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     

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     

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     

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     

Describing function‐based approximations of biomolecular systems

Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of analytical and computational approaches, the authors adapt and develop the method of describing functions to represent the input–output responses of biomolecular signalling systems. They approximate representative systems exhibiting various saturating and hysteretic dynamics in a way that is better than the standard linearisation. Furthermore, they develop analytical upper bounds for the computational error estimates. Finally, they use these error estimates to augment the limit cycle analysis with a simple and quick way to bound the predicted oscillation amplitude. These results provide system approximations that can add more insight into the local behaviour of these systems than standard linearisation, compute responses to other periodic inputs and to analyse limit cycles.Inspec keywords: molecular biophysics, physiological models, approximation theoryOther keywords: describing‐function‐based approximations, mathematical methods, computational approaches, biomolecular signalling systems, hysteretic dynamics, saturating dynamics, analytical upper bounds, computational error estimates, oscillation amplitude     

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     

MPGraph: multi‐view penalised graph clustering for predicting drug–target interactions

Identifying drug–target interactions has been a key step for drug repositioning, drug discovery and drug design. Since it is expensive to determine the interactions experimentally, computational methods are needed for predicting interactions. In this work, the authors first propose a single‐view penalised graph (SPGraph) clustering approach to integrate drug structure and protein sequence data in a structural view. The SPGraph model does clustering on drugs and targets simultaneously such that the known drug–target interactions are best preserved in the clustering results. They then apply the SPGraph to a chemical view with drug response data and gene expression data in NCI‐60 cell lines. They further generalise the SPGraph to a multi‐view penalised graph (MPGraph) version, which can integrate the structural view and chemical view of the data. In the authors'' experiments, they compare their approach with some comparison partners, and the results show that the SPGraph could improve the prediction accuracy in a small scale, and the MPGraph can achieve around 10% improvements for the prediction accuracy. They finally give some new targets for 22 Food and Drug Administration approved drugs for drug repositioning, and some can be supported by other references.Inspec keywords: graphs, drug delivery systems, drugs, proteins, molecular biophysics, molecular configurations, optimisation, eigenvalues and eigenfunctions, Laplace equations, cancer, cellular biophysics, gene therapy, medical computingOther keywords: MPGraph, multiview penalised graph clustering, drug‐target interactions, drug repositioning, drug discovery, drug design, computational methods, single‐view penalized graph clustering approach, drug structure, protein sequence data, SPGraph model, optimisation problem, spectral clustering, eigenvalue decomposition, Laplacian model, gene expression data, NCI‐60 cell lines     

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     

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     

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     

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     

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     

Control of depth of anaesthesia using fractional‐order adaptive high‐gain controller

This study presents a fractional‐order adaptive high‐gain controller for control of depth of anaesthesia. To determine the depth of anaesthesia, the bispectral index (BIS) is utilised. To attain the desired BIS, the propofol infusion rate (as the control signal) should be appropriately adjusted. The effect of the propofol on the human body is modelled with the pharmacokinetic–pharmacodynamic (PK/PD) model. Physical properties of the patient such as gender, age, height and a like determine the parameters of the PK/PD model. This necessitates us to employ an appropriate adaptive controller. To attain this goal, a fractional‐order adaptive high‐gain controller is constructed to solve the tracking problem for minimum phase systems with relative degree two (such as the PK/PD model). This leads to a time‐varying gain adjusting according to a fractional‐order adaptation mechanism. Simulation results performed on various patients (considering the external disturbance and the measurement noise) show the effectiveness of the proposed method.Inspec keywords: medical control systems, gain control, adaptive control, closed loop systems, time‐varying systemsOther keywords: fractional‐order adaptive high‐gain controller, control signal, pharmacokinetic–pharmacodynamic model, fractional‐order adaptation mechanism, anaesthesia depth control, bispectral index, PK‐PD model, propofol infusion rate, tracking problem, minimum phase systems, time‐varying gain, BIS     

Formal reasoning about synthetic biology using higher‐order‐logic theorem proving

Synthetic biology is an interdisciplinary field that uses well‐established engineering principles for performing the analysis of the biological systems, such as biological circuits, pathways, controllers and enzymes. Conventionally, the analysis of these biological systems is performed using paper‐and‐pencil proofs and computer simulation methods. However, these methods cannot ensure accurate results due to their inherent limitations. Higher‐order‐logic (HOL) theorem proving is proposed and used as a complementary approach for analysing linear biological systems, which is based on developing a mathematical model of the genetic circuits and the bio‐controllers used in synthetic biology based on HOL and analysing it using deductive reasoning in an interactive theorem prover. The involvement of the logic, mathematics and the deductive reasoning in this method ensures the accuracy of the analysis. It is proposed to model the continuous dynamics of the genetic circuits and their associated controllers using differential equations and perform their transfer function‐based analysis using the Laplace transform in a theorem prover. For illustration, the genetic circuits of activated and repressed expressions and autoactivation of protein, and phase lag and lead controllers, which are widely used in cancer‐cell identifiers and multi‐input receptors for precise disease detection, are formally analyzed.Inspec keywords: program verification, diseases, genetics, cancer, formal logic, theorem proving, formal verification, differential equations, proteins, transfer functions, inference mechanisms, Laplace transformsOther keywords: biological system, biological circuits, genetic circuits, associated controllers, computer simulation methods, higher‐order‐logic theorem proving, analysing linear biological systems, bio‐controllers, synthetic biology, deductive reasoning, reaction‐based models, transfer function based analysis, differential equation based models, phase lag, lead controllers, computer systems     

Cu‐induced assembly of methanobactin‐modified gold nanoparticles and its peroxidase mimic activity

Methanobactin (Mb) is a small copper‐chelating molecule that functions as an agent for copper acquisition, uptake and copper‐containing methane monooxygenase catalysis in methane‐oxidising bacteria. The UV–visible spectral and fluorescence spectral suggested that Mb/Cu coordination complex as a monomer (Mb‐Cu), dimmer (Mb₂ ‐Cu) and tetramer (Mb₄ ‐Cu) could be obtained at different ratios of Mb to Cu (II). The kinetics of the oxidation of hydroquinone with hydrogen peroxide catalysed by the different Mb/Cu coordination complex were investigated. The results suggested that Mb₂ ‐Cu coordination form has highest catalytic capacity. Further, Mb‐modified gold nanoparticles (AuNPs) were obtained by ligand exchange and assembled into two‐ and three‐D nanocluster structure by metal‐organic coordination as driving force. It has been found that AuNPs increased the catalytic activity of Mb₂ ‐Cu on AuNPs. The more significant catalytic activity was exhibited by the nanocluster assembly with multi‐catalytic centres. This may be attributed to the multivalent collaborative characteristics of the catalytic active centres in the nanocluster network assembly. The assembly of Mb‐modified AuNPs can act as excellent nanoenzyme models for imitating peroxidase.Inspec keywords: nanoparticles, catalysis, oxidation, enzymes, microorganisms, nanobiotechnology, gold, organic compounds, reduction (chemical), visible spectra, molecular biophysics, ultraviolet spectra, biochemistry, copper, nanofabrication, fluorescenceOther keywords: Mb‐modified gold nanoparticles, catalytic active centres, Mb‐modified AuNPs, Cu‐induced assembly, methanobactin‐modified gold nanoparticles, peroxidase mimic activity, copper‐chelating molecule, copper‐containing methane monooxygenase catalysis, methane‐oxidising bacteria, fluorescence, Mb/Cu coordination complex, catalytic activity, UV–visible spectra, nanocluster assembly, Cu, Au     

Overlapping functional modules detection in PPI network with pair‐wise constrained non‐negative matrix tri‐factorisation

A large amount of available protein–protein interaction (PPI) data has been generated by high‐throughput experimental techniques. Uncovering functional modules from PPI networks will help us better understand the underlying mechanisms of cellular functions. Numerous computational algorithms have been designed to identify functional modules automatically in the past decades. However, most community detection methods (non‐overlapping or overlapping types) are unsupervised models, which cannot incorporate the well‐known protein complexes as a priori. The authors propose a novel semi‐supervised model named pairwise constrains nonnegative matrix tri‐factorisation (PCNMTF), which takes full advantage of the well‐known protein complexes to find overlapping functional modules based on protein module indicator matrix and module correlation matrix simultaneously from PPI networks. PCNMTF determinately models and learns the mixed module memberships of each protein by considering the correlation among modules simultaneously based on the non‐negative matrix tri‐factorisation. The experiment results on both synthetic and real‐world biological networks demonstrate that PCNMTF gains more precise functional modules than that of state‐of‐the‐art methods.Inspec keywords: proteins, molecular biophysics, cellular biophysics, matrix algebraOther keywords: overlapping functional module detection, PPI network, pair‐wise constrained nonnegative matrix trifactorisation, protein–protein interaction data, cellular functions, protein complexes, real‐world biological networks, synthetic biological networks     

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