Binding theory equilibrium

Binding Theory. The binding theory is based on the equilibrium between a ligand in solution L and a ligand on the protein P surface L(P)... 

Equation 14.55 is identical to the Langmuir s equation for dilute solutions, expressed in Equation 14.25. This similarity was to be expected because the conditions underlying the Langmuir s adsorption theory and the multiple equilibrium theory are the same, that is, binding (adsorption) equilibrium, and independent and identical binding (adsorption) sites. 

The basic kinetic properties of this allosteric enzyme are clearly explained by combining Monod s theory and these structural results. The tetrameric enzyme exists in equilibrium between a catalytically active R state and an inactive T state. There is a difference in the tertiary structure of the subunits in these two states, which is closely linked to a difference in the quaternary structure of the molecule. The substrate F6P binds preferentially to the R state, thereby shifting the equilibrium to that state. Since the mechanism is concerted, binding of one F6P to the first subunit provides an additional three subunits in the R state, hence the cooperativity of F6P binding and catalysis. ATP binds to both states, so there is no shift in the equilibrium and hence there is no cooperativity of ATP binding. The inhibitor PEP preferentially binds to the effector binding site of molecules in the T state and as a result the equilibrium is shifted to the inactive state. By contrast the activator ADP preferentially binds to the effector site of molecules in the R state and as a result shifts the equilibrium to the R state with its four available, catalytically competent, active sites per molecule. 

Two-state model, a model of proteins that coexists in two states controlled by an equilibrium constant. Molecules with selective affinity for one of the states will produce a bias in that state upon binding to the system. Two-state theory was conceived to describe the function of ion channels but also has relevance to receptors (see Chapter 3.7). 

We shall illustrate the applicability of the GvdW(S) functional above by considering the case of gas-liquid surface tension for the Lennard-Jones fluid. This will also introduce the variational principle by which equilibrium properties are most efficiently found in a density functional theory. Suppose we assume the profile to be of step function shape, i.e., changing abruptly from liquid to gas density at a plane. In this case the binding energy integrals in Ey can be done analytically and we get for the surface tension [9]... 

To make contact with atomic theories of the binding of interstitial hydrogen in silicon, and to extrapolate the solubility to lower temperatures, some thermodynamic analysis of these data is needed a convenient procedure is that of Johnson, etal. (1986). As we have seen in Section II. l,Eqs. (2) et seq., the equilibrium concentration of any interstitial species is determined by the concentration of possible sites for this species, the vibrational partition function for each occupied site, and the difference between the chemical potential p, of the hydrogen and the ground state energy E0 on this type of site. In equilibrium with external H2 gas, /x is accurately known from thermochemical tables for the latter. A convenient source is the... 

The second property is that each term of the PF is proportional to the probability of occurrence of the particular state it represents when the system is at equilibrium. We shall use mainly the second property of the PF. The next section is devoted to this aspect of the theory. Once we have the probabilities of all possible events we can compute average quantities pertaining to the system at equilibrium. Of these, the average occupation number, or the binding isotherm, will be the central quantity to be examined and analyzed in this book. 

In 1985 I was glad to see T. L. Hill s volume entitled Cooperativity Theory in Biochemistry, Steady State and Equilibrium Systems. This was the first book to systematically develop the molecular or statistical mechanical approach to binding systems. Hill demonstrated how and why the molecular approach is so advantageous relative to the prevalent phenomenological approach of that time. On page 58 he wrote the following (my italics) ... 

Many of the 60 known reactions catalyzed by monoclonal antibodies involve kinetically favored reactions e.g., ester hydrolysis), but abzymes can also speed up kinetically disfavored reactions. Stewart and Benkovic apphed transition-state theory to analyze the scope and limitations of antibody catalysis quantitatively. They found the observed rate accelerations can be predicted from the ratio of equilibrium binding constants of the reaction substrate and the transition-state analogue used to raise the antibody. This approach permitted them to rationalize product selectivity displayed in antibody catalysis of disfavored reactions, to predict the degree of rate acceleration that catalytic antibodies may ultimately afford, and to highlight some differences between the way that they and enzymes catalyze reactions. 

The thermodynamics of solute interaction with nonpolar ligates of the stationary phase will be treated later in this chapter within the framework of the solvophobic theory 107-108). According to this theoretical approach the equilibrium constant for the reversible binding of a given eluite to the hydrocarbonaceous ligates at fixed eluent properties and temperature can be approximated by the relationship... 

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