Intrinsic exchange rate

This equation simplifies to kex = kQ if kc << 1c, and to kex = kQk,/kc if 1c, <conformational openings are the rate-limiting step of the exchange and the latter condition is referred to as EX2, where the equilibrium constant for local opening together with the intrinsic exchange rate determine the H-D exchange process. 

FIGURE 10.1 Intrinsic exchange rates of several types of labile hydrogen atoms as functions of solution pH calculated based on the data compiled in Dempsey [71]. Reproduced with permission from Kaltashov and Eyles [72],... 

From the foregoing considerations, may be expressed as = k KJ(K -b 1), i.e., the product of the diffusion limited encounter rate and the fraction of forward reacting encounters, KJ(K -b 1). It has been shown that in regions of pH well above that resulting in the minimum rate, the catalyst is mainly the hydroxide ion and KJ(K + 1) may be approximated by According to the equations above, the electrostatic effect on the intrinsic exchange rates due to the protein structure is contained in the factor and may... 

In Eq. (15.3), m is defined as MG / [denaturant], C, denaturant at the SUPREX transition midpoint, R is the gas constant, T is the temperature in kelvin, (Aiint) is the average intrinsic exchange rate of an amide proton, t is the HDX time, n is the number of subunits in the protein, and [P] is the protein concentration expressed in -mer equivalents. The transition region in the SUPREX curve depicts the range of denaturant concentrations where both the native and the unfolded state of protein are significantly populated. 

The difference in the self-exchange rates of the two cobalt couples favors the oxidative pathway by a factor of 300. (For a further discussion of the above and other self-exchange rates, see B. S. Brunschwig, C. Creutz, D. H. Macartney, T.-K. Sham, and N. Sutin, Faraday Discuss. Chem. Soc., No 74, in press). Evidently the difference in the intrinsic barriers is large enough to compensate for the less favorable driving force for the oxidative pathway. As a result the latter pathway can compete favorably with the reductive pathway. 

Ad. 1. Theoretical considerations including calculations based on the knowledge of anatomical features. While considering whether or not it is reasonable to believe that the non-mono-exponential transverse relaxation reflects an intra- and extra-cellular compartmentalisation, it should be questioned if the slow-exchange assumption is reasonable taking into account the macroscopic features of a muscle cell from a theoretical point of view. The NMR-timescale criterion for exchange limit is comparison of the quantity (rr1 + t"1), where r, and t0 are the average lifetime of a water molecule inside and outside the cell, respectively, with Rt — R , which is the absolute difference in the intrinsic relaxation rates. If R —Rfl > (h 1 + ), the... 

The term F2/CsRT is obtained from the constant capacitance model (Chapter 3.7). Fig. 4.6 gives a plot of the linear free energy relation between the rate constants for water exchange and the intrinsic adsorption rate constant, kads. 

At one extreme diffusivity may be so low that chemical reaction takes place only at suface active sites. In that case p is equal to the fraction of active sites on the surface of the catalyst. Such a polymer-supported phase transfer catalyst would have extremely low activity. At the other extreme when diffusion is much faster than chemical reaction p = 1. In that case the observed reaction rate equals the intrinsic reaction rate. Between the extremes a combination of intraparticle diffusion rates and intrinsic rates controls the observed reaction rates as shown in Fig. 2, which profiles the reactant concentration as a function of distance from the center of a spherical catalyst particle located at the right axis, When both diffusion and intrinsic reactivity control overall reaction rates, there is a gradient of reactant concentration from CAS at the surface, to a lower concentration at the center of the particle. The reactant is consumed as it diffuses into the particle. With diffusional limitations the active sites nearest the surface have the highest turnover numbers. The overall process of simultaneous diffusion and chemical reaction in a spherical particle has been described mathematically for the cases of ion exchange catalysis,63 65) and catalysis by enzymes immobilized in gels 66-67). Many experimental parameters influence the balance between intraparticle diffusional and intrinsic reactivity control of reaction rates with polymer-supported phase transfer catalysts, as shown in Fig. 1. 

The apparent reaction rate ra at the level of one pore results from the exchange of mass between the liquid flow and the porous structure of the catalyst particle as depicted in the close-up of Figure 3. In the absence of external mass transfer limitations, ra equals the product of the intrinsic reaction rate r0 and the particle effectiveness factor rip, the variables being expressed... 

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