for both components m = n = 2, that they have D° values of 10 and 1 respectively. 

An experimentally most useful relationship occurs using Eq. (10), when the free ligand concentration [L] is equal to the dissociation constant fCj, namely. 

Fig. 2.27 GPC spin column ESI-MS determination of MS EC50S. Plot of fraction of known ligand inhibitor non-covalently bound to a fixed amount of kinase protein ([P]o, 5 pM) as a function of initial ligand concentration [L]o. The MS EC50 corresponds to the free ligand concentration [L] when 50% of the initial protein concentration is tied up as protein-ligand complex. At 50% of the...

Li and Wang described a convenient linear plotting protocol that permits one to evaluate stability constants for the formation of reversible metal hgand complexes. Added accuracy is achieved over classical approaches, because their generalized equations quantitatively account for side-reactions of metal ion and/or ligand as well as the difference between the total and free ligand concentration. 

Figure 4. Observed ratio of borate diesters to borate monoesters, scaled by Ilf versus the global free ligand concentration. Standard errors are shown based on multiple fits to individual nB NMR spectra. As the free ligand concentration is also calculated (by difference) from the MB NMR spectra, standard errors are given for this variable as well. The dashed line is the best fit from the model which gives Rg = 88.5 A. For these samples,/was always between 0.2 and 0.6. 

In Figure 5 we plot the ratio of borate esters to borate anion as a function of global free ligand concentration. The borate anion concentration was calculated from the free boron concentration (Bj) observed with 1 B NMR and the pH ... 

Equation 8.15 is the binding isotherm, which shows the hyperbolic dependence of absorbance on free ligand concentration. 

Both binding isotherm (Equation 8.15) and double-reciprocal plots (Equation 8.16) are expressed as a function of free ligand concentration, which is not known. By means of the mass balance on ligand,L can be related to the known total ligand concentration... 

A rearrangement of the relation (5) gives the following expression of the actual free ligand concentration [a]. 

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