Exosomal microRNA concentrations in colorectal cancer: A mathematical model

Colorectal cancer (CRC) is the second leading cause of cancer related deaths in the United States. Early detection increases survival very significantly. Indeed, five year survival for people diagnosed at stage I-II is 90%, while for those diagnosed at stage IV it is only 13%. The gold standard for early detection is colonoscopy, but this procedure is limited due to its invasive nature and its high cost. Hence there is a need to identify non-invasive biomarkers for CRC. Exosomal miRs secreted by cancer cells and overexpressed in the blood have been suggested as biomarkers for cancer. In particular, exosomal miRs 21, 23a, 92a and 1246 are overexpressed in CRC, and thus have the potential to be used as serum biomarkers for early detection of the disease. The present paper develops for the first time a mathematical model for early stage of CRC which includes the effect of these miRs on the growth of the cancer. The model is represented by a system of partial differential equations. Simulations of the model show a relationship between the growth of the tumor diameter and the total mass of these miRs under some of the common mutations which occur in CRC, namely, KRAS, PI3K, APC, p53 and SMAD mutations. The model may serve as a step toward establishing miRs 21, 23a, 92a and 1246 as reliable blood biomarkers for CRC as more experimental results and clinical data become available.