38 research outputs found

    Time scale and dimension analysis of a budding yeast cell cycle model

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    BACKGROUND: The progress through the eukaryotic cell division cycle is driven by an underlying molecular regulatory network. Cell cycle progression can be considered as a series of irreversible transitions from one steady state to another in the correct order. Although this view has been put forward some time ago, it has not been quantitatively proven yet. Bifurcation analysis of a model for the budding yeast cell cycle has identified only two different steady states (one for G1 and one for mitosis) using cell mass as a bifurcation parameter. By analyzing the same model, using different methods of dynamical systems theory, we provide evidence for transitions among several different steady states during the budding yeast cell cycle. RESULTS: By calculating the eigenvalues of the Jacobian of kinetic differential equations we have determined the stability of the cell cycle trajectories of the Chen model. Based on the sign of the real part of the eigenvalues, the cell cycle can be divided into excitation and relaxation periods. During an excitation period, the cell cycle control system leaves a formerly stable steady state and, accordingly, excitation periods can be associated with irreversible cell cycle transitions like START, entry into mitosis and exit from mitosis. During relaxation periods, the control system asymptotically approaches the new steady state. We also show that the dynamical dimension of the Chen's model fluctuates by increasing during excitation periods followed by decrease during relaxation periods. In each relaxation period the dynamical dimension of the model drops to one, indicating a period where kinetic processes are in steady state and all concentration changes are driven by the increase of cytoplasmic growth. CONCLUSION: We apply two numerical methods, which have not been used to analyze biological control systems. These methods are more sensitive than the bifurcation analysis used before because they identify those transitions between steady states that are not controlled by a bifurcation parameter (e.g. cell mass). Therefore by applying these tools for a cell cycle control model, we provide a deeper understanding of the dynamical transitions in the underlying molecular network

    Time scale and dimension analysis of a budding yeast cell cycle model

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    The progress through the eukaryotic cell division cycle is driven by an underlying molecular regulatory network. Cell cycle progression can be considered as a series of irreversible transitions from one steady state to another in the correct order. Although this view has been put forward some time ago, it has not been quantitatively proven yet. Bifurcation analysis of a model for the budding yeast cell cycle has identified only two different steady states (one for G1 and one for mitosis) using cell mass as a bifurcation parameter. By analyzing the same model, using different methods of dynamical systems theory, we provide evidence for transitions among several different steady states during the budding yeast cell cycle. By calculating the eigenvalues of the Jacobian of kinetic differential equations we have determined the stability of the cell cycle trajectories of the Chen model. Based on the sign of the real part of the eigenvalues, the cell cycle can be divided into excitation and relaxation periods. During an excitation period, the cell cycle control system leaves a formerly stable steady state and, accordingly, excitation periods can be associated with irreversible cell cycle transitions like START, entry into mitosis and exit from mitosis. During relaxation periods, the control system asymptotically approaches the new steady state. We also show that the dynamical dimension of the Chen’s model fluctuates by increasing during excitation periods followed by decrease during relaxation periods. In each relaxation period the dynamical dimension of the model drops to one, indicating a period where kinetic processes are in steady state and all concentration changes are driven by the increase of cytoplasmic growth.We apply two numerical methods, which have not been used to analyze biological control systems. These methods are more sensitive than the bifurcation analysis used before because they identify those transitions between steady states that are not controlled by a bifurcation parameter (e.g. cell mass). Therefore by applying these tools for a cell cycle control model, we provide a deeper understanding of the dynamical transitions in the underlying molecular network

    Systematic reduction of complex tropospheric chemical mechanisms using sensitivity and time-scale analyses

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    International audienceExplicit mechanisms describing the complex degradation pathways of atmospheric volatile organic compounds (VOCs) are important, since they allow the study of the contribution of individual VOCS to secondary pollutant formation. They are computationally expensive to solve however, since they contain large numbers of species and a wide range of time-scales causing stiffness in the resulting equation systems. This paper and the following companion paper describe the application of systematic and automated methods for reducing such complex mechanisms, whilst maintaining the accuracy of the model with respect to important species and features. The methods are demonstrated via application to version 2 of the Leeds Master Chemical Mechanism. The methods of local concentration sensitivity analysis and overall rate sensitivity analysis proved to be efficient and capable of removing the majority of redundant reactions and species in the scheme across a wide range of conditions relevant to the polluted troposphere. The application of principal component analysis of the rate sensitivity matrix was computationally expensive due to its use of the decomposition of very large matrices, and did not produce significant reduction over and above the other sensitivity methods. The use of the quasi-steady state approximation (QSSA) proved to be an extremely successful method of removing the fast time-scales within the system, as demonstrated by a local perturbation analysis at each stage of reduction. QSSA species were automatically selected via the calculation of instantaneous QSSA errors based on user-selected tolerances. The application of the QSSA led to the removal of a large number of alkoxy radicals and excited Criegee bi-radicals via reaction lumping. The resulting reduced mechanism was shown to reproduce the concentration profiles of the important species selected from the full mechanism over a wide range of conditions, including those outside of which the reduced mechanism was generated. As a result of a reduction in the number of species in the scheme of a factor of 2, and a reduction in stiffness, the computational time required for simulations was reduced by a factor of 4 when compared to the full scheme

    Systematic reduction of complex tropospheric chemical mechanisms, Part I: sensitivity and time-scale analyses

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    International audienceExplicit mechanisms describing the complex degradation pathways of atmospheric volatile organic compounds (VOCs) are important, since they allow the study of the contribution of individual VOCS to secondary pollutant formation. They are computationally expensive to solve however, since they contain large numbers of species and a wide range of time-scales causing stiffness in the resulting equation systems. This paper and the following companion paper describe the application of systematic and automated methods for reducing such complex mechanisms, whilst maintaining the accuracy of the model with respect to important species and features. The methods are demonstrated via application to version 2 of the Leeds Master Chemical Mechanism. The methods of Jacobian analysis and overall rate sensitivity analysis proved to be efficient and capable of removing the majority of redundant reactions and species in the scheme across a wide range of conditions relevant to the polluted troposphere. The application of principal component analysis of the rate sensitivity matrix was computationally expensive due to its use of the decomposition of very large matrices, and did not produce significant reduction over and above the other sensitivity methods. The use of the quasi-steady state approximation (QSSA) proved to be an extremely successful method of removing the fast time-scales within the system, as demonstrated by a local perturbation analysis at each stage of reduction. QSSA species were automatically selected via the calculation of instantaneous QSSA errors based on user-selected tolerances. The application of the QSSA led to the removal of a large number of alkoxy radicals and excited Criegee bi-radicals via reaction lumping. The resulting reduced mechanism was shown to reproduce the concentration profiles of the important species selected from the full mechanism over a wide range of conditions, including those outside of which the reduced mechanism was generated. As a result of a reduction in the number of species in the scheme of a factor of 2, and a reduction in stiffness, the computational time required for simulations was reduced by a factor of 4 when compared to the full scheme

    Reactions of polycyclic alkylaromatics--VI. Detailed chemical kinetic modeling

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    We developed a detailed chemical kinetics model for the pyrolysis of long-chain polycyclic n-alkylarenes based on a general free-radical mechanism. The model accounts for the two major primary pathways in the pyrolysis network of polycyclic alkylaromatics. Using 1-dodecylpyrene (DDP) as an example, we show that the model qualitatively predicted the effects of time, temperature, and concentration on the product molar yields and the reaction kinetics. The model also predicted the autocatalytic kinetics associated with the cleavage of the aryl---alkyl bond. The model results showed that radical hydrogen transfer was the dominant hydrogenolysis mechanism during all but the very initial stages of the reaction when reverse radical disproportionation dominated. A sensitivity analysis revealed that reactions involving [alpha]-DDP radicals where the most important in determining the reaction kinetics and the product selectivities.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31912/1/0000865.pd

    Automated reaction mechanism generation : improving accuracy and broadening scope

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 169-186).Chemical kinetic modeling plays an important role in the study of reactive chemical systems. Thus, an automated means of constructing chemical kinetic models forms a useful tool in the engineering and science surrounding such systems. This document describes work to further develop one such tool, known as RMG (Reaction Mechanism Generator). Focus is placed on improving the accuracy of parameter estimation in the mechanism generation process and expanding the scope of applicability of the tool. In particular, effort has targeted the generation and use of explicit three-dimensional molecular structures for chemical species considered during reaction mechanism generation. This work has resulted in the generation of a software system integrated with RMG that can automatically generate and use such structures with quantum chemistry or force field codes to obtain more reliable thermochemistry estimates for cyclic structures without human intervention. Ultimately, the result of these updates is improved usefulness and reliability of the software system as a predictive tool. An application of the tool to the high temperature oxidation of JP-10, a jet fuel often used in military applications, is described. Using the newly refined RMG system, a detailed chemical kinetic model was constructed for this system. The resulting model represents a significant improvement upon existing work for JP- 10 oxidation by capturing detailed chemistry for this system. Simulations with this model have been found to produce results for ignition delay and product distribution that compare favorably with experimental results. The successful application of the refined RMG software system to this system demonstrates the practical utility of these updates.by Gregory Russell Magoon.Ph.D

    Estudo teórico da formação de ozônio pela combustão de álcool: simulação do mecanismo de reação

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    As emissões veiculares são a maior fonte de poluição nas grandes cidades, e seus efeitos nocivos são percebidos pela população, vegetação local e até na deterioração de materiais. Estas emissões podem ser compostos primários oriundos dos processos de combustão, principalmente nos motores dos veículos, e perdas evaporativas, que dependem da composição dos combustíveis e da qualidade dos motores (Shi et al., 2008). Os compostos orgânicos (COV) emitidos nos processos de combustão podem reagir na troposfera na presença da luz com radicais hidroxila .OH, oxigênio e os óxidos de nitrogênio, formando o ozônio, e outros oxidantes fotoquímicos. Nos últimos anos, tem sido realizados esforços no sentido de desenvolver combustíveis menos poluentes como os alcoóis, e os ésteres. Em 2004, Pereira et al. apresentaram resultados experimentais obtidos numa câmara de reação onde foram determinados os níveis de ozônio obtidos por reação de vapores de etanol e de gasool. O objetivo geral deste projeto foi construir um modelo químico para reproduzir e explicar os dados experimentais de literatura para a combustão do etanol (Pereira et al., 2004), especialmente os níveis elevados de ozônio para tempos de reação de mais de duas horas. Foram investigados quatros casos para a modelagem do ozônio: etanol puro, etanol com diferentes níveis de radiação solar, etanol contaminado com acetaldeído em concentrações relativas de 0,01%, 0,1%, 1% e 10%, e por fim etanol contaminado com acetaleído em concentrações relativas de 0,01% a 1% respectivamente. Nos dois primeiros casos, as concentrações de ozônio calculadas foram inferiores aos valores do trabalho experimental. A influência da radiação solar é praticamente inexistente neste modelo, e a concentração de ozônio obtida na curva do etanol contaminado com acetaldeído 1% teve um valor de 130 ppb para o tempo de 250 min, próximo ao valor de referência do sistema experimental de 170 ppb, sugerindo que valores acima de 1% podem causar um aumento significativo das concentrações de ozônio fornecendo valores comparáveis aos obtidos nos experimentos
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