Architecture‐dependent robustness in a class of multiple positive feedback loops

Many types of multiple positive feedbacks with each having potentials to generate bistability exist extensively in natural, raising the question of why a particular architecture is present in a cell. In this study, the authors investigate multiple positive feedback loops across three classes: one‐loop class, two‐loop class and three‐loop class, where each class is composed of double positive feedback loop (DPFL) or double negative feedback loop (DNFL) or both. Through large‐scale sampling and robustness analysis, the authors find that for a given class, the homogeneous DPFL circuit (i.e. the coupled circuit that is composed of only DPFLs) is more robust than all the other circuits in generating bistable behaviour. In addition, stochastic simulation shows that the low stable state is more robust than the high stable state in homogeneous DPFL whereas the high‐stable state is more robust than the low‐stable state in homogeneous DNFL circuits. It was argued that this investigation provides insight into the relationship between robustness and network architecture.Inspec keywords: cellular biophysics, feedback, sampling methods, stochastic processesOther keywords: network architecture, low stable state, stochastic simulation, bistable behaviour, homogeneous DPFL circuit, robustness analysis, large‐scale sampling, DNFL, double negative feedback loop, double positive feedback loop, three‐loop class, two‐loop class, one‐loop class, cell architecture, bistability, multiple positive feedback loops, architecture‐dependent robustness     

Synthesising gene clock with toggle switch and oscillator

The usefulness of a genetic clock lies in its role to stimulate a sequence of logic reactions for sequential biological circuits. A clock signal is a periodic square wave, its amplitude alternates at a steady frequency between fixed minimal and maximal levels. Transition between the minimum and the maximum is instantaneous for an ideal square wave; however, the function is unrealisable in physical bio‐systems. This research develops a new genetic clock generator based on a genetic oscillator, in which, a sine wave generator is adopted as a signal oscillator. It is shown that combination of a genetic oscillator with a toggle switch is able to generate clock signals forming an efficient way to generate a near square wave. In silico study confirms the proposed idea.Inspec keywords: genetics, oscillators, biological techniques, square‐wave generators, switchesOther keywords: toggle switch, genetic clock, logic reaction sequence, sequential biological circuits, clock signal, periodic square wave, physical biosystem, genetic clock generator, sine wave generator, signal oscillator, genetic oscillator     

Design of dynamic genetic memory

In electronic systems, dynamic random access memory (DRAM) is one of the core modules in the modern silicon computer. As for a bio‐computer, one would need a mechanism for storage of bio‐information named ‘data’, which, in binary logic, has two levels, logical high and logical low, or in the normalised form, ‘1’ and ‘0’. This study proposes a possible genetic DRAM based on the modified electronic configuration, which uses the biological reaction to fulfil an equivalent RC circuit constituting a memory cell. The authors implement fundamental functions of the genetic DRAM by incorporating a genetic toggle switch for data hold. The results of simulation verify that the basic function can be used on a bio‐storage module for the future bio‐computer.Inspec keywords: DRAM chips, genetic engineering, biocomputers, bioinformatics, equivalent circuits, RC circuitsOther keywords: dynamic genetic memory design, electronic systems, dynamic random access memory, modern silicon computer, biocomputer, bioinformation, binary logic, logical high level, logical low level, normalised form, genetic DRAM, modified electronic configuration, biological reaction, equivalent RC circuit, memory cell, fundamental functions, genetic toggle switch, data hold, biostorage module     

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     

Engineering molecular communications integrated with carbon nanotubes in neural sensor nanonetworks

There have been recent advances in the engineering of molecular communication (MC)‐based networks for nanomedical applications. However, the integration of MC with biomaterials such as carbon nanotubes (CNTs) presents various critical research challenges. In this study, the authors envisaged integrating MC‐based nanonetwork with CNTs to optimise nanonetwork performance. In neural networks, a chronic reduction in the concentration of the neurotransmitter acetylcholine (ACh) eventually leads to the development of neurodegenerative diseases; therefore, they used CNTs as a molecular switch to optimise ACh conductivity supported by artificial MC. Furthermore, MC enables communication between transmitter neurons and receiver neurons for fine‐tuning the ACh release rate according to the feedback concentration of ACh. Subsequently, they proposed a min/max feedback scheme to fine‐tune the expected throughput and ACh transmission efficiency. For demonstration purposes, they deduced analytical forms for the proposed schemes in terms of throughput, incurred traffic rates, and average packet delay.Inspec keywords: carbon nanotubes, cellular biophysics, diseases, feedback, nanomedicine, nanosensors, neural nets, neurophysiologyOther keywords: carbon nanotubes, neural sensor nanonetworks, nanomedical applications, biomaterials, molecular communication‐based nanonetwork, neural networks, neurotransmitter acetylcholine, neurodegenerative diseases, transmitter neurons, receiver neurons     

Small RNA‐mediated switch‐like regulation in bacterial quorum sensing

Quorum sensing (QS) is a signalling mechanism by which bacteria produce, release and then detect and respond to changes in their density and biosignals called autoinducers (AIs). There are multiple feedback loops in the QS system of Vibrio harveyi. However, how these feedback loops function to control signal processing remains unclear. In this study, the authors present a computational model for the switch‐like regulation of signal transduction by small regulatory RNA‐mediated QS based on intertwined network involving AIs, LuxO, LuxU, Qrr sRNAs and LuxR. In agreement with experimental observations, the model suggests that different feedbacks play critical roles in the switch‐like regulation. The authors results reveal that V. harveyi uses multiple feedbacks to precisely control signal transduction.Inspec keywords: biocommunications, biocontrol, biology computing, cellular biophysics, physiological models, RNAOther keywords: RNA‐mediated switch‐like regulation, bacterial quorum sensing, signaling mechanism, autoinducers, Vibrio harveyi, feedback loops function, signal processing control, switch‐like regulation     

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     

Design of synthetic biological logic circuits based on evolutionary algorithm

The construction of an artificial biological logic circuit using systematic strategy is recognised as one of the most important topics for the development of synthetic biology. In this study, a real‐structured genetic algorithm (RSGA), which combines general advantages of the traditional real genetic algorithm with those of the structured genetic algorithm, is proposed to deal with the biological logic circuit design problem. A general model with the cis ‐regulatory input function and appropriate promoter activity functions is proposed to synthesise a wide variety of fundamental logic gates such as NOT, Buffer, AND, OR, NAND, NOR and XOR. The results obtained can be extended to synthesise advanced combinational and sequential logic circuits by topologically distinct connections. The resulting optimal design of these logic gates and circuits are established via the RSGA. The in silico computer‐based modelling technology has been verified showing its great advantages in the purpose.Inspec keywords: biocomputing, biological techniques, combinational circuits, genetic algorithms, logic design, logic gates, sequential circuitsOther keywords: in silico computer‐based modelling, RSGA, sequential logic circuits, XOR gates, NOR gates, NAND gates, OR gates, AND gates, Buffer gates, NOT gates, fundamental logic gates, cis‐regulatory input function, real‐structured genetic algorithm, artiflcial biological logic circuit design     

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     

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     

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     

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     

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     

Bifurcation analysis of bistable and oscillatory dynamics in biological networks using the root‐locus method

Most of the biological systems including gene regulatory networks can be described well by ordinary differential equation models with rational non‐linearities. These models are derived either based on the reaction kinetics or by curve fitting to experimental data. This study demonstrates the applicability of the root‐locus‐based bifurcation analysis method for studying the complex dynamics of such models. The effectiveness of the bifurcation analysis in determining the exact parameter regions in each of which the system shows a certain dynamical behaviour, such as bistability, oscillation, and asymptotically equilibrium dynamics is shown by considering two mostly studied gene regulatory networks, namely Gardner''s genetic toggle switch and p53 gene network possessing two‐phase (mono‐stable/oscillation) dynamics.Inspec keywords: oscillations, curve fitting, differential equations, bifurcation, genetics, nonlinear dynamical systemsOther keywords: nonlinearities, reaction kinetics, root‐locus‐based bifurcation analysis method, complex dynamics, exact parameter regions, dynamical behaviour, equilibrium dynamics, studied gene regulatory networks, p53 gene network, bistable dynamics, oscillatory dynamics, biological networks, root‐locus method, biological systems, ordinary differential equation models     

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     

An analytical approach to bistable biological circuit discrimination using real algebraic geometry

Biomolecular circuits with two distinct and stable steady states have been identified as essential components in a wide range of biological networks, with a variety of mechanisms and topologies giving rise to their important bistable property. Understanding the differences between circuit implementations is an important question, particularly for the synthetic biologist faced with determining which bistable circuit design out of many is best for their specific application. In this work we explore the applicability of Sturm''s theorem—a tool from nineteenth-century real algebraic geometry—to comparing ‘functionally equivalent’ bistable circuits without the need for numerical simulation. We first consider two genetic toggle variants and two different positive feedback circuits, and show how specific topological properties present in each type of circuit can serve to increase the size of the regions of parameter space in which they function as switches. We then demonstrate that a single competitive monomeric activator added to a purely monomeric (and otherwise monostable) mutual repressor circuit is sufficient for bistability. Finally, we compare our approach with the Routh–Hurwitz method and derive consistent, yet more powerful, parametric conditions. The predictive power and ease of use of Sturm''s theorem demonstrated in this work suggest that algebraic geometric techniques may be underused in biomolecular circuit analysis.     

Non‐linear feedback control of the p 53 protein–mdm 2 inhibitor system using the derivative‐free non‐linear Kalman filter

It is proven that the model of the p 53–mdm 2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p 53 protein at the desirable levels. To estimate the non‐measurable elements of the state vector describing the p 53–mdm 2 system dynamics, the derivative‐free non‐linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p 53–mdm 2 system, the derivative‐free non‐linear Kalman filter is re‐designed as a disturbance observer. The derivative‐free non‐linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non‐linear model. The proposed non‐linear feedback control and perturbations compensation method for the p 53–mdm 2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.Inspec keywords: proteins, molecular biophysics, biochemistry, Kalman filters, inverse problems, perturbation theoryOther keywords: nonlinear feedback control, p53 protein‐mdm2 inhibitor system, derivative‐free nonlinear Kalman filter, differential flatness theory, protein synthesis loop, diffeomorphism, protein synthesis model, feedback control law, nonmeasurable elements, modelling uncertainties, inverse transformation, nonlinear model, perturbation compensation method, chemotherapy schemes, medication infusion