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In this paper we consider the unique nonnegative solution to the following generalized version of the stochastic differential equation for a continuous-state branching process.

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The human cytochrome P450 (CYP) enzyme CYP4Z1 is a fatty acid hydroxylase which among human CYPs is unique for being much stronger expressed in the mammary gland than in all other tissues. Moreover, it is strongly overexpressed in all subtypes of breast cancer, and some overexpression has also been found in other types of malignancies, such as ovarian, lung, and prostate cancers, respectively. Due to its unique expression pattern it is conceivable that this enzymes' activity might be exploited for a new therapeutic approach. However, the main challenge for a CYP4Z1-based prodrug strategy (CBPS) for the treatment of breast cancer (and possibly other CYP4Z1-positive malignancies) is the identification of candidate prodrugs that can be activated by this enzyme. In this mini-review we summarize the current knowledge about the enzymatic properties of the CYP4Z1 enzyme as well as on the expression pattern of the CYP4Z1 gene in both normal and cancer cells. Moreover, we present the first homology model of this enzyme and give an outlook on its potential use in cancer treatment strategies.