Toxicants concentration, equation

Several compounds of this series exhibit respectable cytotoxicity and resensitized multidrug resistant cancer cell lines at non-toxic concentrations (Equation 38) [38]. 

Note that K is the slope of the straight line for a semilog plot of toxicant concentration versus time (Figure 6.12). In the preceding equation it is the elimination rate constant that is related to the half-life of the toxicant described earlier in this chapter. The derived C° can be used to calculate the volume of distribution (Vd) of the toxicant as follows ... 

Although both concepts allow the calculation of mixture toxicity on the basis of the toxicity of the individual compounds, there are fundamental differences between CA and IA when it comes to assessing mixtures of low concentrations of toxicants. These differences originate in the opposite conceptual assumptions of both concepts. CA operates on the level of effect concentrations (Equation 4.1), while IA uses the effects of the single toxicants for the calculation of an effect of the mixture (Equation 4.4). Hence, according to CA, every toxicant that is present in the mixture contributes to the overall toxicity (in direct proportion to its toxic unit). In contrast, IA implies that only those components contribute to an overall toxicity that are present in the mixture at a concentration, whose effect—if that concentration would have been applied singly—is greater than 0. 

The title compound, [8-14C]carbovir, 184, a promising anti-AIDS drug182, inhibiting the infectivity and replication of HIV virus at concentrations of approximately 200-400-fold below its toxic concentrations, has been labelled with 14C by treating183 a solution of triethyl [14C] orthoformate in dry chloroform with ds- [4-(2,5-diamino-6-chloro-4-pyrimidinyl)amino]-2-cyclopentyl carbinol 185 and hydrolysis of the crude 186 with 2 N sodium hydroxide (equation 71). 

Curves of cells of Saccharomyces cerevisiae yeast growth in suspension at various concentrations of nickel (II) sulfate may serve as an example (Figure 1) [14], These curves are the evidence of toxic action of nickel (II) ions. Increase of toxicant concentration leads to decrease of rate during the period of exponential growth (parameter p in equation (7)) and maximum size of population of yeast (Parameter p/a in equation(7)) at one and the same initial size of yeast population, N0=100 cells/ml. 

Figure 15. The dependence of roots of characteristic equation of system (37) on toxicant concentration.

BIOACCUMULATION BCF (from regression equations) 24, 37, 40 and 52 may not bioaccumulate because of its toxicity concentration found in fish tissues is expected to be somewhat higher than the average concentration in the water the fish were taken... 

The multiple linear equations given in TABLE 3 indicate a significant relationship of the observed toxicities with several physico-chemical characteristics of these compounds. However, only some 60% of the total variation is explained by equation 3d and the corresponding standard error of the estimate, s = 0.60 is quite large. This means that for a number of compounds the predicted toxic concentrations differ by more than one order of magnitude from those observed experimentally. As there is a spread of close to five orders of magnitude between the molar concentrations of the least and most toxic compounds, the predictive capacity of equation 3d is still of value, though somewhat limited in applicability. This fact stimulates the desire for a closer inspection of the data with a view to delineate more precise relationships for smaller, more easily defined subsets of mono-substituted benzene derivatives. 

An example of the method employed to generate the relationships presented in TABLE 2 follows. By substituting equation 5 (bioconcentration/KQ, relationship) into equations 9 and 11 (toxicity/KQ, relationship), the internal organism toxicant concentration at a given biological endpoint (acute and chronic, respectively) can be estimated from various external toxicant concentrations as described by the QSARs specifically ... 

If all of these aquatic organisms are considered to be at a density of 1.0, the various constants then could be expressed as moles per kilogram of body weight. A summary of estimated constant internal toxicant concentration and the mean value for each toxicity category appears in TABLE 2. Equations 15 and 16 also appear in FIGURE 1. 

As discussed by McCarty et al. (1985), the relationship between internal and external steady-state equilibrium toxicant concentrations appears to be adequately described by a simple one constant equation. Although they were able to show that there appeared to be a constant internal toxicant concentration for certain narcotic organic chemicals and some substituted phenols, they were not able to quantify the relationships. Furthermore, acute and chronic QSARs did not appear to be parallel. When the original data relationships are described by the geometric mean regression technique, the relationships are more accurately described and quantification is possible. 

The internal toxicant concentration can vary, depending on the toxic endpoint being examined, and the mode of toxic action in question. For organisms having significantly different lipid concentrations from those examined herein (about 5%), a clearer understanding of the influence of lipid content in the relationship between and Kg must be obtained. Equation 17 is clearly the... 

To solve the equation for the internal fish toxicant concentration, Cp, the relationship between bioconcentration factors and kinetic constants specifically,... 

Equation 1 (TABLE 2) is the toxicity QSAR for this data set a slope of essentially negative one and r of 0.99 is achieved. Equation 2 is generated using equation 1 and the bioconcentration/Kow relationship of Halfon (1985). It indicates that a whole-body toxicant concentration of approximately 6,500 yumol L or 0.0065 mol L (or mol Kg when the density is about 1.0) is associated with an acutely toxic lethal response in half the exposed population of fathead minnows at essentially infinite time, i.e., threshold. 

TABLE 2 Regression equations for QSAR, QSKRs, and fish toxicant concentration. 

The fitting of non-linear regression equations to time-toxicity data from standard aquatic acute toxicity tests can generate quantifiable first-order, one-compartment kinetics constants when the bioconcentration factor is obtained from other sources and introduced into the equation. The relationship between toxicity-based and bioconcentration-based kinetic parameters is a function of the internal toxicant concentration of endpoint achieved in each of these two experimental protocols. This is a fixed internal concentration of about 0.006 mol L" for acute toxicity and a hydrophobicity-related variable concentration for bioconcentration, for the organisms and organic chemicals studied herein. Therefore, the difference between the endpoints, which is proportional to Kg, can be used to convert toxicity-based kinetic data to bioconcentration-based kinetic data and vice versa. 

In (eco)toxicological QSAR studies, the molecular descriptor of choice is the n-octanol/water partition coefficient (log P), generally used in a simple regression equation. However, sometimes a simple linear regression model is inadequate to model properly the dependence of biological activity (BA) on logF. For example, fish exposed to very hydrophobic chemicals for a limited test duration have insufficient time to achieve a pseudo-steady state partitioning equilibrium between the toxicant concentration in aqueous circumambient phase and the hydrophobic site of action within the fish. Hansch initiated the use of a parabolic model in log P (equation 1) to overcome... 

The fundamental assumption of SAR and QSAR (Structure-Activity Relationships and Quantitative Structure-Activity Relationships) is that the activity of a compound is related to its structural and/or physicochemical properties. In a classic article Corwin Hansch formulated Eq. (15) as a linear frcc-cncrgy related model for the biological activity (e.g.. toxicity) of a group of congeneric chemicals [37, in which the inverse of C, the concentration effect of the toxicant, is related to a hy-drophobidty term, FI, an electronic term, a (the Hammett substituent constant). Stcric terms can be added to this equation (typically Taft s steric parameter, E,). 

It has been shown that carbon dioxide also increases the toxicity of the other gases currently included in the model. For example, the 30 minute plus 24 hour LC50 value of HCN decreases to 75 ppm and that of 02 increases to 6.6% in the presence of 5% C02. However, we empirically found that the effect of the C02 can only be added into this equation once. At this time, we have data on the effect of various concentrations of C02 on CO and only have information on the effect of 5% C02 on the other gases. Since CO is the toxicant most likely to be present in all real fires, we have included the C02 effect into the CO factor. As more information becomes available, the N-Gas equation will be changed to indicate the effect of C02 on the other gases as well. 

A direct method for determining worker exposures is by continuously monitoring the air concentrations of toxicants on-line in a work environment. For continuous concentration data C t) the TWA (time-weighted average) concentration is computed using the equation... 

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