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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]

The ongoing coronavirus disease-2019 (COVID-19) pandemic caused by severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) has serious influences on human health and economy. The available clinical data suggest that patients infected by SARS-CoV-2 have the possibility of simultaneous infection of bacteria. In this study, we present a data-driven mathematical model for coinfection of SARS-CoV-2 and bacteria to investigate the dynamics of COVID-19 progress. Specifically, based on the statistical analysis of different clinical data from China and some other countries, a system model with ordinary differential equations (ODEs) in four variables, i.e. SARS-CoV-2, bacteria, neutrophils and lymphocytes, is established. We further validate our model through theoretical analysis and fitting of different clinical data. Moreover, through numerical simulations and bifurcation analysis, we find that bacterial infection and immune-related parameters in certain ranges lead to the system transitions among three steady states, i.e. mild, severe and death. We also analyzed the influence of the time it takes for patients to switch from a high-risk area to a low-risk area on the recovery time. These results reveal that the coinfection of viruses and bacteria can explain the changes in neutrophils and lymphocytes, and that initial bacterial infection and immune-related parameters have great influences on the severity degree and mortality in COVID-19 patients. Together, our model and quantitative analysis suggest that preventing bacterial infection and enhancing immune ability during the early phase of infections could be a potential treatment option for high-risk COVID-19 patients. [ABSTRACT FROM AUTHOR]

Single-cell RNA transcriptome data present a tremendous opportunity for studying the cellular heterogeneity. Identifying subpopulations based on scRNA-seq data is a hot topic in recent years, although many researchers have been focused on designing elegant computational methods for identifying new cell types; however, the performance of these methods is still unsatisfactory due to the high dimensionality, sparsity and noise of scRNA-seq data. In this study, we propose a new cell type detection method by learning a robust and accurate similarity matrix, named SCCLRR. The method simultaneously captures both global and local intrinsic properties of data based on a low rank representation (LRR) framework mathematical model. The integrated normalized Euclidean distance and cosine similarity are used to balance the intrinsic linear and nonlinear manifold of data in the local regularization term. To solve the non-convex optimization model, we present an iterative optimization procedure using the alternating direction method of multipliers (ADMM) algorithm. We evaluate the performance of the SCCLRR method on nine real scRNA-seq datasets and compare it with seven state-of-the-art methods. The simulation results show that the SCCLRR outperforms other methods and is robust and effective for clustering scRNA-seq data. (The code of SCCLRR is free available for academic https://github.com/wzhangwhu/SCCLRR). [ABSTRACT FROM AUTHOR]

Gag, as the major structural protein of HIV-1, is necessary for the assembly of the HIV-1 sphere shell. An in-depth understanding of its trafficking and polymerization is important for gaining further insights into the mechanisms of HIV-1 replication and the design of antiviral drugs. We developed a mathematical model to simulate two biophysical processes, specifically Gag monomer and dimer transport in the cytoplasm and the polymerization of monomers to form a hexamer underneath the plasma membrane. Using experimental data, an optimization approach was utilized to identify the model parameters, and the identifiability and sensitivity of these parameters were then analyzed. Using our model, we analyzed the weight of the pathways involved in the polymerization reactions and concluded that the predominant pathways for the formation of a hexamer might be the polymerization of two monomers to form a dimer, the polymerization of a dimer and a monomer to form a trimer, and the polymerization of two trimers to form a hexamer. We then deduced that the dimer and trimer intermediates might be crucial in hexamer formation. We also explored four theoretical combined methods for Gag suppression, and hypothesized that the N-terminal glycine residue of the MA domain of Gag might be a promising drug target. This work serves as a guide for future theoretical and experimental efforts aiming to understand HIV-1 Gag trafficking and polymerization, and might help accelerate the efficiency of anti-AIDS drug design. [ABSTRACT FROM AUTHOR]

With the increasing availability of high-throughput data, various computational methods have recently been developed for understanding the cell through protein-protein interaction (PPI) networks at a systems level. However, due to the incompleteness of the original PPI networks those efforts have been significantly hindered. In this paper, we propose a two stage method to predict underlying links between two originally unlinked protein pairs. First, we measure gene expression and gene functional similarly between unlinked protein pairs on Saccharomyces cerevisiae benchmark network and obtain new constructed networks. Then, we select the significant part of the new predicted links by analyzing the difference between essential proteins that have been identified based on the new constructed networks and the original network. Furthermore, we validate the performance of the new method by using the reliable and comprehensive PPI dataset obtained from the STRING database and compare the new proposed method with four other random walk-based methods. Comparing the results indicates that the new proposed strategy performs well in predicting underlying links. This study provides a general paradigm for predicting new interactions between protein pairs and offers new insights into identifying essential proteins. [ABSTRACT FROM AUTHOR]

This study is devoted to the revelation of the dynamical mechanisms of cell growth in response to antibiotics. We establish a mathematical model of ordinary differential equations for an antibiotic-resistant growth system with one positive feedback loop. We perform a dynamical analysis of the behavior of this model system. We present adequate sets of conditions that can guarantee the existence and stability of biologically-reasonable steady states. Using bifurcation analysis and numerical simulation, we show that the relative growth rate, which is defined as the ratio of the cell growth rate to the basal cell growth rate in the absence of antibiotics, can exhibit bistable behavior in an extensive range of parameters that correspond to a growth state and a nongrowth state in biology. We discover that both antibiotic and antibiotic resistance genes can cooperatively enhance bistability, whereas the cooperative coefficient of feedback can contribute to the onset of bistability. These results would contribute to a better understanding of not only the evolution of antibiotics but also the emergence of drug resistance in other diseases. [ABSTRACT FROM AUTHOR]

Abstract: The interferon system provides a powerful and universal intracellular defense mechanism against viruses. As one part of their survival strategies, many viruses have evolved mechanisms to counteract the host type I interferon (IFN-α/β) responses. In this study, we attempt to investigate virus- and double-strand RNA (dsRNA)-triggered type I IFN signaling pathways and understand the inhibition of IFN-α/β induction by viral proteins using mathematical modeling and quantitative analysis. Based on available literature and our experimental data, we develop a mathematical model of virus- and dsRNA-triggered signaling pathways leading to type I IFN gene expression during the primary response, and use the genetic algorithm to optimize all rate constants in the model. The consistency between numerical simulation results and biological experimental data demonstrates that our model is reasonable. Further, we use the model to predict the following phenomena: (1) the dose-dependent inhibition by classical swine fever virus (CSFV) Npro or Erns protein is observed at a low dose and can reach a saturation above a certain dose, not an increase; (2) Erns and Npro have no synergic inhibitory effects on IFN-β induction; (3) the different characters in an important transcription factor, phosphorylated IRF3 (IRF3p), are exhibited because Npro or Erns counteracted dsRNA- and virus-triggered IFN-β induction by targeting the different molecules in the signaling pathways and (4) Npro inhibits the IFN-β expression not only by interacting with IFR3 but also by affecting its complex with MITA. Our approaches help to gain insight into system properties and rational therapy design, as well as to generate hypotheses for further research. [Copyright &y& Elsevier]

• A new framework based on a dynamic optimization problem identifies the adaptive therapeutic schedule for prostate cancer. • A competitive model between drug-sensitive and drug-resistant cells is established and validated using available data. • The stability of equilibrium points and existence of a periodic solution indicate the feasibility of adaptive therapy. • Our therapeutic framework is superior to the current approaches in the total drug dose and the survival time. Adaptive therapy, a new therapeutic strategy, is increasingly applied in the treatment of cancer. According to the evolutionary game theory of cancer cells, adaptive therapy is understood as the dynamic regulation of cancer cells. However, it is a great challenge to identify the therapeutic period and dose in adaptive therapy. In this study, we establish a competitive model between drug-sensitive and drug-resistant cancer cells. Theoretical analysis, including the stability of equilibrium points and the existence of periodic solutions, validates the interpretability of the model. The available data for prostate cancers are used to identify the model parameters. Furthermore, we propose a new dynamic optimization problem with constraints to establish the adaptive therapeutic schedule for prostate cancer, and an optimal set of decisions in this optimization problem represents the therapeutic period and dose in adaptive therapy. Through numerical simulations and quantitative analysis, we compare our therapeutic schedule and current adaptive therapeutic schedules in patients with prostate cancer in three aspects: the total drug dose, the peak number of drug-resistant cancer cells and the survival time. These results demonstrate that our therapeutic framework is superior to the current adaptive therapeutic schedules. The proposed therapeutic framework could provide an identifiable adaptive therapy to achieve personal and precise treatment for prostate cancer. [ABSTRACT FROM AUTHOR]