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     

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.Inspec keywords: genetics, autoregressive processesOther keywords: sparse penalties, gene regulatory networks, time‐course gene expression data, GRN, biological functions, systems biology, sparse linear regression methods, steady‐state gene expression data, adaptive least absolute shrinkage, selection operator, smoothly clipped absolute deviation, autoregressive model, Oracle properties     

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     

Modular bond‐graph modelling and analysis of biomolecular systems

Bond graphs can be used to build thermodynamically‐compliant hierarchical models of biomolecular systems. As bond graphs have been widely used to model, analyse and synthesise engineering systems, this study suggests that they can play the same rôle in the modelling, analysis and synthesis of biomolecular systems. The particular structure of bond graphs arising from biomolecular systems is established and used to elucidate the relation between thermodynamically closed and open systems. Block diagram representations of the dynamics implied by these bond graphs are used to reveal implicit feedback structures and are linearised to allow the application of control‐theoretical methods. Two concepts of modularity are examined: computational modularity where physical correctness is retained and behavioural modularity where module behaviour (such as ultrasensitivity) is retained. As well as providing computational modularity, bond graphs provide a natural formulation of behavioural modularity and reveal the sources of retroactivity. A bond graph approach to reducing retroactivity, and thus inter‐module interaction, is shown to require a power supply such as that provided by the ATP ⇌ ADP + Pi reaction. The mitogen‐activated protein kinase cascade (Raf–MEK–ERK pathway) is used as an illustrative example.Inspec keywords: molecular biophysics, bond graphs, hierarchical systems, thermodynamics, enzymes, physiological models, biology computingOther keywords: signalling networks, behavioural modularity, Michaelis‐Menten kinetics, Raf‐MEK‐ERK pathway, mitogen‐activated protein kinase cascade, ATP⇌ADP + Pi reaction, intermodule interaction, retroactivity, computational modularity, block diagram representations, thermodynamically‐compliant hierarchical models, biomolecular systems, modular bond‐graph modelling     

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     

Structural and practical identifiability analysis of S‐system

In the field of systems biology, biological reaction networks are usually modelled by ordinary differential equations. A sub‐class, the S‐systems representation, is a widely used form of modelling. Existing S‐systems identification techniques assume that the system itself is always structurally identifiable. However, due to practical limitations, biological reaction networks are often only partially measured. In addition, the captured data only covers a limited trajectory, therefore data can only be considered as a local snapshot of the system responses with respect to the complete set of state trajectories over the entire state space. Hence the estimated model can only reflect partial system dynamics and may not be unique. To improve the identification quality, the structural and practical identifiablility of S‐system are studied. The S‐system is shown to be identifiable under a set of assumptions. Then, an application on yeast fermentation pathway was conducted. Two case studies were chosen; where the first case is based on a larger state trajectories and the second case is based on a smaller one. By expanding the dataset which span a relatively larger state space, the uncertainty of the estimated system can be reduced. The results indicated that initial concentration is related to the practical identifiablity.Inspec keywords: biochemistry, differential equations, microorganisms, cellular biophysics, fermentationOther keywords: structural identifiability analysis, practical identifiability analysis, S‐system, system biology, biological reaction networks, ordinary differential equations, local snapshot, state trajectories, estimated model, partial system dynamics, identification quality, yeast fermentation pathway, relatively larger state space     

Crosstalk between pathways enhances the controllability of signalling networks

The control of complex networks is one of the most challenging problems in the fields of biology and engineering. In this study, the authors explored the controllability and control energy of several signalling networks, which consisted of many interconnected pathways, including networks with a bow‐tie architecture. On the basis of the theory of structure controllability, they revealed that biological mechanisms, such as cross‐pathway interactions, compartmentalisation and so on make the networks easier to fully control. Furthermore, using numerical simulations for two realistic examples, they demonstrated that the control energy of normal networks with crosstalk is lower than in networks without crosstalk. These results indicate that the biological networks are optimally designed to achieve their normal functions from the viewpoint of the control theory. The authors’ work provides a comprehensive understanding of the impact of network structures and properties on controllability.Inspec keywords: genetics, numerical analysis, control theoryOther keywords: signalling network controllability, interconnected pathways, bow‐tie architecture, structure controllability, biological mechanisms, cross‐pathway interactions, numerical simulations, biological networks, control theory, gene regulatory network     

M‐matrix‐based stability conditions for genetic regulatory networks with time‐varying delays and noise perturbations

Stability is essential for designing and controlling any dynamic systems. Recently, the stability of genetic regulatory networks has been widely studied by employing linear matrix inequality (LMI) approach, which results in checking the existence of feasible solutions to high‐dimensional LMIs. In the previous study, the authors present several stability conditions for genetic regulatory networks with time‐varying delays, based on M ‐matrix theory and using the non‐smooth Lyapunov function, which results in determining whether a low‐dimensional matrix is a non‐singular M ‐matrix. However, the previous approach cannot be applied to analyse the stability of genetic regulatory networks with noise perturbations. Here, the authors design a smooth Lyapunov function quadratic in state variables and employ M ‐matrix theory to derive new stability conditions for genetic regulatory networks with time‐varying delays. Theoretically, these conditions are less conservative than existing ones in some genetic regulatory networks. Then the results are extended to genetic regulatory networks with time‐varying delays and noise perturbations. For genetic regulatory networks with n genes and n proteins, the derived conditions are to check if an n × n matrix is a non‐singular M ‐matrix. To further present the new theories proposed in this study, three example regulatory networks are analysed.Inspec keywords: genetics, linear matrix inequalities, Lyapunov matrix equations, molecular biophysics, noise, proteinsOther keywords: M‐matrix‐based stability condition, genetic regulatory networks, time‐varying delays, noise perturbations, linear matrix inequality approach, high‐dimensional LMI, Lyapunov function, state variables, M‐matrix theory, proteins, nonsingular M‐matrix     

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     

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     

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     

Non‐fragile reliable control synthesis of the sugarcane borer

This study considers the problem of non‐fragile reliable control synthesis for mathematical model of interaction between the sugarcane borer (Diatraea saccharalis) and its egg parasitoid Trichogramma galloi. In particular, the control could be substituted by periodic releases of a small population of natural enemies and hence it is important to propose the time‐varying controller in sugarcane borer. The main aim of this study is to design a state feedback non‐fragile (time‐varying) reliable controller such that the states of the sugarcane borer system reach the equilibrium point within the desired period. A novel approach is proposed to deal with the uncertain matrices which appear in non‐fragile reliable control. Finally, simulations based on sugarcane borer systems are conducted to illustrate the advantages and effectiveness of the proposed design technique. The result reveals that the proposed non‐fragile control provides good performance in spite of periodic releases of a small population of natural enemies occurs.Inspec keywords: microorganisms, plant diseases, biology computing, state feedback, biocontrol, control system synthesisOther keywords: nonfragile reliable control synthesis, sugarcane borer, mathematical model, Diatraea saccharalis, egg parasitoid, Trichogramma galloi, periodic releases, natural enemies, state feedback nonfragile time‐varying reliable controller, equilibrium point, design technique     

Improved experimental time of ultra‐large bioassays using a parallelised microfluidic biochip architecture/scheduling

Digital microfluidic is an emerging technology to reduce the cost and time of experiments and improve the flexibility, automate‐ability and correctness of biochemical assays. In many of applications such as drug discovery and DNA profiling, a large number of bio‐operations (e.g. the chemical operations used in biology applications) must be done. In these applications, parallelising the operations will be critical in accuracy and cost of the process and digital microfluidic biochips can be considered as a reasonable platform. In this study, a new microfluidic architecture and the corresponding CAD flow is introduced to parallelise the assays on this platform. The authors implemented the proposed architecture and evaluated it using the large real bioassays. The authors’ simulations show that the degree‐of‐parallelism and speed of bioassays are increased more than 4× and the improvements will be better for larger assays. This contribution can open new horizons in drug testing, biology experiments and medical diagnosis operations that contain iterative, time‐consuming and labour experiments.Inspec keywords: microfluidics, lab‐on‐a‐chip, biochemistry, bioMEMS, biomedical equipment, CADOther keywords: biochemical assays, medical diagnosis operations, biology experiments, drug testing, CAD flow, parallelised microfluidic biochip architecture‐scheduling, ultralarge bioassays     

Effective implicit finite‐difference method for sensitivity analysis of stiff stochastic discrete biochemical systems

Simulation of cellular processes is achieved through a range of mathematical modelling approaches. Deterministic differential equation models are a commonly used first strategy. However, because many biochemical processes are inherently probabilistic, stochastic models are often called for to capture the random fluctuations observed in these systems. In that context, the Chemical Master Equation (CME) is a widely used stochastic model of biochemical kinetics. Use of these models relies on estimates of kinetic parameters, which are often poorly constrained by experimental observations. Consequently, sensitivity analysis, which quantifies the dependence of systems dynamics on model parameters, is a valuable tool for model analysis and assessment. A number of approaches to sensitivity analysis of biochemical models have been developed. In this study, the authors present a novel method for estimation of sensitivity coefficients for CME models of biochemical reaction systems that span a wide range of time‐scales. They make use of finite‐difference approximations and adaptive implicit tau‐leaping strategies to estimate sensitivities for these stiff models, resulting in significant computational efficiencies in comparison with previously published approaches of similar accuracy, as evidenced by illustrative applications.Inspec keywords: biochemistry, sensitivity analysis, stochastic processes, cellular biophysics, probability, fluctuations, master equation, reaction kinetics, finite difference methodsOther keywords: effective implicit finite‐difference method, sensitivity analysis, stiff stochastic discrete biochemical systems, cellular processes, mathematical modelling, deterministic differential equation models, inherently probabilistic‐stochastic models, random fluctuations, Chemical Master Equation, biochemical kinetics, kinetic parameter estimation, systems dynamics, CME models, biochemical reaction systems, finite‐difference approximations, adaptive implicit tau‐leaping strategies, computational efficiencies     

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     

Identifying latent dynamic components in biological systems

In computational systems biology, the general aim is to derive regulatory models from multivariate readouts, thereby generating predictions for novel experiments. In the past, many such models have been formulated for different biological applications. The authors consider the scenario where a given model fails to predict a set of observations with acceptable accuracy and ask the question whether this is because of the model lacking important external regulations. Real‐world examples for such entities range from microRNAs to metabolic fluxes. To improve the prediction, they propose an algorithm to systematically extend the network by an additional latent dynamic variable which has an exogenous effect on the considered network. This variable''s time course and influence on the other species is estimated in a two‐step procedure involving spline approximation, maximum‐likelihood estimation and model selection. Simulation studies show that such a hidden influence can successfully be inferred. The method is also applied to a signalling pathway model where they analyse real data and obtain promising results. Furthermore, the technique can be employed to detect incomplete network structures.Inspec keywords: biology computing, RNA, splines (mathematics), maximum likelihood estimation, approximation theory, biochemistryOther keywords: latent dynamic components, biological systems, computational system biology, regulatory models, multivariate readouts, biological applications, external regulations, real‐world examples, microRNA, metabolic fluxes, latent dynamic variables, variable time course, two‐step procedure, spline approximation, maximum‐likelihood estimation, model selection, signalling pathway model, real data, incomplete network structures     

Two faces of competition: target‐mediated reverse signalling in microRNA and mitogen‐activated protein kinase regulatory networks

Biomolecular regulatory networks are organised around hubs, which can interact with a large number of targets. These targets compete with each other for access to their common hubs, but whether the effect of this competition would be significant in magnitude and in function is not clear. In this review, the authors discuss recent in vivo studies that analysed the system level retroactive effects induced by target competition in microRNA and mitogen‐activated protein kinase regulatory networks. The results of these studies suggest that downstream targets can regulate the overall state of their upstream regulators, and thus cannot be ignored in analysing biomolecular networks.Inspec keywords: reviews, RNA, molecular biophysics, enzymesOther keywords: target‐mediated reverse signalling, mitogen‐activated protein kinase regulatory networks, biomolecular regulatory networks, microRNA regulatory networks, review, in vivo study     

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