On the Calculation of System Entropy in Nonlinear Stochastic Biological Networks

An Approximate Method of System Entropy in Discrete-Time Nonlinear Biological Networks

This study discusses the calculation of entropy of discrete-time stochastic biological systems. First, measurement methods of the system entropy of discrete-time linear stochastic networks are introduced. The system entropy is found to be characterized by system matrices of the discrete-time biological systems. Secondly, the system entropy of nonlinear discrete-time stochastic biological systems is discussed and is calculated based on a global linearization method. The approximation of the values of system entropy of nonlinear stochastic systems needs to solve an optimization problem that is constrained by a kind of linear matrix inequality (LMI). Finally, a practical biochemical system is provided to verify the effectiveness of the proposed calculation method.

Entropy as a Robustness Marker in Genetic Regulatory Networks

Genetic regulatory networks have evolved by complexifying their control systems with numerous effectors (inhibitors and activators). That is, for example, the case for the double inhibition by microRNAs and circular RNAs, which introduce a ubiquitous double brake control reducing in general the number of attractors of the complex genetic networks (e.g., by destroying positive regulation circuits), in which complexity indices are the number of nodes, their connectivity, the number of strong connected components and the size of their interaction graph. The stability and robustness of the networks correspond to their ability to respectively recover from dynamical and structural disturbances the same asymptotic trajectories, and hence the same number and nature of their attractors. The complexity of the dynamics is quantified here using the notion of attractor entropy: it describes the way the invariant measure of the dynamics is spread over the state space. The stability (robustness) is characterized by the rate at which the system returns to its equilibrium trajectories (invariant measure) after a dynamical (structural) perturbation. The mathematical relationships between the indices of complexity, stability and robustness are presented in case of Markov chains related to threshold Boolean random regulatory networks updated with a Hopfield-like rule. The entropy of the invariant measure of a network as well as the Kolmogorov-Sinaï entropy of the Markov transition matrix ruling its random dynamics can be considered complexity, stability and robustness indices; and it is possible to exploit the links between these notions to characterize the resilience of a biological system with respect to endogenous or exogenous perturbations. The example of the genetic network controlling the kinin-kallikrein system involved in a pathology called angioedema shows the practical interest of the present approach of the complexity and robustness in two cases, its physiological normal and pathological, abnormal, dynamical behaviors.

Investigating core genetic-and-epigenetic cell cycle networks for stemness and carcinogenic mechanisms, and cancer drug design using big database mining and genome-wide next-generation sequencing data

Recent studies have demonstrated that cell cycle plays a central role in development and carcinogenesis. Thus, the use of big databases and genome-wide high-throughput data to unravel the genetic and epigenetic mechanisms underlying cell cycle progression in stem cells and cancer cells is a matter of considerable interest.

Real genetic-and-epigenetic cell cycle networks (GECNs) of embryonic stem cells (ESCs) and HeLa cancer cells were constructed by applying system modeling, system identification, and big database mining to genome-wide next-generation sequencing data. Real GECNs were then reduced to core GECNs of HeLa cells and ESCs by applying principal genome-wide network projection. In this study, we investigated potential carcinogenic and stemness mechanisms for systems cancer drug design by identifying common core and specific GECNs between HeLa cells and ESCs. Integrating drug database information with the specific GECNs of HeLa cells could lead to identification of multiple drugs for cervical cancer treatment with minimal side-effects on the genes in the common core. We found that dysregulation of miR-29C, miR-34A, miR-98, and miR-215; and methylation of ANKRD1, ARID5B, CDCA2, PIF1, STAMBPL1, TROAP, ZNF165, and HIST1H2AJ in HeLa cells could result in cell proliferation and anti-apoptosis through NFκB, TGF-β, and PI3K pathways. We also identified 3 drugs, methotrexate, quercetin, and mimosine, which repressed the activated cell cycle genes, ARID5B, STK17B, and CCL2, in HeLa cells with minimal side-effects.

Network Biomarkers of Bladder Cancer Based on a Genome-Wide Genetic and Epigenetic Network Derived from Next-Generation Sequencing Data

Epigenetic and microRNA (miRNA) regulation are associated with carcinogenesis and the development of cancer. By using the available omics data, including those from next-generation sequencing (NGS), genome-wide methylation profiling, candidate integrated genetic and epigenetic network (IGEN) analysis, and drug response genome-wide microarray analysis, we constructed an IGEN system based on three coupling regression models that characterize protein-protein interaction networks (PPINs), gene regulatory networks (GRNs), miRNA regulatory networks (MRNs), and epigenetic regulatory networks (ERNs). By applying system identification method and principal genome-wide network projection (PGNP) to IGEN analysis, we identified the core network biomarkers to investigate bladder carcinogenic mechanisms and design multiple drug combinations for treating bladder cancer with minimal side-effects. The progression of DNA repair and cell proliferation in stage 1 bladder cancer ultimately results not only in the derepression of miR-200a and miR-200b but also in the regulation of the TNF pathway to metastasis-related genes or proteins, cell proliferation, and DNA repair in stage 4 bladder cancer. We designed a multiple drug combination comprising gefitinib, estradiol, yohimbine, and fulvestrant for treating stage 1 bladder cancer with minimal side-effects, and another multiple drug combination comprising gefitinib, estradiol, chlorpromazine, and LY294002 for treating stage 4 bladder cancer with minimal side-effects.

Constructing an integrated genetic and epigenetic cellular network for whole cellular mechanism using high-throughput next-generation sequencing data

Background

Epigenetics has been investigated in cancer initiation, and development, especially, since the appearance of epigenomics. Epigenetics may be defined as the mechanisms that lead to heritable changes in gene function and without affecting the sequence of genome. These mechanisms explain how individuals with the same genotype produce phenotypic differences in response to environmental stimuli. Recently, with the accumulation of high-throughput next-generation sequencing (NGS) data, a key goal of systems biology is to construct networks for different cellular levels to explore whole cellular mechanisms. At present, there is no satisfactory method to construct an integrated genetic and epigenetic cellular network (IGECN), which combines NGS omics data with gene regulatory networks (GRNs), microRNAs (miRNAs) regulatory networks, protein-protein interaction networks (PPINs), and epigenetic regulatory networks of methylation using high-throughput NGS data.

Results

We investigated different kinds of NGS omics data to develop a systems biology method to construct an integrated cellular network based on three coupling models that describe genetic regulatory networks, protein–protein interaction networks, microRNA (miRNA) regulatory networks, and methylation regulation. The proposed method was applied to construct IGECNs of gastric cancer and the human immune response to human immunodeficiency virus (HIV) infection, to elucidate human defense response mechanisms. We successfully constructed an IGECN and validated it by using evidence from literature search. The integration of NGS omics data related to transcription regulation, protein-protein interactions, and miRNA and methylation regulation has more predictive power than independent datasets. We found that dysregulation of MIR7 contributes to the initiation and progression of inflammation-induced gastric cancer; dysregulation of MIR9 contributes to HIV-1 infection to hijack CD4+ T cells through dysfunction of the immune and hormone pathways; dysregulation of MIR139-5p, MIRLET7i, and MIR10a contributes to the HIV-1 integration/replication stage; dysregulation of MIR101, MIR141, and MIR152 contributes to the HIV-1 virus assembly and budding mechanisms; dysregulation of MIR302a contributes to not only microvesicle-mediated transfer of miRNAs but also dysfunction of NF-κB signaling pathway in hepatocarcinogenesis.

Conclusion

The coupling dynamic systems of the whole IGECN can allow us to investigate genetic and epigenetic cellular mechanisms via omics data and big database mining, and are useful for further experiments in the field of systems and synthetic biology.