Two-site exchange model

The third and most recent theory comes from Matsumoto and Giese, who suggested that the observed steady-state (SSEPR) spectrum of radical c is due to a superposition of two conformations of the same radical, and that one of these structures has a pyramidalized center. Iwasaki et al. invoked a fourth model, hyperfine modulation, to explain the spectra of the propagating radical. They were able to simulate the observed 9- and 13-line SSEPR spectra using a set of modified Bloch equations for a two-site exchange model between two conformations. 

Fig. 6.25. Simulation of the effect of the diffusion time on the normalized signal decay for the two site exchange model as a function of the diffusion time (A) in a stimulated echo-based diffusion sequence. (Reproduced with permission from ref. [11c]. Copyright 2005 Wiley-VCH.)...

The bound site correlation time can be calculated from this equation,49 though for any practical situation it is unlikely that the two-site exchange model and its corresponding single-site correlation time realistically reflects the actual events in a biochemical medium. Equation (75) may be simply extended to multiplebinding sites, i.e. 

Fig. 6. The fast relaxation rate, R2f, of 87Rb+ in agarose. The form of the line fitted to the first 4 points is R2p = 834( 359) + [agarose] x 976( 67). The last point was omitted as it did not fall within the linear region of the two-site exchange model.

It is possible to reveal very low fluctuation motions by MAS two-site exchange analysis. The rate constant for flip-flop motions of Tyr side chain in Leu -enkephalin trihydrate, for instance, was obtained as 1.3 X 10 s at ambient temperature from NMR by means of spectral simulation utilizing the two-site exchange model [160]. The similar... 

Changes in the NMR spectrum for a two-site exchange system as a function of Model... 

Results of Bo dependency were applied to the two models 1) Static model We assumed a homogeneous population of Na" " in the intracellular fluid, 2) Exchange model We assumed an exchange between Na+ under the slow-motion condition and the Na+ in the extreme narrowing region. Results obtained in this study can be fitted with the two-site exchange... 

The temperature-dependent spectra were interpreted in terms of a two-site hop model, in which the deuterons undergo jumps through a dihedral angle of 103°. This type of motion is consistent with gauche-trans conformational transitions. At -88"C these motions appear static on the time scale of the deuterium NMR experiment, and at +85 °C the motions are in the fast exchange limit. The rate constants for these motions were obtained from the calculated spectra. An Arrhenius plot of these data show that the apparent activation energy is 5.8 kcal/mol. (Dynamic mechanical data (20 Hz) fall on the Arrhenius plot.) The transitions have an intermediate rate on the deuterium NMR time scale at 20 °C, with the correlation time for the motion being 7 x 10 6 s at this temperature. 

These models are based on a supposition that some active centres on the mineral surface react with dissolved components almost instantaneously, whereas the others, very slowly. The simplest and most commonly used such model was proposed by Hussein Magdi Selim (born in 1944) in 1976. His model, which is called two-site adsorption model, deals with two types of adsorption sites on the mineral s surface. One type reacts with dissolved substance quickly, the other one, very slowly. For this reason the exchange process between the mineral and water for each component i has two rates ... 

Jardine et al. (1985b) employed a two-site nonequilibrium transport model to study Al sorption kinetics on kaolinite. They used the transport model of Selim et al. (1976b) and Cameron and Klute (1977). Based on the above model, Jardine et al. (1985a) concluded that there were at least two mechanisms for Al adsorption on Ca-kaolinite. It appeared that there were equilibrium (type-1) reactions on kaolinite that involved instantaneous Ca-Al exchange and rate-limited reaction sites (type-2) involving Al polymerization on kaolinite. The experimental breakthrough curves (BTC) conformed well to the two-site model. 

Wu and Gschwend (1986) reviewed and evaluated several kinetic models to investigate sorption kinetics of hydrophobic organic substances on sediments and soils. They evaluated a first-order model (one-box) where the reaction is evaluated with one rate coefficient (k) as well as a two-site model (two-box) whereby there are two classes of sorbing sites, two chemical reactions in series, or a sorbent with easily accessible sites and difficultly accessible sites. Unfortunately, the latter model has three independent fitting parameters kx, the exchange rate from the solution to the first (accessible sites) box k2, the exchange rate from the first box to the... 

A two-site model has been used (18) to model cesium transport in soils. In this model a Langmuir-type model, Equation 3,was used to represent surface sorption and a first-order model, Equation 1, was used to approximate interparticle diffusion. Extraction with CaC was used to verify the exchangeable site inventory. 

With the cylindrical cryptands, each macrocycle may bind one cation so that both mono- and dinuclear cryptates may be formed. Although the 12-membered (N202) macrocycles of ligand 5 are too small to bind two cations within each of the macrocycles, variable temperature 13C-NMR measurements have revealed intramolecular cation exchange between identical sites at the top and bottom of this cryptand, for Ca2+, Sr2+, and Ba2+. Cation jump between the two sites is fast with respect to intermolecular cation exchange, modeling the elementary jump processes of cations between binding sites in membrane channels (91). 

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