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Recent studies have utilized evolutionary mechanisms to impede the emergence of drug-resistant populations. In this paper, we develop a mathematical model that integrates hormonal treatment, immunotherapy, and the interactions among three cell types: drug-sensitive cancer cells, drug-resistant cancer cells and immune effector cells. Dynamical analysis is performed, examining the existence and stability of equilibria, thereby confirming the model's interpretability. Model parameters are calibrated using available prostate cancer data and literature. Through bifurcation analysis for drug sensitivity under different immune effector cells recruitment responses, we find that resistant cancer cells grow rapidly under weak recruitment response, maintain at a low level under strong recruitment response, and both may occur under moderate recruitment response. To quantify the competitiveness of sensitive and resistant cells, we introduce the comprehensive measures R 1 and R 2 , respectively, which determine the outcome of competition. Additionally, we introduce the quantitative indicators C I E 1 and C I E 2 as comprehensive measures of the immune effects on sensitive and resistant cancer cells, respectively. These two indicators determine whether the corresponding cancer cells can maintain at a low level. Our work shows that the immune system is an important factor affecting the evolution of drug resistance and provides insights into how to enhance immune response to control resistance. • The proposed model is validated by theoretical analysis and experimental data fitting. • MTD treatment promotes and no treatment inhibits resistant cells. • Weaker recruitment of immune effector cells makes drug resistance more likely to occur. • Different drug strategies are suit to patients with varied immune responses. [ABSTRACT FROM AUTHOR]

In vitro , the recombinant HIV-1 Gag protein can generate spherical particles with a diameter of 25–30 nm in a fully defined system. It has approximately 80 building blocks, and its intermediates for assembly are abundant in geometry. Accordingly, there are a large number of nonlinear equations in the classical model. Therefore, it is difficult to compute values of geometry parameters for intermediates and make the mathematical analysis using the model. In this work, we develop a new model of HIV-like particle assembly in vitro by using six-fold symmetry of HIV-like particle assembly to decrease the number of geometry parameters. This method will greatly reduce computational costs and facilitate the application of the model. Then, we prove the existence and uniqueness of the positive equilibrium solution for this model with 79 nonlinear equations. Based on this model, we derive the interesting result that concentrations of all intermediates at equilibrium are independent of three important parameters, including two microscopic on-rate constants and the size of nucleating structure. Before equilibrium, these three parameters influence the concentration variation rates of all intermediates. We also analyze the relationship between the initial concentration of building blocks and concentrations of all intermediates. Furthermore, the bounds of concentrations of free building blocks and HIV-like particles are estimated. These results will be helpful to guide HIV-like particle assembly experiments and improve our understanding of the assembly dynamics of HIV-like particles in vitro . [ABSTRACT FROM AUTHOR]

Abstract: Previous theoretical analyses of evolutionary multi-objective optimization (EMO) mostly focus on obtaining -approximations of Pareto fronts. However, in practical applications, an appropriate value of is critical but sometimes, for a multi-objective optimization problem (MOP) with unknown attributes, difficult to determine. In this paper, we propose a new definition for the finite representation of the Pareto front—the adaptive Pareto front, which can automatically accommodate the Pareto front. Accordingly, it is more practical to take the adaptive Pareto front, or its -approximation (termed the -adaptive Pareto front) as the goal of an EMO algorithm. We then perform a runtime analysis of a ( ) multi-objective evolutionary algorithm (( ) MOEA) for three MOPs, including a discrete MOP with a polynomial Pareto front (denoted as a polynomial DMOP), a discrete MOP with an exponential Pareto front (denoted as an exponential DMOP) and a simple continuous two-objective optimization problem (SCTOP). By employing an estimator-based update strategy in the ( ) MOEA, we show that (1) for the polynomial DMOP, the whole Pareto front can be obtained in the expected polynomial runtime by setting the population size equal to the number of Pareto vectors; (2) for the exponential DMOP, the expected polynomial runtime can be obtained by keeping increasing in the same order as that of the problem size n; and (3) the diversity mechanism guarantees that in the expected polynomial runtime the MOEA can obtain an -adaptive Pareto front of SCTOP for any given precision . Theoretical studies and numerical comparisons with NSGA-II demonstrate the efficiency of the proposed MOEA and should be viewed as an important step toward understanding the mechanisms of MOEAs. [Copyright &y& Elsevier]

Abstract: In evolutionary multi-objective optimization (EMO), the convergence to the Pareto set of a multi-objective optimization problem (MOP) and the diversity of the final approximation of the Pareto front are two important issues. In the existing definitions and analyses of convergence in multi-objective evolutionary algorithms (MOEAs), convergence with probability is easily obtained because diversity is not considered. However, diversity cannot be guaranteed. By combining the convergence with diversity, this paper presents a new definition for the finite representation of a Pareto set, the B-Pareto set, and a convergence metric for MOEAs. Based on a new archive-updating strategy, the convergence of one such MOEA to the B-Pareto sets of MOPs is proved. Numerical results show that the obtained B-Pareto front is uniformly distributed along the Pareto front when, according to the new definition of convergence, the algorithm is convergent. [Copyright &y& Elsevier]

• A novel mathematical model, referred to as a temporal multilayer network, is proposed for exploring complex networked systems with time and space. • Using the mathematical formulation of the fifth-order tensor to represent the temporal multilayer networks. • Based on tensor framework, four important topological metrics are proposed to quantitatively evaluate the temporal multilayer networks. • Two novel iterative refinement centralities are proposed to quantify importance of nodes in temporal multilayer networks. • Using the theory of multilinear algebra and matrix analysis to prove the convergence of two iterative refinement algorithm. Although networks provide a powerful methodology to study a variety of real-world and engineered systems, their current formulation does not typically account for multiple interaction types that vary in space and time, or address interconnected systems such as networks of networks. Unavoidably, ignoring time-dependence and multiple interactions of topological structures might lead to important temporal and structural information loss and may obscure the actual organization. To achieve a deep understanding of the time-varying and interconnected complex networked systems, in this paper, we develop a more general mathematical model, referred to as a temporal multilayer network, which explicitly incorporates time-dependence and multiple relationships of topological structures into a system, and provides a natural and reasonable description for real-world complex systems. Furthermore, using a fifth-order tensorial framework to represent temporal multilayer networks, we generalize four important topological metrics, including overlapping degree, entropy, degree correlation and link overlap, to quantitatively evaluate the temporal multilayer networks. In particular, based on the tensorial framework, we propose two iterative refinement centralities for temporal multilayer networks, referred to as TM-eigenvector and TM-PageRank centralities, which are used to quantitatively evaluate the importance of nodes in real-world complex systems. Moreover, we use the theory of multilinear algebra and matrix analysis to strictly prove the convergence of these iterative algorithms. The proposed mathematical frameworks are validated using two real-world temporal multilayer networked systems related to complex diseases, i.e., influenza and heart diseases. [ABSTRACT FROM AUTHOR]

Type I interferon (IFN) signaling pathways play an essential role in the defense against early viral infections; however, the diverse and intricate molecular mechanisms of virus-triggered type I IFN responses are still poorly understood. In this study, we analyzed and compared two classes of models i.e., deterministic ordinary differential equations (ODEs) and stochastic models to elucidate the dynamics and stochasticity of type I IFN signaling pathways. Bifurcation analysis based on an ODE model reveals that the system exhibits a bistable switch and a one-way switch at high or low levels when the strengths of the negative and positive feedbacks are tuned. Furthermore, we compared the stochastic simulation results under the Master and Langevin equations. Both of the stochastic equations generate the bistable switch phenomenon, and the distance between two stable states are smaller than normal under the simulation of the Langevin equation. The quantitative computations also show that a moderate ratio between positive and negative feedback strengths is required to ensure a reliable switch between the different IFN concentrations that regulate the immune response. Moreover, we propose a multi-state stochastic model based on the above deterministic model to describe the multi-cellular system coupled with the diffusion of IFNs. The perturbation and inhibition analysis showed that the positive feedback, as well as noises, has little effect on the stochastic expression of IFNs, but the negative feedback of ISG56 on the activation of IRF7 has a great influence on IFN stochastic expression. Together, these results reveal that positive feedback stabilizes IFN gene expression, and negative feedback may be the main contribution to the stochastic expression of the IFN gene in the virus-triggered type I IFN response. These findings will provide new insight into the molecular mechanisms of virus-triggered type I IFN signaling pathways. [ABSTRACT FROM AUTHOR]

There are two stages generally recognized in the viral capsid assembly: nucleation and elongation. This paper focuses on the nucleation stage and develops mathematical models for HIV-1 viral capsid nucleation based on six-species dynamical systems. The Particle Swarm Optimization (PSO) algorithm is used for parameter fitting to estimate the association and dissociation rates from biological experiment data. Numerical simulations of capsid protein (CA) multimer concentrations demonstrate a good agreement with experimental data. Sensitivity and elasticity analysis of CA multimer concentrations with respect to the association and dissociation rates further reveals the importance of CA trimer-of- dimers in the nucleation stage of viral capsid self- assembly. [ABSTRACT FROM AUTHOR]

This paper presents a modeling study for the intracellular trafficking and trimerization of the HIV-1 Gag proteins. A set of differential equations including initial and boundary conditions is used to characterize the transport, diffusion, association and dissociation of Gag monomers and trimers for the time period from the initial production of Gag protein monomers to the initial appearance of immature HIV-1 virions near the cell membrane (the time duration T a ). The existence and stability of the steady-state solution of the initial boundary value problems provide a quantitative characterization of the tendency and equilibrium of Gag protein movement. The numerical simulation results further demonstrate Gag trimerization near the cell membrane. Our calculations of T a are in good agreement with published experimental data. Sensitivity analysis of T a to the model parameters indicates that the timing of the initial appearance of HIV-1 virions on the cell membrane is affected by the diffusion and transport processes. These results provide important information and insight into the Gag protein transport and binding and HIV-1 virion formation. [ABSTRACT FROM AUTHOR]