Two state theory

We assume again that the atoms follow straight line trajectories, and we calculate the transition probability, P(b), from the initial to the final state in a collision with a given impact parameter, b. We then compute the cross section by integrating over impact parameter, and, if necessary, angle of v relative to E to obtain the cross section. The central problem is the calculation of the transition probability P(b). The Schroedinger equation for this problem has the Hamiltonian 

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Two-state theory was originally formulated for ion channels. The earliest form, proposed by Del Castillo and Katz [15], was comprised of a channel that when bound to an agonist changed from a closed to an open state. In the absence of agonist, all of the channels are closed ... 

The observation that receptors can demonstrate spontaneous activity necessitated elements of ion two-state theory to be incorporated into receptor theory. 

The extended ternary complex model [23] was conceived after it was clear that receptors could spontaneously activate G-proteins in the absence of agonist. It is an amalgam of the ternary complex model [12] and two-state theory that allows proteins to spontaneously exist in two conformations, each having different properties with respect to other proteins and to ligands. Thus, two receptor species are described [Ra] (active state receptor able to activate G-proteins) and [RJ (inactive state receptors). These coexist according to an allosteric constant (L = [Ra]/[Ri]) ... 

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). 

Two-stage binding reactions, 68, 76 Two-state theory derivation of, 55-56 description of, 42, 47-48 Two-way analysis of variance, 231... 

Most published cytochrome P450 catalytic cycles will show the end-on peroxo coordination as shown in Figure 7.14 (4,5a, 5b). Shaik and co-workers have used density functional theory methods to propose a two-state theory... 

Significant Structure Theory and Eucken s Polymer Model. If we drop the restriction that the bulky species represent only Ice-I-like structures and reserve the term ice-like for water molecules which have merely the same spatial arrangement as ice (i.e., tetrahedrally hydrogen-bonded), we may include in this two-state theory (in which we have a bulky and a dense species) the treatment by Marchi and Eyring (107). This is a special case of the significant structure theory of liquids and introduces, as a specific element, fluidized vacancies in addition to the individual monomers (which, in turn, are assumed capable of free rotation). 

Equations such as (5.1) are also found in the two-states theories of water. These theories aim at explaining all the properties of water via the peculiar features of an open (icelike) and closed qiecies of water (the remainder of the liquid sample). According to these theoretical approaches, the thermodynamic parameters (density, enthalpy, dependence on temperature and pressure of the probability of belonging to one spedes, etc.) characteristic of the two species must be defined via a compromise. In contrast to what happens in the case of density, the definition of these parameters turns out to be unsatisfactory. Geometrical arguments show that it is reasonable to give the... 

Figure 6 illustrates k T), which shows an Arrhenius trend in the range - 20°C to + 100 C with A-28, value which is much greater than A = 1 as predicted by two-state theory. The value of hb ( hb kcal/mol) agrees with the one calculated with data from different experimental techniques... 

It was a matter of some importance to prove this two-state theory ofproteindenaturation.Lumry,BiltonenandBrandts(52)andTanford(8/) suggested as a test of the correctness of this theory a comparison between... 

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