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Alternative splicing makes significant contributions to functional diversity of transcripts and proteins. Many alternatively spliced gene isoforms have been shown to perform specific biological functions under different contexts. In addition to gene-level expression, the advances of high-throughput sequencing offer a chance to estimate isoform-specific exon expression with a high resolution, which is informative for studying splice variants with network analysis. In this study, we propose a novel network-based analysis framework to predict isoform-specific functions from exon-level RNA-Seq data. In particular, based on exon-level expression data, we firstly propose a unified framework, referred to as Iso-Net , to integrate two new mathematical methods (named MINet and RVNet) that infer co-expression networks at different data scenarios. We demonstrate the superior prediction accuracy of Iso-Net over the existing methods for most simulation data, especially in two extreme cases: sample size is very small and exon numbers of two isoforms are quite different. Furthermore, by defining relevant quantitative measures (e.g., Jaccard correlation coefficient) and combining differential co-expression network analysis and GO functional enrichment analysis, a co-expression network analysis framework is developed to predict functions of isoforms and further, to discover their distinct functions within the same gene. We apply Iso-Net to study gene isoforms for several important transcription factors in human myeloid differentiation with the exon-level RNA-Seq data from three different cell lines. Iso-Net is open source and freely available from https://github.com/Dingjie-Wang/Iso-Net. [ABSTRACT FROM AUTHOR]

The assembly of the HIV-1 immature capsid (HIC) is an essential step in the virus life cycle. In vivo, the HIC is composed of ∼ 420 hexameric building blocks, and it takes 5–6 min to complete the assembly process. The involvement of numerous building blocks and the rapid timecourse makes it difficult to understand the HIC assembly process. In this work, we study HIC assembly in vivo by using differential equations. We first obtain a full model with 420 differential equations. Then, we reduce six addition reactions for separate building blocks to a single complex reaction. This strategy reduces the full model to 70 equations. Subsequently, the theoretical analysis of the reduced model shows that it might not be an effective way to decrease the HIC concentration at the equilibrium state by decreasing the microscopic on-rate constants. Based on experimental data, we estimate that the nucleating structure is much smaller than the HIC. We also estimate that the microscopic on-rate constant for nucleation reactions is far less than that for elongation reactions. The parametric collinearity investigation testifies the reliability of these two characteristics, which might explain why free building blocks do not readily polymerize into higher-order polymers until their concentration reaches a threshold value. These results can provide further insight into the assembly mechanisms of the HIC in vivo. [ABSTRACT FROM AUTHOR]

One challenging issue in information science, biological systems and many other field is to determine the most central agents in multilayer networked systems characterized by different types of interrelationships. In this paper, using a fourth-order tensor to represent multilayer networks, we propose a new centrality measure, referred to as the Singular Vector of Tensor (SVT) centrality, which is used to quantitatively evaluate the importance of nodes connected by different types of links in multilayer networks. First, we present a novel iterative method to obtain four alternative metrics that can quantify the hub and authority scores of nodes and layers in multilayer networked systems. Moreover, we use the theory of multilinear algebra to prove that the four metrics converge to four singular vectors of the adjacency tensor of the multilayer network under reasonable conditions. Furthermore, a novel SVT centrality measure is obtained by integrating these four metrics. The experimental results demonstrate that the proposed method is a new centrality measure that significantly outperforms six other published centrality methods on two real-world multilayer networks related to complex diseases, i.e., gastric and colon cancers. [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]

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]

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]

Innate immune response plays an important role in control and clearance of pathogens following viral infection. However, in the majority of virus-infected individuals, the response is insufficient because viruses are known to use different evasion strategies to escape immune response. In this study, we use optimal control theory to investigate how to control the innate immune response. We present an optimal control model based on an ordinary-differential-equation system from a previous study, which investigated the dynamics and regulation of virus-triggered innate immune signaling pathways, and we prove the existence of a solution to the optimal control problem involving antiviral treatment or/and interferon therapy. We conduct numerical experiments to investigate the treatment effects of different control strategies through varying the cost function and control efficiency. The results show that a separate treatment, that is, only inhibiting viral replication (u1(t)) or enhancing interferon activity (u2(t)), has more advantages for controlling viral infection than a mixed treatment, that is, controlling both (u1(t)) and (u2(t)) simultaneously, including the smallest cost and operability. These findings would provide new insight for developing effective strategies for treatment of viral infectious 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]

For the global optimization problems with continuous variables, evolutionary algorithms (EAs) are often used to find the approximate solutions. The number of generations for an EA to find the approximate solutions, called the first hitting time, is an important index to measure the performance of the EA. However, calculating the first hitting time is still difficult in theory. This paper proposes some new drift conditions that are used to estimate the upper bound of the first hitting times of EAs for finding the approximate solutions. Two case studies are given to show how to apply these conditions to estimate the first hitting times. [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]

Abstract: Cells sense several kinds of stimuli and trigger corresponding responses through signaling pathways. As a result, cells must process and integrate multiple signals in parallel to maintain specificity and avoid erroneous cross-talk. In this study, we focus our theoretical effort on understanding specificity of a model network system in yeast, Saccharomyces cerevisiae, which contains three mitogen-activated protein kinase (MAPK) signal transduction cascades that share multiple signaling components. The cellular response to the pheromone, the filamentous growth and osmotic pressure stimuli in yeast is described and an integrative mathematical model for the three MAPK cascades is developed using available literature and experimental data. The theoretical framework for analyzing the specificity of signaling networks [Bardwell, L., Zou, X.F., Nie, Q., Komarova, N.L., 2007. Mathematical models of specificity in cell signaling. Biophys. J. 92, 3425–3441] is extended to include multiple interacting pathways with shared components. Simulations are also performed with any one stimulus, with any two simultaneous stimuli, and with the simultaneous application of the three stimuli. The interactions between the three pathways are systematically investigated. Moreover, the specificity and fidelity of this model system are calculated using our newly developed concept under different stimuli or with specific mutants. Our simulated and calculated results demonstrate that the yeast MAPK signaling network can achieve specificity and fidelity by filtering out spurious cross-talk between the relevant pathways through different mechanisms, such as scaffolding, cross-inhibiting, and feedback control. Proof that Pbs2 and Hog1 are essential for the maintenance of signaling specificity is presented. Our studies provide novel insights into integration of relevant signaling pathways in a biological system and the mechanisms conferring specificity in cellular signaling networks. [Copyright &y& Elsevier]

Abstract: Robustness, the ability to maintain performance in the face of perturbations and uncertainty, is believed to be a necessary property of biological systems. In this paper, we address the issue of robustness in an important signal transduction network—epidermal growth factor receptor (EGFR) network. First, we analyze the robustness in the EGFR signaling network using all rate constants against the Gauss variation which was described as “the reference parameter set” in the previous study [Kholodenko, B.N., Demin, O.V., Moehren, G., Hoek, J.B., 1999. Quantification of short term signaling by the epidermal growth factor receptor. J. Biol. Chem. 274, 30169–30181]. The simulation results show that signal time, signal duration and signal amplitude of the EGRR signaling network are relatively not robust against the simultaneous variation of the reference parameter set. Second, robustness is quantified using some statistical quantities. Finally, a multi-objective evolutionary algorithm (MOEA) is presented to search reaction rate constants which optimize the robustness of network and compared with the NSGA-II, which is a representation of a class of modern multi-objective evolutionary algorithms. Our simulation results demonstrate that signal time, signal duration and signal amplitude of the four key components – the most downstream variable in each of the pathways: R–Sh–G–S, R–PLP, R–G–S and the phosphorylated receptor RP in EGRR signaling network for the optimized parameter sets have better robustness than those for the reference parameter set and the NSGA-II. These results can provide valuable insight into experimental designs and the dynamics of the signal-response relationship between the dimerized and activated EGFR and the activation of downstream proteins. [Copyright &y& Elsevier]

Different cellular signal transduction pathways are often interconnected, so that the potential for undesirable crosstalk between pathways exists. Nevertheless, signaling networks have evolved that maintain specificity from signal to cellular response. Here, we develop a framework for the analysis of networks containing two or more interconnected signaling pathways. We define two properties, specificity and fidelity, that all pathways in a network must possess in order to avoid paradoxical situations where one pathway activates another pathway's output, or responds to another pathway's input, more than its own. In unembellished networks that share components, it is impossible for all pathways to have both mutual specificity and mutual fidelity. However, inclusion of either of two related insulating mechanisms—compartmentalization or the action of a scaffold protein—allows both properties to be achieved, provided deactivation rates are fast compared to exchange rates. [ABSTRACT FROM AUTHOR]

In this article, we propose a fast annealing genetic algorithm (FAGA), based on the principle of the minimal free energy in statistical physics, for solving multi-objective optimization problems. The novelties of FAGA are: (1) providing a new fitness assignment strategy by combining Pareto-dominance relation and Gibbs entropy, (2) introducing a new criterion for selection of new individuals to maintain the diversity of the population. We make many experiments to measure the performance of the proposed FAGA, and estimate its convergence rate for a number of test problems. Simulation results show that the FAGA is a very fast and effective algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new dynamical evolutionary algorithm (DEA) that aims to find the global optimum and give the theoretical explanation from statistical mechanics. The algorithm has been evaluated numerically using a wide set of test functions which are nonlinear, multimodal and multidimensional. The numerical results show that it is possible to obtain global optimum or more accurate solutions than other methods for the investigated hard problems. [ABSTRACT FROM AUTHOR]

The tumor microenvironment (TME) exerts key effects on tumor development, progression and treatment. Therefore, a quantitative understanding of various cellular and molecular interactions in the TME is very important. In this study, we combined a dynamic model and data analysis to quantitatively explore how microenvironmental factors influence tumor growth and three phases of cancer immunoediting. First, we presented a model system of partial differential equations (PDEs) using four main types of cells within the microenvironment of solid tumors and used two sets of published experimental data to validate the model. Accordingly, the partial rank correlation coefficient (PRCC) was calculated to identify the sensitive parameters related to significant biological processes. Furthermore, numerical simulations indicated that the power of tumor proliferation exerts a substantial effect on the state of malignancy, but tumor control is achieved by adjusting sensitive microenvironmental factors, such as immune intensity and the proliferation of cancer-associated fibroblasts (CAFs). Moreover, we used two indicators to quantify three states, i.e., elimination, equilibrium and escape from cancer immunoediting. The quantitative analysis of the TME revealed that immune cells and CAFs dynamically guide the transition of the three states of immunoediting, namely, how these related factors affect the capacity of the immune system to eliminate developing tumor cells, hold them in an equilibrium state, or facilitate their expanded growth. These quantitative results provide new insights into how various microenvironmental changes mediate both natural and therapeutically induced cancer immunoediting responses. [ABSTRACT FROM AUTHOR]

Hepatitis E, as a zoonotic disease, has been a great challenge to global public health. Therefore, it has important research value and practical significance for the transmission and control of hepatitis E virus (HEV). In the exploration of infectious disease transmission dynamics and optimal control, mathematical models are often applied. Among them, the fractional differential model has become an important and practical tool because of its good memory and genetic characteristics. In this paper, an HEV propagation dynamic model is constructed by the Caputo fractional derivative. First, the properties of the model are analyzed, including the existence, non-negativity, boundedness, and stability of the equilibrium points. Then, from the perspective of fractional optimal control (FOC), control measures were proposed, including improving the awareness and prevention of hepatitis E among susceptible people, strengthening the treatment of infected people, and improving environmental hygiene. Then, an FOC model of HEV was constructed. After analyzing the necessary conditions for optimality, the particle swarm optimization is introduced to optimize the control function. In addition, four control strategies are applied. Finally, the numerical simulation is completed by the fractional Adams–Bashforth–Moulton prediction correction algorithm. The four strategies and no control were compared and analyzed. The numerical simulation results of different fractional orders are also compared and analyzed. The results illustrate that the optimal strategy, compared with no control, reduces the HEV control time by nearly 60 days. Therefore, this method would contribute to the study of HEV transmission dynamics and control mechanisms, thus contributing to the development of global public health. [ABSTRACT FROM AUTHOR]

Disease development and cell differentiation both involve dynamic changes; therefore, the reconstruction of dynamic gene regulatory networks (DGRNs) is an important but difficult problem in systems biology. With recent technical advances in single-cell RNA sequencing (scRNA-seq), large volumes of scRNA-seq data are being obtained for various processes. However, most current methods of inferring DGRNs from bulk samples may not be suitable for scRNA-seq data. In this work, we present scPADGRN, a novel DGRN inference method using "time-series" scRNA-seq data. scPADGRN combines the preconditioned alternating direction method of multipliers with cell clustering for DGRN reconstruction. It exhibits advantages in accuracy, robustness and fast convergence. Moreover, a quantitative index called Differentiation Genes' Interaction Enrichment (DGIE) is presented to quantify the interaction enrichment of genes related to differentiation. From the DGIE scores of relevant subnetworks, we infer that the functions of embryonic stem (ES) cells are most active initially and may gradually fade over time. The communication strength of known contributing genes that facilitate cell differentiation increases from ES cells to terminally differentiated cells. We also identify several genes responsible for the changes in the DGIE scores occurring during cell differentiation based on three real single-cell datasets. Our results demonstrate that single-cell analyses based on network inference coupled with quantitative computations can reveal key transcriptional regulators involved in cell differentiation and disease development. Author summary: Single-cell RNA sequencing (scRNA-seq) data are gaining popularity for providing access to cell-level measurements. Currently, time-series scRNA-seq data allow researchers to study dynamic changes during biological processes. This work proposes a novel method, scPADGRN, for application to time-series scRNA-seq data to construct dynamic gene regulatory networks, which are informative for investigating dynamic changes during disease development and cell differentiation. The proposed method shows satisfactory performance on both simulated data and three real datasets concerning cell differentiation. To quantify network dynamics, we present a quantitative index, DGIE, to measure the degree of activity of a certain set of genes in a regulatory network. Quantitative computations based on dynamic networks identify key regulators in cell differentiation and reveal the activity states of the identified regulators. Specifically, Bhlhe40, Msx2, Foxa2 and Dnmt3l might be important regulatory genes involved in differentiation from mouse ES cells to primitive endoderm (PrE) cells. For differentiation from mouse embryonic fibroblast cells to myocytes, Scx, Fos and Tcf12 are suggested to be key regulators. Sox5, Meis2, Hoxb3, Tcf7l1 and Plagl1 critically contribute during differentiation from human ES cells to definitive endoderm cells. These results may guide further theoretical and experimental efforts to understand cell differentiation processes and explore cell heterogeneity. [ABSTRACT FROM AUTHOR]

Background: Networks have been widely used to model the structures of various biological systems. The ultimate aim of research on biological networks is to steer biological system structures to desired states by manipulating signals. Despite great advances in the linear control of single-layer networks, it has been observed that many complex biological systems have a multilayer networked structure and extremely complicated nonlinear processes. Result: In this study, we propose a general framework for controlling nonlinear dynamical systems with multilayer networked structures by formulating the problem as a minimum union optimization problem. In particular, we offer a novel approach for identifying the minimal driver nodes that can steer a multilayered nonlinear dynamical system toward any desired dynamical attractor. Three disease-related biology multilayer networks are used to demonstrate the effectiveness of our approaches. Moreover, in the set of minimum driver nodes identified by the algorithm we proposed, we confirmed that some nodes can act as drug targets in the biological experiments. Other nodes have not been reported as drug targets; however, they are also involved in important biological processes from existing literature. Conclusions: The proposed method could be a promising tool for determining higher drug target enrichment or more meaningful steering nodes for studying complex diseases. [ABSTRACT FROM AUTHOR]

Background: Endometrial Cancer (EC) is one of the most prevalent malignancies that affect the female population globally. In the context of immunotherapy, Tumor Mutation Burden (TMB) in the DNA polymerase epsilon (POLE) subtype of this cancer holds promise as a viable therapeutic target. Methods: We devised a method known as NEM-TIE to forecast the TMB status of patients with endometrial cancer. This approach utilized a combination of the Network Evolution Model, Transfer Information Entropy, Clique Percolation (CP) methodology, and Support Vector Machine (SVM) classification. To construct the Network Evolution Model, we employed an adjacency matrix that utilized transfer information entropy to assess the information gain between nodes of radiomic-clinical features. Subsequently, using the CP algorithm, we unearthed potentially pivotal modules in the Network Evolution Model. Finally, the SVM classifier extracted essential features from the module set. Results: Upon analyzing the importance of modules, we discovered that the dependence count energy in tumor volumes-of-interest holds immense significance in distinguishing TMB statuses among patients with endometrial cancer. Using the 13 radiomic-clinical features extracted via NEM-TIE, we demonstrated that the area under the receiver operating characteristic curve (AUROC) in the test set is 0.98 (95% confidence interval: 0.95–1.00), surpassing the performance of existing techniques such as the mRMR and Laplacian methods. Conclusions: Our study proposed the NEM-TIE method as a means to identify the TMB status of patients with endometrial cancer. The integration of radiomic-clinical data utilizing the NEM-TIE method may offer a novel technology for supplementary diagnosis. [ABSTRACT FROM AUTHOR]

Inference of the biochemical systems (BSs) via experimental data is important for understanding how biochemical components in vivo interact with each other. However, it is not a trivial task because BSs usually function with complex and nonlinear dynamics. As a popular ordinary equation (ODE) model, the S-System describes the dynamical properties of BSs by incorporating the power rule of biochemical reactions but behaves as a challenge because it has a lot of parameters to be confirmed. This work is dedicated to proposing a general method for inference of S-Systems by experimental data, using a biobjective optimization (BOO) model and a specially mixed-variable multiobjective evolutionary algorithm (mv-MOEA). Regarding that BSs are sparse in common sense, we introduce binary variables indicating network connections to eliminate the difficulty of threshold presetting and take data fitting error and the L0-norm as two objectives to be minimized in the BOO model. Then, a selection procedure that automatically runs tradeoff between two objectives is employed to choose final inference results from the obtained nondominated solutions of the mv-MOEA. Inference results of the investigated networks demonstrate that our method can identify their dynamical properties well, although the automatic selection procedure sometimes ignores some weak connections in BSs. [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]

Although differential evolution (DE) algorithms perform well on a large variety of complicated optimization problems, only a few theoretical studies are focused on the working principle of DE algorithms. To make the first attempt to reveal the function of binomial crossover, this paper aims to answer whether it can reduce the approximation error of evolutionary algorithms. By investigating the expected approximation error and the probability of not finding the optimum, we conduct a case study comparing two evolutionary algorithms with and without binomial crossover on two classical benchmark problems: OneMax and Deceptive. It is proven that using binomial crossover leads to the dominance of transition matrices. As a result, the algorithm with binomial crossover asymptotically outperforms that without crossover on both OneMax and Deceptive, and outperforms on OneMax, however, not on Deceptive. Furthermore, an adaptive parameter strategy is proposed which can strengthen the superiority of binomial crossover on Deceptive. [ABSTRACT FROM AUTHOR]

• 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]

The reconstruction of gene regulatory networks (GRNs) from high-throughput experimental data has been considered one of the most important issues in systems biology research. With the development of high-throughput technology and the complexity of biological problems, we need to reconstruct GRNs that contain thousands of genes. However, when many existing algorithms are used to handle these large-scale problems, they will encounter two important issues: low accuracy and high computational cost. To overcome these difficulties, the main goal of this study is to design an effective parallel algorithm to infer large-scale GRNs based on high-performance parallel computing environments. In this study, we proposed a novel asynchronous parallel framework to improve the accuracy and lower the time complexity of large-scale GRN inference by combining splitting technology and ordinary differential equation (ODE)-based optimization. The presented algorithm uses the sparsity and modularity of GRNs to split whole large-scale GRNs into many small-scale modular subnetworks. Through the ODE-based optimization of all subnetworks in parallel and their asynchronous communications, we can easily obtain the parameters of the whole network. To test the performance of the proposed approach, we used well-known benchmark datasets from Dialogue for Reverse Engineering Assessments and Methods challenge (DREAM), experimentally determined GRN of Escherichia coli and one published dataset that contains more than 10 thousand genes to compare the proposed approach with several popular algorithms on the same high-performance computing environments in terms of both accuracy and time complexity. The numerical results demonstrate that our parallel algorithm exhibits obvious superiority in inferring large-scale GRNs. [ABSTRACT FROM AUTHOR]

Although real-coded differential evolution (DE) algorithms can perform well on continuous optimization problems (CoOPs), designing an efficient binary-coded DE algorithm is still a challenging task. Inspired by the learning mechanism in particle swarm optimization (PSO) algorithms, we propose a binary learning differential evolution (BLDE) algorithm that can efficiently locate the global optimal solutions by learning from the last population. Then, we theoretically prove the global convergence of BLDE, and compare it with some existing binary-coded evolutionary algorithms (EAs) via numerical experiments. Numerical results show that BLDE is competitive with the compared EAs. Further study is performed via the change curves of a renewal metric and a refinement metric to investigate why BLDE cannot outperform some compared EAs for several selected benchmark problems. Finally, we employ BLDE in solving the unit commitment problem (UCP) in power systems to show its applicability to practical problems. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) has been used to solve real-parameter optimization problems with nonlinear and multimodal functions for more than a decade of years. However, it is pointed out that this classical DE harbors restricted efficiency and limited local search ability. Inspired by that gradient-based algorithms have powerful local search ability, we propose a new algorithm, which is diversity-maintained DE based on gradient local search (namely, DMGBDE), by incorporating approximate gradient-based algorithms into the DE search while maintaining the diversity of the population. The primary novelties of the proposed DMGBDE are the following: (1) the gradient-based algorithm is embedded into DE in a different manner and (2) a diversity-maintained mutation is introduced to slow down the learning procedure from the searched best individual. We conduct numerical experiments with a number of benchmark problems to measure the performance of the proposed DMGBDE. Simulation results show that the proposed DMGBDE outperforms classical DE and variant without gradient local search or diversity-based mutation. Moreover, comparison with some other recently reported approaches indicates that our proposed DMGBDE is rather competitive. [ABSTRACT FROM AUTHOR]

Owing to the heterogeneity in the evolution of cancer, distinguishing between diverse growth patterns and predicting long-term outcomes based on short-term measurements poses a great challenge. A novel multiscale framework is proposed to unravel the connections between the population dynamics of cancer growth (i.e., aggressive, bounded, and indolent) and the cellular-subclonal dynamics of cancer evolution. This framework employs the non-negative lasso (NN-LASSO) algorithm to forge a link between an ordinary differential equation (ODE)-based population model and a cellular evolution model. The findings of our current work not only affirm the impact of subclonal composition on growth dynamics but also identify two significant subclones within heterogeneous growth patterns. Moreover, the subclonal compositions at the initial time are able to accurately discriminate diverse growth patterns through a machine learning algorithm. The proposed multiscale framework successfully delineates the intricate landscape of cancer evolution, bridging the gap between long-term growth dynamics and short-term measurements, both in simulated and real-world data. This methodology provides a novel avenue for thorough exploration into the realm of cancer evolution. [Display omitted] • A mathematical framework to link the population dynamics and the subclonal dynamics. • The predicted evolutionary landscape reveals the importance of subclonal composition. • Short-term measurements prove effective in predicting long-term growth patterns. [ABSTRACT FROM AUTHOR]

Patients with coronavirus disease 2019 (COVID-19) often exhibit diverse disease progressions associated with various infectious ability, symptoms, and clinical treatments. To systematically and thoroughly understand the heterogeneous progression of COVID-19, we developed a multi-scale computational model to quantitatively understand the heterogeneous progression of COVID-19 patients infected with severe acute respiratory syndrome (SARS)-like coronavirus (SARS-CoV-2). The model consists of intracellular viral dynamics, multicellular infection process, and immune responses, and was formulated using a combination of differential equations and stochastic modeling. By integrating multi-source clinical data with model analysis, we quantified individual heterogeneity using two indexes, i.e., the ratio of infected cells and incubation period. Specifically, our simulations revealed that increasing the host antiviral state or virus induced type I interferon (IFN) production rate can prolong the incubation period and postpone the transition from asymptomatic to symptomatic outcomes. We further identified the threshold dynamics of T cell exhaustion in the transition between mild-moderate and severe symptoms, and that patients with severe symptoms exhibited a lack of naïve T cells at a late stage. In addition, we quantified the efficacy of treating COVID-19 patients and investigated the effects of various therapeutic strategies. Simulations results suggested that single antiviral therapy is sufficient for moderate patients, while combination therapies and prevention of T cell exhaustion are needed for severe patients. These results highlight the critical roles of IFN and T cell responses in regulating the stage transition during COVID-19 progression. Our study reveals a quantitative relationship underpinning the heterogeneity of transition stage during COVID-19 progression and can provide a potential guidance for personalized therapy in COVID-19 patients. Author summary: Coronavirus disease 2019 (COVID-19) is currently destroying both lives and economies. However, patients infected with severe acute respiratory syndrome (SARS)-like coronavirus (SARS-CoV-2) usually present heterogeneous and complicated progressions, such as different incubation periods (short and long), symptoms (asymptomatic and symptomatic) and severity (mild-moderate and severe). Currently, various clinical data and experimental data are available from different countries, which has great significance for integrating different types of data to comprehensively understand the diverse disease progression in COVID-19 patients and guide individual treatment strategies. Here, we developed a multi-scale computational model to describe the dynamical process of patients infected with SARS-CoV-2, including intracellular viral dynamics, multicellular infection process, and immune responses. By combining data integration, stochastic simulation and quantitative analysis based on the multi-scale mathematical model, we addressed an important question regarding how IFN response and T cell exhaustion quantitatively affect heterogeneous progression in patients with respect to incubation periods, symptoms and severity. Furthermore, the efficacy of various therapeutic strategies for treating COVID-19 patients with different severity degrees was evaluated and validated. The computational framework in this study can also be extended to explore the dynamical process of other coronavirus infections. [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]

Background: With the advance of high throughput sequencing, high-dimensional data are generated. Detecting dependence/correlation between these datasets is becoming one of most important issues in multi-dimensional data integration and co-expression network construction. RNA-sequencing data is widely used to construct gene regulatory networks. Such networks could be more accurate when methylation data, copy number aberration data and other types of data are introduced. Consequently, a general index for detecting relationships between high-dimensional data is indispensable. Results: We proposed a Kernel-Based RV-coefficient, named KBRV, for testing both linear and nonlinear correlation between two matrices by introducing kernel functions into RV2 (the modified RV-coefficient). Permutation test and other validation methods were used on simulated data to test the significance and rationality of KBRV. In order to demonstrate the advantages of KBRV in constructing gene regulatory networks, we applied this index on real datasets (ovarian cancer datasets and exon-level RNA-Seq data in human myeloid differentiation) to illustrate its superiority over vector correlation. Conclusions: We concluded that KBRV is an efficient index for detecting both linear and nonlinear relationships in high dimensional data. The correlation method for high dimensional data has possible applications in the construction of gene regulatory network. [ABSTRACT FROM AUTHOR]

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. [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]

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]

Recently, controllability of complex networks has attracted enormous attention in various fields of science and engineering. How to optimize structural controllability has also become a significant issue. Previous studies have shown that an appropriate directional assignment can improve structural controllability; however, the evolution of the structural controllability of complex networks under attacks and cascading has always been ignored. To address this problem, this study proposes a new edge orientation method (NEOM) based on residual degree that changes the link direction while conserving topology and directionality. By comparing the results with those of previous methods in two random graph models and several realistic networks, our proposed approach is demonstrated to be an effective and competitive method for improving the structural controllability of complex networks. Moreover, numerical simulations show that our method is near-optimal in optimizing structural controllability. Strikingly, compared to the original network, our method maintains the structural controllability of the network under attacks and cascading, indicating that the NEOM can also enhance the robustness of controllability of networks. These results alter the view of the nature of controllability in complex networks, change the understanding of structural controllability and affect the design of network models to control such networks. [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]

The early diagnosis and investigation of the pathogenic mechanisms of complex diseases are the most challenging problems in the fields of biology and medicine. Network-based systems biology is an important technique for the study of complex diseases. The present study constructed dynamic protein-protein interaction (PPI) networks to identify dynamical network biomarkers (DNBs) and analyze the underlying mechanisms of complex diseases from a systems level. We developed a model-based framework for the construction of a series of time-sequenced networks by integrating high-throughput gene expression data into PPI data. By combining the dynamic networks and molecular modules, we identified significant DNBs for four complex diseases, including influenza caused by either H3N2 or H1N1, acute lung injury and type 2 diabetes mellitus, which can serve as warning signals for disease deterioration. Function and pathway analyses revealed that the identified DNBs were significantly enriched during key events in early disease development. Correlation and information flow analyses revealed that DNBs effectively discriminated between different disease processes and that dysfunctional regulation and disproportional information flow may contribute to the increased disease severity. This study provides a general paradigm for revealing the deterioration mechanisms of complex diseases and offers new insights into their early diagnoses. [ABSTRACT FROM AUTHOR]