Minimum steering node set of complex networks and its applications to biomolecular networks

Many systems of interests in practices can be represented as complex networks. For biological systems, biomolecules do not perform their functions alone but interact with each other to form so‐called biomolecular networks. A system is said to be controllable if it can be steered from any initial state to any other final state in finite time. The network controllability has become essential to study the dynamics of the networks and understand the importance of individual nodes in the networks. Some interesting biological phenomena have been discovered in terms of the structural controllability of biomolecular networks. Most of current studies investigate the structural controllability of networks in notion of the minimum driver node sets (MDSs). In this study, the authors analyse the network structural controllability in notion of the minimum steering node sets (MSSs). They first develop a graph‐theoretic algorithm to identify the MSS for a given network and then apply it to several biomolecular networks. Application results show that biomolecules identified in the MSSs play essential roles in corresponding biological processes. Furthermore, the application results indicate that the MSSs can reflect the network dynamics and node importance in controlling the networks better than the MDSs.Inspec keywords: molecular biophysics, biocontrol, graph theoryOther keywords: graph‐theoretic algorithm, MSS, minimum driver node sets, structural controllability, network dynamics, network controllability, biological systems, biomolecular networks, complex networks, minimum steering node set     

Signalling pathway impact analysis based on the strength of interaction between genes

Signalling pathway analysis is a popular approach that is used to identify significant cancer‐related pathways based on differentially expressed genes (DEGs) from biological experiments. The main advantage of signalling pathway analysis lies in the fact that it assesses both the number of DEGs and the propagation of signal perturbation in signalling pathways. However, this method simplifies the interactions between genes by categorising them only as activation (+1) and suppression (−1), which does not encompass the range of interactions in real pathways, where interaction strength between genes may vary. In this study, the authors used newly developed signalling pathway impact analysis (SPIA) methods, SPIA based on Pearson correlation coefficient (PSPIA), and mutual information (MSPIA), to measure the interaction strength between pairs of genes. In analyses of a colorectal cancer dataset, a lung cancer dataset, and a pancreatic cancer dataset, PSPIA and MSPIA identified more candidate cancer‐related pathways than were identified by SPIA. Generally, MSPIA performed better than PSPIA.Inspec keywords: genetics, cancer, biology computing, perturbation theory, biological organs, data analysisOther keywords: gene interaction strength, cancer‐related pathways, differentially expressed genes, biological experiments, signal perturbation propagation, signalling pathway impact analysis methods, Pearson correlation coefficient, mutual information, colorectal cancer dataset analysis, pancreatic cancer dataset, PSPIA, MSPIA     

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     

Bogdanov–Takens bifurcation in a neutral BAM neural networks model with delays

In this study, the authors first discuss the existence of Bogdanov–Takens and triple zero singularity of a five neurons neutral bidirectional associative memory neural networks model with two delays. Then, by utilising the centre manifold reduction and choosing suitable bifurcation parameters, the second‐order and the third‐order normal forms of the Bogdanov–Takens bifurcation for the system are obtained. Finally, the obtained normal form and numerical simulations show some interesting phenomena such as the existence of a stable fixed point, a pair of stable non‐trivial equilibria, a stable limit cycles, heteroclinic orbits, homoclinic orbits, coexistence of two stable non‐trivial equilibria and a stable limit cycles in the neighbourhood of the Bogdanov–Takens bifurcation critical point.Inspec keywords: neurophysiology, neural nets, bifurcation, delays, critical pointsOther keywords: Bogdanov‐Takens bifurcation critical point, neutral BAM neural networks, bidirectional associative memory, delays, triple zero singularity, neurons, centre manifold reduction, bifurcation parameters, second‐order normal forms, third‐order normal forms, numerical simulations, stable fixed point, stable nontrivial equilibria, stable limit cycles, heteroclinic orbits, homoclinic orbits     

Bifurcation analysis of insulin regulated mTOR signalling pathway in cancer cells

Insulin induced mTOR signalling pathway is a complex network implicated in many types of cancers. The molecular mechanism of this pathway is highly complex and the dynamics is tightly regulated by intricate positive and negative feedback loops. In breast cancer cell lines, metformin has been shown to induce phosphorylation at specific serine sites in insulin regulated substrate of mTOR pathway that results in apoptosis over cell proliferation. The author models and performs bifurcation analysis to simulate cell proliferation and apoptosis in mTOR signalling pathway to capture the dynamics both in the presence and absence of metformin in cancer cells. Metformin is shown to negatively regulate PI3K through AMPK induced IRS1 phosphorylation and this brings about a reversal of AKT bistablity in codimension‐1 bifurcation diagram from S‐shaped, related to cell proliferation in the absence of drug metformin, to Z‐shaped, related to apoptosis in the presence of drug metformin. The author hypothesises and explains how this negative regulation acts a circuit breaker, as a result of which mTOR network favours apoptosis of cancer cells over its proliferation. The implication of reversing the shape of bistable dynamics from S to Z or vice‐versa in biological networks in general is discussed.Inspec keywords: bifurcation, molecular biophysics, drugs, enzymes, biochemistry, cellular biophysics, cancer, biomedical materialsOther keywords: intricate positive feedback loops, negative feedback loops, breast cancer cell lines, insulin regulated substrate, cell proliferation, cancer cells, AMPK induced IRS1 phosphorylation, codimension‐1 bifurcation diagram, drug metformin, mTOR network, insulin regulated mTOR signalling pathway, bifurcation analysis, PI3K, AKT bistablity     

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     

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     

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     

Comprehensive study of tumour single nucleotide polymorphism array data reveals significant driver aberrations and disrupted signalling pathways in human hepatocellular cancer

The authors describe an integrated method for analysing cancer driver aberrations and disrupted pathways by using tumour single nucleotide polymorphism (SNP) arrays. The authors new method adopts a novel statistical model to explicitly quantify the SNP signals, and therefore infers the genomic aberrations, including copy number alteration and loss of heterozygosity. Examination on the dilution series dataset shows that this method can correctly identify the genomic aberrations even with the existence of severe normal cell contamination in tumour sample. Furthermore, with the results of the aberration identification obtained from multiple tumour samples, a permutation‐based approach is proposed for identifying the statistically significant driver aberrations, which are further incorporated with the known signalling pathways for pathway enrichment analysis. By applying the approach to 286 hepatocellular tumour samples, they successfully uncover numerous driver aberration regions across the cancer genome, for example, chromosomes 4p and 5q, which harbour many known hepatocellular cancer related genes such as alpha‐fetoprotein (AFP) and ectodermal‐neural cortex (ENC1). In addition, they identify nine disrupted pathways that are highly enriched by the driver aberrations, including the systemic lupus erythematosus pathway, the vascular endothelial growth factor (VEGF) signalling pathway and so on. These results support the feasibility and the utility of the proposed method on the characterisation of the cancer genome and the downstream analysis of the driver aberrations and the disrupted signalling pathways.Inspec keywords: cancer, DNA, genetics, genomics, liver, molecular biophysics, molecular configurations, physiological models, polymorphism, statistical analysis, tumoursOther keywords: tumour single nucleotide polymorphism array data, disrupted signalling pathways, human hepatocellular cancer, cancer driver aberrations, statistical model, SNP signals, genomic aberrations, heterozygosity, dilution series dataset, normal cell contamination, permutation‐based approach, statistical significant driver aberrations, hepatocellular tumour samples, cancer genome, hepatocellular cancer related genes, systemic lupus erythematosus pathway, VEGF signalling pathway     

Discovery of significant pathways in breast cancer metastasis via module extraction and comparison

Discovering significant pathways rather than single genes or small gene sets involved in metastasis is becoming more and more important in the study of breast cancer. Many researches have shed light on this problem. However, most of the existing works are relying on some priori biological information, which may bring bias to the models. The authors propose a new method that detects metastasis‐related pathways by identifying and comparing modules in metastasis and non‐metastasis gene co‐expression networks. The gene co‐expression networks are built by Pearson correlation coefficients, and then the modules inferred in these two networks are compared. In metastasis and non‐metastasis networks, 36 and 41 significant modules are identified. Also, 27.8% (metastasis) and 29.3% (non‐metastasis) of the modules are enriched significantly for one or several pathways with p ‐value <0.05. Many breast cancer genes including RB1, CCND1 and TP53 are included in these identified pathways. Five significant pathways are discovered only in metastasis network: glycolysis pathway, cell adhesion molecules, focal adhesion, stathmin and breast cancer resistance to antimicrotubule agents, and cytosolic DNA‐sensing pathway. The first three pathways have been proved to be closely associated with metastasis. The rest two can be taken as a guide for future research in breast cancer metastasis.Inspec keywords: cancer, genetics, genomics, DNA, molecular biophysics, adhesion, cellular biophysicsOther keywords: breast cancer metastasis, module extraction, gene sets, metastasis‐related pathways, nonmetastasis gene coexpression networks, Pearson correlation coefflcients, breast cancer genes, RB1, CCND1, TP53, glycolysis pathway, cell adhesion molecules, focal adhesion, stathmin, breast cancer resistance, antimicrotubule agents, cytosolic DNA‐sensing pathway, breast cancer metastasis     

Classification of drug molecules for oxidative stress signalling pathway

In humans, oxidative stress is involved in the development of diabetes, cancer, hypertension, Alzheimers’ disease, and heart failure. One of the mechanisms in the cellular defence against oxidative stress is the activation of the Nrf2‐antioxidant response element (ARE) signalling pathway. Computation of activity, efficacy, and potency score of ARE signalling pathway and to propose a multi‐level prediction scheme for the same is the main aim of the study as it contributes in a big amount to the improvement of oxidative stress in humans. Applying the process of knowledge discovery from data, required knowledge is gathered and then machine learning techniques are applied to propose a multi‐level scheme. The validation of the proposed scheme is done using the K‐fold cross‐validation method and an accuracy of 90% is achieved for prediction of activity score for ARE molecules which determine their power to refine oxidative stress.Inspec keywords: cancer, cellular biophysics, biochemistry, drugs, molecular biophysics, proteins, learning (artificial intelligence), medical computingOther keywords: oxidative stress, Nrf2‐antioxidant response element signalling pathway, ARE signalling pathway, diabetes, cancer, hypertension, Alzheimers’ disease, heart failure, machine learning techniques, K‐fold cross‐validation method, ARE molecules     

Anisotropic nanomechanical properties of bovine horn using modulus mapping

Bovine horns are durable that they can withstand an extreme loading force which with special structures and mechanical properties. In this study, the authors apply quasi‐static nanoindentation and modulus mapping techniques to research the nanomechanical properties of bovine horn in the transverse direction (TD) and longitudinal direction (LD). In quasi‐static nanoindentation, the horn''s modulus and hardness in the inner layer and the outer layer demonstrated a gradual increase in both TD and LD. Laser scanning confocal microscopy revealed microstructure in the horn with wavy morphology in the TD cross‐section and laminate in the LD cross‐section. When using tensile tests or quasi‐static nanoindentation tests alone, the anisotropy of the mechanical properties of bovine horn were not obvious. However, when using modulus mapping, storage modulus (E ′), loss modulus (E ″) and loss ratio (tan δ) are clearly different depending on the position in the TD and LD. Modulus mapping is proposed as accurately describing the internal structures of bovine horn and helpful in understanding the horn''s energy‐absorption, stiffness and strength that resists forces during fighting.Inspec keywords: laser applications in medicine, proteins, molecular biophysics, high‐speed optical techniques, biomedical optical imaging, viscoelasticity, elastic moduli, biomechanics, biological tissues, nanoindentation, laminates, tensile testing, tensile strengthOther keywords: resists forces, stiffness, energy‐absorption, internal structures, loss ratio, loss modulus, storage modulus, modulus mapping, quasistatic nanoindentation testing, tensile testing, LD cross‐section, laminate, TD cross‐section, wavy morphology, microstructure, laser scanning confocal microscopy, hardness, longitudinal direction, transverse direction, modulus mapping techniques, quasistatic nanoindentation, loading force, bovine horns, modulus mapping, anisotropic nanomechanical properties     

Poly (vinyl alcohol)/poly (acrylamide‐ co ‐diallyldimethyl ammonium chloride) semi‐IPN hydrogels for ciprofloxacin hydrochloride drug delivery

Herein, the authors developed a new and potential semi‐interpenetrating polymer network (semi‐IPN) hydrogels of poly vinyl alcohol (PVA), acryl amide and diallyldimethyl ammonium chloride employing chemical cross‐linker N, N''‐methylene bisacrylamide (NNMBA) and ammonium persulphate as an initiator by radical polymerisation. To analyse the copolymer formation between two monomers and IPN cross‐linking reaction, the resulting hydrogel was characterised by Fourier transform infrared spectroscopy and the surface morphology was analysed using scanning electron microscopy. Differential scanning calorimetry and X‐ray diffraction studies were also carried out for investigating drug loading and distribution and swelling experiments were carried out for the uptake of water. In vitro release of ciprofloxacin hydrochloride from hydrogel was performed at intestinal conditions. The amount of PVA, NNMBA and total monomer concentration was found to strongly control the drug release behaviour from the hydrogels.Inspec keywords: hydrogels, polymer blends, biomedical materials, drug delivery systems, polymerisation, Fourier transform infrared spectra, surface morphology, scanning electron microscopy, differential scanning calorimetry, X‐ray diffraction, swelling, biological organs, ammonium compoundsOther keywords: PVA‐poly(acrylamide‐co‐diallyldimethyl ammonium chloride) semiIPN hydrogels, ciprofloxacin hydrochloride drug delivery, semiinterpenetrating polymer network hydrogels, polyvinyl alcohol, acryl amide, diallyldimethyl ammonium chloride, chemical crosslinker N,N''‐methylene bisacrylamide, ammonium persulphate, radical polymerisation initiator, NNMBA, copolymer formation, IPN crosslinking reaction, Fourier transform infrared spectroscopy, surface morphology, scanning electron microscopy, differential scanning calorimetry, X‐ray diffraction, drug loading, drug distribution, swelling, water uptake, in vitro ciprofloxacin hydrochloride release, intestinal conditions, total monomer concentration, drug release behaviour     

Design of binary subtractor using actin quantum cellular automata

Actin is a biological protein that provides support to the cellular structure and plays a crucial role in cytoskeletal and intra‐cellular signalling events. Logic circuits can be designed with actin filaments with the help of actin quantum automata. The authors use a rule (4,27) to implement some novel designs of logic subtractor circuits on this automata to achieve the difference in two binary bits. Logic design of both half and full binary subtractors is proposed in this study. Actin‐based quantum cellular automata can be used in different combinations of input to get optimised results from the circuits. The authors focus on consolidating the designs inside single automata block to generate output in a less number of timesteps and less overheads. The designs are simulated with Simulink and this way output is verified for these different design approaches. Reliability and fault‐tolerance check is another interesting part of this study. To get a better idea of the optimisation achieved, the authors have also presented a comparative study between the proposed designs in terms of circuit size and efficiency. With all these parameters involved, this study explores opportunities for future implementation of unconventional computing in nano‐scale and cost‐effective bio‐molecular networks.Inspec keywords: cellular automata, molecular biophysics, molecular configurations, biology computing, proteins, logic circuits, biomolecular electronics, cellular biophysics, fault toleranceOther keywords: binary subtractor, actin quantum cellular automata, biological protein, cellular structure, cytoskeletal signalling events, intracellular signalling events, actin filaments, logic subtractor circuits, binary bits, logic design, half binary subtractors, full binary subtractors, optimised results, single automata block, Simulink, design approaches, reliability, fault‐tolerance check, circuit size, circuit efficiency, unconventional computing, nanoscale biomolecular networks, cost‐effective biomolecular networks     

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     

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     

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     

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