Ovarian cancer is the most lethal cancer of the female reproductive system. In that regard, several epidemiological studies suggest that long‐term exposure to estrogen could increase ovarian cancer risk, although its precise role remains controversial. To decipher a mechanism for this, we previously generated a mathematical model of how estrogen‐mediated upregulation of the transcription factor, E2F6, upregulates the ovarian cancer stem/initiating cell marker, c‐Kit, by epigenetic silencing the tumor suppressor miR‐193a, and a competing endogenous (ceRNA) mechanism. In this study, we tested that previous mathematical model, showing that estrogen treatment of immortalized ovarian surface epithelial cells upregulated both E2F6 and c‐KIT, but downregulated miR‐193a. Luciferase assays further confirmed that microRNA‐193a targets both E2F6 and c‐Kit. Interestingly, ChIP‐PCR and bisulphite pyrosequencing showed that E2F6 also epigenetically suppresses miR‐193a, through recruitment of EZH2, and by a complex ceRNA mechanism in ovarian cancer cell lines. Importantly, cell line and animal experiments both confirmed that E2F6 promotes ovarian cancer stemness, whereas E2F6 or EZH2 depletion derepressed miR‐193a, which opposes cancer stemness, by alleviating DNA methylation and repressive chromatin. Finally, 118 ovarian cancer patients with miR‐193a promoter hypermethylation had poorer survival than those without hypermethylation. These results suggest that an estrogen‐mediated E2F6 ceRNA network epigenetically and competitively inhibits microRNA‐193a activity, promoting ovarian cancer stemness and tumorigenesis.

In this paper, we study a class of predator–prey systems of reaction–diffusion type. Specifically, we are interested in the dynamical behaviour for the solution with the initial distribution where the prey species is at the level of the carrying capacity, and the density of the predator species has compact support, or exponentially small tails near . Numerical evidence suggests that this will lead to the formation of a pair of diverging waves propagating outwards from the initial zone. Motivated by this phenomenon, we establish the existence of a family of travelling waves with the minimum speed. Unlike the previous studies, we do not use the shooting argument to show this. Instead, we apply an iteration process based on Berestycki et al 2005 ( Arch. Rational Mech. Anal. 178 57–80) to construct a set of super/sub-solutions. Since the underlying system does not enjoy the comparison principle, such a set of super/sub-solutions is not based on travelling waves, and in fact the super/sub-solutions depend on each other. With the aid of the set of super/sub-solutions, we can construct the solution of the truncated problem on the finite interval, which, via the limiting argument, can in turn generate the wave solution. There are several advantages to this approach. First, it can remove the technical assumptions on the diffusivities of the species in the existing literature. Second, this approach is of PDE type, and hence it can shed some light on the spreading phenomenon indicated by numerical simulation. In fact, we can compute the spreading speed of the predator species for a class of biologically acceptable initial distributions. Third, this approach might be applied to the study of waves in non-cooperative systems (i.e. a system without a comparison principle).

The dynamics of biochemical reaction networks are considered to be responsible for biological functions in living systems. Since real networks are immense and complicated, it is difficult to determine which reactions can cause a significant change of dynamical behaviors, namely, bifurcations. Also to what extent numerical results of network systems depend on the chosen kinetic rate parameters is not known. In this paper, an analytical setting that splits the information of the dynamics into the network structure and reaction kinetics is introduced. This setting possesses a factorization structure for some class of network systems which allows one to determine which subnetworks are responsible for the occurrence of a bifurcation. Subsequently, the bifurcation criteria are reformulated in a manner that allows the efficient determination of relevant reactions for bifurcations.

MicroRNAs (miRNAs) play an important role in gene regulation by degradation or translational inhibition of the targeted mRNAs. It has been experimentally shown that the way miRNAs interact with their targets can be used to explain the indirect interactions among their targets, i.e., competing endogenous RNA (ceRNA). However, whether the protein translated from the targeted mRNAs can play any role in this ceRNA network has not been explored. Here we propose a deterministic model to demonstrate that in a network of one miRNA interacting with multiple-targeted mRNAs, the competition between miRNA-targeted mRNAs is not sufficient for the significant change of those targeted mRNA levels, while dramatic changes of these miRNA-targeted mRNAs require transcriptional inhibition of miRNA by its target proteins. When applied to estrogen receptor signaling pathways, the miR-193a targets E2F6 (a target of estrogen receptor), c-KIT (a marker for cancer stemness), and PBX1 (a transcriptional activator for immunosuppressive cytokine, IL-10) in ovarian cancer, such that epigenetic silencing of miR-193a by E2F6 protein is required for the significant change of c-KIT and PBX1 mRNA level for cancer stemness and immunoevasion, respectively, in ovarian cancer carcinogenesis

Recently we have proposed a monostable reaction-diffusion system to explain the Neolithic transition from hunter-gatherer life to farmer life in Europe. The system is described by a three-component system for the populations of hunter-gatherer (H), sedentary farmer (F1) and migratory one (F2). The conversion between F1 and F2 is specified by such a way that if the total farmers F1 + F2 are overcrowded, F1 actively changes to F2, while if it is less crowded, the situation is vice versa. In order to include this property in the system, the system incorporates a critical parameter (say F0) depending on the development of farming technology in a monotonically increasing way. It determines whether the total farmers are either over crowded (F1 + F2 >F0) or less crowded (F1 + F2 cm(∞).