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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]

The prediction of protein complexes based on the protein interaction network is a fundamental task for the understanding of cellular life as well as the mechanisms underlying complex disease. A great number of methods have been developed to predict protein complexes based on protein–protein interaction (PPI) networks in recent years. However, because the high throughput data obtained from experimental biotechnology are incomplete, and usually contain a large number of spurious interactions, most of the network-based protein complex identification methods are sensitive to the reliability of the PPI network. In this paper, we propose a new method, Identification of Protein Complex based on Refined Protein Interaction Network (IPC-RPIN), which integrates the topology, gene expression profiles and GO functional annotation information to predict protein complexes from the reconstructed networks. To demonstrate the performance of the IPC-RPIN method, we evaluated the IPC-RPIN on three PPI networks of Saccharomycescerevisiae and compared it with four state-of-the-art methods. The simulation results show that the IPC-RPIN achieved a better result than the other methods on most of the measurements and is able to discover small protein complexes which have traditionally been neglected. [ABSTRACT FROM AUTHOR]

The controllability of multilayer networks has become increasingly important in many areas of science and engineering. In this paper, we identify the general rules that determine the controllability and control energy cost of multilayer networks. First, we quantitatively estimate the control energy cost of multilayer networks and investigate the impacts of different coupling strength and coupling patterns on the control energy cost for multilayer networks. The results indicate that the average energy and the coupling strength have an approximately linear relationship in multilayer networks with two layers. Second, we study how the coupling strength and the connection patterns between different layers affect the controllability of multilayer networks from both theoretical and numerical aspects. The obtained piecewise functional relations between the controllability's measure and coupling strength reveal the existence of an optimal coupling strength for the different interconnection strategies in multilayer networks. In particular, the numerical experiments demonstrate that there exists a tradeoff between the optimal controllability and optimal control energy for selecting interlayer connection patterns in multilayer networks. These results provide a comprehensive understanding of the impact of interlayer couplings on the controllability and control energy cost for multilayer networks and provide a methodology for selecting the control nodes and coupling strength to maximize the controllability and minimize the control energy cost. [ABSTRACT FROM AUTHOR]

Considerable evidence suggests that in complex diseases the deteriorations are often abrupt, and can be viewed as a bifurcation or a critical transition from one asymptotically stable equilibrium to another one at a tipping point. Here, we propose some new ideas to detect early-warning signals of such critical transitions from the perspective of qualitative theory of ordinary differential equations. Specifically, we theoretically derive three indicators that serve as a general early-warning signal indicating an imminent bifurcation or sudden deterioration before the critical transition occurs. Then, we verify our theoretical results by numerical simulations for three examples. Our work forms a starting point to motivate new mathematical insights into predictability for critical transitions of dynamical systems from a new perspective. [ABSTRACT FROM AUTHOR]

The controlling of complex networks is one of the most challenging problems in modern network science. Accordingly, the required energy cost of control is a fundamental and significant problem. In this paper, we present the theoretical analysis and numerical simulations to study the controllability of complex networks from the energy perspective. First, by combining theoretical derivation and numerical simulations, we obtain lower bounds of the maximal and minimal energy costs for an arbitrary normal network, which are related to the eigenvalues of the state transition matrix. Second, we deduce that controlling unstable normal networks is easier than controlling stable normal networks with the same size. Third, we demonstrate a tradeoff between the control energy and the average degree (or the maximum degree) of an arbitrary undirected network. Fourth, numerical simulations show that the energy cost is negatively correlated with the degree of nodes. Moreover, the combinations of control nodes with the greater sum of degree need less energy to implement complete control. Finally, we propose a multi-objective optimization model to obtain the control strategy, which not only ensures the fewer control nodes but also guarantees the less energy cost of control. [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]

In this paper, we investigate the complex dynamical behaviors of a biological network that is derived from innate immune responses and that couples positive and negative feedback loops. The stability conditions of the non-negative equilibrium points (EPs) of the system are obtained, using the theory of dynamical systems, and we deduce that no more than three stable EPs exist in this system. Through bifurcation analysis and numerical simulations, we find that the system presents rich dynamical behaviors, such as monostability, bistability and oscillations. These results reveal how positive and negative feedback cooperatively regulate the dynamical behavior of the system. [ABSTRACT FROM AUTHOR]