Stochastic Synchronization of Genetic Oscillator Networks

The study of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. Genetic networks are intrinsically noisy due to natural random intra- and inter-cellular fluctuations. Therefore, it is important to study the effects of noise perturbation on the synchronous dynamics of genetic oscillators. From the synthetic biology viewpoint, it is also important to implement biological systems that minimizing the negative influence of the perturbations. In this paper, based on systems biology approach, we provide a general theoretical result on the synchronization of genetic oscillators with stochastic perturbations. By exploiting the specific properties of many genetic oscillator models, we provide an easy-verified sufficient condition for the stochastic synchronization of coupled genetic oscillators, based on the Lur'e system approach in control theory. A design principle for minimizing the influence of noise is also presented. To demonstrate the effectiveness of our theoretical results, a population of coupled repressillators is adopted as a numerical example. In summary, we present an efficient theoretical method for analyzing the synchronization of genetic oscillator networks, which is helpful for understanding and testing the synchronization phenomena in biological organisms. Besides, the results are actually applicable to general oscillator networks.Comment: 14 pages, 4 figure

High-Order Correlation Integration for Single-Cell or Bulk RNA-seq Data Analysis

Quantifying or labeling the sample type with high quality is a challenging task, which is a key step for understanding complex diseases. Reducing noise pollution to data and ensuring the extracted intrinsic patterns in concordance with the primary data structure are important in sample clustering and classification. Here we propose an effective data integration framework named as HCI (High-order Correlation Integration), which takes an advantage of high-order correlation matrix incorporated with pattern fusion analysis (PFA), to realize high-dimensional data feature extraction. On the one hand, the high-order Pearson's correlation coefficient can highlight the latent patterns underlying noisy input datasets and thus improve the accuracy and robustness of the algorithms currently available for sample clustering. On the other hand, the PFA can identify intrinsic sample patterns efficiently from different input matrices by optimally adjusting the signal effects. To validate the effectiveness of our new method, we firstly applied HCI on four single-cell RNA-seq datasets to distinguish the cell types, and we found that HCI is capable of identifying the prior-known cell types of single-cell samples from scRNA-seq data with higher accuracy and robustness than other methods under different conditions. Secondly, we also integrated heterogonous omics data from TCGA datasets and GEO datasets including bulk RNA-seq data, which outperformed the other methods at identifying distinct cancer subtypes. Within an additional case study, we also constructed the mRNA-miRNA regulatory network of colorectal cancer based on the feature weight estimated from HCI, where the differentially expressed mRNAs and miRNAs were significantly enriched in well-known functional sets of colorectal cancer, such as KEGG pathways and IPA disease annotations. All these results supported that HCI has extensive flexibility and applicability on sample clustering with different types and organizations of RNA-seq data

Measuring robustness of community structure in complex networks

The theory of community structure is a powerful tool for real networks, which can simplify their topological and functional analysis considerably. However, since community detection methods have random factors and real social networks obtained from complex systems always contain error edges, evaluating the robustness of community structure is an urgent and important task. In this letter, we employ the critical threshold of resolution parameter in Hamiltonian function, $\gamma_C$, to measure the robustness of a network. According to spectral theory, a rigorous proof shows that the index we proposed is inversely proportional to robustness of community structure. Furthermore, by utilizing the co-evolution model, we provides a new efficient method for computing the value of $\gamma_C$. The research can be applied to broad clustering problems in network analysis and data mining due to its solid mathematical basis and experimental effects.Comment: 6 pages, 4 figures. arXiv admin note: text overlap with arXiv:1303.7434 by other author

Transient Resetting: A Novel Mechanism for Synchrony and Its Biological Examples

The study of synchronization in biological systems is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. In this paper, by using simple dynamical systems theory, we present a novel mechanism, named transient resetting, for the synchronization of uncoupled biological oscillators with stimuli. This mechanism not only can unify and extend many existing results on (deterministic and stochastic) stimulus-induced synchrony, but also may actually play an important role in biological rhythms. We argue that transient resetting is a possible mechanism for the synchronization in many biological organisms, which might also be further used in medical therapy of rhythmic disorders. Examples on the synchronization of neural and circadian oscillators are presented to verify our hypothesis.Comment: 17 pages, 7 figure

Network biomarkers, interaction networks and dynamical network biomarkers in respiratory diseases

Identification and validation of interaction networks and network biomarkers have become more critical and important in the development of disease-specific biomarkers, which are functionally changed during disease development, progression or treatment. The present review headlined the definition, significance, research and potential application for network biomarkers, interaction networks and dynamical network biomarkers (DNB). Disease-specific interaction networks, network biomarkers, or DNB have great significance in the understanding of molecular pathogenesis, risk assessment, disease classification and monitoring, or evaluations of therapeutic responses and toxicities. Protein-based DNB will provide more information to define the differences between the normal and pre-disease stages, which might point to early diagnosis for patients. Clinical bioinformatics should be a key approach to the identification and validation of disease-specific biomarkers

Spatiotemporal convolutional network for time-series prediction and causal inference

Making predictions in a robust way is not easy for nonlinear systems. In this work, a neural network computing framework, i.e., a spatiotemporal convolutional network (STCN), was developed to efficiently and accurately render a multistep-ahead prediction of a time series by employing a spatial-temporal information (STI) transformation. The STCN combines the advantages of both the temporal convolutional network (TCN) and the STI equation, which maps the high-dimensional/spatial data to the future temporal values of a target variable, thus naturally providing the prediction of the target variable. From the observed variables, the STCN also infers the causal factors of the target variable in the sense of Granger causality, which are in turn selected as effective spatial information to improve the prediction robustness. The STCN was successfully applied to both benchmark systems and real-world datasets, all of which show superior and robust performance in multistep-ahead prediction, even when the data were perturbed by noise. From both theoretical and computational viewpoints, the STCN has great potential in practical applications in artificial intelligence (AI) or machine learning fields as a model-free method based only on the observed data, and also opens a new way to explore the observed high-dimensional data in a dynamical manner for machine learning.Comment: 23 pages, 6 figure