Adaptive modelling of gene regulatory network using Bayesian information criterion‐guided sparse regression approach

Inferring gene regulatory networks (GRNs) from microarray expression data are an important but challenging issue in systems biology. In this study, the authors propose a Bayesian information criterion (BIC)‐guided sparse regression approach for GRN reconstruction. This approach can adaptively model GRNs by optimising the l ₁ ‐norm regularisation of sparse regression based on a modified version of BIC. The use of the regularisation strategy ensures the inferred GRNs to be as sparse as natural, while the modified BIC allows incorporating prior knowledge on expression regulation and thus avoids the overestimation of expression regulators as usual. Especially, the proposed method provides a clear interpretation of combinatorial regulations of gene expression by optimally extracting regulation coordination for a given target gene. Experimental results on both simulation data and real‐world microarray data demonstrate the competent performance of discovering regulatory relationships in GRN reconstruction.Inspec keywords: genetics, Bayes methods, genomics, regression analysis, inference mechanisms, bioinformaticsOther keywords: adaptive modelling, gene regulatory network, Bayesian information criterion‐guided sparse regression approach, GRN, microarray expression data, systems biology, GRN reconstruction, optimisation, l₁ ‐norm regularisation     

Investigating receptor enzyme activity using time‐scale analysis

At early drug discovery, purified protein‐based assays are often used to characterise compound potency. In the context of dose response, it is often perceived that a time‐independent inhibitor is reversible and a time‐dependent inhibitor is irreversible. The legitimacy of this argument is investigated using a simple kinetics model, where it is revealed by model‐based analytical analysis and numerical studies that dose response of an irreversible inhibitor may appear time‐independent under certain parametric conditions. Hence, the observation of time‐independence cannot be used as sole evidence for identification of inhibitor reversibility. It has also been discussed how the synthesis and degradation of a target receptor affect drug inhibition in an in vitro cell‐based assay setting. These processes may also influence dose response of an irreversible inhibitor in such a way that it appears time‐independent under certain conditions. Furthermore, model‐based steady‐state analysis reveals the complexity nature of the drug–receptor process.Inspec keywords: enzymes, molecular biophysics, drugs, biochemistry, reaction kinetics, cellular biophysicsOther keywords: receptor enzyme activity, time‐scale analysis, drug discovery, purified protein‐based assays, compound potency, dose response, reversible time‐independent inhibitor, irreversible time‐dependent inhibitor, kinetics model, target receptor degradation, drug inhibition, in vitro cell‐based assay setting, model‐based steady‐state analysis, drug‐receptor process     

Gene regulatory network discovery using pairwise Granger causality

Discovery of gene regulatory network from gene expression data can yield a useful insight to drug development. Among the methods applied to time‐series data, Granger causality (GC) has emerged as a powerful tool with several merits. Since gene expression data usually have a much larger number of genes than time points therefore a full model cannot be applied in a straightforward manner, GC is often applied to genes pairwisely. In this study, the authors first investigate with synthetic data how spurious causalities (false discoveries) may arise because of the use of pairwise rather than full‐model GC detection. Furthermore, spurious causalities may also arise if the order of the vector autoregressive model is not high enough. As a remedy, the authors demonstrate that model validation techniques can effectively reduce the number of false discoveries. Then, they apply pairwise GC with model validation to the real human HeLa cell‐cycle dataset. They find that Akaike information criterion is generally most suitable for determining model order, but precaution should be taken for extremely short time series. With the authors proposed implementation, degree distributions and network hubs are obtained and compared with existing results, giving a new observation that the hubs tend to act as sources rather than receivers of interactions.Inspec keywords: biology computing, cancer, causality, cellular biophysics, genetics, genomics, time seriesOther keywords: gene regulatory network discovery, pairwise Granger causality, gene expression data, drug development, time‐series data, synthetic data, spurious causalities, full‐model Granger causality detection, vector autoregressive model, real human HeLa cell‐cycle dataset, Akaike information criterion, degree distributions, network hubs     

Mining gene link information for survival pathway hunting

This study proposes a gene link‐based method for survival time‐related pathway hunting. In this method, the authors incorporate gene link information to estimate how a pathway is associated with cancer patient''s survival time. Specifically, a gene link‐based Cox proportional hazard model (Link‐Cox) is established, in which two linked genes are considered together to represent a link variable and the association of the link with survival time is assessed using Cox proportional hazard model. On the basis of the Link‐Cox model, the authors formulate a new statistic for measuring the association of a pathway with survival time of cancer patients, referred to as pathway survival score (PSS), by summarising survival significance over all the gene links in the pathway, and devise a permutation test to test the significance of an observed PSS. To evaluate the proposed method, the authors applied it to simulation data and two publicly available real‐world gene expression data sets. Extensive comparisons with previous methods show the effectiveness and efficiency of the proposed method for survival pathway hunting.Inspec keywords: cancer, physiological models, bioinformatics, genomicsOther keywords: permutation test, pathway survival score, gene link‐based Cox proportional hazard model, cancer patient survival time, survival time‐related pathway hunting, gene link‐based method     

Retrieving relevant time‐course experiments: a study on Arabidopsis microarrays

Understanding time‐course regulation of genes in response to a stimulus is a major concern in current systems biology. The problem is usually approached by computational methods to model the gene behaviour or its networked interactions with the others by a set of latent parameters. The model parameters can be estimated through a meta‐analysis of available data obtained from other relevant experiments. The key question here is how to find the relevant experiments which are potentially useful in analysing current data. In this study, the authors address this problem in the context of time‐course gene expression experiments from an information retrieval perspective. To this end, they introduce a computational framework that takes a time‐course experiment as a query and reports a list of relevant experiments retrieved from a given repository. These retrieved experiments can then be used to associate the environmental factors of query experiment with the findings previously reported. The model is tested using a set of time‐course Arabidopsis microarrays. The experimental results show that relevant experiments can be successfully retrieved based on content similarity.Inspec keywords: botany, lab‐on‐a‐chip, genetics, bioinformatics, information retrieval, data mining, data analysis, associative processingOther keywords: relevant time‐course experiment retrieval, time‐course Arabidopsis microarray, time‐course gene regulation, stimulus response, systems biology, computational method, gene behaviour model, gene networked interaction, latent parameter, model parameter estimation, meta‐analysis, data analysis, time‐course gene expression experiment, information retrieval, computational framework, time‐course experiment query, relevant experiment list, repository, environmental factor, query experiment, experimental content similarity     

Identification of self‐regulatory network motifs in reverse engineering gene regulatory networks using microarray gene expression data

Gene Regulatory Networks (GRNs) are reconstructed from the microarray gene expression data through diversified computational approaches. This process ensues in symmetric and diagonal interaction of gene pairs that cannot be modelled as direct activation, inhibition, and self‐regulatory interactions. The values of gene co‐expressions could help in identifying co‐regulations among them. The proposed approach aims at computing the differences in variances of co‐expressed genes rather than computing differences in values of mean expressions across experimental conditions. It adopts multivariate co‐variances using principal component analysis (PCA) to predict an asymmetric and non‐diagonal gene interaction matrix, to select only those gene pair interactions that exhibit the maximum variances in gene regulatory expressions. The asymmetric gene regulatory interactions help in identifying the controlling regulatory agents, thus lowering the false positive rate by minimizing the connections between previously unlinked network components. The experimental results on real as well as in silico datasets including time‐series RTX therapy, Arabidopsis thaliana, DREAM‐3, and DREAM‐8 datasets, in comparison with existing state‐of‐the‐art approaches demonstrated the enhanced performance of the proposed approach for predicting positive and negative feedback loops and self‐regulatory interactions. The generated GRNs hold the potential in determining the real nature of gene pair regulatory interactions.Inspec keywords: molecular biophysics, principal component analysis, genetics, biology computing, reverse engineeringOther keywords: controlling regulatory agents, interacting genes, unlinked network components, self‐regulatory interactions, gene pair regulatory interactions, self‐regulatory network motifs, reverse engineering gene regulatory networks, microarray gene expression data, diversified computational approaches, symmetric interaction, diagonal interaction, gene pairs, gene co‐expressions, co‐expressed genes, mean expressions, gene regulatory expressions, asymmetric gene regulatory interactions     

Time‐invariant biological networks with feedback loops: structural equation models and structural identifiability

Quantitative analyses of biological networks such as key biological parameter estimation necessarily call for the use of graphical models. While biological networks with feedback loops are common in reality, the development of graphical model methods and tools that are capable of dealing with feedback loops is still in its infancy. Particularly, inadequate attention has been paid to the parameter identifiability problem for biological networks with feedback loops such that unreliable or even misleading parameter estimates may be obtained. In this study, the structural identifiability analysis problem of time‐invariant linear structural equation models (SEMs) with feedback loops is addressed, resulting in a general and efficient solution. The key idea is to combine Mason''s gain with Wright''s path coefficient method to generate identifiability equations, from which identifiability matrices are then derived to examine the structural identifiability of every single unknown parameter. The proposed method does not involve symbolic or expensive numerical computations, and is applicable to a broad range of time‐invariant linear SEMs with or without explicit latent variables, presenting a remarkable breakthrough in terms of generality. Finally, a subnetwork structure of the C. elegans neural network is used to illustrate the application of the authors’ method in practice.Inspec keywords: matrix algebra, least squares approximations, statistical analysis, parameter estimation, biologyOther keywords: structural identifiability analysis problem, time‐invariant linear structural equation models, feedback loops, identifiability equations, time‐invariant linear SEMs, time‐invariant biological networks, graphical model methods, parameter identifiability problem, biological parameter estimation, subnetwork structure, C. elegans neural network     

Multi‐scale approach for simulating time‐delay biochemical reaction systems

This study presents a multi‐scale approach for simulating time‐delay biochemical reaction systems when there are wide ranges of molecular numbers. The authors construct a new efficient approach based on partitioning into slow and fast subsets in conjunction with predictor–corrector methods. This multi‐scale approach is shown to be much more efficient than existing methods such as the delay stochastic simulation algorithm and the modified next reaction method. Numerical testing on several important problems in systems biology confirms the accuracy and computational efficiency of this approach.Inspec keywords: biochemistry, delays, biological techniques, predictor‐corrector methodsOther keywords: multiscale approach, time‐delay biochemical reaction systems, predictor–corrector methods, delay stochastic simulation algorithm, modified next reaction method, numerical testing, systems biology, method accuracy, computational efficiency     

Overshoot in biological systems modelled by Markov chains: a non‐equilibrium dynamic phenomenon

A number of biological systems can be modelled by Markov chains. Recently, there has been an increasing concern about when biological systems modelled by Markov chains will perform a dynamic phenomenon called overshoot. In this study, the authors found that the steady‐state behaviour of the system will have a great effect on the occurrence of overshoot. They showed that overshoot in general cannot occur in systems that will finally approach an equilibrium steady state. They further classified overshoot into two types, named as simple overshoot and oscillating overshoot. They showed that except for extreme cases, oscillating overshoot will occur if the system is far from equilibrium. All these results clearly show that overshoot is a non‐equilibrium dynamic phenomenon with energy consumption. In addition, the main result in this study is validated with real experimental data.Inspec keywords: Markov processes, physiological modelsOther keywords: biological systems, Markov chains, nonequilibrium dynamic phenomenon, overshoot, steady‐state behaviour, oscillating overshoot, simple overshoot     

Hierarchical parameter estimation of GRN based on topological analysis

Reverse engineering of gene regulatory network (GRN) is an important and challenging task in systems biology. Existing parameter estimation approaches that compute model parameters with the same importance are usually computationally expensive or infeasible, especially in dealing with complex biological networks.In order to improve the efficiency of computational modeling, the paper applies a hierarchical estimation methodology in computational modeling of GRN based on topological analysis. This paper divides nodes in a network into various priority levels using the graph‐based measure and genetic algorithm. The nodes in the first level, that correspond to root strongly connected components(SCC) in the digraph of GRN, are given top priority in parameter estimation. The estimated parameters of vertices in the previous priority level ARE used to infer the parameters for nodes in the next priority level. The proposed hierarchical estimation methodology obtains lower error indexes while consuming less computational resources compared with single estimation methodology. Experimental outcomes with insilico networks and a realistic network show that gene networks are decomposed into no more than four levels, which is consistent with the properties of inherent modularity for GRN. In addition, the proposed hierarchical parameter estimation achieves a balance between computational efficiency and accuracy.Inspec keywords: biology computing, network theory (graphs), reverse engineering, graph theory, genetics, genetic algorithms, directed graphs, parameter estimationOther keywords: hierarchical parameter estimation, GRN, topological analysis, gene regulatory network, important task, computational systems biology, compute model parameters, complex biological networks, efficient information, model quality, parameter reliability, computational modelling, study divides nodes, priority levels, graph‐based measure, previous priority level, hierarchical estimation methodology obtains, computational resources, single time estimation, insilico network, realistic network show, computational efficiency     

Impact of negative feedback in metabolic noise propagation

Synthetic biology combines different branches of biology and engineering aimed at designing synthetic biological circuits able to replicate emergent properties useful for the biotechnology industry, human health and environment. The role of negative feedback in noise propagation for a basic enzymatic reaction scheme is investigated. Two feedback control schemes on enzyme expression are considered: one from the final product of the pathway activity, the other from the enzyme accumulation. Both schemes are designed to provide the same steady‐state average values of the involved players, in order to evaluate the feedback performances according to the same working mode. Computations are carried out numerically and analytically, the latter allowing to infer information on which model parameter setting leads to a more efficient noise attenuation, according to the chosen scheme. In addition to highlighting the role of the feedback in providing a substantial noise reduction, our investigation concludes that the effect of feedback is enhanced by increasing the promoter sensitivity for both schemes. A further interesting biological insight is that an increase in the promoter sensitivity provides more benefits to the feedback from the product with respect to the feedback from the enzyme, in terms of enlarging the parameter design space.Inspec keywords: biotechnology, enzymes, biological techniquesOther keywords: negative feedback impact, metabolic noise propagation, mathematical modelling, synthetic biological circuit, biotechnology industry, human health, environment, enzymatic reaction scheme, feedback control scheme, enzyme expression, enzyme accumulation, negative autoregulation, steady‐state average value, feedback performance, stochastic simulation algorithm, stochastic hybrid system modelling, noise attenuation, substantial noise reduction, feedback effect, parameter design space     

Inferring catalysis in biological systems

In systems biology, one is often interested in the communication patterns between several species, such as genes, enzymes or proteins. These patterns become more recognisable when temporal experiments are performed. This temporal communication can be structured by reaction networks such as gene regulatory networks or signalling pathways. Mathematical modelling of data arising from such networks can reveal important details, thus helping to understand the studied system. In many cases, however, corresponding models still deviate from the observed data. This may be due to unknown but present catalytic reactions. From a modelling perspective, the question of whether a certain reaction is catalysed leads to a large increase of model candidates. For large networks the calibration of all possible models becomes computationally infeasible. We propose a method which determines a substantially reduced set of appropriate model candidates and identifies the catalyst of each reaction at the same time. This is incorporated in a multiple‐step procedure which first extends the network by additional latent variables and subsequently identifies catalyst candidates using similarity analysis methods. Results from synthetic data examples suggest a good performance even for non‐informative data with few observations. Applied on CD95 apoptotic pathway our method provides new insights into apoptosis regulation.Inspec keywords: catalysis, catalysts, biochemistry, genetics, enzymes, biology computing, calibration, molecular clustersOther keywords: inferring catalysis, biological systems, systems biology, communication patterns, genes, enzymes, proteins, time‐resolved experiments, time‐resolved communication, reaction networks, gene regulatory networks, biochemical networks, signalling pathways, mathematical data modelling, catalytic reactions, calibration, catalyst, multiple‐step procedure, latent variables, similarity analysis methods, noninformative data, differentiation apoptotic pathway, cluster     

Lung cancer prediction from microarray data by gene expression programming

Lung cancer is a leading cause of cancer‐related death worldwide. The early diagnosis of cancer has demonstrated to be greatly helpful for curing the disease effectively. Microarray technology provides a promising approach of exploiting gene profiles for cancer diagnosis. In this study, the authors propose a gene expression programming (GEP)‐based model to predict lung cancer from microarray data. The authors use two gene selection methods to extract the significant lung cancer related genes, and accordingly propose different GEP‐based prediction models. Prediction performance evaluations and comparisons between the authors’ GEP models and three representative machine learning methods, support vector machine, multi‐layer perceptron and radial basis function neural network, were conducted thoroughly on real microarray lung cancer datasets. Reliability was assessed by the cross‐data set validation. The experimental results show that the GEP model using fewer feature genes outperformed other models in terms of accuracy, sensitivity, specificity and area under the receiver operating characteristic curve. It is concluded that GEP model is a better solution to lung cancer prediction problems.Inspec keywords: lung, cancer, medical diagnostic computing, patient diagnosis, genetic algorithms, feature selection, learning (artificial intelligence), support vector machines, multilayer perceptrons, radial basis function networks, reliability, sensitivity analysisOther keywords: lung cancer prediction, cancer‐related death, cancer diagnosis, gene profiles, gene expression programming‐based model, gene selection, GEP‐based prediction models, prediction performance evaluations, representative machine learning methods, support vector machine, multilayer perceptron, radial basis function neural network, real microarray lung cancer datasets, cross‐data set validation, reliability, receiver operating characteristic curve     

Gaussian graphical model for identifying significantly responsive regulatory networks from time course high‐throughput data

With rapid accumulation of functional relationships between biological molecules, knowledge‐based networks have been constructed and stocked in many databases. These networks provide curated and comprehensive information for functional linkages among genes and proteins, whereas their activities are highly related with specific phenotypes and conditions. To evaluate a knowledge‐based network in a specific condition, the consistency between its structure and conditionally specific gene expression profiling data are an important criterion. In this study, the authors propose a Gaussian graphical model to evaluate the documented regulatory networks by the consistency between network architectures and time course gene expression profiles. They derive a dynamic Bayesian network model to evaluate gene regulatory networks in both simulated and true time course microarray data. The regulatory networks are evaluated by matching network structure with gene expression to achieve consistency measurement. To demonstrate the effectiveness of the authors method, they identify significant regulatory networks in response to the time course of circadian rhythm. The knowledge‐based networks are screened and ranked by their structural consistencies with dynamic gene expression profiling.Inspec keywords: Bayes methods, biology computing, circadian rhythms, Gaussian processes, genetics, genomics, graphs, molecular biophysics, proteinsOther keywords: Gaussian graphical model, responsive regulatory networks, time course high‐throughput data, biological molecules, dynamic gene expression proflling, circadian rhythm, consistency measurement, matching network structure, simulated time course microarray data, true time course microarray data, dynamic Bayesian network model, time course gene expression proflles, network architectures, documented regulatory networks, speciflc gene expression proflling data, phenotypes, proteins, functional linkages, databases, knowledge‐based networks     

Clustering based on multiple biological information: approach for predicting protein complexes

Protein complexes are a cornerstone of many biological processes. Protein–protein interaction (PPI) data enable a number of computational methods for predicting protein complexes. However, the insufficiency of the PPI data significantly lowers the accuracy of computational methods. In the current work, the authors develop a novel method named clustering based on multiple biological information (CMBI) to discover protein complexes via the integration of multiple biological resources including gene expression profiles, essential protein information and PPI data. First, CMBI defines the functional similarity of each pair of interacting proteins based on the edge‐clustering coefficient and the Pearson correlation coefficient. Second, CMBI selects essential proteins as seeds to build the protein complexes. A redundancy‐filtering procedure is performed to eliminate redundant complexes. In addition to the essential proteins, CMBI also uses other proteins as seeds to expand protein complexes. To check the performance of CMBI, the authors compare the complexes discovered by CMBI with the ones found by other techniques by matching the predicted complexes against the reference complexes. The authors use subsequently GO::TermFinder to analyse the complexes predicted by various methods. Finally, the effect of parameters T and R is investigated. The results from GO functional enrichment and matching analyses show that CMBI performs significantly better than the state‐of‐the‐art methods.Inspec keywords: bioinformatics, correlation methods, filtering theory, genetics, genomics, molecular biophysics, pattern clustering, proteinsOther keywords: matching analysis, GO functional enrichment, GO‐TermFinder, redundancy‐filtering procedure, Pearson correlation coefficient, edge‐clustering coefficient, gene expression profiles, multiple biological resources, computational methods, protein‐protein interaction, biological processes, protein complexes, multiple biological information clustering     

Genetic programming‐based approach to elucidate biochemical interaction networks from data

Biochemical systems are characterised by cyclic/reversible reciprocal actions, non‐linear interactions and a mixed relationship structures (linear and non‐linear; static and dynamic). Deciphering the architecture of such systems using measured data to provide quantitative information regarding the nature of relationships that exist between the measured variables is a challenging proposition. Causality detection is one of the methodologies that are applied to elucidate biochemical networks from such data. Autoregressive‐based modelling approach such as granger causality, partial directed coherence, directed transfer function and canonical variate analysis have been applied on different systems for deciphering such interactions, but with limited success. In this study, the authors propose a genetic programming‐based causality detection (GPCD) methodology which blends evolutionary computation‐based procedures along with parameter estimation methods to derive a mathematical model of the system. Application of the GPCD methodology on five data sets that contained the different challenges mentioned above indicated that GPCD performs better than the other methods in uncovering the exact structure with less false positives. On a glycolysis data set, GPCD was able to fill the ‘interaction gaps’ which were missed by other methods.Inspec keywords: autoregressive processes, biochemistry, biology computing, genetic algorithms, parameter estimation, transfer functionsOther keywords: elucidate biochemical interaction networks, biochemical systems, cyclic‐reversible reciprocal actions, nonlinear interactions, autoregressive‐based modelling, granger causality, transfer function, canonical variate analysis, genetic programming‐based causality detection methodology, GPCD methodology, mathematical model, parameter estimation methods