Systematic analysis of the mechanisms of virus-triggered type I IFN signaling pathways through mathematical modeling

Quantification of Type I Interferon Inhibition by Viral Proteins: Ebola Virus as a Case Study

Type I interferons (IFNs) are cytokines with both antiviral properties and protective roles in innate immune responses to viral infection. They induce an antiviral cellular state and link innate and adaptive immune responses. Yet, viruses have evolved different strategies to inhibit such host responses. One of them is the existence of viral proteins which subvert type I IFN responses to allow quick and successful viral replication, thus, sustaining the infection within a host. We propose mathematical models to characterise the intra-cellular mechanisms involved in viral protein antagonism of type I IFN responses, and compare three different molecular inhibition strategies. We study the Ebola viral protein, VP35, with this mathematical approach. Approximate Bayesian computation sequential Monte Carlo, together with experimental data and the mathematical models proposed, are used to perform model calibration, as well as model selection of the different hypotheses considered. Finally, we assess if model parameters are identifiable and discuss how such identifiability can be improved with new experimental data.

Finding Robust Adaptation Gene Regulatory Networks Using Multi-Objective Genetic Algorithm

Robust adaptation plays a key role in gene regulatory networks, and it is thought to be an important attribute for the organic or cells to survive in fluctuating conditions. In this paper, a simplified three-node enzyme network is modeled by the Michaelis-Menten rate equations for all possible topologies, and a family of topologies and the corresponding parameter sets of the network with satisfactory adaptation are obtained using the multi-objective genetic algorithm. The proposed approach improves the computation efficiency significantly as compared to the time consuming exhaustive searching method. This approach provides a systemic way for searching the feasible topologies and the corresponding parameter sets to make the gene regulatory networks have robust adaptation. The proposed methodology, owing to its universality and simplicity, can be used to address more complex issues in biological networks.

Crosstalk between pathways enhances the controllability of signalling networks

The control of complex networks is one of the most challenging problems in the fields of biology and engineering. In this study, the authors explored the controllability and control energy of several signalling networks, which consisted of many interconnected pathways, including networks with a bow-tie architecture. On the basis of the theory of structure controllability, they revealed that biological mechanisms, such as cross-pathway interactions, compartmentalisation and so on make the networks easier to fully control. Furthermore, using numerical simulations for two realistic examples, they demonstrated that the control energy of normal networks with crosstalk is lower than in networks without crosstalk. These results indicate that the biological networks are optimally designed to achieve their normal functions from the viewpoint of the control theory. The authors' work provides a comprehensive understanding of the impact of network structures and properties on controllability.

A New Method for Detecting Protein Complexes based on the Three Node Cliques

The identification of protein complexes in protein-protein interaction (PPI) networks is fundamental for understanding biological processes and cellular molecular mechanisms. Many graph computational algorithms have been proposed to identify protein complexes from PPI networks by detecting densely connected groups of proteins. These algorithms assess the density of subgraphs through evaluation of the sum of individual edges or nodes; thus, incomplete and inaccurate measures may miss meaningful biological protein complexes with functional significance. In this study, we propose a novel method for assessing the compactness of local subnetworks by measuring the number of three node cliques. The present method detects each optimal cluster by growing a seed and maximizing the compactness function. To demonstrate the efficacy of the new proposed method, we evaluate its performance using five PPI networks on three reference sets of yeast protein complexes with five different measurements and compare the performance of the proposed method with four state-of-the-art methods. The results show that the protein complexes generated by the proposed method are of better quality than those generated by four classic methods. Therefore, the new proposed method is effective and useful for detecting protein complexes in PPI networks.

Negative feedback contributes to the stochastic expression of the interferon-β gene in virus-triggered type I interferon signaling pathways

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.

Optimal control strategy for abnormal innate immune response

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.

Deciphering deterioration mechanisms of complex diseases based on the construction of dynamic networks and systems analysis

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.

Mathematical modeling for intracellular transport and binding of HIV-1 Gag proteins

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 Ta). 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 Ta are in good agreement with published experimental data. Sensitivity analysis of Ta 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.