Considerable evidence suggests that during the progression of complex diseases, the deteriorations are not necessarily smooth but are abrupt and may cause a critical transition from one state to another at a tipping point. Here, we develop a model-free method to detect early-warning signals of such critical transitions, even with only a small number of samples. Specifically, we theoretically derive an index based on a dynamical network biomarker (DNB) that serves as a general early-warning signal indicating an imminent bifurcation or sudden deterioration before the critical transition occurs. Based on theoretical analyses, we show that predicting a sudden transition from small samples is achievable provided that there are a large number of measurements for each sample, e.g., high-throughput data. We employ microarray data of three diseases to demonstrate the effectiveness of our method. The relevance of DNBs with the diseases was also validated by related experimental data and functional analysis.

Background: Developing effective strategies for signaling the pre-disease state of complex diseases, a state with high susceptibility before the disease onset or deterioration, is urgently needed because such state usually followed by a catastrophic transition into a worse stage of disease. However, it is a challenging task to identify such pre-disease state or tipping point in clinics, where only one single sample is available and thus results in the failure of most statistic approaches. Methods: In this study, we presented a single-sample-based computational method to detect the early-warning signal of critical transition during the progression of complex diseases. Specifically, given a set of reference samples which were regarded as background, a novel index called single-sample Kullback–Leibler divergence (sKLD), was proposed to explore and quantify the disturbance on the background caused by a case sample. The pre-disease state is then signaled by the significant change of sKLD. Results: The novel algorithm was developed and applied to both numerical simulation and real datasets, including lung squamous cell carcinoma, lung adenocarcinoma, stomach adenocarcinoma, thyroid carcinoma, colon adenocarcinoma, and acute lung injury. The successful identification of pre-disease states and the corresponding dynamical network biomarkers for all six datasets validated the effectiveness and accuracy of our method. Conclusions: The proposed method effectively explores and quantifies the disturbance on the background caused by a case sample, and thus characterizes the criticality of a biological system. Our method not only identifies the critical state or tipping point at a single sample level, but also provides the sKLD-signaling markers for further practical application. It is therefore of great potential in personalized pre-disease diagnosis.

Identifying a critical transition and its leading biomolecular network during the initiation and progression of a complex disease is a challenging task, but holds the key to early diagnosis and further elucidation of the essential mechanisms of disease deterioration at the network level. In this study, we developed a novel computational method for identifying early-warning signals of the critical transition and its leading network during a disease progression, based on high-throughput data using a small number of samples. The leading network makes the first move from the normal state toward the disease state during a transition, and thus is causally related with disease-driving genes or networks. Specifically, we first define a state-transition-based local network entropy (SNE), and prove that SNE can serve as a general early-warning indicator of any imminent transitions, regardless of specific differences among systems. The effectiveness of this method was validated by functional analysis and experimental data.

We develop an auto-reservoir computing framework, Auto-Reservoir Neural Network (ARNN), to efficiently and accurately make multi-step-ahead predictions based on a short-term high-dimensional time series. Different from traditional reservoir computing whose reservoir is an external dynamical system irrelevant to the target system, ARNN directly transforms the observed high-dimensional dynamics as its reservoir, which maps the high-dimensional/spatial data to the future temporal values of a target variable based on our spatiotemporal information (STI) transformation. Thus, the multi-step prediction of the target variable is achieved in an accurate and computationally efficient manner. ARNN is successfully applied to both representative models and real-world datasets, all of which show satisfactory performance in the multi-step-ahead prediction, even when the data are perturbed by noise and when the system is time-varying. Actually, such ARNN transformation equivalently expands the sample size and thus has great potential in practical applications in artificial intelligence and machine learning.

Identifying early warning signals of critical transitions during disease progression is a key to achieving early diagnosis of complex diseases. By exploiting rich information of high-throughput data, a novel model-free method has been developed to detect early warning signals of diseases. Its theoretical foundation is based on dynamical network biomarker (DNB), which is also called as the driver (or leading) network of the disease because components or molecules in DNB actually drive the whole system from one state (e.g. normal state) to another (e.g. disease state). In this article, we first reviewed the concept and main results of DNB theory, and then applied the new method to the analysis of type 2 diabetes mellitus (T2DM). Specifically, based on the temporal-spatial gene expression data of T2DM, we identified tissue-specific DNBs corresponding to the critical transitions occurring in liver, adipose and muscle during T2DM development and progression. Actually, we found that there are two different critical states during T2DM development characterized as responses to insulin resistance and serious inflammation, respectively. Interestingly, a new T2DM-associated function, i.e. steroid hormone biosynthesis, was discovered, and those related genes were significantly dysregulated in liver and adipose at the first critical transition during T2DM deterioration. Moreover, the dysfunction of genes related to responding hormone was also detected in muscle at the similar period. Based on the functional and network analysis on pathogenic molecular mechanism of T2DM, we showed that most of DNB genes, in particular the core ones, tended to be located at the upstream of biological pathways, which implied that DNB genes act as the causal factors rather than the consequence to drive the downstream molecules to change their transcriptional activities. This also validated our theoretical prediction of DNB as the driver network. As shown in this study, DNB can not only signal the emergence of the critical transitions for early diagnosis of diseases, but can also provide the causal network of the transitions for revealing molecular mechanisms of disease initiation and progression at a network level.