IET Systems Biology (IET SYST BIOL)

Publications in this journal

• Article: Symbolic approach to verification and control of deterministic/probabilistic Boolean networks.

  K Kobayashi, K Hiraishi
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  ABSTRACT: A Boolean network (BN) is well known as one of the models of biological networks such as gene regulatory networks, and has been extensively studied. In this study, for a BN, the verification/control problems are discussed. First, a probabilistic model including both synchronous and asynchronous Boolean dynamics is derived. This model can be generalised as a probabilistic BN. Next, a solution method of the verification/control problems is proposed, based on a probabilistic model checker PRISM. Finally, the PRISM-based method is applied to an apoptosis network and a WNT5A network. The proposed approach provides us an easy and convenient tool for analysis and control of biological networks.
  IET Systems Biology 12/2012; 6(6):215-22.
• Article: Computing enclosures for uncertain biochemical systems.

  E August, H Koeppl
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  ABSTRACT: In this study, the authors present a novel method that provides enclosures for state trajectories of a non-linear dynamical system with uncertainties in initial conditions and parameter values. It is based on solving positivity conditions by means of semi-definite programmes and sum of squares decompositions. The method accounts for the indeterminacy of kinetic parameters, measurement uncertainties and fluctuations in the reaction rates because of extrinsic noise. This is particularly useful in the field of systems biology when one seeks to determine model behaviour quantitatively or, if this is not possible, semiquantitatively. The authors also demonstrate the significance of the proposed method to model selection in biology. The authors illustrate the applicability of their method on the mitogen-activated protein kinase signalling pathway, which is an important and reoccurring network motif that apparently also plays a crucial role in the development of cancer.
  IET Systems Biology 12/2012; 6(6):232-40.
• Article: Model of the synthesis of trisporic acid in Mucorales showing bistability.

  S Werner, A Schroeter, C Schimek, S Vlaic, J Wöstemeyer, S Schuster
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  ABSTRACT: An important substance in the signalling between individuals of Mucor-like fungi is trisporic acid (TA). This compound, together with some of its precursors, serves as a pheromone in mating between (+)- and (-)-mating types. Moreover, intermediates of the TA pathway are exchanged between the two mating partners. Based on differential equations, mathematical models of the synthesis pathways of TA in the two mating types of an idealised Mucor-fungus are here presented. These models include the positive feedback of TA on its own synthesis. The authors compare three sub-models in view of bistability, robustness and the reversibility of transitions. The proposed modelling study showed that, in a system where intermediates are exchanged, a reversible transition between the two stable steady states occurs, whereas an exchange of the end product leads to an irreversible transition. The reversible transition is physiologically favoured, because the high-production state of TA must come to an end eventually. Moreover, the exchange of intermediates and TA is compared with the 3-way handshake widely used by computers linked in a network.
  IET Systems Biology 12/2012; 6(6):207-14.
• Article: Design of biomolecular network modifications to achieve adaptation.

  S Waldherr, S Streif, F Allgöwer
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  ABSTRACT: A biomolecular network is called adaptive if its output returns to the original value after a transient response even under a persisting stimulus. The conditions for adaptation have been investigated thoroughly with systems theory approaches in the literature and it is easy to check whether they are satisfied in the linear approximation. In contrast, it is in general not easy to modify a non-adaptive network model such that it gains adaptive behaviour, especially for medium- and large-scale networks. The authors present a systematic approach based on the notion of kinetic perturbations to construct adaptive biomolecular network models from non-adaptive ones. An advantage of kinetic perturbations in this application is that neither the stoichiometry nor the steady state of the system is changed. Furthermore, the method covers both parameter and network structure modifications and can be applied to any reaction rate formalism and even to medium-scale or partially unknown models. The approach is exemplified at a small- and a medium-sized biomolecular network, illustrating its potential to systematically evaluate the different network modifications for adaptation. The proposed method will be useful either in iterative model building to construct mathematical models of adaptive biomolecular networks, or in synthetic biology where it can be applied to design or modify synthetic networks for adaptation.
  IET Systems Biology 12/2012; 6(6):223-31.
• Article: Comparison of statistical and optimisation-based methods for data-driven network reconstruction of biochemical systems.

  B Asadi, M R Maurya, D M Tartakovsky, S Subramaniam
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  ABSTRACT: Data-driven reconstruction of biological networks is a crucial step towards making sense of large volumes of biological data. Although several methods have been developed recently to reconstruct biological networks, there are few systematic and comprehensive studies that compare different methods in terms of their ability to handle incomplete datasets, high data dimensions and noisy data. The authors use experimentally measured and synthetic datasets to compare three popular methods - principal component regression (PCR), linear matrix inequalities (LMI) and least absolute shrinkage and selection operator (LASSO) - in terms of root-mean-squared error (RMSE), average fractional error in the value of the coefficients, accuracy, sensitivity, specificity and the geometric mean of sensitivity and specificity. This comparison enables the authors to establish criteria for selection of an appropriate approach for network reconstruction based on a priori properties of experimental data. For instance, although PCR is the fastest method, LASSO and LMI perform better in terms of accuracy, sensitivity and specificity. Both PCR and LASSO are better than LMI in terms of fractional error in the values of the computed coefficients. Trade-offs such as these suggest that more than one aspect of each method needs to be taken into account when designing strategies for network reconstruction. [Includes supplementary material].
  IET Systems Biology 10/2012; 6(5):155-163.
• Article: Analysis of a bio-dynamic model via Lyapunov principle and small-world network for tuberculosis.

  H-Y Chung, C-Y Chung, S-C Ou
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  ABSTRACT: The study will apply Lyapunov principle to construct a dynamic model for tuberculosis (TB). The Lyapunov principle is commonly used to examine and determine the stability of a dynamic system. To simulate the transmissions of vector-borne diseases and discuss the related health policies effects on vector-borne diseases, the authors combine the multi-agent-based system, social network and compartmental model to develop an epidemic simulation model. In the identity level, the authors use the multi-agent-based system and the mirror identity concept to describe identities with social network features such as daily visits, long-distance movement, high degree of clustering, low degree of separation and local clustering. The research will analyse the complex dynamic mathematic model of TB epidemic and determine its stability property by using the popular Matlab/Simulink software and relative software packages. Facing the current TB epidemic situation, the development of TB and its developing trend through constructing a dynamic bio-mathematical system model of TB is investigated. After simulating the development of epidemic situation with the solution of the SMIR epidemic model, the authors will come up with a good scheme to control epidemic situation to analyse the parameter values of a model that influence epidemic situation evolved. The authors will try to find the quarantining parameters that are the most important factors to control epidemic situation. The SMIR epidemic model and the results via numerical analysis may offer effective prevention with reference to controlling epidemic situation of TB.
  IET Systems Biology 10/2012; 6(5):196-206.
• Article: Systemic modelling of human bioenergetics and blood circulation.

  K M Lim, S-H Yang, E B Shim
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  ABSTRACT: This work reviews the main aspects of human bioenergetics and the dynamics of the cardiovascular system, with emphasis on modelling their physiological characteristics. The methods used to study human bioenergetics and circulation dynamics, including the use of mathematical models, are summarised. The main characteristics of human bioenergetics, including mitochondrial metabolism and global energy balance, are first described, and the systemic aspects of blood circulation and related physiological issues are introduced. The authors also discuss the present status of studies of human bioenergetics and blood circulation. Then, the limitations of the existing studies are described in an effort to identify directions for future research towards integrated and comprehensive modelling. This review emphasises that a multi-scale and multi-physical approach to bioenergetics and blood circulation that considers multiple scales and physiological factors are necessary for the appropriate clinical application of computational models.
  IET Systems Biology 10/2012; 6(5):187-195.
• Article: Editorial: Modelling noise in biochemical reaction networks.

  R Grima, J Kim
  IET Systems Biology 08/2012; 6(4):101.
• Article: Linear noise approximation is valid over limited times for any chemical system that is sufficiently large.

  E W J Wallace, D T Gillespie, K R Sanft, L R Petzold
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  ABSTRACT: The linear noise approximation (LNA) is a way of approximating the stochastic time evolution of a well-stirred chemically reacting system. It can be obtained either as the lowest order correction to the deterministic chemical reaction rate equation (RRE) in van Kampen's system-size expansion of the chemical master equation (CME), or by linearising the two-term-truncated chemical Kramers-Moyal equation. However, neither of those derivations sheds much light on the validity of the LNA. The problematic character of the system-size expansion of the CME for some chemical systems, the arbitrariness of truncating the chemical Kramers-Moyal equation at two terms, and the sometimes poor agreement of the LNA with the solution of the CME, have all raised concerns about the validity and usefulness of the LNA. Here, the authors argue that these concerns can be resolved by viewing the LNA as an approximation of the chemical Langevin equation (CLE). This view is already implicit in Gardiner's derivation of the LNA from the truncated Kramers-Moyal equation, as that equation is mathematically equivalent to the CLE. However, the CLE can be more convincingly derived in a way that does not involve either the truncated Kramers-Moyal equation or the system-size expansion. This derivation shows that the CLE will be valid, at least for a limited span of time, for any system that is sufficiently close to the thermodynamic (large-system) limit. The relatively easy derivation of the LNA from the CLE shows that the LNA shares the CLE's conditions of validity, and it also suggests that what the LNA really gives us is a description of the initial departure of the CLE from the RRE as we back away from the thermodynamic limit to a large but finite system. The authors show that this approach to the LNA simplifies its derivation, clarifies its limitations, and affords an easier path to its solution.
  IET Systems Biology 08/2012; 6(4):102-15.
• Article: Anomalous diffusion and multifractional Brownian motion: simulating molecular crowding and physical obstacles in systems biology.

  T T Marquez-Lago, A Leier, K Burrage
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  ABSTRACT: There have been many recent studies from both experimental and simulation perspectives in order to understand the effects of spatial crowding in molecular biology. These effects manifest themselves in protein organisation on the plasma membrane, on chemical signalling within the cell and in gene regulation. Simulations are usually done with lattice- or meshless-based random walks but insights can also be gained through the computation of the underlying probability density functions of these stochastic processes. Until recently much of the focus had been on continuous time random walks, but some very recent work has suggested that fractional Brownian motion may be a good descriptor of spatial crowding effects in some cases. The study compares both fractional Brownian motion and continuous time random walks and highlights how well they can represent different types of spatial crowding and physical obstacles. Simulated spatial data, mimicking experimental data, was first generated by using the package Smoldyn. We then attempted to characterise this data through continuous time anomalously diffusing random walks and multifractional Brownian motion (MFBM) by obtaining MFBM paths that match the statistical properties of our sample data. Although diffusion around immovable obstacles can be reasonably characterised by a single Hurst exponent, we find that diffusion in a crowded environment seems to exhibit multifractional properties in the form of a different short- and long-time behaviour.
  IET Systems Biology 08/2012; 6(4):134-42.
• Article: Simulation of mRNA diffusion in the nuclear environment.

  M R Roussel, T Tang
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  ABSTRACT: A mathematical model is devised to study the diffusion of mRNA in the nucleus from the site of synthesis to a nuclear pore where it is exported to the cytoplasm. This study examines the role that nuclear structure can play in determining the kinetics of export by considering models in which elements of the nuclear skeleton and confinement by chromatin direct the mRNA movement. As a rule, a dense chromatin layer favours rapid export by reducing the effective volume for diffusion. However, it may also result in a heavy tail in the export time distribution because of the low mobility of molecules that accidentally find their way deep into the dense layer. An anisotropic solid-state transport system can also assist export. There exist both an optimal ratio of the anisotropy and an optimal depth of the solid-state transport layer that favour rapid export. [Includes supplementary material].
  IET Systems Biology 08/2012; 6(4):125-33.
• Article: Non-linear corrections to the time-covariance function derived from a multi-state chemical master equation.

  M Scott
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  ABSTRACT: The time-covariance function captures the dynamics of biochemical fluctuations and contains important information about the underlying kinetic rate parameters. Intrinsic fluctuations in biochemical reaction networks are typically modelled using a master equation formalism. In general, the equation cannot be solved exactly and approximation methods are required. For small fluctuations close to equilibrium, a linearisation of the dynamics provides a very good description of the relaxation of the time-covariance function. As the number of molecules in the system decrease, deviations from the linear theory appear. Carrying out a systematic perturbation expansion of the master equation to capture these effects results in formidable algebra; however, symbolic mathematics packages considerably expedite the computation. The authors demonstrate that non-linear effects can reveal features of the underlying dynamics, such as reaction stoichiometry, not available in linearised theory. Furthermore, in models that exhibit noise-induced oscillations, non-linear corrections result in a shift in the base frequency along with the appearance of a secondary harmonic.
  IET Systems Biology 08/2012; 6(4):116-24.
• Article: Influence of cell-to-cell variability on spatial pattern formation.

  B Greese, K Wester, R Bensch, O Ronneberger, J Timmer, M Hülskamp, C Fleck
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  ABSTRACT: Many spatial patterns in biology arise through differentiation of selected cells within a tissue, which is regulated by a genetic network. This is specified by its structure, parameterisation and the noise on its components and reactions. The latter, in particular, is not well examined because it is rather difficult to trace. The authors use suitable local mathematical measures based on the Voronoi diagram of experimentally determined positions of epidermal plant hairs (trichomes) to examine the variability or noise in pattern formation. Although trichome initiation is a highly regulated process, the authors show that the experimentally observed trichome pattern is substantially disturbed by cell-to-cell variations. Using computer simulations, they find that the rates concerning the availability of the protein complex that triggers trichome formation plays a significant role in noise-induced variations of the pattern. The focus on the effects of cell noise yields further insights into pattern formation of trichomes. The authors expect that similar strategies can contribute to the understanding of other differentiation processes by elucidating the role of naturally occurring fluctuations in the concentration of cellular components or their properties.
  IET Systems Biology 08/2012; 6(4):143-153.
• Article: Model of lymphoma from stochastic analysis.

  J M Chrobak, H Herrero
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  ABSTRACT: In this work, the authors introduce a stochastic model of lymphoma. Two clonotypes of T cells of the immune system compete with each other and with other clonotypes for survival stimuli. One of the clonotypes is normal and the other is tumourous. To model the tumourous clonotype the authors include a rate of influx of new naive T cells (descendants of mutated precursor cells) from the thymus. The authors obtain a deterministic approximation to the stochastic model and analyse eight cases of competition between the two clonotypes of T cells. The authors obtain two possible scenarios, depending on the values of parameters: either both clonotypes survive in the repertoire or the clonotype of the normal T cells becomes extinct, meanwhile the clonotype of the tumourous T cells is maintained, after achieving some maximum level of growth. The authors show that if the income of the new tumourous T cells from the thymus is augmented, then the tumourous clonotype, would never be removed from the repertoire; meanwhile the normal clonotype could become extinct if it was not specialised enough to compete effectively for survival stimuli provided by professional cells.
  IET Systems Biology 06/2012; 6(3):94-9.
• Article: Mathematical modelling unravels regulatory mechanisms of interferon-γ-induced STAT1 serine-phosphorylation and MUC4 expression in pancreatic cancer cells.

  C Kossow, D Jose, R Jaster, O Wolkenhauer, K Rateitschak
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  ABSTRACT: Interferon-γ (IFNγ)-mediated signal transduction via upregulation of signal transducer and activator of transcription (STAT) 1 leads to the expression of the mucin (MUC) 4 gene in pancreatic cancer cells. Upregulation of STAT1 may also implicate STAT1 tyrosine- or serine-phosphorylation. Experimental data indicate that reaction steps involved in IFN-γ induced serine-phosphorylation of STAT1 vary between cell types in contrast to conserved IFN-γ induced tyrosine-phosphorylation of STAT1. The above observations raise the following two questions: (i) How does IFNγ stimulation regulates serine-phosphorylation of STAT1 in the pancreatic cancer cell line CD18/HPAF? (ii) Which type of STAT1 acts as a transcription factor of MUC4? Our objective is to address these two questions by data-driven mathematical modelling. Simulation results of the parameterised ordinary differential equation models show that serine-phosphorylation of unphosphorylated STAT1 occurs in the cytoplasm. In contrast, serine-phosphorylation of tyrosine-phosphorylated STAT1 can take place in the cytoplasm or in the nucleus. In addition, our results propose that unphosphorylated or serine-phosphorylated STAT1 can act as transcription factors of MUC4, either alone by progressive binding to different sites in the promoter or both together.
  IET Systems Biology 06/2012; 6(3):73-85.
• Article: Feedback motif for the pathogenesis of Parkinson's disease.

  M Cloutier, R Middleton, P Wellstead
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  ABSTRACT: Previous article on the integrative modelling of Parkinson's disease (PD) described a mathematical model with properties suggesting that PD pathogenesis is associated with a feedback-induced biochemical bistability. In this article, the authors show that the dynamics of the mathematical model can be extracted and distilled into an equivalent two-state feedback motif whose stability properties are controlled by multi-factorial combinations of risk factors and genetic mutations associated with PD. Based on this finding, the authors propose a principle for PD pathogenesis in the form of the switch-like transition of a bistable feedback process from 'healthy' homeostatic levels of reactive oxygen species and the protein α-synuclein, to an alternative 'disease' state in which concentrations of both molecules are stable at the damagingly high-levels associated with PD. The bistability is analysed using the rate curves and steady-state response characteristics of the feedback motif. In particular, the authors show how a bifurcation in the feedback motif marks the pathogenic moment at which the 'healthy' state is lost and the 'disease' state is initiated. Further analysis shows how known risks (such as: age, toxins and genetic predisposition) modify the stability characteristics of the feedback motif in a way that is compatible with known features of PD, and which explain properties such as: multi-factorial causality, variability in susceptibility and severity, multi-timescale progression and the special cases of familial Parkinson's and Parkinsonian symptoms induced purely by toxic stress.
  IET Systems Biology 06/2012; 6(3):86-93.
• Article: Dynamic modelling of protein and oxidative metabolisms simulates the pathogenesis of Parkinson's disease.

  M Cloutier, P Wellstead
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  ABSTRACT: Research into Parkinson's disease (PD) is difficult and time consuming. It is a complex condition that develops over many decades in the human brain. For such apparently intractable diseases, mathematical models can offer an additional means of investigation. As a contribution to this process, the authors have developed an ordinary differential equation model of the most important cellular processes that have been associated with PD. The model describes the following processes: (i) cellular generation and scavenging of reactive oxygen species; (ii) the possible damage and removal of the protein -synuclein and, (iii) feedback interactions between damaged α-synuclein and reactive oxygen species. Simulation results show that the Parkinsonian condition, with elevated oxidative stress and misfolded α-synuclein accumulation, can be induced in the model by known PD risk factors such as ageing, exposure to toxins and genetic defects. The significant outcome of the paper is the demonstration that it is possible to reproduce in silico the multi-factorial interactions that characterise the pathogenesis of PD. As such, the model provides a systematic explanation of the variability and heterogeneity of PD and provides the basis for computational studies of further facets of this complex multi-factorial condition. [Includes supplementary material].
  IET Systems Biology 06/2012; 6(3):65-72.
• Article: Empirically determining the sample size for large-scale gene network inference algorithms.

  G Altay
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  ABSTRACT: The performance of genome-wide gene regulatory network inference algorithms depends on the sample size. It is generally considered that the larger the sample size, the better the gene network inference performance. Nevertheless, there is not adequate information on determining the sample size for optimal performance. In this study, the author systematically demonstrates the effect of sample size on information-theory-based gene network inference algorithms with an ensemble approach. The empirical results showed that the inference performances of the considered algorithms tend to converge after a particular sample size region. As a specific example, the sample size region around ≃64 is sufficient to obtain the most of the inference performance with respect to precision using the representative algorithm C3NET on the synthetic steady-state data sets of Escherichia coli and also time-series data set of a homo sapiens subnetworks. The author verified the convergence result on a large, real data set of E. coli as well. The results give evidence to biologists to better design experiments to infer gene networks. Further, the effect of cutoff on inference performances over various sample sizes is considered. [Includes supplementary material].
  IET Systems Biology 04/2012; 6(2):35-43.