Sigmoidal relationship

Fig. 2.6 Trendships between percentage human PPB (hPPB%) and octanol-water log D " [20]. Note the around 2 log units downshift of the sigmoidal relationship for acids as compared to neutrals and basics. (With kind permission of Springer-Kluwer.)...

Fig. 5.3 Sigmoidal relationship of intestinal absorption with TPSA for 20 representative drugs.

For 31 passively transported dmgs, excellent sigmoidal relationships were found between human intestinal absorption and their H-bond acceptor and donor factors [65] ... 

Figure 2 The permeability in Caco-2 cell monolayers as a function of distribution coefficient (octonol/water, pH 7.4) for 5-fluorouraciI and prodrugs. A sigmoidal relationship can be observed. (Replot from Ref. 26, with kind permission from Elsevier Science-NL, Amsterdam, The Netherlands.)...

Liposome partitioning of ionizable drugs can be determined by titration, and has been correlated with human absorption [102-104]. A new absorption potential parameter has been suggested, as calculated from liposome distribution data and the solubility-dose ratio, which shows an excellent sigmoidal relationship with human passive intestinal absorption (Eq. 2) [102, 103]. 

Fig. 4.1. Relationship between the absorbed vivo perfusion of the human jejunum (B) (data fraction (FA) of structurally diverse sets of compiled from publications by Lennernas orally administered drugs and permeability laboratory [63, 115]). Sigmoidal relationships coefficients obtained in Caco-2 cell monolayers were obtained between FA and the (A) (data compiled from publications by permeability coefficients in both models.

A Michaelis-Menten type graph for an allosteric enzyme shows not the usual hyperbolic shape as shown in Section 1.4, but a sigmoidal relationship between [S] and activity. 

Many companies have tried to develop peptidic renin inhibitors. Unfortunately these are rather large molecules and not unexpectedly poor absorption was often observed. The role of physicochemical properties has been discussed for this class of compounds. One of the conclusions was that compounds with higher lipophilicity were better absorbed from the intestine [29]. Absorption and bile elimination rate are both MW-dependent. Lower MW results in better absorption and less bile excretion. The combined influence of molecular size and lipophilicity on absorption of a series of renin inhibitors can be seen from Figure 1.7. The observed iso-size curves are believed to be part of a general sigmoidal relationship between permeability and lipophilicity [30-31] (for further details see Chapter 3). 

As mentioned above, hydrogen bonding and molecular size, in combination with lipophilicity have an important influence on oral absorption. A number of methods are available to compute these properties. A further example of the correlation between H-bonding, expressed as polar surface area, is found in Figure 3.12 [24,25]. Such a sigmoidal relationship is found for compounds which are absorbed by passive diffusion only and not hindered by efflux or metabolism, and which are not involved in active uptake. Otherwise deviations will be foimd [25]. 

The review article by Egan examines several predictive approaches, from fairly simple ones, using only one variable and showing a sigmoidal relationship [55], to increasingly more complex approaches where non-linear equations were successfully used to predict percent protein binding for neutral, basic and zwitterionic compounds across a set of 302 compounds, but where a similar attempt was used for acidic compounds the result was a poor fitting model [59]. 

A detailed discussion of the mechanism for 5 -AMP deamination is at present premature. The sigmoid relationship for substrate saturation and activation by monovalent cations and adenine nucleotides is consistent with mechanisms involving active site-effector site interaction. However, the activation brought about by this site-site interaction is a relatively... 

There was a sigmoidal relationship between the logarithms of stress and strain rate. 

The previous section illustrated how allosteric cooperativity can result in a sigmoidal relationship between binding saturation and substrate concentration. In this section, we demonstrate how a sigmoidal relationship between product concentration and time can arise from enzyme kinetics with time lags. 

The plasma concentration of ascorbate shows a sigmoidal relationship with intake. Below about 30 mg per day, the plasma concentration is extremely low and does not reflect increasing intake to any significant extent. As the intake rises above 30 mg per day, so the plasma concentration begins to increase sharply, reaching a plateau of 70 to 85 /rmol per L, at intakes between 70 to 100 mg per day, when the renal threshold is reached and the vitamin is excreted quantitatively with increasing intake. 

The k (retention factor) values are then plotted versus the s pH values, and the inflection point of this sigmoidal relationship could be taken as the sp of that particular compound at particular hydro-organic mixture. The ipKa determined at 30v/v% MeCN was determined to be 3.9 (using nonlinear regression analysis program MathCad 8). This corresponds well to our original estimation of IpKa 3.7. 

All these coefficients are unknown and are estimated by fitting experimental results to the model. The question is then how to construct the model. The authors reasoned that the quadratic relationship between log k and O requires 3 levels and that the sigmoid relationship between log A and pH could be described by four or five points. They... 

The 4PL (Eq. (9.2)) provides an accurate representation of the sigmoidal relationship between the anal3dical response and the logarithm of the analyte concentration in immunoassays ... 

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