Complex biological systems do not always develop smoothly but occasionally undergo a sharp transition; i.e. there exists a critical transition or tipping point at which a drastic qualitative shift occurs. Hunting for such a critical transition is important to prevent or delay the occurrence of catastrophic consequences, such as disease deterioration. However, the identification of the critical state for complex biological systems is still a challenging problem when using high-dimensional small sample data, especially where only a certain sample is available, which often leads to the failure of most traditional statistical approaches. In this study, a novel quantitative method, sample-perturbed network entropy (SPNE), is developed based on the sample-perturbed directed network to reveal the critical state of complex biological systems at the single-sample level. Specifically, the SPNE approach effectively quantifies the perturbation effect caused by a specific sample on the directed network in terms of network entropy and thus captures the criticality of biological systems. This model-free method was applied to both bulk and single-cell expression data. Our approach was validated by successfully detecting the early warning signals of the critical states for six real datasets, including four tumor datasets from The Cancer Genome Atlas (TCGA) and two single-cell datasets of cell differentiation. In addition, the functional analyses of signaling biomarkers demonstrated the effectiveness of the analytical and computational results.

The critical point or pivotal threshold of cell transition occurs in early embryonic development when cell differentiation culminates in its transition to specific cell fates, at which the cell population undergoes an abrupt and qualitative shift. Revealing such critical points of cell transitions can track cellular heterogeneity and shed light on the molecular mechanisms of cell differentiation. However, precise detection of critical state transitions proves challenging when relying on single-cell RNA sequencing data due to their inherent sparsity, noise, and heterogeneity. In this study, diverging from conventional methods like differential gene analysis or static techniques that emphasize classification of cell types, an innovative computational approach, single-cell gene association entropy (SGAE), is designed for the analysis of single-cell RNA-seq data and utilizes gene association information to reveal critical states of cell transitions. More specifically, through the translation of gene expression data into local SGAE scores, the proposed SGAE can serve as an index to quantitatively assess the resilience and critical properties of genetic regulatory networks, consequently detecting the signal of cell transitions. Analyses of five single-cell datasets for embryonic development demonstrate that the SGAE method achieves better performance in facilitating the characterization of a critical phase transition compared with other existing methods. Moreover, the SGAE value can effectively discriminate cellular heterogeneity over time and performs well in the temporal clustering of cells. Besides, biological functional analysis also indicates the effectiveness of the proposed approach.

Tipping points or critical transitions widely exist during the progression of many biological processes. It is of great importance to detect the tipping point with the measured omics data, which may be a key to achieving predictive or preventive medicine. We present the tipping point detector (TPD), a web tool for the detection of the tipping point during the dynamic process of biological systems, and further its leading molecules or network, based on the input high-dimensional time series or stage course data. With the solid theoretical background of dynamic network biomarker (DNB) and a series of computational methods for DNB detection, TPD detects the potential tipping point/critical state from the input omics data and outputs multifarious visualized results, including a suggested tipping point with a statistically significant P value, the identified key genes and their functional biological information, the dynamic change in the DNB/leading network that may drive the critical transition and the survival analysis based on DNB scores that may help to identify 'dark' genes (nondifferential in terms of expression but differential in terms of DNB scores). TPD fits all current browsers, such as Chrome, Firefox, Edge, Opera, Safari and Internet Explorer. TPD is freely accessible at http://www.rpcomputationalbiology.cn/TPD.

The dynamics of complex diseases are not always smooth; they are occasionally abrupt, i.e. there is a critical state transition or tipping point at which the disease undergoes a sudden qualitative shift. There are generally a few significant differences in the critical state in terms of gene expressions or other static measurements, which may lead to the failure of traditional differential expression-based biomarkers to identify such a tipping point. In this study, we propose a computational method, the direct interaction network-based divergence, to detect the critical state of complex diseases by exploiting the dynamic changes in multivariable distributions inferred from observable samples and local biomolecular direct interaction networks. Such a method is model-free and applicable to both bulk and single-cell expression data. Our approach was validated by successfully identifying the tipping point just before the occurrence of a critical transition for both a simulated data set and seven real data sets, including those from The Cancer Genome Atlas and two single-cell RNA-sequencing data sets of cell differentiation. Functional and pathway enrichment analyses also validated the computational results from the perspectives of both molecules and networks.

MOTIVATION: Catastrophic transitions are ubiquitous in the dynamic progression of complex biological systems; that is, a critical transition at which complex systems suddenly shift from one stable state to another occurs. Identifying such a critical point or tipping point is essential for revealing the underlying mechanism of complex biological systems. However, it is difficult to identify the tipping point since few significant differences in the critical state are detected in terms of traditional static measurements. RESULTS: In this study, by exploring the dynamic changes in gene cooperative effects between the before-transition and critical states, we presented a model-free approach, the directed-network rank score (DNRS), to detect the early-warning signal of critical transition in complex biological systems. The proposed method is applicable to both bulk and single-cell RNA-sequencing (scRNA-seq) data. This computational method was validated by the successful identification of the critical or pre-transition state for both simulated and six real datasets, including three scRNA-seq datasets of embryonic development and three tumor datasets. In addition, the functional and pathway enrichment analyses suggested that the corresponding DNRS signaling biomarkers were involved in key biological processes. AVAILABILITY AND IMPLEMENTATION: The source code is freely available at https://github.com/zhongjiayuan/DNRS. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Bioinformatics (2009) doi:10.1093/bioinformatics/btz758 In the above article the funding source was given incorrectly as ‘Guangdong Natural Science Funds for Distinguished Young Scholar (No. 2019B151502062).’ This has now been corrected to ‘Guangdong Basic and Applied Basic Research Foundation (No. 2019B151502062).’

MOTIVATION: The time evolution or dynamic change of many biological systems during disease progression is not always smooth but occasionally abrupt, that is, there is a tipping point during such a process at which the system state shifts from the normal state to a disease state. It is challenging to predict such disease state with the measured omics data, in particular when only a single sample is available. RESULTS: In this study, we developed a novel approach, i.e. single-sample landscape entropy (SLE) method, to identify the tipping point during disease progression with only one sample data. Specifically, by evaluating the disorder of a network projected from a single-sample data, SLE effectively characterizes the criticality of this single sample network in terms of network entropy, thereby capturing not only the signals of the impending transition but also its leading network, i.e. dynamic network biomarkers. Using this method, we can characterize sample-specific state during disease progression and thus achieve the disease prediction of each individual by only one sample. Our method was validated by successfully identifying the tipping points just before the serious disease symptoms from four real datasets of individuals or subjects, including influenza virus infection, lung cancer metastasis, prostate cancer and acute lung injury. AVAILABILITY AND IMPLEMENTATION: https://github.com/rabbitpei/SLE. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Identifying the critical state or pre-transition state just before the occurrence of a phase transition is a challenging task, because the state of the system may show little apparent change before this critical transition during the gradual parameter variations. Such dynamics of phase transition is generally composed of three stages, i.e. before-transition state, pre-transition state and after-transition state, which can be considered as three different Markov processes. RESULTS: By exploring the rich dynamical information provided by high-throughput data, we present a novel computational method, i.e. hidden Markov model (HMM) based approach, to detect the switching point of the two Markov processes from the before-transition state (a stationary Markov process) to the pre-transition state (a time-varying Markov process), thereby identifying the pre-transition state or early-warning signals of the phase transition. To validate the effectiveness, we apply this method to detect the signals of the imminent phase transitions of complex systems based on the simulated datasets, and further identify the pre-transition states as well as their critical modules for three real datasets, i.e. the acute lung injury triggered by phosgene inhalation, MCF-7 human breast cancer caused by heregulin and HCV-induced dysplasia and hepatocellular carcinoma. Both functional and pathway enrichment analyses validate the computational results. AVAILABILITY AND IMPLEMENTATION: The source code and some supporting files are available at https://github.com/rabbitpei/HMM_based-method CONTACTS: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Identifying the pre-transition state just before the occurrence of a critical transition during a complex biological process is a challenging task, because the state of the system may show little apparent change or clear phenomenon before this critical transition during the biological processes. By regarding that the pre-transition state is the end or change-point of a stationary Markov process, we present a novel computational method, hidden Markov model (HMM) based state-transition forward method, which is a non-parametric estimation and can identify the pre-transition state. To validate the effectiveness, we apply this method to detect the signal of the imminent critical deterioration of complex diseases based on both simulated dataset and the rich information provided by high-throughput microarray data. We identify the pre-transition states and a number of related modules for the acute lung injury triggered by phosgene inhalation. Both functional and pathway enrichment analyses validate the results.

To get a better understanding of the ongoing in situ environmental changes preceding the brain tumorigenesis, we assessed cerebrospinal fluid (CSF) proteome profile changes in a glioma rat model in which brain tumor invariably develop after a single in utero exposure to the neurocarcinogen ethylnitrosourea (ENU). Computationally, the CSF proteome profile dynamics during the tumorigenesis can be modeled as non-smooth or even abrupt state changes. Such brain tumor environment transition analysis, correlating the CSF composition changes with the development of early cellular hyperplasia, can reveal the pathogenesis process at network level during a time before the image detection of the tumors. In this controlled rat model study, matched ENU and salineexposed rats' CSF proteomics changes were quantified at approximately 30, 60, 90, 120, 150 days of age (P30, P60, P90, P120, P150). We applied our transition-based network entropy (TNE) method to compute the CSF proteome changes in the ENU rat model and test the hypothesis of the critical transition state prior to impending hyperplasia. Our analysis identified a dynamic driver network (DDN) of CSF proteins related with the emerging tumorigenesis progressing from the non-hyperplasia state. The DDN associated leading network CSF proteins can allow the early detection of such dynamics before the catastrophic shift to the clear clinical landmarks in gliomas. An improved understanding of the critical transition state (P60) during the brain tumor progression can provide the scientific groundwork to device novel therapeutics preventing tumor formation.

In a content centric network, packet forwarding is performed over data names instead of IP addresses. Since data names are order-of-magnitude larger in number and complexity, CAM-based or Trie-based techniques are not applicable any more. and new forwarding schemes are proposed to solve the problem. These schemes use hashing to store the large routing table for named data into relatively abundant off-chip memory, and use some on-chip Bloom filter to minimize expensive off-chip memory access by quickly screen out table lookup queries for unrecorded names. In this paper we propose to add a `summary vector' to the on-chip Bloom filter that can help in constructing an efficient off-chip hash table for better storage and lookup performance: a dynamic collision-free hash table that only needs to read into only one routing record for any lookup queries.