Parabolic Quantitative Structure‐Activity Relationships and Photodynamic Therapy: Application of a Three‐Compartment Model with Clearance to the In Vivo Quantitative Structure‐Activity Relationships of a Congeneric Series of Pyropheophorbide Derivatives Used as Photosensitizers for Photodynamic Therapy

Abstract

An open three-compartment pharmacokinetic model was applied to the in vivo quantitative structure-activity relationship (QSAR) data of a homologous series of pyropheophorbide photosensitizers for photodynamic therapy (PDT). The physical model was a lipid compartment sandwiched between two identical aqueous compartments. The first compartment was assumed to clear irreversibly at a rate K0. The measured octanol-water partition coefficients, P(i) (where i is the number of carbons in the alkyl chain) and the clearance rate K0 determined the clearance kinetics of the drugs. Solving the coupled differential equations of the three-compartment model produced clearance kinetics for each of the sensitizers in each of the compartments. The third compartment was found to contain the target of PDT. This series of compounds is quite lipophilic. Therefore these drugs are found mainly in the second compartment. The drug level in the third compartment represents a small fraction of the tissue level and is thus not accessible to direct measurement by extraction. The second compartment of the model accurately predicted the clearance from the serum of mice of the hexyl ether of pyropheophorbide a, one member of this series of compounds. The diffusion and clearance rate constants were those found by fitting the pharmacokinetics of the third compartment to the QSAR data. This result validated the magnitude and mechanistic significance of the rate constants used to model the QSAR data. The PDT response to dose theory was applied to the kinetic behavior of the target compartment drug concentration. This produced a pharmacokinetic-based function connecting PDT response to dose as a function of time postinjection. This mechanistic dose-response function was fitted to published, single time point QSAR data for the pheophorbides. As a result, the PDT target threshold dose together with the predicted QSAR as a function of time postinjection was found.

Mechanisms in photodynamic therapy: part one—photosensitizers, photochemistry and cellular localization

“…There are signs that this is starting to happen. Well-designed structure-function studies on rationally chosen sets of candidate PS molecules may allow more or less general conclusions to be deduced [93,94]. These experiments may have to be carried out both in vitro and in vivo.…”

Porphycenes: Facts and Prospects in Photodynamic Therapy of Cancer

“…chemical design and prediction of biological activity, only few QSAR studies on pharmacokinetics, subcellular localization, and tumor photosensitization of new PSs have been published [42, [227][228][229][230][231][232][233], and also very limited information about QSAR of porphycene PSs is available [234][235][236].…”

Progress with heterocyclic photosensitizers for the photodynamic therapy (PDT) of tumours

“…An example is provided by the preparation of a series of ether derivatives, based on 3(1-alkoxyethyl)-3-devinyl-pyropheophorbide a, in which lipophilicity increases as the alkyl chain length increases. The preparative route (Scheme 3) shows the hexyl ether, at which point along the homologous series the PDT activity has been found to be greatest [32,33]. Chlorophyll a 13 suffers thermal decarboxymethylation in hot collidine to give pyropheophorbide a, isolated as the methyl ester 14.…”