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     

Identifying genuine protein–protein interactions within communities of gene co‐expression networks using a deconvolution method

Direct relationships between biological molecules connected in a gene co‐expression network tend to reflect real biological activities such as gene regulation, protein–protein interactions (PPIs), and metabolisation. As correlation‐based networks contain numerous indirect connections, those direct relationships are always ‘hidden’ in them. Compared with the global network, network communities imply more biological significance on predicting protein function, detecting protein complexes and studying network evolution. Therefore, identifying direct relationships in communities is a pervasive and important topic in the biological sciences. Unfortunately, this field has not been well studied. A major thrust of this study is to apply a deconvolution algorithm on communities stemming from different gene co‐expression networks, which are constructed by fixing different thresholds for robustness analysis. Using the fifth Dialogue on Reverse Engineering Assessment and Methods challenge (DREAM5) framework, the authors demonstrate that nearly all new communities extracted from a ‘deconvolution filter’ contain more genuine PPIs than before deconvolution.Inspec keywords: proteins, deconvolution, genetics, bioinformatics, biology computing, molecular biophysicsOther keywords: identifying genuine protein–protein interactions, gene co‐expression network, deconvolution method, direct relationships, biological molecules, biological activities, gene regulation, correlation‐based networks, numerous indirect connections, global network, network communities, biological significance, protein function, protein complexes, studying network evolution, biological sciences, different gene co‐expression networks     

Contribution of time delays to p53 oscillation in DNA damage response

Although the oscillatory dynamics of the p53 network have been extensively studied, the understanding of the mechanism of delay‐induced oscillations is still limited. In this paper, a comprehensive mathematical model of p53 network is studied, which contains two delayed negative feedback loops. By studying the model with and without explicit delays, the results indicate that the time delay of Mdm2 protein synthesis can well control the pulse shape but cannot induce p53 oscillation alone, while the time delay required for Wip1 protein synthesis induces a Hopf bifurcation to drive p53 oscillation. In addition, the synergy of the two delays will cause the p53 network to oscillate in advance, indicating that p53 begins the repair process earlier in the damaged cell. Furthermore, the stability and bifurcation of the model are addressed, which may highlight the role of time delay in p53 oscillations.Inspec keywords: proteins, cellular biophysics, DNA, molecular biophysics, biomolecular effects of radiation, bifurcation, physiological models, cellular effects of radiation, oscillations, geneticsOther keywords: highlight, time delay, delayed negative feedback loops, murine double minute 2, Wip1 protein synthesis, explicit delays, Mdm2 protein synthesis, p53 network     

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     

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     

Review of tools and algorithms for network motif discovery in biological networks

Network motifs are recurrent and over‐represented patterns having biological relevance. This is one of the important local properties of biological networks. Network motif discovery finds important applications in many areas such as functional analysis of biological components, the validity of network composition, classification of networks, disease discovery, identification of unique subunits etc. The discovery of network motifs is a computationally challenging task due to the large size of real networks, and the exponential increase of search space with respect to network size and motif size. This problem also includes the subgraph isomorphism check, which is Nondeterministic Polynomial (NP)‐complete. Several tools and algorithms have been designed in the last few years to address this problem with encouraging results. These tools and algorithms can be classified into various categories based on exact census, mapping, pattern growth, and so on. In this study, critical aspects of network motif discovery, design principles of background algorithms, and their functionality have been reviewed with their strengths and limitations. The performances of state‐of‐art algorithms are discussed in terms of runtime efficiency, scalability, and space requirement. The future scope, research direction, and challenges of the existing algorithms are presented at the end of the study.Inspec keywords: computational complexity, graph theory, biology, search problemsOther keywords: network size, motif size, network motif discovery, biological networks, network composition, recurrent patterns, over‐represented patterns, local properties, search space, subgraph isomorphism check, NP‐complete problem, NP‐complete problem, exact census, design principles, background algorithms, runtime efficiency, space requirement     

Efficient prediction of drug–drug interaction using deep learning models

A drug–drug interaction or drug synergy is extensively utilised for cancer treatment. However, prediction of drug–drug interaction is defined as an ill‐posed problem, because manual testing is only implementable on small group of drugs. Predicting the drug–drug interaction score has been a popular research topic recently. Recently many machine learning models have proposed in the literature to predict the drug–drug interaction score efficiently. However, these models suffer from the over‐fitting issue. Therefore, these models are not so‐effective for predicting the drug–drug interaction score. In this work, an integrated convolutional mixture density recurrent neural network is proposed and implemented. The proposed model integrates convolutional neural networks, recurrent neural networks and mixture density networks. Extensive comparative analysis reveals that the proposed model significantly outperforms the competitive models.Inspec keywords: cancer, learning (artificial intelligence), drugs, recurrent neural nets, convolutional neural nets, drug delivery systemsOther keywords: drug synergy, drug–drug interaction score, drug–drug interaction prediction, deep learning, cancer treatment, machine learning, convolutional mixture density recurrent neural network     

Estimation of skin impedance models with experimental data and a proposed model for human skin impedance

The skin is a complex biological tissue whose impedance varies with frequency. The properties and structure of skin changes with the location on the body, age, geographical location and other factors. Considering these factors, skin impedance analysis is a sophisticated data analysis. However, despite all these variations, various researchers have always worked to develop an equivalent electrical model of the skin. The two most important categories of electrical models are RC‐based model and CPE‐based model which focus on the physiological stratification and biological properties of skin, respectively. In this work, experimental skin impedance data is acquired from ten sites on the body to find the fitting model. It is observed that a hybrid of fractional‐order CPE‐based model and higher‐order RC layered‐based model can provide the best fitting electrical model of skin. A new model is developed with this hybrid orders. Genetic algorithm is used for the extraction of parameter components. Least error of fitting has been observed for the proposed model as compared with the other models. This model can be used in correlating many skin problems and in the development of diagnostic tools. It will offer an additional supportive tool in‐vitro to the medical specialist.Inspec keywords: genetic algorithms, skin, data analysis, bioelectric phenomena, medical computing, electric impedance, patient diagnosisOther keywords: skin impedance models, human skin impedance, skin impedance analysis, data analysis, electrical models, RC‐based model, biological properties, experimental skin impedance data, fractional‐order CPE‐based model, skin problems, complex biological tissue, higher‐order RC layered‐based model, genetic algorithm, diagnostic tools     

Identification of specific microRNA–messenger RNA regulation pairs in four subtypes of breast cancer

Four subtypes of breast cancer, luminal A, luminal B, basal‐like, human epidermal growth factor receptor‐enriched, have been identified based on gene expression profiles of human tumours. The goal of this study is to find whether the same groups'' genes would exhibit different networks among the four subtypes. Differential expressed genes between each of the four subtypes and the normal samples were identified. The overlaps between the four groups of differentially expressed genes were used to construct regulations networks for each of the four subtypes. Univariate and multivariate Cox regressions were employed to test the genes in the four regulation networks. This study demonstrated that the common genes in four subtypes showed different regulation. Also, the hsa‐miR‐182 and decorin pair performs different functions among the four subtypes of breast cancer. The result indicated that heterogeneity of breast cancer is not only reflected in the different expression patterns among different genes, but also in the different regulatory networks of the same group of genes.Inspec keywords: genetics, cellular biophysics, tumours, molecular biophysics, RNA, biochemistry, cancer, proteins, biology computingOther keywords: decorin pair performs different functions, breast cancer heterogeneity, regulatory networks, specific microRNA–messenger, regulation pairs, human epidermal growth factor receptor, gene expression profiles, differentially expressed genes, regulations networks, hsa‐miR‐182, decorin pair, human tumours     

Functional tunability of biological circuits from additional toggle switches

In many complex regulatory networks with interlinked feedback loops, the simple core circuits are sufficient to achieve the specific biological functions of the whole networks, naturally raising a question: what is the role of the additional feedback loops. By investigating the effect of an additional toggle switch on the auto‐activation circuit responsible for competent switch in Bacillus subtilits and on the activator–repressor circuit responsible for cell cycle in Xenopus embryonic, the authors show that the additional toggle switch can elaborate the dynamical behaviour of both circuits. Specifically, the additional toggle switch in B. subtilits does not significantly affect the saturation level of the competent state but can tune the activation threshold (i.e. the minimal stimulus required to switch the system from the non‐competent state to the competent state). For the activator–repressor circuit in X. embryonic cell cycle, the additional toggle switch can tune the oscillation frequency but does not change the oscillation amplitude. The proposed detailed results not only provide guidelines to the engineering of synthetic genetic circuits, but also imply a significant fact that additional toggle switches in a complex network are not really redundant but play a role of tuning network functions.Inspec keywords: biochemistry, cellular biophysics, microorganismsOther keywords: functional tunability, biological circuits, toggle switches, complex regulatory networks, interlinked feedback loops, Bacillus subtilits, autoactivation circuit, activator‐repressor circuit, Xenopus embryonic     

Effective sampling trajectory optimisation for sensitivity analysis of biological systems

Sensitivity analysis has been widely applied to study the biological systems, including metabolic networks, signalling pathways, and genetic circuits. The Morris method is a kind of screening sensitivity analysis approach, which can fast identify a few key factors from numerous biological parameters and inputs. The parameter or input space is randomly sampled to produce a very limited number of trajectories for the calculation of elementary effects. It is clear that the sampled trajectories are not enough to cover the whole uncertain space, which eventually causes unstable sensitivity measures. This paper presents a novel trajectory optimisation algorithm for the Morris‐based sensitivity calculation to ensure a good scan throughout the whole uncertain space. The paper demonstrates that this presented method gets more consistent sensitivity results through a benchmark example. The application to a previously published ordinary differential equation model of a cellular signalling network is presented. In detail, the parameter sensitivity analysis verifies the good agreement with data of the literatures.Inspec keywords: genetics, differential equations, sensitivity analysis, biology, sampling methods, optimisationOther keywords: biological systems, metabolic networks, genetic circuits, Morris‐based sensitivity calculation, ordinary differential equation, sampling trajectory optimisation, sensitivity analysis, parameter sensitivity analysis, cellular signalling network     

System‐based strategies for p53 recovery

The authors have proposed a systems theory‐based novel drug design approach for the p53 pathway. The pathway is taken as a dynamic system represented by ordinary differential equations‐based mathematical model. Using control engineering practices, the system analysis and subsequent controller design is performed for the re‐activation of wild‐type p53. p53 revival is discussed for both modes of operation, i.e. the sustained and oscillatory. To define the problem in control system paradigm, modification in the existing mathematical model is performed to incorporate the effect of Nutlin. Attractor point analysis is carried out to select the suitable domain of attraction. A two‐loop negative feedback control strategy is devised to drag the system trajectories to the attractor point and to regulate cellular concentration of Nutlin, respectively. An integrated framework is constituted to incorporate the pharmacokinetic effects of Nutlin in the cancerous cells. Bifurcation analysis is also performed on the p53 model to see the conditions for p53 oscillation.Inspec keywords: proteins, tumours, cancer, cellular biophysics, molecular biophysics, molecular configurations, biochemistry, differential equations, closed loop systems, bifurcation, biology computingOther keywords: system‐based strategies, p53 recovery, systems theory‐based novel drug design approach, dynamic system, ordinary differential equations‐based mathematical model, control engineering practices, subsequent controller design, wild‐type p53, p53 revival, oscillatory, control system paradigm, mathematical model, Nutlin effect, attractor point analysis, domain‐of‐attraction, two‐loop negative feedback control strategy, cellular concentration, pharmacokinetic effects, cancerous cells, bifurcation analysis, p53 oscillation, anomalous cell     

Application of conditional robust calibration to ordinary differential equations models in computational systems biology: a comparison of two sampling strategies

Mathematical modelling is a widely used technique for describing the temporal behaviour of biological systems. One of the most challenging topics in computational systems biology is the calibration of non‐linear models; i.e. the estimation of their unknown parameters. The state‐of‐the‐art methods in this field are the frequentist and Bayesian approaches. For both of them, the performance and accuracy of results greatly depend on the sampling technique employed. Here, the authors test a novel Bayesian procedure for parameter estimation, called conditional robust calibration (CRC), comparing two different sampling techniques: uniform and logarithmic Latin hypercube sampling. CRC is an iterative algorithm based on parameter space sampling and on the estimation of parameter density functions. They apply CRC with both sampling strategies to the three ordinary differential equations (ODEs) models of increasing complexity. They obtain a more precise and reliable solution through logarithmically spaced samples.Inspec keywords: sampling methods, parameter estimation, Bayes methods, differential equations, iterative methodsOther keywords: CRC, parameter space sampling, parameter density functions, sampling strategies, ordinary differential equations models, logarithmically spaced samples, computational systems biology, mathematical modelling, temporal behaviour, biological systems, challenging topics, nonlinear models, unknown parameters, frequentist approaches, Bayesian approaches, sampling technique, novel Bayesian procedure, parameter estimation, called conditional robust calibration, different sampling techniques     

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     

Algorithm to identify the optimal perturbation based on the net basin‐of‐state of perturbed states in Boolean network

Boolean networks are widely used to model gene regulatory networks and to design therapeutic intervention strategies to affect the long‐term behavior of systems. Here, the authors investigate the 1 bit perturbation, which falls under the category of structural intervention. The authors’ idea is that, if and only if a perturbed state evolves from a desirable attractor to an undesirable attractor or from an undesirable attractor to a desirable attractor, then the size of basin of attractor of a desirable attractor may decrease or increase. In this case, if the authors obtain the net BOS of the perturbed states, they can quickly obtain the optimal 1 bit perturbation by finding the maximum value of perturbation gain. Results from both synthetic and real biological networks show that the proposed algorithm is not only simpler and but also performs better than the previous basin‐of‐states (BOS)‐based algorithm by Hu et al..Inspec keywords: perturbation theory, genetics, Boolean functionsOther keywords: optimal perturbation, perturbed states, Boolean network, gene regulatory networks, basin‐of‐states‐based algorithm, state‐transition diagram, structural intervention, perturbation gain, synthetic biological networks, real biological networks, 1 bit perturbation     

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