Transition Yet Energy Consuming for Tumor Growth Regulated by the Colored Microenvironment

Transition or metastasis is a main characteristic of tumor developmental processes. However, the mechanism behind the transition and what costs involved are obscure when the tumor is exposed to a colored microscopic environment. Here, focusing on the regulatory role of noises from its strength and correlation time on phenotypic diversity of tumors, we show that (1) when the noise strength (NS) is fixed, extending the autocorrelation time (AT) of multiplicative noise can regulate bidirectionally the tumor phenotype, i.e., it can promote the diffusion also contribute to killing cancer cells simultaneously; (2) AT of additive noise can reduce the occurrence probability of cancer cells, but the NS can increase this probability; (3) the effect of the cross-correlated strength (CS) on cell phenotype is twofold, i.e., increasing CS may urge the mean first passage time (MFPT) of switching to the tumor state to have the minimum and maximum values but the cross-correlation time (CT) always makes the MFPT to have a minimum value. In addition, NS can make MFPT to have a peak. Moreover, by reconstructing the reaction network from the mesoscopic scale, we further show that AT of multiplicative noise can increase energy consumption, and there exists a trade-off between NS and AT of additive noise. We also show that the energy consumption is monotonically decreasing with increasing the CT but the CS can amplify the difference of this dependence. The overall analysis implies that tumor cells would make use of external noise to survive in fluctuating environments.