An S-System Parameter Estimation Method (SPEM) for biological networks

Reverse engineering genetic networks using nonlinear saturation kinetics

A gene regulatory network (GRN) represents a set of genes along with their regulatory interactions. Cellular behavior is driven by genetic level interactions. Dynamics of such systems show nonlinear saturation kinetics which can be best modeled by Michaelis-Menten (MM) and Hill equations. Although MM equation is being widely used for modeling biochemical processes, it has been applied rarely for reverse engineering GRNs. In this paper, we develop a complete framework for a novel model for GRN inference using MM kinetics. A set of coupled equations is first proposed for modeling GRNs. In the coupled model, Michaelis-Menten constant associated with regulation by a gene is made invariant irrespective of the gene being regulated. The parameter estimation of the proposed model is carried out using an evolutionary optimization method, namely, trigonometric differential evolution (TDE). Subsequently, the model is further improved and the regulations of different genes by a given gene are made distinct by allowing varying values of Michaelis-Menten constants for each regulation. Apart from making the model more relevant biologically, the improvement results in a decoupled GRN model with fast estimation of model parameters. Further, to enhance exploitation of the search, we propose a local search algorithm based on hill climbing heuristics. A novel mutation operation is also proposed to avoid population stagnation and premature convergence. Real life benchmark data sets generated in vivo are used for validating the proposed model. Further, we also analyze realistic in silico datasets generated using GeneNetweaver. The comparison of the performance of proposed model with other existing methods shows the potential of the proposed model.

Evaluation of artificial time series microarray data for dynamic gene regulatory network inference

High-throughput technology like microarrays is widely used in the inference of gene regulatory networks (GRNs). We focused on time series data since we are interested in the dynamics of GRNs and the identification of dynamic networks. We evaluated the amount of information that exists in artificial time series microarray data and the ability of an inference process to produce accurate models based on them. We used dynamic artificial gene regulatory networks in order to create artificial microarray data. Key features that characterize microarray data such as the time separation of directly triggered genes, the percentage of directly triggered genes and the triggering function type were altered in order to reveal the limits that are imposed by the nature of microarray data on the inference process. We examined the effect of various factors on the inference performance such as the network size, the presence of noise in microarray data, and the network sparseness. We used a system theory approach and examined the relationship between the pole placement of the inferred system and the inference performance. We examined the relationship between the inference performance in the time domain and the true system parameter identification. Simulation results indicated that time separation and the percentage of directly triggered genes are crucial factors. Also, network sparseness, the triggering function type and noise in input data affect the inference performance. When two factors were simultaneously varied, it was found that variation of one parameter significantly affects the dynamic response of the other. Crucial factors were also examined using a real GRN and acquired results confirmed simulation findings with artificial data. Different initial conditions were also used as an alternative triggering approach. Relevant results confirmed that the number of datasets constitutes the most significant parameter with regard to the inference performance.

A scalable algorithm for structure identification of complex gene regulatory network from temporal expression data

Background

Gene regulatory interactions are of fundamental importance to various biological functions and processes. However, only a few previous computational studies have claimed success in revealing genome-wide regulatory landscapes from temporal gene expression data, especially for complex eukaryotes like human. Moreover, recent work suggests that these methods still suffer from the curse of dimensionality if a network size increases to 100 or higher.

Results

Here we present a novel scalable algorithm for identifying genome-wide gene regulatory network (GRN) structures, and we have verified the algorithm performances by extensive simulation studies based on the DREAM challenge benchmark data. The highlight of our method is that its superior performance does not degenerate even for a network size on the order of 10⁴, and is thus readily applicable to large-scale complex networks. Such a breakthrough is achieved by considering both prior biological knowledge and multiple topological properties (i.e., sparsity and hub gene structure) of complex networks in the regularized formulation. We also validate and illustrate the application of our algorithm in practice using the time-course gene expression data from a study on human respiratory epithelial cells in response to influenza A virus (IAV) infection, as well as the CHIP-seq data from ENCODE on transcription factor (TF) and target gene interactions. An interesting finding, owing to the proposed algorithm, is that the biggest hub structures (e.g., top ten) in the GRN all center at some transcription factors in the context of epithelial cell infection by IAV.

Conclusions

The proposed algorithm is the first scalable method for large complex network structure identification. The GRN structure identified by our algorithm could reveal possible biological links and help researchers to choose which gene functions to investigate in a biological event. The algorithm described in this article is implemented in MATLAB ^Ⓡ, and the source code is freely available from https://github.com/Hongyu-Miao/DMI.git.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-017-1489-z) contains supplementary material, which is available to authorized users.

Reverse engineering gene regulatory networks from measurement with missing values

Background

Gene expression time series data are usually in the form of high-dimensional arrays. Unfortunately, the data may sometimes contain missing values: for either the expression values of some genes at some time points or the entire expression values of a single time point or some sets of consecutive time points. This significantly affects the performance of many algorithms for gene expression analysis that take as an input, the complete matrix of gene expression measurement. For instance, previous works have shown that gene regulatory interactions can be estimated from the complete matrix of gene expression measurement. Yet, till date, few algorithms have been proposed for the inference of gene regulatory network from gene expression data with missing values.

Results

We describe a nonlinear dynamic stochastic model for the evolution of gene expression. The model captures the structural, dynamical, and the nonlinear natures of the underlying biomolecular systems. We present point-based Gaussian approximation (PBGA) filters for joint state and parameter estimation of the system with one-step or two-step missing measurements. The PBGA filters use Gaussian approximation and various quadrature rules, such as the unscented transform (UT), the third-degree cubature rule and the central difference rule for computing the related posteriors. The proposed algorithm is evaluated with satisfying results for synthetic networks, in silico networks released as a part of the DREAM project, and the real biological network, the in vivo reverse engineering and modeling assessment (IRMA) network of yeast Saccharomyces cerevisiae.

Conclusion

PBGA filters are proposed to elucidate the underlying gene regulatory network (GRN) from time series gene expression data that contain missing values. In our state-space model, we proposed a measurement model that incorporates the effect of the missing data points into the sequential algorithm. This approach produces a better inference of the model parameters and hence, more accurate prediction of the underlying GRN compared to when using the conventional Gaussian approximation (GA) filters ignoring the missing data points.

Electronic supplementary material

The online version of this article (doi:10.1186/s13637-016-0055-8) contains supplementary material, which is available to authorized users.

Use of systems biology to decipher host-pathogen interaction networks and predict biomarkers

In systems biology, researchers aim to understand complex biological systems as a whole, which is often achieved by mathematical modelling and the analyses of high-throughput data. In this review, we give an overview of medical applications of systems biology approaches with special focus on host-pathogen interactions. After introducing general ideas of systems biology, we focus on (1) the detection of putative biomarkers for improved diagnosis and support of therapeutic decisions, (2) network modelling for the identification of regulatory interactions between cellular molecules to reveal putative drug targets and (3) module discovery for the detection of phenotype-specific modules in molecular interaction networks. Biomarker detection applies supervised machine learning methods utilizing high-throughput data (e.g. single nucleotide polymorphism (SNP) detection, RNA-seq, proteomics) and clinical data. We demonstrate structural analysis of molecular networks, especially by identification of disease modules as a novel strategy, and discuss possible applications to host-pathogen interactions. Pioneering work was done to predict molecular host-pathogen interactions networks based on dual RNA-seq data. However, currently this network modelling is restricted to a small number of genes. With increasing number and quality of databases and data repositories, the prediction of large-scale networks will also be feasible that can used for multidimensional diagnosis and decision support for prevention and therapy of diseases. Finally, we outline further perspective issues such as support of personalized medicine with high-throughput data and generation of multiscale host-pathogen interaction models.

Towards Semantic Biomedical Problem Solving

Biological and medical intelligence (BMI) has been studied in solos, lacking a systematic methodology. In this paper, we describe how Semantic Computing can enhance biological and medical intelligence. Specifically, we show how Structured Natural Language (SNL) can express many problems in BMI with a finite number of sentence patterns, and show how biological tools, OLAP, data mining tools and statistical analysis tools may be linked to solve problems related to biomedical data.

Properties of sparse penalties on inferring gene regulatory networks from time-course gene expression data

Genes regulate each other and form a gene regulatory network (GRN) to realise biological functions. Elucidating GRN from experimental data remains a challenging problem in systems biology. Numerous techniques have been developed and sparse linear regression methods become a promising approach to infer accurate GRNs. However, most linear methods are either based on steady-state gene expression data or their statistical properties are not analysed. Here, two sparse penalties, adaptive least absolute shrinkage and selection operator and smoothly clipped absolute deviation, are proposed to infer GRNs from time-course gene expression data based on an auto-regressive model and their Oracle properties are proved under mild conditions. The effectiveness of those methods is demonstrated by applications to in silico and real biological data.

Inference of nonlinear gene regulatory networks through optimized ensemble of support vector regression and dynamic Bayesian networks

Comprehensive understanding of gene regulatory networks (GRNs) is a major challenge in systems biology. Most methods for modeling and inferring the dynamics of GRNs, such as those based on state space models, vector autoregressive models and G1DBN algorithm, assume linear dependencies among genes. However, this strong assumption does not make for true representation of time-course relationships across the genes, which are inherently nonlinear. Nonlinear modeling methods such as the S-systems and causal structure identification (CSI) have been proposed, but are known to be statistically inefficient and analytically intractable in high dimensions. To overcome these limitations, we propose an optimized ensemble approach based on support vector regression (SVR) and dynamic Bayesian networks (DBNs). The method called SVR-DBN, uses nonlinear kernels of the SVR to infer the temporal relationships among genes within the DBN framework. The two-stage ensemble is further improved by SVR parameter optimization using Particle Swarm Optimization. Results on eight insilico-generated datasets, and two real world datasets of Drosophila Melanogaster and Escherichia Coli, show that our method outperformed the G1DBN algorithm by a total average accuracy of 12%. We further applied our method to model the time-course relationships of ovarian carcinoma. From our results, four hub genes were discovered. Stratified analysis further showed that the expression levels Prostrate differentiation factor and BTG family member 2 genes, were significantly increased by the cisplatin and oxaliplatin platinum drugs; while expression levels of Polo-like kinase and Cyclin B1 genes, were both decreased by the platinum drugs. These hub genes might be potential biomarkers for ovarian carcinoma.

Properties of sparse penalties on inferring gene regulatory networks from time-course gene expression data

Genes regulate each other and form a gene regulatory network (GRN) to realise biological functions. Elucidating GRN from experimental data remains a challenging problem in systems biology. Numerous techniques have been developed and sparse linear regression methods become a promising approach to infer accurate GRNs. However, most linear methods are either based on steady-state gene expression data or their statistical properties are not analysed. Here, two sparse penalties, adaptive least absolute shrinkage and selection operator and smoothly clipped absolute deviation, are proposed to infer GRNs from time-course gene expression data based on an auto-regressive model and their Oracle properties are proved under mild conditions. The effectiveness of those methods is demonstrated by applications to in silico and real biological data.

A group LASSO-based method for robustly inferring gene regulatory networks from multiple time-course datasets

BACKGROUND

As an abstract mapping of the gene regulations in the cell, gene regulatory network is important to both biological research study and practical applications. The reverse engineering of gene regulatory networks from microarray gene expression data is a challenging research problem in systems biology. With the development of biological technologies, multiple time-course gene expression datasets might be collected for a specific gene network under different circumstances. The inference of a gene regulatory network can be improved by integrating these multiple datasets. It is also known that gene expression data may be contaminated with large errors or outliers, which may affect the inference results.

RESULTS

A novel method, Huber group LASSO, is proposed to infer the same underlying network topology from multiple time-course gene expression datasets as well as to take the robustness to large error or outliers into account. To solve the optimization problem involved in the proposed method, an efficient algorithm which combines the ideas of auxiliary function minimization and block descent is developed. A stability selection method is adapted to our method to find a network topology consisting of edges with scores. The proposed method is applied to both simulation datasets and real experimental datasets. It shows that Huber group LASSO outperforms the group LASSO in terms of both areas under receiver operating characteristic curves and areas under the precision-recall curves.

CONCLUSIONS

The convergence analysis of the algorithm theoretically shows that the sequence generated from the algorithm converges to the optimal solution of the problem. The simulation and real data examples demonstrate the effectiveness of the Huber group LASSO in integrating multiple time-course gene expression datasets and improving the resistance to large errors or outliers.

Biochemical Systems Theory: A Review

Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools that facilitate the analysis of dynamic biological systems. This paper depicts major developments in BST up to the current state of the art in 2012. It discusses its rationale, describes the typical strategies and methods of designing, diagnosing, analyzing, and utilizing BST models, and reviews areas of application. The paper is intended as a guide for investigators entering the fascinating field of biological systems analysis and as a resource for practitioners and experts.