Predicting RNA polymerase II transcriptional elongation pausing and associated histone code.

RNA Polymerase II (Pol II) transcriptional elongation pausing is an integral part of the dynamic regulation of gene transcription in the genome of metazoans. It plays a pivotal role in many vital biological processes and disease progression. However, experimentally measuring genome-wide Pol II pausing is technically challenging and the precise governing mechanism underlying this process is not fully understood. Here, we develop RP3 (RNA Polymerase II Pausing Prediction), a network regularized logistic regression machine learning method, to predict Pol II pausing events by integrating genome sequence, histone modification, gene expression, chromatin accessibility, and protein-protein interaction data. RP3 can accurately predict Pol II pausing in diverse cellular contexts and unveil the transcription factors that are associated with the Pol II pausing machinery. Furthermore, we utilize a forward feature selection framework to systematically identify the combination of histone modification signals associated with Pol II pausing. RP3 is freely available at https://github.com/AMSSwanglab/RP3.

Delay induced stability switch in a mathematical model of CD8 T-cell response to SARS-CoV-2 mediated by receptor ACE2.

The pathogen SARS-CoV-2 binds to the receptor angiotensin-converting enzyme 2 (ACE2) of the target cells and then replicates itself through the host, eventually releasing free virus particles. After infection, the CD8 T-cell response is triggered and appears to play a critical role in the defense against virus infections. Infected cells and their activated CD8 T-cells can cause tissue damage. Here, we established a mathematical model of within-host SARS-CoV-2 infection that incorporates the receptor ACE2, the CD8 T-cell response, and the damaged tissues. According to this model, we can get the basic reproduction number R0 and the immune reproduction number R1. We provide the theoretical proof for the stability of the disease-free equilibrium, immune-inactivated equilibrium, and immune-activated equilibrium. Finally, our numerical simulations show that the time delay in CD8 T-cell production can induce complex dynamics such as stability switching. These results provide insights into the mechanisms of SARS-CoV-2 infection and may help in the development of effective drugs against COVID-19.

SpecLoop predicts cell type-specific chromatin loop via transcription factor cooperation.

Cell-type-Specific Chromatin Loops (CSCLs) are crucial for gene regulation and cell fate determination. However, the mechanisms governing their establishment remain elusive. Here, we present SpecLoop, a network regularization-based machine learning framework, to investigate the role of transcription factors (TFs) cooperation in CSCL formation. SpecLoop integrates multi-omics data, including gene expression, chromatin accessibility, sequence, protein-protein interaction, and TF binding motif data, to predict CSCLs and identify TF cooperations. Using high resolution Hi-C data as the gold standard, SpecLoop accurately predicts CSCL in GM12878, IMR90, HeLa-S3, K562, HUVEC, HMEC, and NHEK seven cell types, with the AUROC values ranging from 0.8645 to 0.9852 and AUPR values ranging from 0.8654 to 0.9734. Notably SpecLoop demonstrates improved accuracy in predicting long-distance CSCLs and identifies TF complexes with strong predictive ability. Our study systematically explores the TFs and TF pairs associated with CSCL through effective integration of diverse omics data. SpecLoop is freely available at https://github.com/AMSSwanglab/SpecLoop.

Stability and persistence analysis of a microorganism flocculation model with infinite delay.

In this paper, we study the global stability and persistence of a microorganism flocculation model with infinite delay. First, we make a complete theoretical analysis on the local stability of the boundary equilibrium (microorganism-free equilibrium) and the positive equilibrium (microorganism co-existent equilibrium), and give a sufficient condition for the global stability of the boundary equilibrium (applicable to the forward bifurcation and the backward bifurcation). Then, for the persistence of the model, we present an explicit estimate of the eventual lower bound of any positive solution for which only the parameter threshold $ R_0 > 1 $ is required. The obtained results extend some of the conclusions of the existing literatures on the case of discrete time delay.

A COVID-19 Infection Model Considering the Factors of Environmental Vectors and Re-Positives and Its Application to Data Fitting in Japan and Italy.

COVID-19, which broke out globally in 2019, is an infectious disease caused by a novel strain of coronavirus, and its spread is highly contagious and concealed. Environmental vectors play an important role in viral infection and transmission, which brings new difficulties and challenges to disease prevention and control. In this paper, a type of differential equation model is constructed according to the spreading functions and characteristics of exposed individuals and environmental vectors during the virus infection process. In the proposed model, five compartments were considered, namely, susceptible individuals, exposed individuals, infected individuals, recovered individuals, and environmental vectors (contaminated with free virus particles). In particular, the re-positive factor was taken into account (i.e., recovered individuals who have lost sufficient immune protection may still return to the exposed class). With the basic reproduction number R0 of the model, the global stability of the disease-free equilibrium and uniform persistence of the model were completely analyzed. Furthermore, sufficient conditions for the global stability of the endemic equilibrium of the model were also given. Finally, the effective predictability of the model was tested by fitting COVID-19 data from Japan and Italy.

Global asymptotic stability of a delay differential equation model for SARS-CoV-2 virus infection mediated by ACE2 receptor protein.

The COVID-19 pandemic has brought a serious threat to human life safety worldwide. SARS-CoV-2 virus mainly binds to the target cell surface receptor ACE2 (Angiotensin-converting enzyme 2 ) through the S protein expressed on the surface of the virus, resulting in infection of target cells. During this infection process, the target cell ACE2 receptor plays a very important mediating role. In this paper, a delay differential equation model containing the mediated effect of target cell receptor is established according to the mechanism of SARS-CoV-2 virus invasion of target cells, and the global stability of the infection-free equilibrium and the infected equilibrium of the model is obtained by using the basic reproduction number  ℛ 0  and constructing the appropriate Lyapunov functional. The expression of the basic reproduction number  ℛ 0  intuitively gives the dependence on the expression ratio of the target cell surface ACE2 receptor, which is helpful for the understanding of the mechanism of SARS-CoV-2 virus infection.

Periodic oscillation for a class of in-host MERS-CoV infection model with CTL immune response.

The purpose of this paper is to give some sufficient conditions for the existence of periodic oscillation of a class of in-host MERS-Cov infection model with cytotoxic T lymphocyte (CTL) immune response. A new technique is developed to obtain a lower bound of the state variable characterizing CTL immune response in the model. Our results expand on some previous works.

Global dynamics of an SI epidemic model with nonlinear incidence rate, feedback controls and time delays.

In this paper, we consider a class of SI epidemic model with nonlinear incidence, feedback controls and four different discrete time delays. By skillfully constructing appropriate Lyapunov functionals, and combining Lyapunov-LaSalle invariance principle and Barbalat's lemma, the global dynamics of the model are established. Our results extend and improve related works in the existing literatures.

The differential equation model of pathogenesis of Kawasaki disease with theoretical analysis.

Fever is a extremely common symptom in infants and young children. Due to the lowresistance of infants and young, long-term fever may cause damage to the child's body. Clinically,some children with long-term fever was eventually diagnosed with Kawasaki disease (KD). KD, anautoimmune disease, is a systemic vasculitis mainly affecting children younger than 5 years old. Dueto the delayed therapy and diagnosis, coronary artery abnormalities (CAAs) develop in children with KD, and leads to a high risk of acquired heart disease. Later, patients may have myocardial infarctionor even die a sudden death. Unfortunately, at present, the pathogenesis of KD remains unknownand KD lacks of specific and sensitive biomarkers, thus bringing difficulties to diagnosis and therapy.Therefore it is a highly focused topic to research on the mechanism of KD. Some scholars believethat KD is caused by the cross reaction of external infection and organ tissue composition, herebytriggering disorder of the immune system and producing a variety of cytokines. On the basis ofconsidering the cytokines such as vascular endothelial cells, inflammatory factors, adhesion factorsand chemokines, endothelial cell growth factors, put forward a kind of dynamic model of pathogenesisof KD by the theory of ordinary differential equation. It is found that the dynamic model can showcomplex dynamic behavior, such as the forward and backward bifurcation of the equilibria. This articlereveals the possible complexity of KD infection, and provides a theoretical references for the researchof pathogenic mechanism and clinical treatment of KD.

Corrigendum to "Modeling Inhibitory Effect on the Growth of Uninfected T Cells Caused by Infected T Cells: Stability and Hopf Bifurcation".

[This corrects the article DOI: 10.1155/2018/3176893.].

Remarks on a variant of Lyapunov-LaSalle theorem.

The aim of this paper is to give some global stability criteria on a variant of Lyapunov-LaSalle theorem for a class of delay di erential system.

Modeling Inhibitory Effect on the Growth of Uninfected T Cells Caused by Infected T Cells: Stability and Hopf Bifurcation.

We consider a class of viral infection dynamic models with inhibitory effect on the growth of uninfected T cells caused by infected T cells and logistic target cell growth. The basic reproduction number R 0 is derived. It is shown that the uninfected equilibrium is globally asymptotically stable if R 0 < 1. Sufficient conditions for the existence of Hopf bifurcation at the infected equilibrium are investigated by analyzing the distribution of eigenvalues. Furthermore, the properties of Hopf bifurcation are determined by the normal form theory and the center manifold. Numerical simulations are carried out to support the theoretical analysis.

A Novel Dynamic Model Describing the Spread of the MERS-CoV and the Expression of Dipeptidyl Peptidase 4.

The Middle East respiratory syndrome (MERS) coronavirus, a newly identified pathogen, causes severe pneumonia in humans. MERS is caused by a coronavirus known as MERS-CoV, which attacks the respiratory system. The recently defined receptor for MERS-CoV, dipeptidyl peptidase 4 (DPP4), is generally expressed in endothelial and epithelial cells and has been shown to be present on cultured human nonciliated bronchiolar epithelium cells. In this paper, a class of novel four-dimensional dynamic model describing the infection of MERS-CoV is given, and then global stability of the equilibria of the model is discussed. Our results show that the spread of MERS-CoV can also be controlled by decreasing the expression rate of DPP4.

Stability and Hopf Bifurcation in a Delayed HIV Infection Model with General Incidence Rate and Immune Impairment.

We investigate the dynamical behavior of a delayed HIV infection model with general incidence rate and immune impairment. We derive two threshold parameters, the basic reproduction number R 0 and the immune response reproduction number R 1. By using Lyapunov functional and LaSalle invariance principle, we prove the global stability of the infection-free equilibrium and the infected equilibrium without immunity. Furthermore, the existence of Hopf bifurcations at the infected equilibrium with CTL response is also studied. By theoretical analysis and numerical simulations, the effect of the immune impairment rate on the stability of the infected equilibrium with CTL response has been studied.

[Advances in the pathway and molecular mechanism for the biodegradation of microcystins].

With increasing discharge of wastewater containing nitrogen and phosphorus into rivers and lakes, harmful cyanobacterial blooms have become more frequent worldwide. The main harm of cyanobacterial blooms is producing and releasing a great amount of algal toxins mainly containing microcystins (MCs). Since MCs are extremely harmful to plants and animals and difficult to be removed efficiently by the traditional processing methods, how to control harmful cyanobacterial blooms and remove MCs have become an unsolved problem in the field of environmental science all over the world. This paper summarized the structure and toxicity of MCs, the MCs-biodegrading bacterial strains, the enzymes, the genes, and the biodegradation pathway and molecular mechanism of MCs. The further research subjects were also proposed. It was hoped that this review could provide a reference for restoring MCs-polluted lakes and reservoirs and ensuring drinking water safety.

Analysis of SIR epidemic models with nonlinear incidence rate and treatment.

This paper deals with the nonlinear dynamics of a susceptible-infectious-recovered (SIR) epidemic model with nonlinear incidence rate, vertical transmission, vaccination for the newborns of susceptible and recovered individuals, and the capacity of treatment. It is assumed that the treatment rate is proportional to the number of infectives when it is below the capacity and constant when the number of infectives reaches the capacity. Under some conditions, it is shown that there exists a backward bifurcation from an endemic equilibrium, which implies that the disease-free equilibrium coexists with an endemic equilibrium. In such a case, reducing the basic reproduction number less than unity is not enough to control and eradicate the disease, extra measures are needed to ensure that the solutions approach the disease-free equilibrium. When the basic reproduction number is greater than unity, the model can have multiple endemic equilibria due to the effect of treatment, vaccination and other parameters. The existence and stability of the endemic equilibria of the model are analyzed and sufficient conditions on the existence and stability of a limit cycle are obtained. Numerical simulations are presented to illustrate the analytical results.

A dynamic model describing heterotrophic culture of Chlorella and its stability analysis.

Chlorella is an important species of microorganism, which includes about 10 species. Chlorella USTB01 is a strain of microalga which is isolated from Qinghe River in Beijing and has strong ability in the utilization of organic compounds and was identified as Chlorella sp. (H. Yan et al, Isolation and heterotrophic culture of Chlorella sp., J. Univ. Sci. Tech. Beijing, 2005, 27:408-412). In this paper, based on the standard Chemostat models and the experimental data on the heterotrophic culture of Chlorella USTB01, a dynamic model governed by differential equations with three variables (Chlorella, carbon source and nitrogen source) is proposed. For the model, there always exists a boundary equilibrium, i.e. Chlorella-free equilibrium. Furthermore, under additional conditions, the model also has the positive equilibria, i.e., the equilibira for which Chlorella, carbon source and nitrogen source are coexistent. Then, local and global asymptotic stability of the equilibria of the model have been discussed. Finally, the parameters in the model are determined according to the experimental data, and numerical simulations are given. The numerical simulations show that the trajectories of the model fit the trends of the experimental data well.

Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate.

In this paper, based on SIR and SEIR epidemic models with a general nonlinear incidence rate, we incorporate time delays into the ordinary differential equation models. In particular, we consider two delay differential equation models in which delays are caused (i) by the latency of the infection in a vector, and (ii) by the latent period in an infected host. By constructing suitable Lyapunov functionals and using the Lyapunov-LaSalle invariance principle, we prove the global stability of the endemic equilibrium and the disease-free equilibrium for time delays of any length in each model. Our results show that the global properties of equilibria also only depend on the basic reproductive number and that the latent period in a vector does not affect the stability, but the latent period in an infected host plays a positive role to control disease development.

An improved model of T cell development in the thymus and its stability analysis.

Based on some important experimental dates, in this paper we shall introduce time delays into Mehrs's non-linear differential system model which is used to describe proliferation, differentiation and death of T cells in the thymus (see, for example, [3], [6], [7] and [9]) and give a revised nonlinear differential system model with time delays. By using some classical analysis techniques of functional differential equations, we also consider local and global asymptotic stability of the equilibrium and the permanence of the model.