Based on the transcriptional regulatory mechanisms between microRNA-200 and transcription factor ZEB in an individual cancer cell, a minimal dynamic model is proposed to study the epithelial-mesenchymal transition (EMT) and mesenchymal-epithelial transition (MET) processes of cancer cells. It is shown that each cancer cell can exit in any of three phenotypic states: the epithelial (E) state, the mesenchymal (M) state, and the epithelial/mesenchymal (E/M) hybrid state, and the state of cancer cell can interconvert between different states. The phase diagram shows that there are monostable, bistable, and tristable phenotypic states regions in a parameters plane. It is found that different pathway in the phase diagram can correspond to the EMT or the MET process of cancer cells, and there are two possible EMT processes. It is important that the experimental phenomenon of E/M hybrid state appearing in the EMT process but rather in the MET process can be understood through different pathways in the phase diagram. Our numerical simulations show that the effects of noise are opposite to these of time delay on the expression of transcription factor ZEB, and there is competition between noise and time delay in phenotypic transitions process of cancer cells.

In this paper we propose a mathematical model of bone remodeling with time delays of both osteoclast-derived paracrine signaling of tumor and tumor-derived paracrine signaling of osteoclast. The effects of time delays on the growth of tumor cells and bone system are studied in multiple myeloma-induced bone disease. In the case of small osteoclast-derived paracrine signaling, it is found that the growth of tumor cells slows down, the oscillation period of the ratio of osteoclasts to osteoblasts is extended with increasing time delay, and there is a competition between the delay and osteoclast-derived paracrine signaling. In the case of large tumor-derived paracrine signaling, the tumor-derived paracrine signaling can induce a more significant decline in tumor growth for long time delay, and thus slowing down the progression of bone disease. There is an optimal coupling between the tumor-derived paracrine signaling of osteoclasts and time delay during the progressions of bone diseases, which suppresses the tumor growth and the regression of bone disease.

The differential sensitivity to merocyanine 540 (MC540)-sensitized photoirradiation of leukemia cells, selected solid tumor cells, and normal pluripotent hematopoietic stem cells has been successfully exploited for the extracorporeal purging of simulated autologous remission bone marrow grafts. In this communication, we compare the effects of fractionated vs continuous irradiation upon the MC540-sensitized photoinactivation of L1210 and K562 leukemia cells. Exposure to MC540 (15 micrograms/mL) and fractionated doses of white light inactivated fewer in vitro clonogenic cells than exposure to an equivalent dose of continuous irradiation, provided the irradiation doses were small (8.1-16.2 kJ/m2) and spaced 1-2 h apart. The dye-sensitized photoinactivation of leukemia cells was enhanced when cells were stored at 4 degrees C instead of 37 degrees C between irradiation periods, most likely in part because the cells were unable to repair sublethal photodynamic damages at the lower temperature. These data suggest that cells can recover from sublethal damage inflicted by the plasma membrane-active photosensitizer, MC540.