McFarland probability model

Figure 13 McFarland probability model (eqs. 87 — 90). Symmetrical curves with linear ascending and descending sides result from eq. 90 (reproduced from Figure 1 and redrawn from Figure 3 of ref. [436] with permission from the American Chemical Society, Washington, DC, USA).

The bilinear model of Kubinyi (1977, 1993) was derived from a reconsideration of the McFarland probability model and takes into account the different volumes of the aqueous and the organic target phases in biological systems ... 

Another cutoff model, which deals with nonlinearity in biological systems, is one defined by McFarland (191). It attempts to elucidate the dependency of drug transport on hydrophobicity in multicompartment models. McFarland addressed the probability of drug molecules traversing several aqueous lipid barriers from the first aqueous compartment to a distant, final aqueous compartment. The probability of a drug molecule to access the final compartment n of a biological system was used to define the drug concentration in this compartment. 

Theoretical approaches were followed by others, the first one laying the foundation for all other theoretical models. McFarland considered the rate constants k (transport from the aqueous phase into an organic phase) and I (transport in the reverse direction) to be related to the probabilities of a molecule to enter either the lipid phase (eq. 87) or the aqueous phase (eq. 88) from an aqueous/lipid interface (Pi,j = probabilities) [436]. 

Sustaining the transport model, further non-linear representations of the observed structure-activity relationships were derived. According to the McFarland model (Seydel and Schaper, 1979 Kubinyi 1993), the probability of a drug reaching the receptor after passing several membranes depends on its lipophilicity in a symmetrical manner with linearly increasing and decreasing sides of the curve ... 

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