Binding constant defined

The square model is simpler than the linear model. Since all the sites are identical, in a weak sense, we have only one (first) intrinsic binding constant defined by... 

This binding may be described by a binding constant defined by the equilibrium... 

The binding constant is defined by the equiHbrium constant for the reaction... 

Thermodynamic control (Figure 1, right) is based on adsorption of substances until quasi-equilibrium stage. In this case, the surface ratio of the adsorbed species is defined by the ratio of products of their concentration and binding constant. This deposition is much less influenced by poorly controllable fluctuations of external conditions and provides much better reproducibility. The total coverage can be almost 100%. Because of these reasons, the thermodynamic control is advantageous for preparation of mixed nanostructured monolayers for electrochemical applications including a formation of spreader-bar structures for their application as molecular templates for synthesis of nanoparticles. 

The stability of a trivial assembly is simply determined by the thermodynamic properties of the discrete intermolecular binding interactions involved. Cooperative assembly processes involve an intramolecular cyclization, and this leads to an enhanced thermodynamic stability compared with the trivial analogs. The increase in stability is quantified by the parameter EM, the effective molarity of the intramolecular process, as first introduced in the study of intramolecular covalent cyclization reactions (6,7). EM is defined as the ratio of the binding constant of the intramolecular interaction to the binding constant of the corresponding intermolecular interaction (Scheme 2). The former can be determined by measuring the stability of the self-assembled structure, and the latter value is determined using simple monofunctional reference compounds. 

Such internal thermodynamic equilibria where A is a protein are found for non-metal components, including free coenzymes and substrates where B is a small molecule, or where free M is an ion of either a non-metal, e.g. Cl" or HCOj, or a metal, e.g. K+ or Mg2+, or is H+, and they are involved in, even necessary for, catalysis, pumping and cooperative controls of many metabolic paths. All such combinations reach equilibrium, as long as exchange is fast, where a fast rate can be taken as, say, 10-3 s for dissociation in cells. Note that equilibria with defined binding constants for AB or AM formation in any system reduce the number of variables and hence AB and AM concentrations are defined by those of free A, B and M, leaving two independent variables for each equilibrium. In some cases, the... 

In just the way that Km defines the dissociation of an enzyme from its substrate, K (the inhibitor constant) defines the strength of binding of a reversible inhibitor to the enzyme. 

It becomes obvious from the clustered data points that the binding constant for the 7 -enantiomer is too small to be accurately determined by this method. Hence, indirect affinity CE (resolution method) was utilized to determine the binding constant for the 7 -enantiomer. Indirect affinity CE makes use of the knowledge of the constant for one enantiomer (here, A s) and in addition of experimental separation data as obtained with the racemate of DNB-Leu in presence of the tBuCQN selector as BGE additive. By use of Equation 1.10, an enantioselectivity factor may be defined as the ratio of the binding constants of S- and 7 -enantiomers yielding the following equation ... 

Clearly, this is a simple Langmuir (see Section 2.4) isotherm with a binding constant for site a that is an average of the binding constants for site a in a system at states L and H, with weights andX, respectively. Similarly, we define the conditional probability of finding site a occupied given that site b is occupied which, for the... 

We define the following seven intrinsic binding constants,... 

It is sometimes convenient to introduce conditional intrinsic binding constants. These are defined in the same way as the conditional probabilities, namely,... 

In summary, the intrinsic binding constant to be used throughout this book always refers to a specific set of sites. They are defined in terms of the molecular properties of the system through the corresponding canonical PFs. They are also interpreted as probability ratios or as free energies of binding processes. In subsequent chapters we shall see how to extract from these quantities various correlation functions or, equivalently, cooperativities. 

Throughout the remainder of this book we shall use only the intrinsic binding constant as defined by the corresponding canonical PFs in Section 2.2. The are the quantities that are obtained directly from experiments. However, if we wish to interpret these quantities, say in terms of cooperativity, we must convert to the... 

We now define the intrinsic binding constant k as the ratio QiVfKolQid) (Section... 

At this point we again stress the sequence of definitions leading to Eq. (4.2.16). First, the correlation function is defined as a measure of the extent of the dependence between the two events in Eq. (4.2.12) [or, equivalently, in Eq. (4.2.13)]. The probabilities used in the definition of g a, b) were read from the GPF of the system, e.g., (4.2.1). This side of g a, b) allows us to investigate the molecular content of the correlation function, which is the central issue of this book. The other side of g a, b) follows from the recognition that the limiting value of g(a, b), denoted by g a, b), connects the binding constants ah and kg A. This side of g a, b) allows us to extract information on the cooperativity of the system from the experimental data. In other words, these relationships may be used to calculate the correlation fimction from experimental data, on the one hand, and to interpret these correlation functions in terms of molecular properties, on the other. 

The more traditional approach is to define an interaction coefficient [the equivalent of our g a, b)] in terms of the experimental binding constants by... 

The binding constants and correlation functions are defined as in Chapter 4. For instance. 

The first, 7(0, can be determined from the experimental data for any finite value of C. The second, 7,<0, may be interpreted as the same integral 7(0, but computed for a hypothetical system of independent sites. As we shall see below, this interpretation is somewhat risky and should be avoided. The function 7,.(Q is better viewed as defined in Eq. (5.8.10), with the binding constants determined in Eq. (5.8.8). 

In terms of the two functions 7(0 and I C) and the intrinsic binding constants we define the quantity... 

For all the above reasons we have defined g(C) without reference to any hypothetical, independent-site system. One simply extracts both 1(C) and all from the experimental data, and then constructs the quantity g(C). When the sites are identical in a weak sense, i.e., all k = k, some of the correlations for a given / might differ. For example, four identical subunits arranged in a square will have only one intrinsic binding constant k, but two different pair correlation functions. For this particular example we have four nearest-neighbor pair correlations g (2), and two second-nearest-neighbor pair correlations gJJ)- The average correlation for this case is... 

Ackers et al. (1982, 1986) analyzed data on the binding of the X repressor to the left and right operators obtained by footprinting titration. In order to obtain the correlations in this system, they wrote the following relations between the (overall) macroscopic binding constants Ki (i = 1,2, 3), defined in Section 2.3, and the intrinsic binding constants kf, and k ... 

The phenomenological approach developed mainly by Wyman, and used by Ackers et al., starts by defining all the binding constants as equilibrium constants for the binding process. Thus, is defined in terms of the standard free-energy change for the process, written symbolically as... 

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