Stochastic S-system modeling of gene regulatory network

Filter feature selection based Boolean Modelling for Genetic Network Inference

The reconstruction of Gene Regulatory Networks (GRNs) from time series gene expression data is highly relevant for the discovery of complex biological interactions and dynamics. Various computational strategies have been developed for this task, but most approaches have low computational efficiency and are not able to cope with high-dimensional, low sample-number, gene expression data. In this paper, we introduce a novel combined filter feature selection approach for efficient and accurate inference of GRNs. A Boolean framework for network modelling is used to demonstrate the efficacy of the proposed approach. Using discretized microarray expression data, the genes most relevant to each target gene are first filtered using ReliefF, an instance-based feature ranking method that is here applied for the first time to GRN inference. Then, further gene selection from the filtered-gene list is done using a mutual information-based min-redundancy max-relevance criterion by eliminating irrelevant genes. This combined method is executed on resampled datasets to finalize the optimal set of regulatory genes. Building upon our previous research, a Pearson correlation coefficient-based Boolean modelling approach is utilized for the efficient identification of the optimal regulatory rules associated with selected regulatory genes. The proposed approach was evaluated using gene expression datasets from small-scale and medium-scale real gene networks, and was observed to be more effective than Linear Discriminant Analysis, performed better than the individual feature selection methods, and obtained improved Structural Accuracy with a higher number of true positives than other state-of-the-art methods, while outperforming these methods with respect to Dynamic Accuracy and efficiency.

Reverse engineering gene regulatory network based on complex-valued ordinary differential equation model

BACKGROUND

The growing researches of molecular biology reveal that complex life phenomena have the ability to demonstrating various types of interactions in the level of genomics. To establish the interactions between genes or proteins and understand the intrinsic mechanisms of biological systems have become an urgent need and study hotspot.

RESULTS

In order to forecast gene expression data and identify more accurate gene regulatory network, complex-valued version of ordinary differential equation (CVODE) is proposed in this paper. In order to optimize CVODE model, a complex-valued hybrid evolutionary method based on Grammar-guided genetic programming and complex-valued firefly algorithm is presented.

CONCLUSIONS

When tested on three real gene expression datasets from E. coli and Human Cell, the experiment results suggest that CVODE model could improve 20-50% prediction accuracy of gene expression data, which could also infer more true-positive regulatory relationships and less false-positive regulations than ordinary differential equation.

Root locus-based stability analysis for biological systems

Background: The first objective for realizing and handling biological systems is to choose a suitable model prototype and then perform structure and parameter identification. Afterwards, a theoretical analysis is needed to understand the characteristics, abilities, and limitations of the underlying systems. Generalized Michaelis-Menten kinetics (MM) and S-systems are two well-known biochemical system theory-based models. Research on steady-state estimation of generalized MM systems is difficult because of their complex structure. Further, theoretical analysis of S-systems is still difficult because of the power-law structure, and even the estimation of steady states can be easily achieved via algebraic equations. Aim: We focus on how to flexibly use control technologies to perform deeper biological system analysis. Methods: For generalized MM systems, the root locus method (proposed by Walter R. Evans) is used to predict the direction and rate (flux) limitations of the reaction and to estimate the steady states and stability margins (relative stability). Mode analysis is additionally introduced to discuss the transient behavior and the setting time. For S-systems, the concept of root locus, mode analysis, and the converse theorem are used to predict the dynamic behavior, to estimate the setting time and to analyze the relative stability of systems. Theoretical results were examined via simulation in a Simulink/MATLAB environment. Results: Four kinds of small functional modules (a system with reversible MM kinetics, a system with a singular or nearly singular system matrix and systems with cascade or branch pathways) are used to describe the proposed strategies clearly. For the reversible MM kinetics system, we successfully predict the direction and the rate (flux) limitations of reactions and obtain the values of steady state and net flux. We observe that theoretically derived results are consistent with simulation results. Good prediction is observed ([Formula: see text]% accuracy). For the system with a (nearly) singular matrix, we demonstrate that the system is neither globally exponentially stable nor globally asymptotically stable but globally semistable. The system possesses an infinite gain margin (GM denoting how much the gain can increase before the system becomes unstable) regardless of how large or how small the values of independent variables are, but the setting time decreases and then increases or always decreases as the values of independent variables increase. For S-systems, we first demonstrate that the stability of S-systems can be determined by linearized systems via root loci, mode analysis, and block diagram-based simulation. The relevant S-systems possess infinite GM for the values of independent variables varying from zero to infinity, and the setting time increases as the values of independent variables increase. Furthermore, the branch pathway maintains oscillation until a steady state is reached, but the oscillation phenomenon does not exist in the cascade pathway because in this system, all of the root loci are located on real lines. The theoretical predictions of dynamic behavior for these two systems are consistent with the simulation results. This study provides a guideline describing how to choose suitable independent variables such that systems possess satisfactory performance for stability margins, setting time and dynamic behavior. Conclusion: The proposed root locus-based analysis can be applied to any kind of differential equation-based biological system. This research initiates a method to examine system dynamic behavior and to discuss operating principles.

Uncovering cancer gene regulation by accurate regulatory network inference from uninformative data

The interactions among the components of a living cell that constitute the gene regulatory network (GRN) can be inferred from perturbation-based gene expression data. Such networks are useful for providing mechanistic insights of a biological system. In order to explore the feasibility and quality of GRN inference at a large scale, we used the L1000 data where ~1000 genes have been perturbed and their expression levels have been quantified in 9 cancer cell lines. We found that these datasets have a very low signal-to-noise ratio (SNR) level causing them to be too uninformative to infer accurate GRNs. We developed a gene reduction pipeline in which we eliminate uninformative genes from the system using a selection criterion based on SNR, until reaching an informative subset. The results show that our pipeline can identify an informative subset in an overall uninformative dataset, allowing inference of accurate subset GRNs. The accurate GRNs were functionally characterized and potential novel cancer-related regulatory interactions were identified.

A non-linear reverse-engineering method for inferring genetic regulatory networks

Hematopoiesis is a highly complex developmental process that produces various types of blood cells. This process is regulated by different genetic networks that control the proliferation, differentiation, and maturation of hematopoietic stem cells (HSCs). Although substantial progress has been made for understanding hematopoiesis, the detailed regulatory mechanisms for the fate determination of HSCs are still unraveled. In this study, we propose a novel approach to infer the detailed regulatory mechanisms. This work is designed to develop a mathematical framework that is able to realize nonlinear gene expression dynamics accurately. In particular, we intended to investigate the effect of possible protein heterodimers and/or synergistic effect in genetic regulation. This approach includes the Extended Forward Search Algorithm to infer network structure (top-down approach) and a non-linear mathematical model to infer dynamical property (bottom-up approach). Based on the published experimental data, we study two regulatory networks of 11 genes for regulating the erythrocyte differentiation pathway and the neutrophil differentiation pathway. The proposed algorithm is first applied to predict the network topologies among 11 genes and 55 non-linear terms which may be for heterodimers and/or synergistic effect. Then, the unknown model parameters are estimated by fitting simulations to the expression data of two different differentiation pathways. In addition, the edge deletion test is conducted to remove possible insignificant regulations from the inferred networks. Furthermore, the robustness property of the mathematical model is employed as an additional criterion to choose better network reconstruction results. Our simulation results successfully realized experimental data for two different differentiation pathways, which suggests that the proposed approach is an effective method to infer the topological structure and dynamic property of genetic regulations.

Modeling Long ncRNA-Mediated Regulation in the Mammalian Cell Cycle

Long noncoding RNAs (lncRNAs) are transcripts longer than 200 nucleotides that are not translated into proteins. They have recently gained widespread attention due to the finding that tens of thousands of lncRNAs reside in the human genome, and due to an increasing number of lncRNAs that are found to be associated with disease. Some lncRNAs, including disease-associated ones, play different roles in regulating the cell cycle. Mathematical models of the cell cycle have been useful in better understanding this biological system, such as how it could be robust to some perturbations and how the cell cycle checkpoints could act as a switch. Here, we discuss mathematical modeling techniques for studying lncRNA regulation of the mammalian cell cycle. We present examples on how modeling via network analysis and differential equations can provide novel predictions toward understanding cell cycle regulation in response to perturbations such as DNA damage.

Dynamic modeling and network approaches for omics time course data: overview of computational approaches and applications

Inferring networks and dynamics of genes, proteins, cells and other biological entities from high-throughput biological omics data is a central and challenging issue in computational and systems biology. This is essential for understanding the complexity of human health, disease susceptibility and pathogenesis for Predictive, Preventive, Personalized and Participatory (P4) system and precision medicine. The delineation of the possible interactions of all genes/proteins in a genome/proteome is a task for which conventional experimental techniques are ill suited. Urgently needed are rapid and inexpensive computational and statistical methods that can identify interacting candidate disease genes or drug targets out of thousands that can be further investigated or validated by experimentations. Moreover, identifying biological dynamic systems, and simultaneously estimating the important kinetic structural and functional parameters, which may not be experimentally accessible could be important directions for drug-disease-gene network studies. In this article, we present an overview and comparison of recent developments of dynamic modeling and network approaches for time-course omics data, and their applications to various biological systems, health conditions and disease statuses. Moreover, various data reduction and analytical schemes ranging from mathematical to computational to statistical methods are compared including their merits, drawbacks and limitations. The most recent software, associated web resources and other potentials for the compared methods are also presented and discussed in detail.

Simulink-Based Analysis for Coupled Metabolic Systems

Stability analysis and dynamic simulation are important for researchers to capture the performance and the properties of underling systems. S-systems have good potential for characterizing dynamic interactive behaviour of large scale metabolic and genetic systems. It is important to develop a platform to achieve timely dynamic behaviour of S-systems to various situations. In this study, we first set up the respective block diagrams of S-systems for module-based simulation. We then derive reasonable theorems to examine the stability of S-systems and find out what kinds of environmental situations will make systems stable. Three canonical systems are used to examine the results which are carried out in the Matlab/Simulink environments.

Computational dynamic approaches for temporal omics data with applications to systems medicine

Modeling and predicting biological dynamic systems and simultaneously estimating the kinetic structural and functional parameters are extremely important in systems and computational biology. This is key for understanding the complexity of the human health, drug response, disease susceptibility and pathogenesis for systems medicine. Temporal omics data used to measure the dynamic biological systems are essentials to discover complex biological interactions and clinical mechanism and causations. However, the delineation of the possible associations and causalities of genes, proteins, metabolites, cells and other biological entities from high throughput time course omics data is challenging for which conventional experimental techniques are not suited in the big omics era. In this paper, we present various recently developed dynamic trajectory and causal network approaches for temporal omics data, which are extremely useful for those researchers who want to start working in this challenging research area. Moreover, applications to various biological systems, health conditions and disease status, and examples that summarize the state-of-the art performances depending on different specific mining tasks are presented. We critically discuss the merits, drawbacks and limitations of the approaches, and the associated main challenges for the years ahead. The most recent computing tools and software to analyze specific problem type, associated platform resources, and other potentials for the dynamic trajectory and interaction methods are also presented and discussed in detail.

External Noise and External Signal Induced Transition of Gene Switch and Coherence Resonance in the Genetic Regulatory System

The transition of gene switch induced by external noises (multiplicative external noise and additive external noise) and external signals is investigated in the genetic regulatory system. Results show that the state-to-state transition of gene switch as well as resonant behaviors, such as the explicit coherence resonance (ECR), implicit coherence resonance (ICR) and control parameter coherence biresonance (CPCBR), can appear when noises are injected into the genetic regulatory system. The ECR is increased with the increase of the control parameter value when starting from the supercritical Hopf bifurcation parameter point, and there exists a critical control parameter value for the occurrence of ECR. However, the ICR is decreased as the control parameter value is increased when starting from the subcritical Hopf bifurcation point. In particular, the coherence of ECR is higher and more sensitive to noise than that of ICR. When an external signal is introduced into the system, the enhancement or suppression of the CPCBR and the number of peaks strongly depend on the frequency and amplitude of the external signal. Furthermore, the gene regulation system can selectively enhance or decrease the noise-induced oscillation signals at preferred frequency and amplitude of an external signal.

A novel algorithm with differential evolution and coral reef optimization for extreme learning machine training

Extreme learning machine (ELM) is a novel and fast learning method to train single layer feed-forward networks. However due to the demand for larger number of hidden neurons, the prediction speed of ELM is not fast enough. An evolutionary based ELM with differential evolution (DE) has been proposed to reduce the prediction time of original ELM. But it may still get stuck at local optima. In this paper, a novel algorithm hybridizing DE and metaheuristic coral reef optimization (CRO), which is called differential evolution coral reef optimization (DECRO), is proposed to balance the explorative power and exploitive power to reach better performance. The thought and the implement of DECRO algorithm are discussed in this article with detail. DE, CRO and DECRO are applied to ELM training respectively. Experimental results show that DECRO-ELM can reduce the prediction time of original ELM, and obtain better performance for training ELM than both DE and CRO.