Kinetic perfection

There is some similarity between Ferry s treatment of concentrated systems (14), (123) [eq. (4.4)] and Cerf s just mentioned approach. In both cases the normal coordinate transformation is assumed to be possible along the lines given for infinitely dilute solutions of kinetically perfectly flexible chains (Rouse, Zimm). Only afterwards, different external (Ferry) or internal (Cerf) friction factors are ascribed to the various normal modes. 

Another way of evaluating enzymatic activity is by comparing k2 values. This first-order rate constant reflects the capacity of the enzyme-substrate complex ES to form the product P. Confusingly, k2 is also known as the catalytic constant and is sometimes written as kcal. It is in fact the equivalent of the enzyme s TOF, since it defines the number of catalytic cycles the enzyme can undergo in one time unit. The k2 (or kcat) value is obtained from the initial reaction rate, and thus pertains to the rate at high substrate concentrations. Some enzymes are so fast and so selective that their k2/Km ratio approaches molecular diffusion rates (108—109 m s-1). This means that every substrate/enzyme collision is fruitful, and the reaction rate is limited only by how fast the substrate molecules diffuse to the enzyme. Such enzymes are called kinetically perfect enzymes [26],... 

Some enzymes are so fast and so selective that their k2/Km ratio approaches the molecular diffusion rates (108-109m s-1). Such enzymes are called kinetically perfect [21]. With these enzymes, the reaction rate is diffusion controlled, and every collision is an effective one. However, since the active site is very small compared to the entire enzyme, there must be some extra forces which draw the substrate to the active sites (otherwise, there would be many fruitless collisions). The work of these forces was dubbed by William Jencks in 1975 as the Circe effect [22], after the mythological sorceress of the island of Aeaea, who lured Odysseus men to a feast and then turned them into pigs [23,24]. 

During the evolution of a natural enzyme, selection is not solely dependent on rate improvement. Therefore, there is no requirement for enzymes to be kinetically perfect, and it should be possible to develop catalytic antibodies that are faster than their natural counterparts. The designed substrate 52 has a rate of 1.4 s-1 with 84G3-catalyzed retro-aldol reaction (Zhong et al., 1999). Its kinetic parameters hold the current world record for antibody catalysis (KM = 4.2 /ulM, = 2 X... 

In the liquid phase diffusion to the catalyst may become the limiting step. Diffusion limitations provides an upper bound to the observed reaction rate (see Chapter 8). It appears that some enzyme catalytic reactions are so fast, e.g. carbonic anhydrase or acetyl cholesterase, that they exhibit this phenomenon. Catalysis under such condition is called "kinetic perfection". 

The fecat/J M ratios of the enzymes superoxide dismutase, acetylcholinesterase, and triosephosphate isomerase are between 10 and lO" s Enzymes such as these that have fecat/ M ratios at the upper limits have attained kinetic perfection. Their catalytic velocity is restricted only by the rate at which they encounter substrate in the solution (Table 8.8). Any further gain in catalytic rate can come only by decreasing the time for diffusion. Remember that the active site is only a small part of the total enzyme structure. Yet, for catalytically perfect enzymes, every encounter between enzyme and substrate is productive. In these cases, there may be attractive electrostatic forces on the enzyme that entice the substrate to the active site. These forces are sometimes referred to poetically as Circe effects. 

Explain the significance of K, k2, fecat> and bca/l M- C>efine kinetic perfection as it pertains to enzyme catalysis. 

It is important to note that the model calculation of the maximal accumulation rate of a GS conjugate in vacuoles exploiting different energy sources clearly demonstrates kinetic perfection of ABC transporters direct energisation maximally allows vacuolar accumulation by a factor of 4 x 10 compared to a factor of 100 or 3.2 only for AH - or A P-dependent energisation, respectively (Kreuz et al., 1996). Thus, if potentially toxic molecules need to be removed from the cytosol against a steep concentration gradient, ABC transporters can be expected to be more efficient than antiporters. 

For large wavelength and for an adsorption-desorption controlled transfer, the stability seems to be always guaranteed whatever be the sorption kinetics (perfect gas, Langmuir, B.E.T.)... 

Qualitative examples abound. Perfect crystals of sodium carbonate, sulfate, or phosphate may be kept for years without efflorescing, although if scratched, they begin to do so immediately. Too strongly heated or burned lime or plaster of Paris takes up the first traces of water only with difficulty. Reactions of this type tend to be autocat-alytic. The initial rate is slow, due to the absence of the necessary linear interface, but the rate accelerates as more and more product is formed. See Refs. 147-153 for other examples. Ruckenstein [154] has discussed a kinetic model based on nucleation theory. There is certainly evidence that patches of product may be present, as in the oxidation of Mo(lOO) surfaces [155], and that surface defects are important [156]. There may be catalysis thus reaction VII-27 is catalyzed by water vapor [157]. A topotactic reaction is one where the product or products retain the external crystalline shape of the reactant crystal [158]. More often, however, there is a complicated morphology with pitting, cracking, and pore formation, as with calcium carbonate [159]. 

For example, the measurements of solution osmotic pressure made with membranes by Traube and Pfeffer were used by van t Hoff in 1887 to develop his limit law, which explains the behavior of ideal dilute solutions. This work led direcdy to the van t Hoff equation. At about the same time, the concept of a perfectly selective semipermeable membrane was used by MaxweU and others in developing the kinetic theory of gases. 

Determination of Crystallization Kinetics. Under steady-state conditions, the total number production rate of crystals in a perfectly mixed crystallizer is identical to the nucleation rate, B. Accordingly,... 

Figure 16-27 compares the various constant pattern solutions for R = 0.5. The curves are of a similar shape. The solution for reaction kinetics is perfectly symmetrical. The cui ves for the axial dispersion fluid-phase concentration profile and the linear driving force approximation are identical except that the latter occurs one transfer unit further down the bed. The cui ve for external mass transfer is exactly that for the linear driving force approximation turned upside down [i.e., rotated 180° about cf= nf = 0.5, N — Ti) = 0]. The hnear driving force approximation provides a good approximation for both pore diffusion and surface diffusion. 

The name continuous flow-stirred tank reactor is nicely descriptive of a type of reactor that frequently for both production and fundamental kinetic studies. Unfortunately, this name, abbreviated as CSTR, misses the essence of the idealization completely. The ideality arises from the assumption in the analysis that the reactor is perfectly mixed, and that it is homogeneous. A better name for this model might be continuous perfectly mixed reactor (CPMR). 

But k must always be greater than or equal to k h / (A i + kf). That is, the reaction can go no faster than the rate at which E and S come together. Thus, k sets the upper limit for A ,. In other words, the catalytic effieiency of an enzyme cannot exceed the diffusion-eontroUed rate of combination of E and S to form ES. In HgO, the rate constant for such diffusion is approximately (P/M - sec. Those enzymes that are most efficient in their catalysis have A , ratios approaching this value. Their catalytic velocity is limited only by the rate at which they encounter S enzymes this efficient have achieved so-called catalytic perfection. All E and S encounters lead to reaction because such catalytically perfect enzymes can channel S to the active site, regardless of where S hits E. Table 14.5 lists the kinetic parameters of several enzymes in this category. Note that and A , both show a substantial range of variation in this table, even though their ratio falls around 10 /M sec. 

The rate (or kinetics) and form of a corrosion reaction will be affected by a variety of factors associated with the metal and the metal surface (which can range from a planar outer surface to the surface within pits or fine cracks), and the environment. Thus heterogeneities in a metal (see Section 1.3) may have a marked effect on the kinetics of a reaction without affecting the thermodynamics of the system there is no reason to believe that a perfect single crystal of pure zinc completely free from lattic defects (a hypothetical concept) would not corrode when immersed in hydrochloric acid, but it would probably corrode at a significantly slower rate than polycrystalline pure zinc, although there is no thermodynamic difference between these two forms of zinc. Furthermore, although heavy metal impurities in zinc will affect the rate of reaction they cannot alter the final position of equilibrium. 

There is a reasonable explanation for this type of deviation. The kinetic theory, which explains the pressure-volume behavior, is based upon the assumption that the particles exert no force on each other. But real molecules do exert force on each other The condensation of every gas on cooling shows that there are always attractive forces. These forces are not very important when the molecules are far apart (that is, at low pressures) but they become noticeable at higher pressures. With this explanation, we see that the kinetic theory is based on an idealized gas—one for which the molecules exert no force on each other whatsoever. Every gas approaches such ideal behavior if the pressure is low enough. Then ihe molecules are, on the average, so far apart that then-attractive forces are negligible. A gas that behaves as though the molecules exert no force on each other is called an ideal gas or a perfect gas. 

Avogadro s Hypothesis is consistent with the kinetic theory. Therefore a perfect gas follows Avogadro s Hypothesis. At one atmosphere pressure and 0°C, one mole (6.02 X 10 molecules) of a perfect gas occupies 22.414 liters. How closely real gases approximate a perfect gas at one atmosphere pressure and 0°C is shown by measur-... 

Fig. 1. Examples of the kinetic curves during ethylene polymerization by chromium oxide catalysts. Support—SiOs temperature—80°C polymerization at constant ethylene pressure in perfect mixing reactor. Curve 1—catalyst reduced by CO at 300°C. Curve 2— catalyst activated in vacuum (400°C) polymerization in the case of (1) and (2) in solvent (heptane) ethylene pressure 10 kg/cm2 02 content in ethylene 1 ppm, HsO 3 ppm. Curves 3, 4, 5, 6—catalyst activated in vacuum (400°C) polymerization without solvent ethylene pressure 19 (curve 3), 13 (curve 4), 4 (curve 5), and 2 (curve 6) kg/cm2 02 content in ethylene 1 ppm, HsO = 12 ppm.

In summary, the Third Law predicts that ordering processes are favored as the temperature is lowered, so that eventually perfect order should be obtained in any solid as its temperature approaches 0 K. But kinetic effects are such that the equilibration times needed to achieve this order are sometimes very long. 

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