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Single cell technologies provide an unprecedented opportunity to explore the heterogeneity in a biological process at the level of single cells. One major challenge in analyzing single cell data is to identify cell subpopulations, stable cell states, and cells in transition between states. To elucidate the transition mechanisms in cell fate dynamics, it is highly desirable to quantitatively characterize cellular states and intermediate states. Here, we present scRCMF, an unsupervised method that identifies stable cell states and transition cells by adopting a nonlinear optimization model that infers the latent substructures from a gene-cell matrix. We incorporate a random coefficient matrix-based regularization into the standard nonnegative matrix decomposition model to improve the reliability and stability of estimating latent substructures. To quantify the transition capability of each cell, we propose two new measures: single-cell transition entropy (scEntropy) and transition probability (scTP). When applied to two simulated and three published scRNA-seq datasets, scRCMF not only successfully captures multiple subpopulations and transition processes in large-scale data, but also identifies transition states and some known marker genes associated with cell state transitions and subpopulations. Furthermore, the quantity scEntropy is found to be significantly higher for transition cells than other cellular states during the global differentiation, and the scTP predicts the "fate decisions" of transition cells within the transition. The present study provides new insights into transition events during differentiation and development.

As a new tumor therapeutic strategy, adaptive therapy involves utilizing the competition between cancer cells to suppress the growth of drug-resistant cells, maintaining a certain tumor burden. However, it is difficult to determine the appropriate time and drug dose. In this paper, we consider the competition model between drug-sensitive cells and drug-resistant cells, propose the problem of drug concentration, and provide two state constraints: the upper limit of the maximum allowable drug concentration and the tumor burden. Using relevant theories, we propose the best treatment strategy. Through a numerical simulation and quantitative analysis, the effects of drug concentrations and different tumor burdens on treatments are studied, and the effects of cell-to-cell competitive advantage on cell changes are taken into account. The clinical dose titration method is further simulated; the results show that our therapeutic regimen can better suppress the growth of drug-resistant cells, control the tumor burden, limit drug toxicity, and extend the effective treatment time. [ABSTRACT FROM AUTHOR]

It is of critical importance to comprehend the biological environment and core tumor populations when trying to design successful therapeutic solutions for fighting cancers. In several diseases, G9a has been recognized as a novel epigenetic therapeutic target, and its blockage can shift tumor cells (TCs) toward tumor propagating cells (TPCs). This study combines mathematical modeling based on ordinary differential equations and dynamical analysis to quantitatively and qualitatively understand the interactions among G9a, TCs, and TPCs, denoted as G9a-TC-TPC. We propose four different dynamical systems with the impact of the strong Allee effect, named the Hill–Hill system, Logistic–Logistic system, Hill–Logistic system and Logistic–Hill system, to simulate different biological processes through the Hill functions and the Logistic functions that are often used in the models of biological systems. Based on theoretical analysis of these models, including the positivity, boundedness and stability of equilibria, we find that the Hill–Logistic system can display bistable states that correspond to the wild-type tumors and the aggressive tumors. Consequently, we use bifurcation analysis and numerical simulations to illustrate the complicated dynamical behavior of this system. It has been shown that under a specific therapy that changes the relative apoptotic rate of TCs (G9a suppresses the apoptosis of TCs), which can affect the bistability and instability of the system, the wide-type state can be obtained. We also discover that the relative handling time of TCs and TPCs can cooperatively enhance bistability, whereas the cooperative coefficient of feedback can contribute to all tumor cells moving from high-level monostability to bistable states in a restricted region, then to low-level stable states. These results offer new insights for more precisely understanding epigenetic therapy treatments with G9a. [ABSTRACT FROM AUTHOR]