Inference of biological S-system using the separable estimation method and the genetic algorithm

The identifiability of gene regulatory networks: the role of observation data

Identifying gene regulatory networks (GRN) from observation data is significant to understand biological systems. Conventional studies focus on improving the performance of identification algorithms. However, besides algorithm performance, the GRN identification is strongly depended on the observation data. In this work, for three GRN S-system models, three observation data collection schemes are used to perform the identifiability test procedure. A modified genetic algorithm-particle swarm optimization algorithm is proposed to implement this task, including the multi-level mutation operation and velocity limitation strategy. The results show that, in scheme 1 (starting from a special initial condition), the GRN systems are of identifiability using the sufficient transient observation data. In scheme 2, the observation data are short of sufficient system dynamic. The GRN systems are not of identifiability even though the state trajectories can be reproduced. As a special case of scheme 2, i.e., the steady-state observation data, the equilibrium point analysis is given to explain why it is infeasible for GRN identification. In schemes 1 and 2, the observation data are obtained from zero-input GRN systems, which will evolve to the steady state at last. The sufficient transient observation data in scheme 1 can be obtained by changing the experimental conditions. Additionally, the valid observation data can be also obtained by means of adding impulse excitation signal into GRN systems (scheme 3). Consequently, the GRN systems are identifiable using scheme 3. Owing to its universality and simplicity, these results provide a guide for biologists to collect valid observation data for identifying GRNs and to further understand GRN dynamics.

D3GRN: a data driven dynamic network construction method to infer gene regulatory networks

BACKGROUND

To infer gene regulatory networks (GRNs) from gene-expression data is still a fundamental and challenging problem in systems biology. Several existing algorithms formulate GRNs inference as a regression problem and obtain the network with an ensemble strategy. Recent studies on data driven dynamic network construction provide us a new perspective to solve the regression problem.

RESULTS

In this study, we propose a data driven dynamic network construction method to infer gene regulatory network (D3GRN), which transforms the regulatory relationship of each target gene into functional decomposition problem and solves each sub problem by using the Algorithm for Revealing Network Interactions (ARNI). To remedy the limitation of ARNI in constructing networks solely from the unit level, a bootstrapping and area based scoring method is taken to infer the final network. On DREAM4 and DREAM5 benchmark datasets, D3GRN performs competitively with the state-of-the-art algorithms in terms of AUPR.

CONCLUSIONS

We have proposed a novel data driven dynamic network construction method by combining ARNI with bootstrapping and area based scoring strategy. The proposed method performs well on the benchmark datasets, contributing as a competitive method to infer gene regulatory networks in a new perspective.

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

The key processes in biological and chemical systems are described by networks of chemical reactions. From molecular biology to biotechnology applications, computational models of reaction networks are used extensively to elucidate their non-linear dynamics. The model dynamics are crucially dependent on the parameter values which are often estimated from observations. Over the past decade, the interest in parameter and state estimation in models of (bio-) chemical reaction networks (BRNs) grew considerably. The related inference problems are also encountered in many other tasks including model calibration, discrimination, identifiability, and checking, and optimum experiment design, sensitivity analysis, and bifurcation analysis. The aim of this review paper is to examine the developments in literature to understand what BRN models are commonly used, and for what inference tasks and inference methods. The initial collection of about 700 documents concerning estimation problems in BRNs excluding books and textbooks in computational biology and chemistry were screened to select over 270 research papers and 20 graduate research theses. The paper selection was facilitated by text mining scripts to automate the search for relevant keywords and terms. The outcomes are presented in tables revealing the levels of interest in different inference tasks and methods for given models in the literature as well as the research trends are uncovered. Our findings indicate that many combinations of models, tasks and methods are still relatively unexplored, and there are many new research opportunities to explore combinations that have not been considered-perhaps for good reasons. The most common models of BRNs in literature involve differential equations, Markov processes, mass action kinetics, and state space representations whereas the most common tasks are the parameter inference and model identification. The most common methods in literature are Bayesian analysis, Monte Carlo sampling strategies, and model fitting to data using evolutionary algorithms. The new research problems which cannot be directly deduced from the text mining data are also discussed.

Coevolutionary Structure-Redesigned-Based Bacterial Foraging Optimization

This paper presents a Coevolutionary Structure-Redesigned-Based Bacteria Foraging Optimization (CSRBFO) based on the natural phenomenon that most living creatures tend to cooperate with each other so as to fulfill tasks more effectively. Aiming at lowering computational complexity while maintaining the critical search capability of standard bacterial foraging optimization (BFO), we employ a general loop to replace the nested loop and eliminate the reproduction step of BFO. Hence, the proposed CSRBFO only consists of two main steps: (1) chemotaxis and (2) elimination & dispersal. A coevolutionary strategy by which all bacteria can learn from each other and search for optima cooperatively is incorporated into the chemotactic step to accelerate convergence and facilitate accurate search. In the elimination & dispersal step, the three-stage evolutionary strategy with different learning methods for maintaining diversity is studied. An evaluation of the convergence status is then added to determine whether bacteria should move on to the next stage or not. The combination of coevolutionary strategy and convergence status evaluation is expected to balance exploration and exploitation. Experimental results comparing seven well-known heuristic algorithms on 24 benchmark functions demonstrate that the proposed CSRBFO outperforms the comparison algorithms significantly in most of the cases.

Inference of Biochemical S-Systems via Mixed-Variable Multiobjective Evolutionary Optimization

Inference of the biochemical systems (BSs) via experimental data is important for understanding how biochemical components in vivo interact with each other. However, it is not a trivial task because BSs usually function with complex and nonlinear dynamics. As a popular ordinary equation (ODE) model, the S-System describes the dynamical properties of BSs by incorporating the power rule of biochemical reactions but behaves as a challenge because it has a lot of parameters to be confirmed. This work is dedicated to proposing a general method for inference of S-Systems by experimental data, using a biobjective optimization (BOO) model and a specially mixed-variable multiobjective evolutionary algorithm (mv-MOEA). Regarding that BSs are sparse in common sense, we introduce binary variables indicating network connections to eliminate the difficulty of threshold presetting and take data fitting error and the L₀-norm as two objectives to be minimized in the BOO model. Then, a selection procedure that automatically runs tradeoff between two objectives is employed to choose final inference results from the obtained nondominated solutions of the mv-MOEA. Inference results of the investigated networks demonstrate that our method can identify their dynamical properties well, although the automatic selection procedure sometimes ignores some weak connections in BSs.

Recurrent neural network-based modeling of gene regulatory network using elephant swarm water search algorithm

Correct inference of genetic regulations inside a cell from the biological database like time series microarray data is one of the greatest challenges in post genomic era for biologists and researchers. Recurrent Neural Network (RNN) is one of the most popular and simple approach to model the dynamics as well as to infer correct dependencies among genes. Inspired by the behavior of social elephants, we propose a new metaheuristic namely Elephant Swarm Water Search Algorithm (ESWSA) to infer Gene Regulatory Network (GRN). This algorithm is mainly based on the water search strategy of intelligent and social elephants during drought, utilizing the different types of communication techniques. Initially, the algorithm is tested against benchmark small and medium scale artificial genetic networks without and with presence of different noise levels and the efficiency was observed in term of parametric error, minimum fitness value, execution time, accuracy of prediction of true regulation, etc. Next, the proposed algorithm is tested against the real time gene expression data of Escherichia Coli SOS Network and results were also compared with others state of the art optimization methods. The experimental results suggest that ESWSA is very efficient for GRN inference problem and performs better than other methods in many ways.

Reverse engineering of gene regulatory networks based on S-systems and Bat algorithm

The correct inference of gene regulatory networks for the understanding of the intricacies of the complex biological regulations remains an intriguing task for researchers. With the availability of large dimensional microarray data, relationships among thousands of genes can be simultaneously extracted. Among the prevalent models of reverse engineering genetic networks, S-system is considered to be an efficient mathematical tool. In this paper, Bat algorithm, based on the echolocation of bats, has been used to optimize the S-system model parameters. A decoupled S-system has been implemented to reduce the complexity of the algorithm. Initially, the proposed method has been successfully tested on an artificial network with and without the presence of noise. Based on the fact that a real-life genetic network is sparsely connected, a novel Accumulative Cardinality based decoupled S-system has been proposed. The cardinality has been varied from zero up to a maximum value, and this model has been implemented for the reconstruction of the DNA SOS repair network of Escherichia coli. The obtained results have shown significant improvements in the detection of a greater number of true regulations, and in the minimization of false detections compared to other existing methods.

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.

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.

PSO based PI controller design for a solar charger system

Due to global energy crisis and severe environmental pollution, the photovoltaic (PV) system has become one of the most important renewable energy sources. Many previous studies on solar charger integrated system only focus on load charge control or switching Maximum Power Point Tracking (MPPT) and charge control modes. This study used two-stage system, which allows the overall portable solar energy charging system to implement MPPT and optimal charge control of Li-ion battery simultaneously. First, this study designs a DC/DC boost converter of solar power generation, which uses variable step size incremental conductance method (VSINC) to enable the solar cell to track the maximum power point at any time. The voltage was exported from the DC/DC boost converter to the DC/DC buck converter, so that the voltage dropped to proper voltage for charging the battery. The charging system uses constant current/constant voltage (CC/CV) method to charge the lithium battery. In order to obtain the optimum PI charge controller parameters, this study used intelligent algorithm to determine the optimum parameters. According to the simulation and experimental results, the control parameters resulted from PSO have better performance than genetic algorithms (GAs).

Multiobjective identification of controlling areas in neuronal networks

In this paper, we investigate the multiobjective identification of controlling areas in the neuronal network of a cat's brain by considering two measures of controllability simultaneously. By utilizing nondominated sorting mechanisms and composite differential evolution (CoDE), a reference-point-based nondominated sorting composite differential evolution (RP-NSCDE) is developed to tackle the multiobjective identification of controlling areas in the neuronal network. The proposed RP-NSCDE shows its promising performance in terms of accuracy and convergence speed, in comparison to nondominated sorting genetic algorithms II. The proposed method is also compared with other representative statistical methods in the complex network theory, single objective, and constraint optimization methods to illustrate its effectiveness and reliability. It is shown that there exists a tradeoff between minimizing two objectives, and therefore pareto fronts (PFs) can be plotted. The developed approaches and findings can also be applied to coordination control of various kinds of real-world complex networks including biological networks and social networks, and so on.

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.