Showing papers in "Iet Systems Biology in 2012"

Linear noise approximation is valid over limited times for any chemical system that is sufficiently large

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.

Building blocks of biological networks: a review on major network motif discovery algorithms.

Abstract: In recent years, there has been a great interest in studying different aspects of complex networks in a range of fields. One important local property of networks is network motifs, recurrent and statistically significant sub-graphs or patterns, which assists researchers in the identification of functional units in the networks. Although network motifs may provide a deep insight into the network's functional abilities, their detection is computationally challenging. Therefore several algorithms have been introduced to resolve this computationally hard problem. These algorithms can be classified under various paradigms such as exact counting methods, sampling methods, pattern growth methods and so on. Here, the authors will give a review on computational aspects of major algorithms and enumerate their related benefits and drawbacks from an algorithmic perspective.

Network-based analysis of complex diseases

Abstract: Complex diseases are commonly believed to be caused by the breakdown of several correlated genes rather than individual genes. The availability of genome-wide data of high-throughput experiments provides us with new opportunity to explore this hypothesis by analysing the disease-related biomolecular networks, which are expected to bridge genotypes and disease phenotypes and further reveal the biological mechanisms of complex diseases. In this study, the authors review the existing network biology efforts to study complex diseases, such as breast cancer, diabetes and Alzheimer's disease, using high-throughput data and computational tools. Specifically, the authors categorise these existing methods into several classes based on the research topics, that is, disease genes, dysfunctional pathways, network signatures and drug-target networks. The authors also summarise the pros and cons of those methods from both computation and application perspectives, and further discuss research trends and future topics of this promising field.

Anomalous diffusion and multifractional Brownian motion: simulating molecular crowding and physical obstacles in systems biology

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.

Feedback motif for the pathogenesis of Parkinson's disease.

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.

Dynamic modelling of protein and oxidative metabolisms simulates the pathogenesis of Parkinson's disease

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 α-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]

Empirically determining the sample size for large-scale gene network inference algorithms

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]

Symbolic approach to verification and control of deterministic/probabilistic Boolean networks

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.

Design of biomolecular network modifications to achieve adaptation.

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.

Comparison of statistical and optimisation-based methods for data-driven network reconstruction of biochemical systems.

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.

Non-linear corrections to the time-covariance function derived from a multi-state chemical master equation

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.

Influence of cell-to-cell variability on spatial pattern formation

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.

Model of the synthesis of trisporic acid in Mucorales showing bistability.

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.

Growth-related model of the GAL system in Saccharomyces cerevisiae predicts behaviour of several mutant strains.

Abstract: The genetic regulatory network responds dynamically to perturbations in the intracellular and extracellular environments of an organism The GAL system in the yeast Saccharomyces cerevisiae has evolved to utilise galactose as an alternative carbon and energy source, in the absence of glucose in the environment This work contains a modified dynamic model for GAL system in S cerevisiae, which includes a novel mechanism for Gal3p activation upon induction with galactose The modification enables the model to simulate the experimental observation that in absence of galactose, oversynthesis of Gal3p can also induce the GAL system Subsequently, the model is related to growth on galactose and glucose in a structured manner The growth-related models are validated with experimental data for growth on individual substrates as well as mixed substrates Finally, the model is tested for its prediction of a variety of known mutant behaviours The exercise shows that the authors' model with a single set of parameters is able to capture the rich behaviour of the GAL system in S cerevisiae [Includes supplementary material]

Mathematical modelling unravels regulatory mechanisms of interferon-γ-induced STAT1 serine-phosphorylation and MUC4 expression in pancreatic cancer cells

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 IFNγ-induced serine-phosphorylation of STAT1 vary between cell types in contrast to conserved IFNγ-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.

Simulation of mRNA diffusion in the nuclear environment

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]

Identifying similar functional modules by a new hybrid spectral clustering method.

Abstract: Recently, a large number of researches have focused on finding cellular modules within protein–protein interaction networks. Until now, most of the works have concentrated on finding small modules and protein complexes. The authors have extended the concept of functional module and have identified larger functional modules which are the most similar to the entire network. To this end, a new hybrid spectral-based method is proposed here. First, the original graph is transformed into a line graph. Next, the nodes of the new graph are represented in the Euclidean space by using spectral methods and finally, a self-organising map is applied to the points in the new feature space. The experimental results show that similar modules, obtained from the proposed method, have own local hubs and lots of significant functional subunits concerning each other. These modules not only detect general biological processes that each protein is involved in, but also due to great similarities to the original network, it can be used as significant subnetworks for predicting protein function as detailed as possible. Some interesting properties of these modules are also investigated in this research. [Includes supplementary material]

DoGeNetS: Using optimisation to discriminate regulatory network topologies based on gene expression data

Abstract: Gene regulatory networks (GRNs) determine the dynamics of gene expression. Interest often focuses on the topological structure of a GRN while numerical parameters (e.g. decay rates) are unknown and less important. For larger GRNs, inference of structure from gene expression data is prohibitively difficult. Models are often proposed based on integrative interpretation of multiple sources of information. We have developed DoGeNetS (Discrimination of Gene Network Structures), a method to directly assess candidate models of GRN structure against a target gene expression data set. The transsys language serves to model GRN structures. Numeric parameters are optimised to approximate the target data. Multiple restarts of optimisation yield score sets that provide a basis to statistically discriminate candidate models according to their potential to explain the target data. We demonstrate discrimination power of the DoGeNetS method by relating structural divergence to divergence between gene expression data sets. Known models are used to generate target expression data, and a set of candidate models with a defined structural divergence to the true model is produced. Structural divergence and divergence of expression profiles after optimisation are strongly correlated. We further show that discrimination is possible at noise levels exceeding those typical of contemporary microarray data. DoGeNetS is capable of discriminating the best GRN structure from among a small number of candidates. p values indicate whether differences in divergence of expression are significant. Although this study uses single gene knockouts, the DoGeNetS method can be adapted to simulate a virtually unlimited range of experimental conditions. [Includes supplementary material]

Analysis of a bio-dynamic model via Lyapunov principle and small-world network for tuberculosis.

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.

Optimal ratio of scaffold complex to free Fus3 to maximise the accumulation of phosphorylated Fus3 in yeast pheromone signalling pathway

Abstract: In this study, the author considers the design rule of the intracellular signalling pathway. In yeast pheromone signalling pathway, scaffold Ste5 tethers the components of signalling pathway, Ste11, Ste7 and Fus3. Even though scaffold complex is independently produced before stimuli, excessively expressed Fus3 as compared with scaffold exists in cytoplasm as free kinase. How the ratio of scaffold complex to the free Fus3 is determined is not clear yet. First, the contribution of free Fus3 to signal transduction is theoretically shown by using a simplified model of pheromone signalling pathway. Next, the optimum expression levels of Ste5, Ste11, Ste7 and Fus3 are systematically explored by using the detailed model and genetic algorithm under the constraint that the total expression level of these four genes is limited. Excessive expression of Fus3 is advantageous for the efficient signalling without stall of the signal transduction. The result suggests that the component of signalling pathway is optimally expressed to maximise the accumulation of phosphorylated Fus3 at a fixed time point under the constraint that the total gene expression is limited. The proposed model provides further insight into the signalling network from the point of view of not only its function but also its optimality.

Spatial localisation of chaperone distribution in the endoplasmic reticulum of yeast

Abstract: In eukaryotes, the endoplasmic reticulum (ER) serves as the first membrane-enclosed organelle in the secretory pathway, with functions including protein folding, maturation and transport. Molecular chaperones, of the Hsp70 family of proteins, participate in assisting these processes and are essential to cellular function and survival. BiP is a resident Hsp70 chaperone in the ER of Saccharomyces cerevisiae. In this study the authors have created a partial differential equation model to examine how BiP interacts with the membrane-bound co-chaperone Sec63 in translocation, a process in which BiP assists in guiding a nascent protein into the ER lumen. It has been found that when Sec63 participates in translocation through localisation at the membrane, the spatial distribution of BiP is inhomogeneous, with more BiP at the surface. When translocation is inhibited through a disabling of Sec63's membrane tether, the concentration of BiP throughout the ER becomes homogeneous. The computational simulations suggest that Sec63's localisation and the resulting binding to BiP near the membrane surface of the ER enable a heterogeneous distribution of BiP within the ER, and may facilitate BiP's role in translocation. [Includes supplementary material].

Systemic modelling of human bioenergetics and blood circulation.

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.

Computing enclosures for uncertain biochemical systems

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.

Model of lymphoma from stochastic analysis

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.

Modelling noise in biochemical reaction networks

Abstract: It is now well appreciated that noise pervades the dynamics of intracellular reaction kinetics. Intrinsic noise is typical inside cells because of the inherent low copy number of several types of molecules. Equally important though much less studied are extrinsic sources of noise such as temporal variability in the ribosome number per cell and in the concentration of macromolecular crowding agents in the cytoplasm. Modelling is an important tool in Systems Biology to study how the interplay of these various noise sources impacts the dynamics on cellular and multi-cellular scales.