Evolutionary modeling and inference of gene network

GRNMOPT: Inference of gene regulatory networks based on a multi-objective optimization approach

BACKGROUND AND OBJECTIVE

The reconstruction of gene regulatory networks (GRNs) stands as a vital approach in deciphering complex biological processes. The application of nonlinear ordinary differential equations (ODEs) models has demonstrated considerable efficacy in predicting GRNs. Notably, the decay rate and time delay are pivotal in authentic gene regulation, yet their systematic determination in ODEs models remains underexplored. The development of a comprehensive optimization framework for the effective estimation of these key parameters is essential for accurate GRN inference.

METHOD

This study introduces GRNMOPT, an innovative methodology for inferring GRNs from time-series and steady-state data. GRNMOPT employs a combined use of decay rate and time delay in constructing ODEs models to authentically represent gene regulatory processes. It incorporates a multi-objective optimization approach, optimizing decay rate and time delay concurrently to derive Pareto optimal sets for these factors, thereby maximizing accuracy metrics such as AUROC (Area Under the Receiver Operating Characteristic curve) and AUPR (Area Under the Precision-Recall curve). Additionally, the use of XGBoost for calculating feature importance aids in identifying potential regulatory gene links.

RESULTS

Comprehensive experimental evaluations on two simulated datasets from DREAM4 and three real gene expression datasets (Yeast, In vivo Reverse-engineering and Modeling Assessment [IRMA], and Escherichia coli [E. coli]) reveal that GRNMOPT performs commendably across varying network scales. Furthermore, cross-validation experiments substantiate the robustness of GRNMOPT.

CONCLUSION

We propose a novel approach called GRNMOPT to infer GRNs based on a multi-objective optimization framework, which effectively improves inference accuracy and provides a powerful tool for GRNs inference.

Inference of gene regulatory networks based on nonlinear ordinary differential equations

Motivation

Gene regulatory networks (GRNs) capture the regulatory interactions between genes, resulting from the fundamental biological process of transcription and translation. In some cases, the topology of GRNs is not known, and has to be inferred from gene expression data. Most of the existing GRNs reconstruction algorithms are either applied to time-series data or steady-state data. Although time-series data include more information about the system dynamics, steady-state data imply stability of the underlying regulatory networks.

Results

In this article, we propose a method for inferring GRNs from time-series and steady-state data jointly. We make use of a non-linear ordinary differential equations framework to model dynamic gene regulation and an importance measurement strategy to infer all putative regulatory links efficiently. The proposed method is evaluated extensively on the artificial DREAM4 dataset and two real gene expression datasets of yeast and Escherichia coli. Based on public benchmark datasets, the proposed method outperforms other popular inference algorithms in terms of overall score. By comparing the performance on the datasets with different scales, the results show that our method still keeps good robustness and accuracy at a low computational complexity.

Availability and implementation

The proposed method is written in the Python language, and is available at: https://github.com/lab319/GRNs_nonlinear_ODEs

Supplementary information

Supplementary data are available at Bioinformatics online.

Metabolic network discovery by top-down and bottom-up approaches and paths for reconciliation

The primary focus in the network-centric analysis of cellular metabolism by systems biology approaches is to identify the active metabolic network for the condition of interest. Two major approaches are available for the discovery of the condition-specific metabolic networks. One approach starts from genome-scale metabolic networks, which cover all possible reactions known to occur in the related organism in a condition-independent manner, and applies methods such as the optimization-based Flux-Balance Analysis to elucidate the active network. The other approach starts from the condition-specific metabolome data, and processes the data with statistical or optimization-based methods to extract information content of the data such that the active network is inferred. These approaches, termed bottom-up and top-down, respectively, are currently employed independently. However, considering that both approaches have the same goal, they can both benefit from each other paving the way for the novel integrative analysis methods of metabolome data- and flux-analysis approaches in the post-genomic era. This study reviews the strengths of constraint-based analysis and network inference methods reported in the metabolic systems biology field; then elaborates on the potential paths to reconcile the two approaches to shed better light on how the metabolism functions.

Massive exploration of perturbed conditions of the blood coagulation cascade through GPU parallelization

The introduction of general-purpose Graphics Processing Units (GPUs) is boosting scientific applications in Bioinformatics, Systems Biology, and Computational Biology. In these fields, the use of high-performance computing solutions is motivated by the need of performing large numbers of in silico analysis to study the behavior of biological systems in different conditions, which necessitate a computing power that usually overtakes the capability of standard desktop computers. In this work we present coagSODA, a CUDA-powered computational tool that was purposely developed for the analysis of a large mechanistic model of the blood coagulation cascade (BCC), defined according to both mass-action kinetics and Hill functions. coagSODA allows the execution of parallel simulations of the dynamics of the BCC by automatically deriving the system of ordinary differential equations and then exploiting the numerical integration algorithm LSODA. We present the biological results achieved with a massive exploration of perturbed conditions of the BCC, carried out with one-dimensional and bi-dimensional parameter sweep analysis, and show that GPU-accelerated parallel simulations of this model can increase the computational performances up to a 181× speedup compared to the corresponding sequential simulations.

A review on the computational approaches for gene regulatory network construction

Many biological research areas such as drug design require gene regulatory networks to provide clear insight and understanding of the cellular process in living cells. This is because interactions among the genes and their products play an important role in many molecular processes. A gene regulatory network can act as a blueprint for the researchers to observe the relationships among genes. Due to its importance, several computational approaches have been proposed to infer gene regulatory networks from gene expression data. In this review, six inference approaches are discussed: Boolean network, probabilistic Boolean network, ordinary differential equation, neural network, Bayesian network, and dynamic Bayesian network. These approaches are discussed in terms of introduction, methodology and recent applications of these approaches in gene regulatory network construction. These approaches are also compared in the discussion section. Furthermore, the strengths and weaknesses of these computational approaches are described.

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.

Parameter estimation using meta-heuristics in systems biology: a comprehensive review

This paper gives a comprehensive review of the application of meta-heuristics to optimization problems in systems biology, mainly focussing on the parameter estimation problem (also called the inverse problem or model calibration). It is intended for either the system biologist who wishes to learn more about the various optimization techniques available and/or the meta-heuristic optimizer who is interested in applying such techniques to problems in systems biology. First, the parameter estimation problems emerging from different areas of systems biology are described from the point of view of machine learning. Brief descriptions of various meta-heuristics developed for these problems follow, along with outlines of their advantages and disadvantages. Several important issues in applying meta-heuristics to the systems biology modelling problem are addressed, including the reliability and identifiability of model parameters, optimal design of experiments, and so on. Finally, we highlight some possible future research directions in this field.

Genetic networks and soft computing

The analysis of gene regulatory networks provides enormous information on various fundamental cellular processes involving growth, development, hormone secretion, and cellular communication. Their extraction from available gene expression profiles is a challenging problem. Such reverse engineering of genetic networks offers insight into cellular activity toward prediction of adverse effects of new drugs or possible identification of new drug targets. Tasks such as classification, clustering, and feature selection enable efficient mining of knowledge about gene interactions in the form of networks. It is known that biological data is prone to different kinds of noise and ambiguity. Soft computing tools, such as fuzzy sets, evolutionary strategies, and neurocomputing, have been found to be helpful in providing low-cost, acceptable solutions in the presence of various types of uncertainties. In this paper, we survey the role of these soft methodologies and their hybridizations, for the purpose of generating genetic networks.

Finding alternatives and reduced formulations for process-based models

This paper addresses the problem of model complexity commonly arising in constructing and using process-based models with intricate interactions. Apart from complex process details the dynamic behavior of such systems is often limited to a discrete number of typical states. Thus, models reproducing the system's processes in all details are often too complex and over-parameterized. In order to reduce simulation times and to get a better impression of the important mechanisms, simplified formulations are desirable. In this work a data adaptive model reduction scheme that automatically builds simple models from complex ones is proposed. The method can be applied to the transformation and reduction of systems of ordinary differential equations. It consists of a multistep approach using a low dimensional projection of the model data followed by a Genetic Programming/Genetic Algorithm hybrid to evolve new model systems. As the resulting models again consist of differential equations, their process-based interpretation in terms of new state variables becomes possible. Transformations of two simple models with oscillatory dynamics, simulating a mathematical pendulum and predator-prey interactions respectively, serve as introductory examples of the method's application. The resulting equations of force indicate the predator-prey system's equivalence to a nonlinear oscillator. In contrast to the simple pendulum it contains driving and damping forces that produce a stable limit cycle.

Inferring adaptive regulation thresholds and association rules from gene expression data through combinatorial optimization learning

There is a need to design computational methods to support the prediction of gene regulatory networks. Such models should offer both biologically-meaningful and computationally-accurate predictions, which in combination with other techniques may improve large-scale, integrative studies. This paper presents a new machine learning method for the prediction of putative regulatory associations from expression data, which exhibit properties never or only partially addressed by other techniques recently published. The method was tested on a Saccharomyces cerevisiae gene expression dataset. The results were statistically validated and compared with the relationships inferred by two machine learning approaches to gene regulatory network prediction. Furthermore, the resulting predictions were assessed using domain knowledge. The proposed algorithm may be able to accurately predict relevant biological associations between genes. One of the most relevant features of this new method is the prediction of adaptive regulation thresholds for the discretization of gene expression values, which is required prior to the rule association learning process. Moreover, an important advantage consists of its low computational cost to infer association rules. The proposed system may significantly support exploratory, large-scale studies of automated identification of potentially-relevant gene expression associations.

Identification of biochemical networks by S-tree based genetic programming

MOTIVATION

Most previous approaches to model biochemical networks have focused either on the characterization of a network structure with a number of components or on the estimation of kinetic parameters of a network with a relatively small number of components. For system-level understanding, however, we should examine both the interactions among the components and the dynamic behaviors of the components. A key obstacle to this simultaneous identification of the structure and parameters is the lack of data compared with the relatively large number of parameters to be estimated. Hence, there are many plausible networks for the given data, but most of them are not likely to exist in the real system.

RESULTS

We propose a new representation named S-trees for both the structural and dynamical modeling of a biochemical network within a unified scheme. We further present S-tree based genetic programming to identify the structure of a biochemical network and to estimate the corresponding parameter values at the same time. While other evolutionary algorithms require additional techniques for sparse structure identification, our approach can automatically assemble the sparse primitives of a biochemical network in an efficient way. We evaluate our algorithm on the dynamic profiles of an artificial genetic network. In 20 trials for four settings, we obtain the true structure and their relative squared errors are <5% regardless of releasing constraints about structural sparseness. In addition, we confirm that the proposed algorithm is robust within +/-10% noise ratio. Furthermore, the proposed approach ensures a reasonable estimate of a real yeast fermentation pathway. The comparatively less important connections with non-zero parameters can be detected even though their orders are below 10(-2). To demonstrate the usefulness of the proposed algorithm for real experimental biological data, we provide an additional example on the transcriptional network of SOS response to DNA damage in Escherichia coli. We confirm that the proposed algorithm can successfully identify the true structure except only one relation.

Computation intelligent for eukaryotic cell-cycle gene network

Computational intelligent approaches is adopted to construct the S-system of eukaryotic cell cycle for further analysis of genetic regulatory networks. A highly nonlinear power-law differential equation is constructed to describe the transcriptional regulation of gene network from the time-courses dataset. Global artificial algorithm, based on hybrid differential evolution, can achieve global optimization for the highly nonlinear differential gene network modeling. The constructed gene regulatory networks will be a reference for researchers to realize the inhibitory and activatory operator for genes synthesis and decomposition in Eukaryotic cell cycle.

Reverse engineering of biochemical equations from time-course data by means of genetic programming

Increased research aimed at simulating biological systems requires sophisticated parameter estimation methods. All current approaches, including genetic algorithms, need pre-existing equations to be functional. A generalized approach to predict not only parameters but also biochemical equations from only observable time-course information must be developed and a computational method to generate arbitrary equations without knowledge of biochemical reaction mechanisms must be developed. We present a technique to predict an equation using genetic programming. Our technique can search topology and numerical parameters of mathematical expression simultaneously. To improve the search ability of numeric constants, we added numeric mutation to the conventional procedure. As case studies, we predicted two equations of enzyme-catalyzed reactions regarding adenylate kinase and phosphofructokinase. Our numerical experimental results showed that our approach could obtain correct topology and parameters that were close to the originals. The mean errors between given and simulation-predicted time-courses were 1.6 x 10(-5)% and 2.0 x 10(-3)%, respectively. Our equation prediction approach can be applied to identify metabolic reactions from observable time-courses.

Mathematical and computational techniques to deduce complex biochemical reaction mechanisms

Time series data can now be routinely collected for biochemical reaction pathways, and recently, several methods have been proposed to infer reaction mechanisms for metabolic pathways and networks. In this paper we provide a survey of mathematical techniques for determining reaction mechanisms for time series data on the concentration or abundance of different reacting components, with little prior information about the pathways involved.