The ubiquitin-proteasome pathway is the principal pathway for intracellular protein degradation1,2 (Fig 1). This pathway selectively degrades an extensive number of short-lived regulatory proteins involved in the control of normal cellular processes. In order to be degraded, proteins targeted by the ubiquitin-proteasome pathway are covalently tagged by polyubiquitination, via a three-step enzymatic process, which ultimately leads to their recognition and degradation, by the 26S proteasome in a highly specific and regulated manner. This process is accomplished by the sequential action of three enzymes: an ATP-dependent ubiquitin-activating enzyme (E1), an ubiquitin-conjugating enzyme (E2) and an ubiquitin-pro-tein ligase (E3).3 This cascade covalently links the C terminus of ubiquitin to a free amino group on the target protein, usually the e-amino of a lysine residue.

In the QSAR (quantitative structure-activity relationship) and QSPR (quantitative structure-property-activity relationship) study physico-chemical property, lipophilicity is used, to predict bioactivity of the newly synthesized coumarin compounds. Lipophilicity is a property of a molecule which depends on and can be changed by modifications in molecular structure. The parameter of the lipophilicity, partition coefficient (log P), is commonly used in drug designing and it is a numeric characteristic of lipophilicity of the examined substance, potential drug. The synthesis of 4-arylaminocoumarins derivatives from 4-hydroxycoumarin, has been carried out. In this work we described the fragmental method of calculation of partition coefficient according to the Rekker's method, because the best correlation between calculated and experimental values log P was determined according to the Rekker model. 4-Arylaminocoumarin has negative value of log P, but substitution with alkyl or allyl groups on the position 3 increases lipofilicity. Introduction of methyl or ethyl group into position 3 increases lipofilicity, suggesting that by increasing the chain length the values of log P become higher. The influence of allyl substituent in position three increases lipophilicity similar to methyl group. The aryl supstitent decreases lipoflicity, but a general relationship among them could not be established. The results obtained in this study enable further synthesis of new coumarin derivatives and predict their biological activity and properties.