Apparent value

This means that the potential some distance away appears to follow Eq. V-13, but with an apparent value of AkTjze, which is independent of the actual value. For monovalent ions at room temperature this apparent would be 100 mV. 

It is because of these complications, both theoretical and practical, that it is doubtful that calculated surface energies for solids will ever serve as more than a guide as to what to expect experimentally. Corollaries are that different preparations of the same substance may give different values and that widely different experimental methods may yield different apparent values for a given preparation. In this last connection, see Section VII-5 especially. 

It can be seen from Table 2 that the intrinsic values of the pK s are close to the model compound value that we use for Cys(8.3), and that interactions with surrounding titratable residues are responsible for the final apparent values of the ionization constants. It can also be seen that the best agreement with the experimental value is obtained for the YPT structure suplemented with the 27 N-terminal amino acids, although both the original YPT structure and the one with the crystal water molecule give values close to the experimentally determined one. Minimization, however, makes the agreement worse, probably because it w s done without the presence of any solvent molecules, which are important for the residues on the surface of the protein. For the YTS structure, which refers to the protein crystallized with an SO4 ion, the results with and without the ion included in the calculations, arc far from the experimental value. This may indicate that con-... 

The value of the saturation concentration,, is the spatial average of the value determined from a clean water performance test and is not corrected for gas-side oxygen depletion therefore K ji is an apparent value because it is determined on the basis of an uncorrected. A tme volumetric mass transfer coefficient can be evaluated by correcting for the gas-side oxygen depletion. However, for design purposes, can be estimated from the surface saturation concentration and effective saturation depth by... 

The hnearity between M and makes the concept of absorbance so usehil that measurements made by sampling methods other than transmission are usually converted to a scale proportional to absorbance. The linearity between M and i is maintained only if the resolution of the spectrometer is adequate to eliminate contributions from wavelengths not absorbed by the species being measured. In addition, the apparent value of a is very dependent on resolution because a is 2l strong function of wavelength (30,31). 

Under some citcumstances the crack tip stress intensity is different than far-field stresses would indicate because of microstmctural effects behind the crack tip, such as fibers, whiskers, and bridging grains. Often far-field values indicate the crack is propagating at a stress intensity value higher than Kj and this apparent value usually increases as crack length increases. In spite of indications to the contrary, bonds continue to break at the same value of the stress intensity however, the crack tip is being shielded from some of the appHed stress intensity. To minimize confusion about Kj it has been suggested that the farfield value of the stress intensity be called When there are no microstmctural features that effectively reduce the crack tip stress intensity,... 

For adsorbent materials, experimental tortuosity factors generally fall in the range 2-6 and generally decrease as the particle porosity is increased. Higher apparent values may be obtained when the experimental measurements are affected by other resistances, while v ues much lower than 2 generally indicate that surface or solid diffusion occurs in parallel to pore diffusion. 

The quantum efflciency of die inadiatioii of a hydrogen-chlorine mixture has the apparent value between 10" and 10 , but the coiTesponding value for the parallel bromine reaction is only about 10. Of course die real quantum efflciency can only reach the value of unity as an upper limit, and the large apparent value for the chlorine reaction indicates that once two chlorine atoms... 

Remember that the modulus E = o/ . will increase during creep at constant o. This will give a lower apparent value of E. Long tests give large creep strains and even lower apparent moduli. 

Decrea.se in cooperativity of snb.strate. satnradon curve. Effector A lowers the apparent value of L. 

The converse situation applies in the presence of I, which binds only to T. T binding will lead to an increase in the population of T conformers, at the expense of Rq (Figure 15.11). The decline in [Rq] means that it is less likely for S (or A) to bind. Consequently, the presence of I increases the cooperativity (that is, the sigmoidicity) of the substrate saturation curve, as evidenced by the shift of this curve to the right (Figure 15.11). The presence of I raises the apparent value of L. 

FIGURE 15.12 71 versus [S] curves for an allosteric V system. The V system fits the model of Moiiod, Wyman, and Chaiigeux, given the following conditions (1) R and T have the affinity for the substrate, S. (2) The effectors A and I have different affinities for R and T and thus can shift the relative T/R distribution. (That is, A and I change the apparent value of L.) Assume as before that A binds only to the R state and I binds only to the T state. (3) R and T differ in their catalytic ability. Assume that R is the enzymatically active form, whereas T is inactive. Because A perturbs the T/R equilibrium in favor of more R, A increases the apparent Vmax- I favors transition to the inactive T state. 

When the temperature of the analyzed sample is increased continuously and in a known way, the experimental data on desorption can serve to estimate the apparent values of parameters characteristic for the desorption process. To this end, the most simple Arrhenius model for activated processes is usually used, with obvious modifications due to the planar nature of the desorption process. Sometimes, more refined models accounting for the surface mobility of adsorbed species or other specific points are applied. The Arrhenius model is to a large extent merely formal and involves three effective (apparent) parameters the activation energy of desorption, the preexponential factor, and the order of the rate-determining step in desorption. As will be dealt with in Section II. B, the experimental arrangement is usually such that the primary records reproduce essentially either the desorbed amount or the actual rate of desorption. After due correction, the output readings are converted into a desorption curve which may represent either the dependence of the desorbed amount on the temperature or, preferably, the dependence of the desorption rate on the temperature. In principle, there are two approaches to the treatment of the desorption curves. 

Increases in reaction rate with temperature are often found to obey the Arrhenius equation, from which the apparent values of the reaction frequency factor, A, and the activation energy, E, are calculated. The possibility that the kinetic obedience changes with temperature must also be considered. 

Pavlyuchenko and co-workers [649] have shown that mercury is a more effective inhibitor of HgO decomposition than oxygen. Apparent values of E for the reaction of red HgO at 0.01 Torr vary with temperature ... 

Wydeven [865] concludes that, in the presence of Co304 (6.8%), up to 60% of the reactant NaC103 decomposed in the solid state. During subsequent melting, there was an increase in reaction rate. The catalytic activity of the additive was ascribed to the electron accepting properties of the oxide (Co304 is a p-type semi-conductor). The apparent value of E increased from 120 to 200 kJ mole 1 between a = 0.05 and 0.5. 

The 5 and 520,w obtained from Eqs. 1-3 will be apparent values because of the effects of solution non-ideality, deriving from co-exclusion and—for charged polysaccharides—polyelectrolyte effects [30]. To eUminate the effects of non-ideality it is necessary to measure either s or S2o,w for a range of different cell loading concentrations c, and perform an extrapolation to zero concentration. For polysaccharides this has been conventionally achieved from a plot of I/5 (or 1/S20,w) versus c [30] ... 

One of the main characteristic of polyelectrolyte is the pK of the - COOH function as usually with polyelectrolyte only the intrinsic pK (pKo) extrapolated to zero charge characterizes the polymer [41] one gets 3.30 which is in same range as other carboxylic polymers the apparent values of pK (pKa) depends on the charge distribution, on the polymer concentration, on the ionic strength of the solution and on the nature of the counterions. 

However, as stated above, the partition coefficients measured by the shake-flask method or by potenhometric titration can be influenced by the potenhal difference between the two phases, and are therefore apparent values which depend on the experimental condihons (phase volume ratio, nature and concentrahons of all ions in the solutions). In particular, it has been shown that the difference between the apparent and the standard log Pi depends on the phase volume raho and that this relationship itself depends on the lipophilicity of the ion [80]. In theory, the most relevant case for in vivo extrapolation is when V /V 1 as it corresponds to the phase ratio encountered by a drug as it distributes within the body. The measurement of apparent log Pi values does not allow to differentiate between ion-pairing effect and partihoning of the ions due to the Galvani potential difference, and it has been shown that the apparent lipophilicity of a number of quaternary ion drugs is not due to ion-pair partitioning as inihally thought [80]. 

Reliable determination of all three functions depends on the information content associated with the experiments. The conventional experimental design does not provide sufficient information to determine all three functions accurately [34], Another consideration is that conventional analyses are all based on the assumption that the sample is uniform, and use an average value for porosity and an apparent value for permeability. Clearly, these properties vary spatially, and failure to account for the effects of spatial variations in the properties will lead to errors in the estimates of the functions [16]. 

An inhibitor that binds exclusively to the free enzyme (i.e., for which a = °°) is said to be competitive because the binding of the inhibitor and the substrate to the enzyme are mutually exclusive hence these inhibitors compete with the substrate for the pool of free enzyme molecules. Referring back to the relationships between the steady state kinetic constants and the steps in catalysis (Figure 2.8), one would expect inhibitors that conform to this mechanism to affect the apparent value of KM (which relates to formation of the enzyme-substrate complex) and VmJKM, but not the value of Vmax (which relates to the chemical steps subsequent to ES complex formation). The presence of a competitive inhibitor thus influences the steady state velocity equation as described by Equation (3.1) ... 

Because noncompetitive inhibitors bind to both the free enzyme and the ES complex, or subsequent species in the reaction pathway, we would expect these molecules to exert a kinetic effect on the E + S —> ES" process, thus effecting the apparent values of both VmdX/KM (influenced by both the K and al, terms) and Vmax (influenced by the aK term). This is reflected in the velocity equation for noncompetitive inhibition ... 

Referring back to Equation (3.2), we see that the effect of a noncompetitive inhibitor on the kinetic constants is to lower the apparent value of Vmax and to increase, decrease, or leave unaffected the apparent value of Ku, depending on whether a is >1, <1 or =1, respectively (see Table 3.3). These effects are apparent in plots... 

Table 3.3 Effects of inhibitors of different modalities on the apparent values of steady state kinetic constants and on specific steps in catalysis... 

Figure 3.9 Apparent value of the dissociation constant (K,) for a labeled inhibitor, I, as a function of the concentration of a second inhibitor, J when measured by equilibrium binding methods. The solid circles represent the behavior expected when compounds I and J bind in a mutually exclusive fashion with one another. The other symbols represent the behavior expected when compounds I and J bind in a nonexclusive, but antagonistic (i.e., noncompetitive, a > 1) fashion, to separate binding sites. The data for mutually exclusive binding were fit to the equation (apparent)K, = A, 1 + ([f ] A",) I and that for nonexclusive binding were fit to the equation (apparent)Kt = ( [J] + Kj / Kj + f[I]/y) ) for y values of 5 (closed triangles), 10 (open squares), 20 (closed squares), and 50 (open circles).

An inhibitor that binds exclusively to the ES complex, or a subsequent species, with little or no affinity for the free enzyme is referred to as uncompetitive. Inhibitors of this modality require the prior formation of the ES complex for binding and inhibition. Hence these inhibitors affect the steps in catalysis subsequent to initial substrate binding that is, they affect the ES —> ES1 step. One might then expect that these inhibitors would exclusively affect the apparent value of Vm and not influence the value of KM. This, however, is incorrect. Recall, as illustrated in Figure 3.1, that the formation of the ESI ternary complex represents a thermodynamic cycle between the ES, El, and ESI states. Hence the augmentation of the affinity of an uncompetitive inhibitor that accompanies ES complex formation must be balanced by an equal augmentation of substrate affinity for the El complex. The result of this is that the apparent values of both Vmax and Ku decrease with increasing concentrations of an uncompetitive inhibitor (Table 3.3). The velocity equation for uncompetitive inhibition is as follows ... 

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