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Active Transport

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Irina Badralexi – One of the best experts on this subject based on the ideXlab platform.

  • A stochastic model for intracellular Active Transport
    BIOMATH, 2018
    Co-Authors: Raluca Purnichescu-purtan, Irina Badralexi

    Abstract:

    We develop a stochastic model for an intracellular Active Transport problem. Our aims are to calculate the probability that a molecular motor reaches a hidden target, to study what influences this probability and to calculate the time required for the molecular motor to hit the target (Mean First Passage Time). We study different biologically relevant scenarios, which include the possibility of multiple hidden targets (which breed competition) and the presence of obstacles. The purpose of including obstacles is to illustrate actual disruptions of the intracellular Transport (which can result, for example, in several neurological disorders. From a mathematical point of view, the intracellular Active Transport is modelled by two independent continuous-time, discrete space Markov chains: one for the dynamics of the molecular motor in the space intervals and one for the domain of target. The process is time homogeneous and independent of the position of the molecular motor.

  • A stochastic model for Active Transport
    Texts in Biomathematics, 2018
    Co-Authors: Raluca Purnichescu-purtan, Irina Badralexi

    Abstract:

    We develop a stochastic model for an intracellular Active Transport problem. Our aims are to calculate the probability that a molecular motor reaches a hidden target, to study what influences this probability and to calculate the time required for the molecular motor to hit the target (mean first passage time). We study different biologically relevant scenarios, which include the possibility of multiple hidden targets (which breed competition) and the presence of obstacles. The purpose of including obstacles is to illustrate actual disruptions of the intracellular Transport (which can result, for example, in several neurological disorders. From a mathematical point of view, the intracellular Active Transport is modelled by two independent continuous-time, discrete space Markov chains: one for the dynamics of the molecular motor in the space intervals and one for the domain of target. The process is time homogeneous and independent of the position of the molecular motor.

  • A stochastic model for intracellular Active Transport
    Biomath Communications Supplement, 2018
    Co-Authors: Raluca Purnichescu Purtan, Irina Badralexi

    Abstract:

    We develop a stochastic model for an intracellular Active Transport problem. Our aims are to calculate the probability that a molecular motor reaches a hidden target, to study what influences this probability and to calculate the time required for the molecular motor to hit the target (mean first passage time).  We will study different biologically relevant scenarios, which include the possibility of multiple hidden targets (which breed competition), the presence of moving targets and moving obstacles. The purpose of including obstacles is to illustrate actual disruptions of the intracellular Transport (which can result, for example, in several neurological disorders [1])  From a mathematical point of view, the intracellular Active Transport is modelled by two independent continuous-time, discrete space Markov chains: one for the dynamics of the molecular motor in the space intervals and one for the domain of target. The process is time homogeneous and independent of the position of the molecular motor.

Vanessa Styles – One of the best experts on this subject based on the ideXlab platform.

  • A Cahn–Hilliard–Darcy model for tumour growth with chemotaxis and Active Transport
    Mathematical Models and Methods in Applied Sciences, 2016
    Co-Authors: Harald Garcke, Emanuel Sitka, Kei Fong Lam, Vanessa Styles

    Abstract:

    Using basic thermodynamic principles we derive a Cahn–Hilliard–Darcy model for tumour growth including nutrient diffusion, chemotaxis, Active Transport, adhesion, apoptosis and proliferation. In contrast to earlier works, the model is based on a volume-averaged velocity and in particular includes Active Transport mechanisms which ensure thermodynamic consistency. We perform a formally matched asymptotic expansion and develop several sharp interface models. Some of them are classical and some are new which for example include a jump in the nutrient density at the interface. A linear stability analysis for a growing nucleus is performed and in particular the role of the new Active Transport term is analysed. Numerical computations are performed to study the influence of the Active Transport term for specific growth scenarios.

  • a cahn hilliard darcy model for tumour growth with chemotaxis and Active Transport
    Mathematical Models and Methods in Applied Sciences, 2016
    Co-Authors: Harald Garcke, Emanuel Sitka, Vanessa Styles

    Abstract:

    Using basic thermodynamic principles we derive a Cahn–Hilliard–Darcy model for tumour growth including nutrient diffusion, chemotaxis, Active Transport, adhesion, apoptosis and proliferation. In contrast to earlier works, the model is based on a volume-averaged velocity and in particular includes Active Transport mechanisms which ensure thermodynamic consistency. We perform a formally matched asymptotic expansion and develop several sharp interface models. Some of them are classical and some are new which for example include a jump in the nutrient density at the interface. A linear stability analysis for a growing nucleus is performed and in particular the role of the new Active Transport term is analysed. Numerical computations are performed to study the influence of the Active Transport term for specific growth scenarios.

  • a cahn hilliard darcy model for tumour growth with chemotaxis and Active Transport
    arXiv: Analysis of PDEs, 2015
    Co-Authors: Harald Garcke, Emanuel Sitka, Vanessa Styles

    Abstract:

    Using basic thermodynamic principles we derive a Cahn–Hilliard–Darcy model for tumour growth including nutrient diffusion, chemotaxis, Active Transport, adhesion, apoptosis and proliferation. The model generalises earlier models and in particular includes Active Transport mechanisms which ensure thermodynamic consistency. We perform a formally matched asymptotic expansion and develop several sharp interface models. Some of them are classical and some are new which for example include a jump in the nutrient density at the interface. A linear stability analysis for a growing nucleus is performed and in particular the role of the new Active Transport term is analysed. Numerical computations are performed to study the influence of the Active Transport term for specific growth scenarios.

Harald Garcke – One of the best experts on this subject based on the ideXlab platform.

  • A Cahn–Hilliard–Darcy model for tumour growth with chemotaxis and Active Transport
    Mathematical Models and Methods in Applied Sciences, 2016
    Co-Authors: Harald Garcke, Emanuel Sitka, Kei Fong Lam, Vanessa Styles

    Abstract:

    Using basic thermodynamic principles we derive a Cahn–Hilliard–Darcy model for tumour growth including nutrient diffusion, chemotaxis, Active Transport, adhesion, apoptosis and proliferation. In contrast to earlier works, the model is based on a volume-averaged velocity and in particular includes Active Transport mechanisms which ensure thermodynamic consistency. We perform a formally matched asymptotic expansion and develop several sharp interface models. Some of them are classical and some are new which for example include a jump in the nutrient density at the interface. A linear stability analysis for a growing nucleus is performed and in particular the role of the new Active Transport term is analysed. Numerical computations are performed to study the influence of the Active Transport term for specific growth scenarios.

  • a cahn hilliard darcy model for tumour growth with chemotaxis and Active Transport
    Mathematical Models and Methods in Applied Sciences, 2016
    Co-Authors: Harald Garcke, Emanuel Sitka, Vanessa Styles

    Abstract:

    Using basic thermodynamic principles we derive a Cahn–Hilliard–Darcy model for tumour growth including nutrient diffusion, chemotaxis, Active Transport, adhesion, apoptosis and proliferation. In contrast to earlier works, the model is based on a volume-averaged velocity and in particular includes Active Transport mechanisms which ensure thermodynamic consistency. We perform a formally matched asymptotic expansion and develop several sharp interface models. Some of them are classical and some are new which for example include a jump in the nutrient density at the interface. A linear stability analysis for a growing nucleus is performed and in particular the role of the new Active Transport term is analysed. Numerical computations are performed to study the influence of the Active Transport term for specific growth scenarios.

  • a cahn hilliard darcy model for tumour growth with chemotaxis and Active Transport
    arXiv: Analysis of PDEs, 2015
    Co-Authors: Harald Garcke, Emanuel Sitka, Vanessa Styles

    Abstract:

    Using basic thermodynamic principles we derive a Cahn–Hilliard–Darcy model for tumour growth including nutrient diffusion, chemotaxis, Active Transport, adhesion, apoptosis and proliferation. The model generalises earlier models and in particular includes Active Transport mechanisms which ensure thermodynamic consistency. We perform a formally matched asymptotic expansion and develop several sharp interface models. Some of them are classical and some are new which for example include a jump in the nutrient density at the interface. A linear stability analysis for a growing nucleus is performed and in particular the role of the new Active Transport term is analysed. Numerical computations are performed to study the influence of the Active Transport term for specific growth scenarios.