CPMI: comprehensive neighborhood-based perturbed mutual information for identifying critical states of complex biological processes.

BACKGROUND: There exists a critical transition or tipping point during the complex biological process. Such critical transition is usually accompanied by the catastrophic consequences. Therefore, hunting for the tipping point or critical state is of significant importance to prevent or delay the occurrence of catastrophic consequences. However, predicting critical state based on the high-dimensional small sample data is a difficult problem, especially for single-cell expression data. RESULTS: In this study, we propose the comprehensive neighbourhood-based perturbed mutual information (CPMI) method to detect the critical states of complex biological processes. The CPMI method takes into account the relationship between genes and neighbours, so as to reduce the noise and enhance the robustness. This method is applied to a simulated dataset and six real datasets, including an influenza dataset, two single-cell expression datasets and three bulk datasets. The method can not only successfully detect the tipping points, but also identify their dynamic network biomarkers (DNBs). In addition, the discovery of transcription factors (TFs) which can regulate DNB genes and nondifferential 'dark genes' validates the effectiveness of our method. The numerical simulation verifies that the CPMI method is robust under different noise strengths and is superior to the existing methods on identifying the critical states. CONCLUSIONS: In conclusion, we propose a robust computational method, i.e., CPMI, which is applicable in both the bulk and single cell datasets. The CPMI method holds great potential in providing the early warning signals for complex biological processes and enabling early disease diagnosis.

New results on bifurcation for fractional-order octonion-valued neural networks involving delays.

This work chiefly explores fractional-order octonion-valued neural networks involving delays. We decompose the considered fractional-order delayed octonion-valued neural networks into equivalent real-valued systems via Cayley-Dickson construction. By virtue of Lipschitz condition, we prove that the solution of the considered fractional-order delayed octonion-valued neural networks exists and is unique. By constructing a fairish function, we confirm that the solution of the involved fractional-order delayed octonion-valued neural networks is bounded. Applying the stability theory and basic bifurcation knowledge of fractional order differential equations, we set up a sufficient condition remaining the stability behaviour and the appearance of Hopf bifurcation for the addressed fractional-order delayed octonion-valued neural networks. To illustrate the justifiability of the derived theoretical results clearly, we give the related simulation results to support these facts. Simultaneously, the bifurcation plots are also displayed. The established theoretical results in this work have important guiding significance in devising and improving neural networks.

mNFE: microbiome network flow entropy for detecting pre-disease states of type 1 diabetes.

In the development of Type 1 diabetes (T1D), there are critical states just before drastic changes, and identifying these pre-disease states may predict T1D or provide crucial early-warning signals. Unlike gene expression data, gut microbiome data can be collected noninvasively from stool samples. Gut microbiome sequencing data contain different levels of phylogenetic information that can be utilized to detect the tipping point or critical state in a reliable manner, thereby providing accurate and effective early-warning signals. However, it is still difficult to detect the critical state of T1D based on gut microbiome data due to generally non-significant differences between healthy and critical states. To address this problem, we proposed a new method - microbiome network flow entropy (mNFE) based on a single sample from each individual - for detecting the critical state before seroconversion and abrupt transitions of T1D at various taxonomic levels. The numerical simulation validated the robustness of mNFE under different noise levels. Furthermore, based on real datasets, mNFE successfully identified the critical states and their dynamic network biomarkers (DNBs) at different taxonomic levels. In addition, we found some high-frequency species, which are closely related to the unique clinical characteristics of autoantibodies at the four levels, and identified some non-differential 'dark species' play important roles during the T1D progression. mNFE can robustly and effectively detect the pre-disease states at various taxonomic levels and identify the corresponding DNBs with only a single sample for each individual. Therefore, our mNFE method provides a new approach not only for T1D pre-disease diagnosis or preventative treatment but also for preventative medicine of other diseases by gut microbiome.

MIWE: detecting the critical states of complex biological systems by the mutual information weighted entropy.

Complex biological systems often undergo sudden qualitative changes during their dynamic evolution. These critical transitions are typically characterized by a catastrophic progression of the system. Identifying the critical point is critical to uncovering the underlying mechanisms of complex biological systems. However, the system may exhibit minimal changes in its state until the critical point is reached, and in the face of high throughput and strong noise data, traditional biomarkers may not be effective in distinguishing the critical state. In this study, we propose a novel approach, mutual information weighted entropy (MIWE), which uses mutual information between genes to build networks and identifies critical states by quantifying molecular dynamic differences at each stage through weighted differential entropy. The method is applied to one numerical simulation dataset and four real datasets, including bulk and single-cell expression datasets. The critical states of the system can be recognized and the robustness of MIWE method is verified by numerical simulation under the influence of different noises. Moreover, we identify two key transcription factors (TFs), CREB1 and CREB3, that regulate downstream signaling genes to coordinate cell fate commitment. The dark genes in the single-cell expression datasets are mined to reveal the potential pathway regulation mechanism.

GPDRP: a multimodal framework for drug response prediction with graph transformer.

BACKGROUND: In the field of computational personalized medicine, drug response prediction (DRP) is a critical issue. However, existing studies often characterize drugs as strings, a representation that does not align with the natural description of molecules. Additionally, they ignore gene pathway-specific combinatorial implication. RESULTS: In this study, we propose drug Graph and gene Pathway based Drug response prediction method (GPDRP), a new multimodal deep learning model for predicting drug responses based on drug molecular graphs and gene pathway activity. In GPDRP, drugs are represented by molecular graphs, while cell lines are described by gene pathway activity scores. The model separately learns these two types of data using Graph Neural Networks (GNN) with Graph Transformers and deep neural networks. Predictions are subsequently made through fully connected layers. CONCLUSIONS: Our results indicate that Graph Transformer-based model delivers superior performance. We apply GPDRP on hundreds of cancer cell lines' bulk RNA-sequencing data, and it outperforms some recently published models. Furthermore, the generalizability and applicability of GPDRP are demonstrated through its predictions on unknown drug-cell line pairs and xenografts. This underscores the interpretability achieved by incorporating gene pathways.

Potential network markers and signaling pathways for B cells of COVID-19 based on single-cell condition-specific networks.

To explore the potential network markers and related signaling pathways of human B cells infected by COVID-19, we performed standardized integration and analysis of single-cell sequencing data to construct conditional cell-specific networks (CCSN) for each cell. Then the peripheral blood cells were clustered and annotated based on the conditional network degree matrix (CNDM) and gene expression matrix (GEM), respectively, and B cells were selected for further analysis. Besides, based on the CNDM of B cells, the hub genes and 'dark' genes (a gene has a significant difference between case and control samples not in a gene expression level but in a conditional network degree level) closely related to COVID-19 were revealed. Interestingly, some of the 'dark' genes and differential degree genes (DDGs) encoded key proteins in the JAK-STAT pathway, which had antiviral effects. The protein p21 encoded by the 'dark' gene CDKN1A was a key regulator for the COVID-19 infection-related signaling pathway. Elevated levels of proteins encoded by some DDGs were directly related to disease severity of patients with COVID-19. In short, the proteins encoded by 'dark' genes complement some missing links in COVID-19 and these signaling pathways played an important role in the growth and activation of B cells.

Revealing Tissue Heterogeneity and Spatial Dark Genes from Spatially Resolved Transcriptomics by Multiview Graph Networks.

Spatially resolved transcriptomics (SRT) is capable of comprehensively characterizing gene expression patterns and providing an unbiased image of spatial composition. To fully understand the organizational complexity and tumor immune escape mechanism, we propose stMGATF, a multiview graph attention fusion model that integrates gene expression, histological images, spatial location, and gene association. To better extract information, stMGATF exploits SimCLRv2 for visual feature exaction and employs edge feature enhanced graph attention networks for the learning potential embedding of each view. A global attention mechanism is used to adaptively integrate 3 views to obtain low-dimensional representation. Applied to diverse SRT datasets, stMGATF is robust and outperforms other methods in detecting spatial domains and denoising data even with different resolutions and platforms. In particular, stMGATF contributes to the elucidation of tissue heterogeneity and extraction of 3-dimensional expression domains. Importantly, considering the associations between genes in tumors, stMGATF can identify the spatial dark genes ignored by traditional methods, which can be used to predict tumor-driving transcription factors and reveal tumor immune escape mechanisms, providing theoretical evidence for the development of new immunotherapeutic strategies.

Exploration on dynamics in a discrete predator-prey competitive model involving feedback controls.

In this work, we set up a new discrete predator-prey competitive model with time-varying delays and feedback controls. By virtue of the difference inequality knowledge, a sufficient condition which guarantees the permanence of the established discrete predator-prey competitive model with time-varying delays and feedback controls is derived. Under some appropriate parameter conditions, we have proved that the periodic solution of the system without delay exists and globally attractive. To verify the correctness of the derived theoretical fruits, we give two examples and execute computer simulations. Our obtained results are novel and complement previous known results.

Specific network information gain for detecting the critical state of colorectal cancer based on gut microbiome.

There generally exists a critical state or tipping point from a stable state to another in the development of colorectal cancer (CRC) beyond which a significant qualitative transition occurs. Gut microbiome sequencing data can be collected non-invasively from fecal samples, making it more convenient to obtain. Furthermore, intestinal microbiome sequencing data contain phylogenetic information at various levels, which can be used to reliably identify critical states, thereby providing early warning signals more accurately and effectively. Yet, pinpointing the critical states using gut microbiome data presents a formidable challenge due to the high dimension and strong noise of gut microbiome data. To address this challenge, we introduce a novel approach termed the specific network information gain (SNIG) method to detect CRC's critical states at various taxonomic levels via gut microbiome data. The numerical simulation indicates that the SNIG method is robust under different noise levels and that it is also superior to the existing methods on detecting the critical states. Moreover, utilizing SNIG on two real CRC datasets enabled us to discern the critical states preceding deterioration and to successfully identify their associated dynamic network biomarkers at different taxonomic levels. Notably, we discovered certain 'dark species' and pathways intimately linked to CRC progression. In addition, we accurately detected the tipping points on an individual dataset of type I diabetes.

New exploration on bifurcation for fractional-order quaternion-valued neural networks involving leakage delays.

During the past decades, many works on Hopf bifurcation of fractional-order neural networks are mainly concerned with real-valued and complex-valued cases. However, few publications involve the quaternion-valued neural networks which is a generalization of real-valued and complex-valued neural networks. In this present study, we explorate the Hopf bifurcation problem for fractional-order quaternion-valued neural networks involving leakage delays. Taking advantage of the Hamilton rule of quaternion algebra, we decompose the addressed fractional-order quaternion-valued delayed neural networks into the equivalent eight real valued networks. Then the delay-inspired bifurcation condition of the eight real valued networks are derived by making use of the stability criterion and bifurcation theory of fractional-order differential dynamical systems. The impact of leakage delay on the bifurcation behavior of the involved fractional-order quaternion-valued delayed neural networks has been revealed. Software simulations are implemented to support the effectiveness of the derived fruits of this study. The research supplements the work of Huang et al. (Neural Netw 117:67-93, 2019).

Detecting the Critical States of Type 2 Diabetes Mellitus Based on Degree Matrix Network Entropy by Cross-Tissue Analysis.

Type 2 diabetes mellitus (T2DM) is a metabolic disease caused by multiple etiologies, the development of which can be divided into three states: normal state, critical state/pre-disease state, and disease state. To avoid irreversible development, it is important to detect the early warning signals before the onset of T2DM. However, detecting critical states of complex diseases based on high-throughput and strongly noisy data remains a challenging task. In this study, we developed a new method, i.e., degree matrix network entropy (DMNE), to detect the critical states of T2DM based on a sample-specific network (SSN). By applying the method to the datasets of three different tissues for experiments involving T2DM in rats, the critical states were detected, and the dynamic network biomarkers (DNBs) were successfully identified. Specifically, for liver and muscle, the critical transitions occur at 4 and 16 weeks. For adipose, the critical transition is at 8 weeks. In addition, we found some "dark genes" that did not exhibit differential expression but displayed sensitivity in terms of their DMNE score, which is closely related to the progression of T2DM. The information uncovered in our study not only provides further evidence regarding the molecular mechanisms of T2DM but may also assist in the development of strategies to prevent this disease.

Research on Potential Network Markers and Signaling Pathways in Type 2 Diabetes Based on Conditional Cell-Specific Network.

Traditional methods concerning type 2 diabetes (T2D) are limited to grouped cells instead of each single cell, and thus the heterogeneity of single cells is erased. Therefore, it is still challenging to study T2D based on a single-cell and network perspective. In this study, we construct a conditional cell-specific network (CCSN) for each single cell for the GSE86469 dataset which is a single-cell transcriptional set from nondiabetic (ND) and T2D human islet samples, and obtain a conditional network degree matrix (CNDM). Since beta cells are the key cells leading to T2D, we search for hub genes in CCSN of beta cells and find that ATP6AP2 is essential for regulation and storage of insulin, and the renin-angiotensin system involving ATP6AP2 is related to most pathological processes leading to diabetic nephropathy. The communication between beta cells and other endocrine cells is performed and three gene pairs with obvious interaction are found. In addition, different expression genes (DEGs) are found based on CNDM and the gene expression matrix (GEM), respectively. Finally, 'dark' genes are identified, and enrichment analysis shows that NFATC2 is involved in the VEGF signaling pathway and indirectly affects the production of Prostacyclin (PGI2), which may be a potential biomarker for diabetic nephropathy.

Detecting the critical states during disease development based on temporal network flow entropy.

Complex diseases progression can be generally divided into three states, which are normal state, predisease/critical state and disease state. The sudden deterioration of diseases can be viewed as a bifurcation or a critical transition. Therefore, hunting for the tipping point or critical state is of great importance to prevent the disease deterioration. However, it is still a challenging task to detect the critical states of complex diseases with high-dimensional data, especially based on an individual. In this study, we develop a new method based on network fluctuation of molecules, temporal network flow entropy (TNFE) or temporal differential network flow entropy, to detect the critical states of complex diseases on the basis of each individual. By applying this method to a simulated dataset and six real diseases, including respiratory viral infections and tumors with four time-course and two stage-course high-dimensional omics datasets, the critical states before deterioration were detected and their dynamic network biomarkers were identified successfully. The results on the simulated dataset indicate that the TNFE method is robust under different noise strengths, and is also superior to the existing methods on detecting the critical states. Moreover, the analysis on the real datasets demonstrated the effectiveness of TNFE for providing early-warning signals on various diseases. In addition, we also predicted disease deterioration risk and identified drug targets for cancers based on stage-wise data.

Identifying Critical States of Complex Diseases by Single-Sample Jensen-Shannon Divergence.

MOTIVATION: The evolution of complex diseases can be modeled as a time-dependent nonlinear dynamic system, and its progression can be divided into three states, i.e., the normal state, the pre-disease state and the disease state. The sudden deterioration of the disease can be regarded as the state transition of the dynamic system at the critical state or pre-disease state. How to detect the critical state of an individual before the disease state based on single-sample data has attracted many researchers' attention. METHODS: In this study, we proposed a novel approach, i.e., single-sample-based Jensen-Shannon Divergence (sJSD) method to detect the early-warning signals of complex diseases before critical transitions based on individual single-sample data. The method aims to construct score index based on sJSD, namely, inconsistency index (ICI). RESULTS: This method is applied to five real datasets, including prostate cancer, bladder urothelial carcinoma, influenza virus infection, cervical squamous cell carcinoma and endocervical adenocarcinoma and pancreatic adenocarcinoma. The critical states of 5 datasets with their corresponding sJSD signal biomarkers are successfully identified to diagnose and predict each individual sample, and some "dark genes" that without differential expressions but are sensitive to ICI score were revealed. This method is a data-driven and model-free method, which can be applied to not only disease prediction on individuals but also targeted drug design of each disease. At the same time, the identification of sJSD signal biomarkers is also of great significance for studying the molecular mechanism of disease progression from a dynamic perspective.

Global asymptotical stability of almost periodic solutions for a non-autonomous competing model with time-varying delays and feedback controls.

In this paper, we are concerned with a non-autonomous competing model with time delays and feedback controls. Applying the comparison theorem of differential equations and by constructing a suitable Lyapunov functional, some sufficient conditions which guarantee the existence of a unique globally asymptotically stable nonnegative almost periodic solution of the system are established. An example with its numerical simulations is given to illustrate the feasibility of our results.

Oscillatory dynamics in a discrete predator-prey model with distributed delays.

This work aims to discuss a predator-prey system with distributed delay. Various conditions are presented to ensure the existence and global asymptotic stability of positive periodic solution of the involved model. The method is based on coincidence degree theory and the idea of Lyapunov function. At last, simulation results are presented to show the correctness of theoretical findings.

Exponential Stability of Almost Periodic Solutions for Memristor-Based Neural Networks with Distributed Leakage Delays.

In this letter, we deal with a class of memristor-based neural networks with distributed leakage delays. By applying a new Lyapunov function method, we obtain some sufficient conditions that ensure the existence, uniqueness, and global exponential stability of almost periodic solutions of neural networks. We apply the results of this solution to prove the existence and stability of periodic solutions for this delayed neural network with periodic coefficients. We then provide an example to illustrate the effectiveness of the theoretical results. Our results are completely new and complement the previous studies Chen, Zeng, and Jiang ( 2014 ) and Jiang, Zeng, and Chen ( 2015 ).

Oscillations for a delayed predator-prey model with Hassell-Varley-type functional response.

In this paper, a delayed predator-prey model with Hassell-Varley-type functional response is investigated. By choosing the delay as a bifurcation parameter and analyzing the locations on the complex plane of the roots of the associated characteristic equation, the existence of a bifurcation parameter point is determined. It is found that a Hopf bifurcation occurs when the parameter τ passes through a series of critical values. The direction and the stability of Hopf bifurcation periodic solutions are determined by using the normal form theory and the center manifold theorem due to Faria and Maglhalaes (1995). In addition, using a global Hopf bifurcation result of Wu (1998) for functional differential equations, we show the global existence of periodic solutions. Some numerical simulations are presented to substantiate the analytical results. Finally, some biological explanations and the main conclusions are included.