SPNE: sample-perturbed network entropy for revealing critical states of complex biological systems.

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.

Identifying the critical states and dynamic network biomarkers of cancers based on network entropy.

BACKGROUND: There are sudden deterioration phenomena during the progression of many complex diseases, including most cancers; that is, the biological system may go through a critical transition from one stable state (the normal state) to another (the disease state). It is of great importance to predict this critical transition or the so-called pre-disease state so that patients can receive appropriate and timely medical care. In practice, however, this critical transition is usually difficult to identify due to the high nonlinearity and complexity of biological systems. METHODS: In this study, we employed a model-free computational method, local network entropy (LNE), to identify the critical transition/pre-disease states of complex diseases. From a network perspective, this method effectively explores the key associations among biomolecules and captures their dynamic abnormalities. RESULTS: Based on LNE, the pre-disease states of ten cancers were successfully detected. Two types of new prognostic biomarkers, optimistic LNE (O-LNE) and pessimistic LNE (P-LNE) biomarkers, were identified, enabling identification of the pre-disease state and evaluation of prognosis. In addition, LNE helps to find "dark genes" with nondifferential gene expression but differential LNE values. CONCLUSIONS: The proposed method effectively identified the critical transition states of complex diseases at the single-sample level. Our study not only identified the critical transition states of ten cancers but also provides two types of new prognostic biomarkers, O-LNE and P-LNE biomarkers, for further practical application. The method in this study therefore has great potential in personalized disease diagnosis.

Data-driven energy landscape reveals critical genes in cancer progression.

The evolution of cancer is a complex process characterized by stable states and transitions among them. Studying the dynamic evolution of cancer and revealing the mechanisms of cancer progression based on experimental data is an important topic. In this study, we aim to employ a data-driven energy landscape approach to analyze the dynamic evolution of cancer. We take Kidney renal clear cell carcinoma (KIRC) as an example. From the energy landscape, we introduce two quantitative indicators (transition probability and barrier height) to study critical shifts in KIRC cancer evolution, including cancer onset and progression, and identify critical genes involved in these transitions. Our results successfully identify crucial genes that either promote or inhibit these transition processes in KIRC. We also conduct a comprehensive biological function analysis on these genes, validating the accuracy and reliability of our predictions. This work has implications for discovering new biomarkers, drug targets, and cancer treatment strategies in KIRC.

Identifying the critical state of cancers by single-sample Markov flow entropy.

Background: The progression of complex diseases sometimes undergoes a drastic critical transition, at which the biological system abruptly shifts from a relatively healthy state (before-transition stage) to a disease state (after-transition stage). Searching for such a critical transition or critical state is crucial to provide timely and effective scientific treatment to patients. However, in most conditions where only a small sample size of clinical data is available, resulting in failure when detecting the critical states of complex diseases, particularly only single-sample data. Methods: In this study, different from traditional methods that require multiple samples at each time, a model-free computational method, single-sample Markov flow entropy (sMFE), provides a solution to the identification problem of critical states/pre-disease states of complex diseases, solely based on a single-sample. Our proposed method was employed to characterize the dynamic changes of complex diseases from the perspective of network entropy. Results: The proposed approach was verified by unmistakably identifying the critical state just before the occurrence of disease deterioration for four tumor datasets from The Cancer Genome Atlas (TCGA) database. In addition, two new prognostic biomarkers, optimistic sMFE (O-sMFE) and pessimistic sMFE (P-sMFE) biomarkers, were identified by our method and enable the prognosis evaluation of tumors. Conclusions: The proposed method has shown its capability to accurately detect pre-disease states of four cancers and provide two novel prognostic biomarkers, O-sMFE and P-sMFE biomarkers, to facilitate the personalized prognosis of patients. This is a remarkable achievement that could have a major impact on the diagnosis and treatment of complex diseases.

Phosphate removal from digested sludge supernatant using modified fly ash.

The removal of phosphate in digested sludge supernatant by modified coal fly ash was investigated in this study. Modification of the fly ash by the addition of sulfuric acid could significantly enhance its immobilization ability. The experimental results also showed that adsorption of phosphate by the modified fly ash was rapid with the removal percentage of phosphate reaching an equilibrium of 98.62% in less than 5 minutes. The optimum pH for phosphate removal was 9 and the removal percentage increased with increasing adsorbent dosage. The effect of temperature on phosphate removal efficiency was not significant from 20 to 40 degrees C. X-ray diffraction and scanning electron microscope analyses showed that phosphate formed an amorphous precipitate with water-soluble calcium, aluminum, and iron ions in the modified fly ash.