Half-value concentration

H-abstraction intramolecular, 378 Half-value concentration, 181 Half-band width, 69 Half quenching concentration, 173 Hamiltonian operator, 65 perturbing, 67 Hammet equation, 110 He-Ne laser, 318 Heavy atom perturbation, 70 external, 145 intermolecular, 71 intramolecular, 71... 

Only a subset of the parameter values in the O Flaherfy model require inputs from the user to simulate blood and tissue lead concentrations. Lead-related parameters for which values can be entered into the model include fractional absorption from the gastrointestinal tract partition coefficients for lead in nonbone tissues and in the surface region of bone maximum capacity and half-saturation concentration for capacity-limited binding in the erythrocyte elimination clearance fractional clearance of lead from plasma into forming bone and the restricted permeability coefficients for lead diffusion within bone, from plasma into bone, and from bone into plasma (O Flaherty 1991a). 

When concentration of A was doubled, half-life reduces to its half value, i.e. 

In Eq. (1), a is the equilibrium stress (Nm 2) supported by the swollen specimen a is the stretched specimen length divided by the unstretched length (extension ratio) v2 is the volume fraction of dry protein and p is the density of dry protein. In the common case of tetrafunctional crosslinks, the concentration of network chains n (mol network chains/g polymer) is exactly one-half the concentration of crosslinks, so that n = 2c. The hypothesis that a specimen behaves as if it were an ideal rubber can be confirmed by observing a linear relation with zero intercept between a and the strain function (a — 1/a2) and by establishing a direct proportionality between a and the absolute temperature at constant value of the extension ratio, as stipulated by Eq. (1). 

Figure 12.4 Comparison of the reaction rate functions Eqs. 12-27 (curve 1) and 12-28 (curve 2). The straight line through the origin indicates the initial slope of size k. Half-saturation concentrations are at ln2 (J/k) and (J/k), respectively. Parameter values J= 1, k = 1.

If the recombination is delayed, e.g., by migration of excited electrons, luminescence takes place by a second-order bimolecular reaction. The probability of a luminescent recombination of the excited electron with the holes is then proportional to the product of the concentration of electrons and the concentration of holes. The lower the initial intensity is, and the further the decay has progressed, the slower the decay to the half value is. This hyperbolic decay law is only of limited validity. If the excited electron is momentarily trapped before recombination, very complex interactions can arise. 

No health hazard data are available and no limits for workplace exist. Ozonated water in high concentrations can lead to eye and skin irritation. Langlais et al. (1991) summarize some LC50-values (concentration that is lethal to half of the test animals) found in fish... 

From the preliminary research described in the previous section, it appears that the small oxidation wave with half-value potential (EV2) of ca. 0.21V vs. SCE offers favourable perspectives for the amperometric determination of relatively high hydrogen peroxide concentrations. In contrast to the second oxidation wave with I2=0.76 V vs. SCE, the pseudo-limiting currents obtained in the prewave do not satisfy the relation of Levich (Chapter 1, Equationl.15). However, they are almost completely independent of the rotation rate of the electrode, revealing that these limiting currents are not controlled by transport of electroactive species but by (an) other process(es). This is illustrated in Fig.4.5. 

The confirmation of a compound s identity is only one half of the overall confirmation procedure quantitative confirmation is the other half. Compound concentrations calculated from analyses on two columns or two detectors must be in agreement. The EPA recommends a 40 percent difference (calculated as the RPD shown in Equation 1, Table 2.2) as a threshold value for making decisions on the presence or absence of a compound (EPA, 1996a). This means that the concentrations obtained from two columns or two detectors that agree within 40 percent indicate the presence of an analyte, provided that the retention time confirmation criterion has been also met. 

The implication for the therapeutic application of these rifampicins is quite obvious. Highly lipophilic derivatives may fail in therapy despite low in vitro MIC values (high intrinsic activity) because the time needed for the diffusion into the bacterial cell might be too long compared with their biological half-life (concentration-time profile in the serum). 

It is clear that the levels of the individual acids in rancid milk can be considerably lower than the threshold values reported by Scanlan et al. (1965), which do not include the levels contributed by the fresh milk, (i.e., approximately half the concentrations shown in the second column). Thus, the flavor of the combination of the acids in rancid milk is apparently sufficient to exceed the threshold for detection of rancidity. 

Follow-up testing performed after confirmation is usually to determine IC50 or EC50 values. These tests require preparation of each compound in a series of different concentrations according to twofold diluting schemas (the concentration of each consequent point is half the concentration of the previous point in the series with the half log, every other point would differ in a magnitude of concentration). The number of concentration points in a series can range from 2 to 12 (Quintero et al., 2007 Turner and Charlton, 2005). 

Equation 18.12 shows that the inverse of the concentration at any time is a linear function of time, the slope of the line being determined by the coagulation constant. Experimental data from both mono-disperse and polydisperse aerosols follow this general form, at least initially. As will be discussed later, the coagulation constant may be appreciably larger than the theoretical value. If th is defined as the half-value time, i.e., the time in which the concentration decreases by a factor of 2, then... 

The other alkali metals have been less extensively studied. The propagation rates of polystyrylsodium, -potassium, -rubidium and -cesium have been measured in benzene and cyclohexane [72, 73]. The sodium compound still shows half order kinetics in active centre concentration and is presumably associated to dimers. The rates for the rubidium and cesium compounds are directly proportional to the concentrations of the active chains which are presumably unassociated in solution. Absolute kp values can be determined from the propagation rate in this case. Poly-styrylpotassium shows intermediate behaviour (Fig. 11), the reaction order being close to unity at a concentration of the potassium compound near 5 x 10 M and close to one half at concentrations around 10" M. It could be shown by viscosity measurements that association was absent in the low concentration range. In this system both K2 and kp can be measured. The results are summarized in Table 2. The half order reactions show a large increase in kpK between lithium and potassium which... 

Also in this case results showed a significant minimum at a depth of about 150 m in spite of the fact that the values that they reported along the entire water column were about half the concentrations measured in different oceanic areas. This low concentration measured in deep water seems in contrast to the cumulative Cu increase from the Atlantic to the North Pacific (12). 

Values of the population densities of levels v = 1,2 and half the concentration of 0-atoms have been plotted against time in Fig. 27. Deactivation by 0-atoms causes populations to decrease for t > tmax bringing N to its Boltzmann value at Tg. 

A° values can be obtained experimentally from eq. 23, which defines the half-quenching concentration, permitting calculation of a corresponding value. These are shown In Table 1 for a variety of donor-acceptor pairs. 

For this procedure one, once again, sets the substrate concentration at one face (now the cis face) of the membrane at a limitingly high level—as defined in the preceding subsection (if the system is such that this condition can be fulfilled). One now measures the net cis to trans flow of substrate when the substrate concentration at the trans face is set at various levels. In the complete absence of trans substrate, the net flow of substrate has a maximal value and is of course equal to the maximal velocity of the corresponding zero trans experiment, i.e., Vf2 or Vf. As the substrate concentration at the trans face is increased, the net cis to trans flow is reduced, since the substrate can, in general, move in the trans to cis direction. One can define /(2 i and K as the half-saturation concentration of substrate at the trans face, which is just sufficient to reduce the net flow of substrate in the cis to trans direction to one-half of the maximal value. 

For this procedure, we take Sj as the concentration at the trans face and let S2 become limitingly high in Eqn. 12 or 13. Then the surprising result is obtained that the unidirectional flux in the cis-to-trans direction is zero at all finite values of S,. An equation of the form of Eqn. 3 cannot be obtained. There is no maximum velocity in the infinite trans procedure at accessible substrate concentrations and a finite value for the half-saturation concentration K 2 cannot be obtained. The conclusion follows ... 

If the infinite trans procedure yields a finite value for the half-saturation concentration, the simple-pore model of Fig. 5 cannot be an adequate description of the system and the simple-pore model is to be rejected. 

If now the cis side concentration, S, is set at a limitingly high value the net flow of substrate is equal to l// i2- This is the maximum zero trans velocity and this value will not change as S2 is increased to any finite concentration. (This is so by definition since with S, limitingly high, no finite value of 83 can affect the value of the numerator or denominator of Eqn. 17.) An equation of the form of Eqn. 4 with a finite half-saturation concentration at the trans face K cannot be obtained for a simple pore. Once again, if the infinite cis experiment can be performed so that a finite value of the half-saturation concentration KH is measurable, the simple-pore model must be rejected. 

The fact that the infinite cis and trans experiments can be performed and yield finite values of the respective half-saturation concentration leads, as we have seen, to the rejection of the simple-pore model (and its more complex form). The simple carrier can then temporarily be considered acceptable for such systems as yield finite half-saturation concentrations for these procedures. But the actual value of these parameters may or may not be consistent with the simple carrier and hence one can develop rejection criteria for the simple carrier in terms of the experimentally measurable parameters. The point of such an analysis is the following For a system which behaves as a simple carrier, the unidirectional flux Eqn. 30 is appropriate and will serve to account for all steady-state experiments involving the single substrate S. Yet Eqn. 30 contains only four independently variable parameters—one form in K and three forms in R (since the forms are connected by /Jqo + ee 12 21)-... 

Depending on the values of the resistance terms / , one may get very different values for the measured half-saturation concentrations for the various transport procedures. Nevertheless, all these are derivable (if the carrier model holds) from the intrinsic dissociation constant K and the appropriate pair of resistance terms. 

In general, one will not be surprised to find a marked asymmetry in transport parameters. The transport rate constants can have any values subject only to the constraint that in the absence of an external source of energy there is no net movement of substrate when the concentration at each face of the membrane is the same. This implies that h,/2 = for the simple pore or that h,/2k = 2/1 2 for the simple carrier. It is the value of the transport resistance / ,2 and /(ji hat will determine whether or not the system will behave asymmetrically. This can be seen by taking the ratio of the derivable half-saturation concentration and maximum velocities as follows ... 

The relationship between Na-K ATPase activity and active trans-membrane transport of Na" " and K, discussed in detail in earlier reviews [6,127,128] rests on the following arguments. Both Na-K ATPase and Na - K transport are activated by the simultaneous presence of internal ATP, Mg and Na and external K and both are inhibited by externally present cardiac glycosides like ouabain. The half-maximal activating concentrations of Na and K, the values for ATP and the half-inhibitory concentrations of ouabain are nearly equal for the two activities in the systems where they have been determined. For a large variety of tissues there is a remarkably constant ratio of 3 Na transported per ATP hydrolyzed ([6] pp. 271-272 [128] p. 158). The 3Na /2K stoichiometry for the transport agrees with the ratio of Na released to K bound upon phosphorylation of the enzyme (Section 2). Definitive proof for the involvement of the enzyme in transmembrane transport of Na and K has come from reconstitution studies in which a purified... 

The range of substrate concentration should include the K value. Ideally, K should be the half value of that range ... 

For robust estimation of the ratio of Vm to Ka of an enzyme. So can be paeset at a value below 10% of Km to simplify Equ.(2) into Bqu.(9). Steady-state data from a reaction curve can be analyzed after data transformation according to the left part in Equ.(9). For validating Equ.(9), it is proposed that So should be below 1% of Km (Meyler-Almes Auer, 2000). The use of extremely low So requires special methods to monitor enzyme reaction curves and steady-state reaction can not always be achieved with enzymes of low intrinsic catalytic activities. On the other hand, the use of So below 10% of Kn is reasonable to estimate the ratio of Vm to Kn (Liao, et al., 2001). To estimate the ratio of Vm to Kn, the use of Equ.(9) to analyze data is robust and resistant to variations of So if Equ.(9) is valid this property makes the estimation of the ratio of Vm to Kn for screening reversible inhibitors superior to the estimation of the half-inhibition concentrations (Cheng Prusoff, 1973). 

For this modelling the Monod kinetic approach was chosen. In this work the primary redox reaction sequence (1A)-(5A) was set up introducing appropriate threshold values (half satmation concentrations) as reaction limiting factors. The contribution of a given electron acceptor i to the overall DOC degradation is given by... 

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