A mathematical model for the regulation of tumor dormancy based on enzyme kinetics

In this paper we present a two-compartment model for tumor dormancy based on an idea of Zetter [1998, Ann. Rev. Med. 49, 407-422] to wit: The vascularization of a secondary (daughter) tumor can be suppressed by an inhibitor originating from a larger primary (mother) tumor. We apply this idea at the avascular level to develop a model for the remote suppression of secondary avascular tumors via the secretion of primary avascular tumor inhibitors. The model gives good agreement with the observations of [De Giorgi et al., 2003, Derm. Surgery 29, 664-667]. These authors reported on the emergence of a polypoid melanoma at a site remote from a primary polypoid melanoma after excision of the latter. The authors observed no recurrence of the melanoma at the primary site, but did observe secondary tumors at secondary sites 5-7 cm from the primary site within a period of 1 month after the excision of the primary site. We attempt to provide a reasonable biochemical/cell biological model for this phenomenon. We show that when the tumors are sufficiently remote, the primary tumor will not influence the secondary tumor while, if they are too close together, the primary tumor can effectively prevent the growth of the secondary tumor, even after it is removed. It should be possible to use the model as the basis for a testable hypothesis.