15 research outputs found

    The slow-scale linear noise approximation:an accurate, reduced stochastic description of biochemical networks under timescale separation conditions

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    <p>Abstract</p> <p>Background</p> <p>It is well known that the deterministic dynamics of biochemical reaction networks can be more easily studied if timescale separation conditions are invoked (the quasi-steady-state assumption). In this case the deterministic dynamics of a large network of elementary reactions are well described by the dynamics of a smaller network of effective reactions. Each of the latter represents a group of elementary reactions in the large network and has associated with it an effective macroscopic rate law. A popular method to achieve model reduction in the presence of intrinsic noise consists of using the effective macroscopic rate laws to heuristically deduce effective probabilities for the effective reactions which then enables simulation via the stochastic simulation algorithm (SSA). The validity of this heuristic SSA method is <it>a priori</it> doubtful because the reaction probabilities for the SSA have only been rigorously derived from microscopic physics arguments for elementary reactions.</p> <p>Results</p> <p>We here obtain, by rigorous means and in closed-form, a reduced linear Langevin equation description of the stochastic dynamics of monostable biochemical networks in conditions characterized by small intrinsic noise and timescale separation. The slow-scale linear noise approximation (ssLNA), as the new method is called, is used to calculate the intrinsic noise statistics of enzyme and gene networks. The results agree very well with SSA simulations of the non-reduced network of elementary reactions. In contrast the conventional heuristic SSA is shown to overestimate the size of noise for Michaelis-Menten kinetics, considerably under-estimate the size of noise for Hill-type kinetics and in some cases even miss the prediction of noise-induced oscillations.</p> <p>Conclusions</p> <p>A new general method, the ssLNA, is derived and shown to correctly describe the statistics of intrinsic noise about the macroscopic concentrations under timescale separation conditions. The ssLNA provides a simple and accurate means of performing stochastic model reduction and hence it is expected to be of widespread utility in studying the dynamics of large noisy reaction networks, as is common in computational and systems biology.</p

    Methods in Computational Biology

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    Modern biology is rapidly becoming a study of large sets of data. Understanding these data sets is a major challenge for most life sciences, including the medical, environmental, and bioprocess fields. Computational biology approaches are essential for leveraging this ongoing revolution in omics data. A primary goal of this Special Issue, entitled “Methods in Computational Biology”, is the communication of computational biology methods, which can extract biological design principles from complex data sets, described in enough detail to permit the reproduction of the results. This issue integrates interdisciplinary researchers such as biologists, computer scientists, engineers, and mathematicians to advance biological systems analysis. The Special Issue contains the following sections:•Reviews of Computational Methods•Computational Analysis of Biological Dynamics: From Molecular to Cellular to Tissue/Consortia Levels•The Interface of Biotic and Abiotic Processes•Processing of Large Data Sets for Enhanced Analysis•Parameter Optimization and Measuremen

    Micro-, Meso- and Macro-Connectomics of the Brain

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    Neurosciences, Neurolog

    Semi-analytical solutions for the reversible Selkov model with feedback delay

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    Semi-analytical solutions for the reversible Selkov, or glycolytic oscillations model, are considered. The model is coupled with feedback at the boundary and considered in one-dimensional reaction-diffusion cell. This experimentally feasible scenario is analogous to feedback scenarios in a continuously stirred tank reactor. The Galerkin method is applied, which approximates the spatial structure of both the reactant and autocatalyst concentrations. This approach is used to obtain a lower-order, ordinary differential equation model for the system of governing equations. Steady-state solutions, bifurcation diagrams and the region of parameter space, in which Hopf bifurcations occur, are all found. The effect of feedback strength and delay response on the parameter region in which oscillatory solutions occur, is examined. It is found that varying the strength of the feedback response can stabilize or destabilize the system while increasing the delay response usually destabilizes the reaction-diffusion cell. The semi-analytical model is shown to be highly accurate, in comparison with numerical solutions of the governing equations

    A Language-centered Approach to support environmental modeling with Cellular Automata

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    Die Anwendung von Methodiken und Technologien aus dem Bereich der Softwaretechnik auf den Bereich der Umweltmodellierung ist eine gemeinhin akzeptierte Vorgehensweise. Im Rahmen der "modellgetriebenen Entwicklung"(MDE, model-driven engineering) werden Technologien entwickelt, die darauf abzielen, Softwaresysteme vorwiegend auf Basis von im Vergleich zu Programmquelltexten relativ abstrakten Modellen zu entwickeln. Ein wesentlicher Bestandteil von MDE sind Techniken zur effizienten Entwicklung von "domänenspezifischen Sprachen"( DSL, domain-specific language), die auf Sprachmetamodellen beruhen. Die vorliegende Arbeit zeigt, wie modellgetriebene Entwicklung, und insbesondere die metamodellbasierte Beschreibung von DSLs, darüber hinaus Aspekte der Pragmatik unterstützen kann, deren Relevanz im erkenntnistheoretischen und kognitiven Hintergrund wissenschaftlichen Forschens begründet wird. Hierzu wird vor dem Hintergrund der Erkenntnisse des "modellbasierten Forschens"(model-based science und model-based reasoning) gezeigt, wie insbesondere durch Metamodelle beschriebene DSLs Möglichkeiten bieten, entsprechende pragmatische Aspekte besonders zu berücksichtigen, indem sie als Werkzeug zur Erkenntnisgewinnung aufgefasst werden. Dies ist v.a. im Kontext großer Unsicherheiten, wie sie für weite Teile der Umweltmodellierung charakterisierend sind, von grundsätzlicher Bedeutung. Die Formulierung eines sprachzentrierten Ansatzes (LCA, language-centered approach) für die Werkzeugunterstützung konkretisiert die genannten Aspekte und bildet die Basis für eine beispielhafte Implementierung eines Werkzeuges mit einer DSL für die Beschreibung von Zellulären Automaten (ZA) für die Umweltmodellierung. Anwendungsfälle belegen die Verwendbarkeit von ECAL und der entsprechenden metamodellbasierten Werkzeugimplementierung.The application of methods and technologies of software engineering to environmental modeling and simulation (EMS) is common, since both areas share basic issues of software development and digital simulation. Recent developments within the context of "Model-driven Engineering" (MDE) aim at supporting the development of software systems at the base of relatively abstract models as opposed to programming language code. A basic ingredient of MDE is the development of methods that allow the efficient development of "domain-specific languages" (DSL), in particular at the base of language metamodels. This thesis shows how MDE and language metamodeling in particular, may support pragmatic aspects that reflect epistemic and cognitive aspects of scientific investigations. For this, DSLs and language metamodeling in particular are set into the context of "model-based science" and "model-based reasoning". It is shown that the specific properties of metamodel-based DSLs may be used to support those properties, in particular transparency, which are of particular relevance against the background of uncertainty, that is a characterizing property of EMS. The findings are the base for the formulation of an corresponding specific metamodel- based approach for the provision of modeling tools for EMS (Language-centered Approach, LCA), which has been implemented (modeling tool ECA-EMS), including a new DSL for CA modeling for EMS (ECAL). At the base of this implementation, the applicability of this approach is shown

    Using Mathematical Modelling and Electrochemical Analysis to Investigate Age‐Associated Disease

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    People are living longer. With this rise in life expectancy, a concomitant rise in morbidity in later life is observed; with conditions including cardiovascular disease (CVD), and cancer. However, ageing and the pathogenesis of age related disease, can be difficult to study, as the ageing process is a complex process, which affects multiple systems and mechanisms. The aim of this research was two‐fold. The first aim was to use mathematical modelling to investigate the mechanisms underpinning cholesterol metabolism, as aberrations to this system are associated with an increased risk for CVD. To better understand cholesterol from a mechanistic perspective, a curated kinetic model of whole body cholesterol metabolism, from the BioModels database, was expanded in COPASI, to produce a model with a broader range of mechanisms which underpin cholesterol metabolism. A range of time course data, and local and global parameter scans were utilised to examine the effect of cholesterol feeding, saturated fat feeding, ageing, and cholesterol ester transfer protein (CETP) genotype. These investigations revealed: the model behaved as a hypo‐responder to cholesterol feeding, the robustness of the cholesterol biosynthesis pathway, and the impact CETP can have on healthy ageing. The second aim of this work was to use electrochemical techniques to detect DNA methylation within the engrailed homeobox 1 (EN1) gene promoter, which has been implicated in cancer. Hypermethylation of this gene promoter is often observed in a diseased state. Synthetic DNA, designed to represent methylated and unmethylated variants, were adsorbed onto a gold rotating disk electrode for electrochemical analysis by 1) electrochemical impedance spectroscopy (EIS), 2) cyclic voltammetry (CV) and 3) differential pulse voltammetry (DPV). The technique was then applied to bisulphite modified and asymmetrically amplified DNA from the breast cancer cell line MCF‐7. Results indicated that electrochemical techniques could detect DNA methylation in both synthetic and cancer derived DNA, with EIS producing superiorresults. These non‐traditional techniques ofstudying age related disease were effective for the investigation of cholesterol metabolism and DNA methylation, and this work highlights how these techniques could be used to elucidate mechanisms or diagnose/monitor disease pathogenesis, to reduce morbidity in older peopl

    Metabolic flux analysis of Streptomyces fradiae C373-10

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    In order to obtain high yields of antibiotics, the flow of carbon through the primary metabolic pathways (i.e., glycolysis, the TCA cycle, pentose phosphate pathway, etc) must be radically redirected from the pathways that normally support balanced growth, towards pathways that support antibiotic synthesis. Such metabolic flux alterations directly oppose the enzyme level control mechanisms that are responsible for maintaining flux distributions optimal for growth. This enzyme resistance is referred to, as metabolic or network rigidity, which must be removed in order to attain improvements in product yield. Although modifications of the primary metabolism can be achieved through molecular biology, the choice of enzymes to be amplified or attenuated to mitigate network rigidity remains uncertain, and yield enhancements via metabolic modifications are largely pursued by trial and error. Hence, there is a clear need to develop a robust technique to identify limitations in the primary metabolism. To this end, Metabolic Flux Analysis (MFA) has been used to map the flow of carbon through primary metabolic pathways of Streptomyces fradiae C373-10 during batch cultures grown on a number of different carbon sources. MFA has been researched synergistically by a number of researchers, who have employed vastly different mathematical styles. Metabolic flux analysis (MFA) is a theoretical methodology used to determine fluxes through metabolic pathways, in terms of specific rates of reactions through a stoichiometric model of cellular reactions, using mass balances for the intracellular metabolites. Two approaches have generally been used; (1) the monomeric composition (amino acids, lipids, carbohydrates, RNA & DNA) and extracellular measurements of the cell are used to build a simple arithmetic model of cellular metabolism, (2) differential equations are used to model metabolism from extracellular metabolites only. In essence they are trying to achieve the same objectives. The alternative approach of Harry Holms (1986) has been adopted by this laboratory in the past. It offers a logical place to start, building compositional tables that need to be constructed to undertake any form of flux analysis. The main aim of this project was to prepare such a theoretical material balance of Streptomyces fradiae fermentations in batch culture. It would be of interest to see which of the approaches could be best applied to a Streptomyces fermentations, in the same way as MFA has been applied, to well defined bacteria such as E. coli (Holms, 1986, 1991, 1996, 1997, 2001; Aristidou et al., 1998; Varma et al., 1993a, 1993b, Varma & Palsson, 1994a, 1994b, 1995; Van Gulik & Heijnen, 1995; Pramanik & Keasling, 1997; Yang, 1999; Yang et al., 1999a, b) & Corynebacterium glutamicum (Vallino & Stephanopoulos, 1993, 1994a, b). It was therefore necessary to develop an adequate defined medium, to acquire all of the data for S. fradiae biomass required to calculate these fluxes. Additional information that was needed to achieve this objective is listed below. (1) A number of different medium compositions were tested for their suitability, optimised, and stepped up to bench top fermentation. To undertake a flux analysis, the main requirements are simple nitrogen and carbon sources that produce, reasonable antibiotic yields (Chapter 4). (2) Determine the macromolecular composition of S. fradiae C373-10 & S. coelicolor 1147 during exponential growth phase. (3) Investigate methods for the fractionation of biomass into its macromolecular and monomeric contents. Previous workers have shown considerable analytical error and reproducibility of standard assay techniques to collect bacterial compositional data. The intension was to reduce the inconsistencies in calculating compositional data by applying a number of analytical protocols and reconciling the data (see Chapter 8, discussion). (4) Determine the elemental composition of S. fradiae C373-10. Although this was not required for calculation of the fluxes, it would give an overall view of the composition of the biomass. (5) Investigate the differences between the elemental, monomeric, and macromolecular content of the biomass; inaccuracies of 20 % or more are commonly accepted in the literature. Since the molecular composition should directly define the elemental composition further investigation is needed. One theory is that metabolites such as shunt metabolites or cell wall material are not adequately accounted for. (6) The monomeric composition of S. coelicolor 1147, S. fradiae C373-10, and E. coli ML308 will be converted to compositional tables as Holms (1986)[see Chapter 6 and Appendix B]. Where appropriate the monomeric composition will be used to determine the (monomeric) composition of S. fradiae & S. coelicolor. In addition macromolecular data will be used where monomeric data analysis was not feasible, i.e., monomer content for DNA may be obtained from the macromolecular content; for example, approximately 70 % of Streptomyces DNA is comprised of guanine and cytosine bases (Pridham & Tresner, 1974). The DNA content may be expressed in terms of its bases. However, not all monomer amounts can be calculated from the macromolecular composition. For example, for the monomeric content of amino acids; high pressure liquid chromatography (HPLC) was undertaken. (7) Investigate the amino acid composition of S. fradiae C373-10 & S. coelicolor 1147; it will be of interest to see, how the amino acid contents of these streptomycetes differ due to the consequences of codon bias. (8) Collect the following information throughout the fermentations. specific rates of substrate uptake, specific growth rate, specific oxygen uptake and specific carbon dioxide evolution. (9) Identify and quantify the excretion rates of organic acids of S. fradiae C373-10 & S. coelicolor 1147 under different growth conditions. (10) Identify and quantify secondary metabolites excreted by S. fradiae C373-10 through out the fermentation, to allow for the determination of fluxes to these metabolites. (11) Determine the throughputs and fluxes through the central metabolic pathways of S. fradiae C373-10 & S. coelicolor 1147 to biomass. The throughputs would be calculated from the monomeric compositional data using the Holms (1986) approach. Assumptions were made, that central metabolic pathways were similar to E. coli, when there was no literature available to prove otherwise. (12) Compare the fluxes through the central metabolic pathways of S. fradiae C373-10 & S. coelicolor 1147 to biomass and to antibiotic production. Although the magnitude of fluxes in batch culture will be significantly different even between similar cultures. It should be possible to compare the ratio of flux to biosynthesis, to identify alterations in fluxes with the view of highlighting possible sites of regulation. (13) To investigate and develop on existing matrix algebra flux based techniques to the analysis of the fluxes through the central metabolic pathways of S. fradiae C373-10 & S. coelicolor 1147. The ultimate goal being to compare the strategies for flux analysis and undertake a further investigation in sensitivity analysis. With the main emphasis on defining how differences in compositional data and isoenzymes may affect the overall partitioning of flux. The above research has been undertaken; to investigate whether observations on specific rates of substrate uptake, the fate of individual medium components, specific growth rate, antibiotic production, shunt metabolites, oxygen uptake and carbon dioxide evolution could identify the enzymes or metabolic pathways most responsible for the overall reaction rate. This could result in the identification of areas concerned with regulation of these fluxes. Identification of such areas by flux determination would provide a foundation upon which further physiological and genetic studies could be based, thus contributing to a further understanding of the switch from primary to secondary metabolism in Streptomyces.In order to obtain high yields of antibiotics, the flow of carbon through the primary metabolic pathways (i.e., glycolysis, the TCA cycle, pentose phosphate pathway, etc) must be radically redirected from the pathways that normally support balanced growth, towards pathways that support antibiotic synthesis. Such metabolic flux alterations directly oppose the enzyme level control mechanisms that are responsible for maintaining flux distributions optimal for growth. This enzyme resistance is referred to, as metabolic or network rigidity, which must be removed in order to attain improvements in product yield. Although modifications of the primary metabolism can be achieved through molecular biology, the choice of enzymes to be amplified or attenuated to mitigate network rigidity remains uncertain, and yield enhancements via metabolic modifications are largely pursued by trial and error. Hence, there is a clear need to develop a robust technique to identify limitations in the primary metabolism. To this end, Metabolic Flux Analysis (MFA) has been used to map the flow of carbon through primary metabolic pathways of Streptomyces fradiae C373-10 during batch cultures grown on a number of different carbon sources. MFA has been researched synergistically by a number of researchers, who have employed vastly different mathematical styles. Metabolic flux analysis (MFA) is a theoretical methodology used to determine fluxes through metabolic pathways, in terms of specific rates of reactions through a stoichiometric model of cellular reactions, using mass balances for the intracellular metabolites. Two approaches have generally been used; (1) the monomeric composition (amino acids, lipids, carbohydrates, RNA & DNA) and extracellular measurements of the cell are used to build a simple arithmetic model of cellular metabolism, (2) differential equations are used to model metabolism from extracellular metabolites only. In essence they are trying to achieve the same objectives. The alternative approach of Harry Holms (1986) has been adopted by this laboratory in the past. It offers a logical place to start, building compositional tables that need to be constructed to undertake any form of flux analysis. The main aim of this project was to prepare such a theoretical material balance of Streptomyces fradiae fermentations in batch culture. It would be of interest to see which of the approaches could be best applied to a Streptomyces fermentations, in the same way as MFA has been applied, to well defined bacteria such as E. coli (Holms, 1986, 1991, 1996, 1997, 2001; Aristidou et al., 1998; Varma et al., 1993a, 1993b, Varma & Palsson, 1994a, 1994b, 1995; Van Gulik & Heijnen, 1995; Pramanik & Keasling, 1997; Yang, 1999; Yang et al., 1999a, b) & Corynebacterium glutamicum (Vallino & Stephanopoulos, 1993, 1994a, b). It was therefore necessary to develop an adequate defined medium, to acquire all of the data for S. fradiae biomass required to calculate these fluxes. Additional information that was needed to achieve this objective is listed below. (1) A number of different medium compositions were tested for their suitability, optimised, and stepped up to bench top fermentation. To undertake a flux analysis, the main requirements are simple nitrogen and carbon sources that produce, reasonable antibiotic yields (Chapter 4). (2) Determine the macromolecular composition of S. fradiae C373-10 & S. coelicolor 1147 during exponential growth phase. (3) Investigate methods for the fractionation of biomass into its macromolecular and monomeric contents. Previous workers have shown considerable analytical error and reproducibility of standard assay techniques to collect bacterial compositional data. The intension was to reduce the inconsistencies in calculating compositional data by applying a number of analytical protocols and reconciling the data (see Chapter 8, discussion). (4) Determine the elemental composition of S. fradiae C373-10. Although this was not required for calculation of the fluxes, it would give an overall view of the composition of the biomass. (5) Investigate the differences between the elemental, monomeric, and macromolecular content of the biomass; inaccuracies of 20 % or more are commonly accepted in the literature. Since the molecular composition should directly define the elemental composition further investigation is needed. One theory is that metabolites such as shunt metabolites or cell wall material are not adequately accounted for. (6) The monomeric composition of S. coelicolor 1147, S. fradiae C373-10, and E. coli ML308 will be converted to compositional tables as Holms (1986)[see Chapter 6 and Appendix B]. Where appropriate the monomeric composition will be used to determine the (monomeric) composition of S. fradiae & S. coelicolor. In addition macromolecular data will be used where monomeric data analysis was not feasible, i.e., monomer content for DNA may be obtained from the macromolecular content; for example, approximately 70 % of Streptomyces DNA is comprised of guanine and cytosine bases (Pridham & Tresner, 1974). The DNA content may be expressed in terms of its bases. However, not all monomer amounts can be calculated from the macromolecular composition. For example, for the monomeric content of amino acids; high pressure liquid chromatography (HPLC) was undertaken. (7) Investigate the amino acid composition of S. fradiae C373-10 & S. coelicolor 1147; it will be of interest to see, how the amino acid contents of these streptomycetes differ due to the consequences of codon bias. (8) Collect the following information throughout the fermentations. specific rates of substrate uptake, specific growth rate, specific oxygen uptake and specific carbon dioxide evolution. (9) Identify and quantify the excretion rates of organic acids of S. fradiae C373-10 & S. coelicolor 1147 under different growth conditions. (10) Identify and quantify secondary metabolites excreted by S. fradiae C373-10 through out the fermentation, to allow for the determination of fluxes to these metabolites. (11) Determine the throughputs and fluxes through the central metabolic pathways of S. fradiae C373-10 & S. coelicolor 1147 to biomass. The throughputs would be calculated from the monomeric compositional data using the Holms (1986) approach. Assumptions were made, that central metabolic pathways were similar to E. coli, when there was no literature available to prove otherwise. (12) Compare the fluxes through the central metabolic pathways of S. fradiae C373-10 & S. coelicolor 1147 to biomass and to antibiotic production. Although the magnitude of fluxes in batch culture will be significantly different even between similar cultures. It should be possible to compare the ratio of flux to biosynthesis, to identify alterations in fluxes with the view of highlighting possible sites of regulation. (13) To investigate and develop on existing matrix algebra flux based techniques to the analysis of the fluxes through the central metabolic pathways of S. fradiae C373-10 & S. coelicolor 1147. The ultimate goal being to compare the strategies for flux analysis and undertake a further investigation in sensitivity analysis. With the main emphasis on defining how differences in compositional data and isoenzymes may affect the overall partitioning of flux. The above research has been undertaken; to investigate whether observations on specific rates of substrate uptake, the fate of individual medium components, specific growth rate, antibiotic production, shunt metabolites, oxygen uptake and carbon dioxide evolution could identify the enzymes or metabolic pathways most responsible for the overall reaction rate. This could result in the identification of areas concerned with regulation of these fluxes. Identification of such areas by flux determination would provide a foundation upon which further physiological and genetic studies could be based, thus contributing to a further understanding of the switch from primary to secondary metabolism in Streptomyces

    Metabolomics Data Processing and Data Analysis—Current Best Practices

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    Metabolomics data analysis strategies are central to transforming raw metabolomics data files into meaningful biochemical interpretations that answer biological questions or generate novel hypotheses. This book contains a variety of papers from a Special Issue around the theme “Best Practices in Metabolomics Data Analysis”. Reviews and strategies for the whole metabolomics pipeline are included, whereas key areas such as metabolite annotation and identification, compound and spectral databases and repositories, and statistical analysis are highlighted in various papers. Altogether, this book contains valuable information for researchers just starting in their metabolomics career as well as those that are more experienced and look for additional knowledge and best practice to complement key parts of their metabolomics workflows

    Role of adipose tissue in the pathogenesis and treatment of metabolic syndrome

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    Š Springer International Publishing Switzerland 2014. Adipocytes are highly specialized cells that play a major role in energy homeostasis in vertebrate organisms. Excess adipocyte size or number is a hallmark of obesity, which is currently a global epidemic. Obesity is not only the primary disease of fat cells, but also a major risk factor for the development of Type 2 diabetes, cardiovascular disease, hypertension, and metabolic syndrome (MetS). Today, adipocytes and adipose tissue are no longer considered passive participants in metabolic pathways. In addition to storing lipid, adipocytes are highly insulin sensitive cells that have important endocrine functions. Altering any one of these functions of fat cells can result in a metabolic disease state and dysregulation of adipose tissue can profoundly contribute to MetS. For example, adiponectin is a fat specific hormone that has cardio-protective and anti-diabetic properties. Inhibition of adiponectin expression and secretion are associated with several risk factors for MetS. For this purpose, and several other reasons documented in this chapter, we propose that adipose tissue should be considered as a viable target for a variety of treatment approaches to combat MetS
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