Detecting small attractors of large Boolean networks by function‐reduction‐based strategy

Boolean networks (BNs) are widely used to model gene regulatory networks and to design therapeutic intervention strategies to affect the long‐term behaviour of systems. A central aim of Boolean‐network analysis is to find attractors that correspond to various cellular states, such as cell types or the stage of cell differentiation. This problem is NP‐hard and various algorithms have been used to tackle it with considerable success. The idea is that a singleton attractor corresponds to n consistent subsequences in the truth table. To find these subsequences, the authors gradually reduce the entire truth table of Boolean functions by extending a partial gene activity profile (GAP). Not only does this process delete inconsistent subsequences in truth tables, it also directly determines values for some nodes not extended, which means it can abandon the partial GAPs that cannot lead to an attractor as early as possible. The results of simulation show that the proposed algorithm can detect small attractors with length p = 4 in BNs of up to 200 nodes with average indegree K = 2.Inspec keywords: Boolean functions, genetics, cellular biophysicsOther keywords: detecting small attractors, function‐reduction‐based strategy, model gene regulatory networks, therapeutic intervention strategies, Boolean‐network analysis, cellular states, NP‐hard, singleton attractor, Boolean functions, partial gene activity profile, cell differentiation     

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     

Period–amplitude co‐variation in biomolecular oscillators

The period and amplitude of biomolecular oscillators are functionally important properties in multiple contexts. For a biomolecular oscillator, the overall constraints in how tuning of amplitude affects period, and vice versa, are generally unclear. Here, the authors investigate this co‐variation of the period and amplitude in mathematical models of biomolecular oscillators using both simulations and analytical approximations. The authors computed the amplitude–period co‐variation of 11 benchmark biomolecular oscillators as their parameters were individually varied around a nominal value, classifying the various co‐variation patterns such as a simultaneous increase/decrease in period and amplitude. Next, the authors repeated the classification using a power norm‐based amplitude metric, to account for the amplitudes of the many biomolecular species that may be part of the oscillations, finding largely similar trends. Finally, the authors calculate ‘scaling laws’ of period–amplitude co‐variation for a subset of these benchmark oscillators finding that as the approximated period increases, the upper bound of the amplitude increases, or reaches a constant value. Based on these results, the authors discuss the effect of different parameters on the type of period–amplitude co‐variation as well as the difficulty in achieving an oscillation with large amplitude and small period.Inspec keywords: molecular biophysics, oscillations, biology computing, circadian rhythmsOther keywords: period‐amplitude co‐variation, biomolecular oscillators, mathematical models, analytical approximations, co‐variation patterns, power norm‐based amplitude metric, scaling laws     

Non‐normality can facilitate pulsing in biomolecular circuits

Non‐normality can underlie pulse dynamics in many engineering contexts. However, its role in pulses generated in biomolecular contexts is generally unclear. Here, the authors address this issue using the mathematical tools of linear algebra and systems theory on simple computational models of biomolecular circuits. They find that non‐normality is present in standard models of feedforward loops. They used a generalised framework and pseudospectrum analysis to identify non‐normality in larger biomolecular circuit models, finding that it correlates well with pulsing dynamics. Finally, they illustrate how these methods can be used to provide analytical support to numerical screens for pulsing dynamics as well as provide guidelines for design.Inspec keywords: linear algebra, feedforward, eigenvalues and eigenfunctions, network analysis, molecular biophysicsOther keywords: nonnormality, biomolecular circuits, pulse dynamics, engineering contexts, biomolecular contexts, linear algebra, systems theory, simple computational models, standard models, larger biomolecular circuit models     

Experimental evidence for constraints in amplitude‐timescale co‐variation of a biomolecular pulse generating circuit design

Understanding constraints on the functional properties of biomolecular circuit dynamics, such as the possible variations of amplitude and timescale of a pulse, is an important part of biomolecular circuit design. While the amplitude‐timescale co‐variations of the pulse in an incoherent feedforward loop have been investigated computationally using mathematical models, experimental support for any such constraints is relatively unclear. Here, the authors address this using experimental measurement of an existing pulse generating incoherent feedforward loop circuit realisation in the context of a standard mathematical model. They characterise the trends of co‐variation in the pulse amplitude and rise time computationally by randomly exploring the parameter space. They experimentally measured the co‐variation by varying inducers and found that larger amplitude pulses have a slower rise time. They discuss the gap between the experimental measurements and predictions of the standard model, highlighting model additions and other biological factors that might bridge the gap.Inspec keywords: pulse generators, molecular electronics, integrated circuit designOther keywords: biomolecular pulse, functional properties, biomolecular circuit dynamics, biomolecular circuit design, incoherent feedforward loop, loop circuit realisation, pulse amplitude, amplitude‐timescale covariation, biomolecular pulse generating circuit, biological factors     

On‐chip label‐free impedance‐based detection of antibiotic permeation

Biosensors are analytical tools used for the analysis of biomaterial samples and provide an understanding about the biocomposition, structure, and function of biomolecules and/or biomechanisms by converting the biological response into an electrical and/or optical signal. In particular, with the rise in antibiotic resistance amongst pathogenic bacteria, the study of antibiotic activity and transport across cell membranes in the field of biosensors has been gaining widespread importance. Herein, for the rapid and label‐free detection of antibiotic permeation across a membrane, a microelectrode integrated microfluidic device is presented. The integrated chip consists of polydimethylsiloxane based microfluidic channels bonded onto microelectrodes on‐glass and enables us to recognize the antibiotic permeation across a membrane into the model membranes based on electrical impedance measurement, while also allowing optical monitoring. Impedance testing is label free and therefore allows the detection of both fluorescent and non‐fluorescent antibiotics. As a model membrane, Giant Unilamellar Vesicles (GUVs) are used and impedance measurements were performed by a precision inductance, capacitance, and resistance metre. The measured signal recorded from the device was used to determine the change in concentration inside and outside of the GUVs. We have found that permeation of antibiotic molecules can be easily monitored over time using the proposed integrated device. The results also show a clear difference between bilayer permeation that occurs through the lipidic bilayer and porin‐mediated permeation through the porin channels inserted in the lipid bilayer.     

Investigation of graphene‐on‐metal substrates for SPR‐based sensor using finite‐difference time domain

In this study, the authors investigated the effects of a single layer graphene as a coating layer on top of metal thin films such as silver, gold, aluminum and copper using finite‐difference time domain method. To enhance the resolution of surface plasmon resonance (SPR) sensor, it is necessary to increase the SPR reflectivity and decrease the full‐width‐half maximum (FWHM) of the SPR curve so that there is minimum uncertainty in the determination of the resonance dip. Numerical data was verified with analytical and experimental data where all the data were in good agreement with resonance angle differing in <10% due to noise present in components such as humidity and temperature. In further analysis, reflectivity and FWHM were compared among four types of metal with various thin film thicknesses where graphene was applied on top of the metal layers, and data was compared against pure conventional metal thin films. A 60 nm‐thick Au thin film results in higher performance with reflectivity of 92.4% and FWHM of 0.88° whereas single layer graphene‐on‐60 nm‐thick Au gave reflectivity of 91.7% and FWHM of 1.32°. However, a graphene‐on‐40 nm‐thick Ag also gave good performance with narrower FWHM of 0.88° and reflection spectra of 89.2%.Inspec keywords: graphene, surface plasmon resonance, finite difference time‐domain analysis, reflectivity, metallic thin films, silver, gold, aluminium, copper, chemical sensors, biological techniquesOther keywords: graphene‐on‐metal substrates, SPR‐based sensor, finite‐difference time domain, metal thin films, surface plasmon resonance sensor, SPR curve, resonance angles, reflectivity, C, Ag, Au, Al, Cu     

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     

Chattering‐ free hybrid adaptive neuro‐fuzzy inference system‐particle swarm optimisation data fusion‐based BG‐level control

In this study, a closed‐loop control scheme is proposed for the glucose–insulin regulatory system in type‐1 diabetic mellitus (T1DM) patients. Some innovative hybrid glucose–insulin regulators have combined artificial intelligence such as fuzzy logic and genetic algorithm with well known Palumbo model to regulate the blood glucose (BG) level in T1DM patients. However, most of these approaches have focused on the glucose reference tracking, and the qualitative of this tracking such as chattering reduction of insulin injection has not been well‐studied. Higher‐order sliding mode (HoSM) controllers have been employed to attenuate the effect of chattering. Owing to the delayed nature and non‐linear property of glucose–insulin mechanism as well as various unmeasurable disturbances, even the HoSM methods are partly successful. In this study, data fusion of adaptive neuro‐fuzzy inference systems optimised by particle swarm optimisation has been presented. The excellent performance of the proposed hybrid controller, i.e. desired BG‐level tracking and chattering reduction in the presence of daily glucose‐level disturbances is verified.Inspec keywords: fuzzy control, variable structure systems, particle swarm optimisation, neurocontrollers, fuzzy neural nets, blood, genetic algorithms, closed loop systems, medical control systems, fuzzy reasoning, diseases, nonlinear control systems, sugarOther keywords: data fusion, adaptive neuro‐fuzzy inference systems, particle swarm optimisation, hybrid controller, desired BG‐level tracking, chattering reduction, daily glucose‐level disturbances, closed‐loop control scheme, glucose–insulin regulatory system, type‐1 diabetic mellitus patients, innovative hybrid glucose–insulin regulators, artificial intelligence, fuzzy logic, genetic algorithm, Palumbo model, blood glucose level, T1DM patients, glucose reference tracking, insulin injection, mode controllers, glucose–insulin mechanism, chattering‐free hybrid adaptive neuro‐fuzzy inference system, particle swarm optimisation data fusion‐based BG‐level control     

Review of the systems biology of the immune system using agent‐based models

The immune system is an inherent protection system in vertebrate animals including human beings that exhibit properties such as self‐organisation, self‐adaptation, learning, and recognition. It interacts with the other allied systems such as the gut and lymph nodes. There is a need for immune system modelling to know about its complex internal mechanism, to understand how it maintains the homoeostasis, and how it interacts with the other systems. There are two types of modelling techniques used for the simulation of features of the immune system: equation‐based modelling (EBM) and agent‐based modelling. Owing to certain shortcomings of the EBM, agent‐based modelling techniques are being widely used. This technique provides various predictions for disease causes and treatments; it also helps in hypothesis verification. This study presents a review of agent‐based modelling of the immune system and its interactions with the gut and lymph nodes. The authors also review the modelling of immune system interactions during tuberculosis and cancer. In addition, they also outline the future research directions for the immune system simulation through agent‐based techniques such as the effects of stress on the immune system, evolution of the immune system, and identification of the parameters for a healthy immune system.Inspec keywords: reviews, cancerOther keywords: review, system biology, agent‐based models, immune system, vertebrate animals, human beings, disease, gut nodes, lymph nodes, tuberculosis, cancer     

In vitro evaluation of biodegradable nHAP‐Chitosan‐Gelatin‐based scaffold for tissue engineering application

The present study focuses on fabrication and characterisation of porous composite scaffold containing hydroxyapatite (HAP), chitosan, and gelatin with an average pore size of 250–1010 nm for improving wound repair and regeneration by Electrospinning method. From the results of X ‐Ray Diffraction (XRD) study, the peaks correspond to crystallographic structure of HAP powder. The presence of functional group bonds of HAP powder, Chitosan and scaffold was studied using Fourier Transform Infrared Spectroscopy (FTIR). The surface morphology of the scaffold was observed using Scanning Electron Microscope (SEM). The Bioactivity of the Nano composite scaffolds was studied using simulated body fluid solution at 37 ± 1°C. The biodegradability test was studied using Tris‐Buffer solution for the prepared nanocomposites [nano Chitosan, nano Chitosan gelatin, Nano based Hydroxyapatite Chitosan gelatin]. The cell migration and potential biocompatibility of nHAP‐chitosan‐gelatin scaffold was assessed via wound scratch assay and were compared to povedeen as control. Cytocompatibility evaluation for Vero Cells using wound scratch assay showed that the fabricated porous nanocomposite scaffold possess higher cell proliferation and growth than that of povedeen. Thus, the study showed that the developed nanocomposite scaffolds are potential candidates for regenerating damaged cell tissue in wound healing process.Inspec keywords: nanofabrication, tissue engineering, electrospinning, wounds, cellular biophysics, scanning electron microscopy, surface morphology, X‐ray diffraction, biomedical materials, nanomedicine, porosity, biodegradable materials, nanoporous materials, calcium compounds, gelatin, nanocomposites, Fourier transform infrared spectra, nanoparticles, precipitation (physical chemistry)Other keywords: average pore size, wound repair, crystallographic structure, HAP powder, functional group bonds, simulated body fluid solution, biodegradability test, Tris‐Buffer solution, cell migration, wound scratch assay, tissue engineering, electrospinning method, X‐ray diffraction, Fourier transform infrared spectroscopy, scanning electron microscopy, biocompatibility, cytocompatibility, porous nanocomposite scaffold, cell tissue, nHAP‐chitosan‐gelatin scaffold composites, wet chemical precipitation method, surface morphology, nanohydroxyapatite‐nanochitosan‐gelatin scaffold composites, cell proliferation, wound healing, (Ca₁₀ (PO₄)₆ (OH)₂)     

Observer‐based resilient finite‐time control of blood gases model during extra‐corporeal circulation

This study aims at designing an observer‐based resilient controller to regulate the amount of oxygen and carbon dioxide in the blood of patients during the extra‐corporeal blood circulation process. More precisely, in this study, a suitable observer‐based resilient controller is constructed to regulate the levels of patient blood gases in a finite interval of time. The finite‐time boundedness with the prescribed H∞ performance index of the considered blood gases control system against modelling uncertainty and external disturbances is ensured by using Lyapunov stability analysis. Moreover, a set of sufficient conditions for obtaining the controller gain is developed in the form of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed robust finite‐time control scheme is verified through simulation results. The result reveals that the blood gases are maintained in their physiological ranges during a stable extra‐corporeal circulation process via the proposed observer‐based resilient controller.Inspec keywords: blood, haemodynamics, oxygen, carbon compounds, controllers, medical control systems, biomedical equipment, Lyapunov methods, linear matrix inequalitiesOther keywords: observer‐based resilient finite‐time control, observer‐based resilient controller, oxygen amount, carbon dioxide amount, extracorporeal blood circulation process, patient blood gas levels, finite time interval, finite‐time boundedness, H_∞ performance index, blood gases control system, Lyapunov stability analysis, controller gain, linear matrix inequalities, physiological ranges, LMIs, CO₂ , O₂      

Anti‐triangle centrality‐based community detection in complex networks

Community detection has been extensively studied in the past decades largely because of the fact that community exists in various networks such as technological, social and biological networks. Most of the available algorithms, however, only focus on the properties of the vertices, ignoring the roles of the edges. To explore the roles of the edges in the networks for community discovery, the authors introduce the novel edge centrality based on its antitriangle property. To investigate how the edge centrality characterises the community structure, they develop an approach based on the edge antitriangle centrality with the isolated vertex handling strategy (EACH) for community detection. EACH first calculates the edge antitriangle centrality scores for all the edges of a given network and removes the edge with the highest score per iteration until the scores of the remaining edges are all zero. Furthermore, EACH is characterised by being free of the parameters and independent of any additional measures to determine the community structure. To demonstrate the effectiveness of EACH, they compare it with the state‐of‐the art algorithms on both the synthetic networks and the real world networks. The experimental results show that EACH is more accurate and has lower complexity in terms of community discovery and especially it can gain quite inherent and consistent communities with a maximal diameter of four jumps.Inspec keywords: biology computing, complex networks, graph theory, social sciences computingOther keywords: antitriangle centrality‐based community detection, complex networks, technological networks, social networks, biological networks, vertex properties, edge roles, community discovery, antitriangle property, community structure, edge antitriangle centrality, isolated vertex handling strategy, EACH, antitriangle centrality scores, synthetic networks, real world networks     

Lamivudine‐conjugated and efavirenz‐loaded G2 dendrimers: Novel anti‐retroviral nano drug delivery systems

Infection with human immunodeficiency virus (HIV)‐1 causes immunological disorders and death worldwide which needs to be further assisted by novel anti‐retroviral drug delivery systems. Consequently, finding newer anti‐retroviral pharmaceuticals by using biocompatible, biodegradable nanomaterials comprising a nanoparticle as core and a therapeutic agent is of high global interest. In this experiment, a second generation of a negatively charged nano‐biopolymer linear globular G2 dendrimer was carefully conjugated and loaded with well‐known anti‐HIV drugs lamivudine and efavirenz, respectively. They were characterised by a variety of analytical methods such as Zetasizer, Fourier‐transform infrared spectroscopy, elemental analysis and liquid chromatography‐mass spectroscopy. Additionally, conjugated lamivudine and loaded efazirenz with globular PEGylated G2 dendrimer were tested on an HEK293 T cell infected by single‐cycle replicable HIV‐1 virion and evaluated using XTT test and HIV‐1 P24 protein load. The results showed that lamivudine‐conjugated G2 significantly decreased retroviral activity without any cell toxicity. This effect was more or less observed by efavirenz‐loaded G2. These nano‐constructs are strongly suggested for further in vivo anti‐HIV assays.     

Microelectromechanical system‐based biosensor for label‐free detection of human cytomegalovirus

The human cytomegalovirus (HCMV) is an asymptomatic common virus that is typically harmless, but in some cases, it can be life threatening. Thus, there is an urgent need to develop novel diagnostic methods and strengthen the efforts to combat this virus. A microcantilever‐based biosensor functionalised with the UL83‐antibody of HCMV (UL83‐HCMV antibody) has been developed to detect the UL83‐antigen of HCMV (UL83‐HCMV antigen) at different concentrations ranging from 0.3 to 300 ng/ml. The response of the biosensor to the presence of UL83‐HCMV antigen was measured through the shift in resonance frequency before and after antigen–antibody binding. The system shows a low detection limit of 84 pg/ml, which is comparable to traditional sensors, and a detection time of less than 15 min was achieved. The selectivity of the sensor was demonstrated using three different proteins with and without the UL83‐HCMV antigen. The biosensor shows high selectivity for the UL83‐HCMV antigen. Mass loading by the UL83‐HCMV antigen was roughly estimated with a sensitivity of ∼30 fg/Hz. This technique is crucial for the fabrication of portable and low‐cost biosensors that can be used in real‐time monitoring and enables early medical diagnosis.     

Describing functions for nonlinear optical systems

The concept of describing functions is useful for analyzing and designing nonlinear systems. A proposal for using the idea of describing functions for studying the behavior of a nonlinear optical processing system is given. The describing function can be used in the same way that a coherent transfer function or optical transfer function is used to characterize linear, shift-invariant optical processors. Two coherent optical systems for measuring the magnitude of the describing function of nonlinear optical processors are suggested.     

Hilbert transform‐based time‐series analysis of the circadian gene regulatory network

In this work, the authors propose the Hilbert transform (HT)‐based numerical method to analyse the time series of the circadian rhythms. They demonstrate the application of HT by taking both deterministic and stochastic time series that they get from the simulation of the fruit fly model Drosophila melanogaster and show how to extract the period, construct phase response curves, determine period sensitivity of the parameters to perturbations and build Arnold tongues to identify the regions of entrainment. They also derive a phase model that they numerically simulate to capture whether the circadian time series entrains to the forcing period completely (phase locking) or only partially (phase slips) or neither. They validate the phase model, and numerics with the experimental time series forced under different temperature cycles. Application of HT to the circadian time series appears to be a promising tool to extract the characteristic information about circadian rhythms.Inspec keywords: time series, genetics, Hilbert transforms, stochastic processes, circadian rhythms, signal processing, medical signal processingOther keywords: phase model, experimental time series, circadian time series, circadian rhythms, circadian gene regulatory network, deterministic time series, stochastic time series, fruit fly model, phase response curves, period sensitivity, phase locking, phase slips, Hilbert transform, time‐series analysis, signal processing     

Fuzzy logic and Lyapunov‐based non‐linear controllers for HCV infection

Hepatitis C is the liver disease caused by the Hepatitis C virus (HCV) which can lead to serious health problems such as liver cancer. In this research work, the non‐linear model of HCV having three state variables (uninfected hepatocytes, infected hepatocytes and virions) and two control inputs has been taken into account, and four non‐linear controllers namely non‐linear PID controller, Lyapunov Redesign controller, Synergetic controller and Fuzzy Logic‐Based controller have been proposed to control HCV infection inside the human body. The controllers have been designed for the anti‐viral therapy in order to control the amount of uninfected hepatocytes to the desired safe limit and to track the amount of infected hepatocytes and virions to their reference value which is zero. One control input is the Pegylated interferon (peg‐IFN‐α) which acts in reducing the infected hepatocytes and the other input is ribavirin which blocks the production of virions. By doing so, the uninfected hepatocytes increase and achieve the required safe limit. Lyapunov stability analysis has been used to prove the stability of the whole system. The comparative analysis of the proposed nonlinear controllers using MATLAB/Simulink have been done with each other and with linear PID. These results depict that the infected hepatocytes and virions are reduced to the desired level, enhancing the rate of sustained virologic response (SVR) and reducing the treatment period as compared with previous strategies introduced in the literature.     

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