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Naoki Kubota – One of the best experts on this subject based on the ideXlab platform.

  • Continuity for the asymptotic shape in the frog model with random initial configurations
    Stochastic Processes and their Applications, 2020
    Co-Authors: Naoki Kubota
    Abstract:

    Abstract We consider the so-called frog model with random initial configurations, which is described by the following evolution mechanism of simple random walks on the multidimensional cubic lattice: Some Particles are randomly assigned to any site of the multidimensional cubic lattice. Initially, only Particles at the origin are Active and they independently perform simple random walks. The other Particles are sleeping and do not move at first. When sleeping Particles are hit by an Active Particle, they become Active and start doing independent simple random walks. An interest of this model is how initial configurations affect the asymptotic shape of the set of all sites visited by Active Particles up to a certain time. Thus, in this paper, we prove continuity for the asymptotic shape in the law of the initial configuration.

  • Deviation bounds for the first passage time in the frog model
    Advances in Applied Probability, 2019
    Co-Authors: Naoki Kubota
    Abstract:

    AbstractWe consider the so-called frog model with random initial configurations. The dynamics of this model are described as follows. Some Particles are randomly assigned to any site of the multidimensional cubic lattice. Initially, only Particles at the origin are Active and these independently perform simple random walks. The other Particles are sleeping and do not move at first. When sleeping Particles are hit by an Active Particle, they become Active and start moving in a similar fashion. The aim of this paper is to derive large deviation and concentration bounds for the first passage time at which an Active Particle reaches a target site.

  • Deviation bounds for the first passage time in the frog model
    Advances in Applied Probability, 2019
    Co-Authors: Naoki Kubota
    Abstract:

    We consider the so-called frog model with random initial configurations. The dynamics of this model is described as follows: Some Particles are randomly assigned on any site of the multidimensional cubic lattice. Initially, only Particles at the origin are Active and these independently perform simple random walks. The other Particles are sleeping and do not move at first. When sleeping Particles are hit by an Active Particle, they become Active and start moving in a similar fashion. The aim of this paper is to derive large deviation and concentration bounds for the first passage time at which an Active Particle reaches a target site.

Hartmut Löwen – One of the best experts on this subject based on the ideXlab platform.

  • Theory of Active Particle penetration through a planar elastic membrane
    New Journal of Physics, 2019
    Co-Authors: Abdallah Daddi-moussa-ider, Benno Liebchen, Andreas M. Menzel, Hartmut Löwen
    Abstract:

    With the rapid advent of biomedical and biotechnological innovations, a deep understanding of the nature of interaction between nanomaterials and cell membranes, tissues, and organs, has become increasingly important. Active penetration of nanoParticles through cell membranes is a fascinating phenomenon that may have important implications in various biomedical and clinical applications. Using a fully analytical theory supplemented by Particle-based computer simulations, the penetration process of an Active Particle through a planar two-dimensional elastic membrane is studied. The membrane is modeled as a self-assembled sheet of Particles, uniformly arranged on a square lattice. A coarse-grained model is introduced to describe the mutual interactions between the membrane Particles. The Active penetrating Particle is assumed to interact sterically with the membrane Particles. State diagrams are presented to fully characterize the system behavior as functions of the relevant control parameters governing the transition between different dynamical states. Three distinct scenarios are identified. These compromise trapping of the Active Particle, penetration through the membrane with subsequent self-healing, in addition to penetration with permanent disruption of the membrane. The latter scenario is accompanied by a partial fragmentation of the membrane and creation of a hole of a size exceeding the interaction range of the membrane components. Our analytical theory is based on a combination of a perturbative expansion technique and a discrete-to-continuum formulation. Our approach might be helpful for the prediction of the transition threshold between the trapping and penetration in real-space experiments involving motile swimming bacteria or artificial Active Particles.

  • Membrane penetration and trapping of an Active Particle
    Journal of Chemical Physics, 2019
    Co-Authors: Abdallah Daddi-moussa-ider, Benno Liebchen, Christian Hoell, Arnold J. T. M. Mathijssen, Francisca Guzmán-lastra, Christian Schölz, Andreas M. Menzel, Hartmut Löwen
    Abstract:

    The interaction between nano- or micro-sized Particles and cell membranes is of crucial importance in many biological and biomedical applications such as drug and gene delivery to cells and tissues. During their cellular uptake, the Particles can pass through cell membranes via passive endocytosis or by Active penetration to reach a target cellular compartment or organelle. In this manuscript, we develop a simple model to describe the interaction of a self-driven spherical Particle (moving through an effective constant Active force) with a minimal membrane system, allowing for both penetration and trapping. We numerically calculate the state diagram of this system, the membrane shape, and its dynamics. In this context, we show that the Active Particle may either get trapped near the membrane or penetrate through it, where the membrane can either be permanently destroyed or recover its initial shape by self-healing. Additionally, we systematically derive a continuum description allowing us to accurately predict most of our results analytically. This analytical theory helps in identifying the generic aspects of our model, suggesting that most of its ingredients should apply to a broad range of membranes, from simple model systems composed of magnetic microParticles to lipid bilayers. Our results might be useful to predict the mechanical properties of synthetic minimal membranes.

  • membrane penetration and trapping of an Active Particle
    arXiv: Soft Condensed Matter, 2019
    Co-Authors: Abdallah Daddimoussaider, Benno Liebchen, Christian Hoell, Arnold J. T. M. Mathijssen, Christian Schölz, Andreas M. Menzel, Segun Goh, Francisca Guzmanlastra, Hartmut Löwen
    Abstract:

    The interaction between nano- or micro-sized Particles and cell membranes is of crucial importance in many biological and biomedical applications such as drug and gene delivery to cells and tissues. During their cellular uptake, the Particles can pass through cell membranes via passive endocytosis or by Active penetration to reach a target cellular compartment or organelle. In this manuscript, we develop a simple model to describe the interaction of a self-driven spherical Particle (moving through an effective constant Active force) with a minimal membrane system, allowing for both penetration and trapping. We numerically calculate the state diagram of this system, the membrane shape, and its dynamics. In this context, we show that the Active Particle may either get trapped near the membrane or penetrates through it, where the membrane can either be permanently destroyed or recover its initial shape by self-healing. Additionally, we systematically derive a continuum description allowing to accurately predict most of our results analytically. This analytical theory helps identifying the generic aspects of our model, suggesting that most of its ingredients should apply to a broad range of membranes, from simple model systems composed of magnetic microParticles to lipid bilayers. Our results might be useful to predict mechanical properties of synthetic minimal membranes.

Abdallah Daddi-moussa-ider – One of the best experts on this subject based on the ideXlab platform.

  • Theory of Active Particle penetration through a planar elastic membrane
    New Journal of Physics, 2019
    Co-Authors: Abdallah Daddi-moussa-ider, Benno Liebchen, Andreas M. Menzel, Hartmut Löwen
    Abstract:

    With the rapid advent of biomedical and biotechnological innovations, a deep understanding of the nature of interaction between nanomaterials and cell membranes, tissues, and organs, has become increasingly important. Active penetration of nanoParticles through cell membranes is a fascinating phenomenon that may have important implications in various biomedical and clinical applications. Using a fully analytical theory supplemented by Particle-based computer simulations, the penetration process of an Active Particle through a planar two-dimensional elastic membrane is studied. The membrane is modeled as a self-assembled sheet of Particles, uniformly arranged on a square lattice. A coarse-grained model is introduced to describe the mutual interactions between the membrane Particles. The Active penetrating Particle is assumed to interact sterically with the membrane Particles. State diagrams are presented to fully characterize the system behavior as functions of the relevant control parameters governing the transition between different dynamical states. Three distinct scenarios are identified. These compromise trapping of the Active Particle, penetration through the membrane with subsequent self-healing, in addition to penetration with permanent disruption of the membrane. The latter scenario is accompanied by a partial fragmentation of the membrane and creation of a hole of a size exceeding the interaction range of the membrane components. Our analytical theory is based on a combination of a perturbative expansion technique and a discrete-to-continuum formulation. Our approach might be helpful for the prediction of the transition threshold between the trapping and penetration in real-space experiments involving motile swimming bacteria or artificial Active Particles.

  • Membrane penetration and trapping of an Active Particle
    Journal of Chemical Physics, 2019
    Co-Authors: Abdallah Daddi-moussa-ider, Benno Liebchen, Christian Hoell, Arnold J. T. M. Mathijssen, Francisca Guzmán-lastra, Christian Schölz, Andreas M. Menzel, Hartmut Löwen
    Abstract:

    The interaction between nano- or micro-sized Particles and cell membranes is of crucial importance in many biological and biomedical applications such as drug and gene delivery to cells and tissues. During their cellular uptake, the Particles can pass through cell membranes via passive endocytosis or by Active penetration to reach a target cellular compartment or organelle. In this manuscript, we develop a simple model to describe the interaction of a self-driven spherical Particle (moving through an effective constant Active force) with a minimal membrane system, allowing for both penetration and trapping. We numerically calculate the state diagram of this system, the membrane shape, and its dynamics. In this context, we show that the Active Particle may either get trapped near the membrane or penetrate through it, where the membrane can either be permanently destroyed or recover its initial shape by self-healing. Additionally, we systematically derive a continuum description allowing us to accurately predict most of our results analytically. This analytical theory helps in identifying the generic aspects of our model, suggesting that most of its ingredients should apply to a broad range of membranes, from simple model systems composed of magnetic microParticles to lipid bilayers. Our results might be useful to predict the mechanical properties of synthetic minimal membranes.

Andreas M. Menzel – One of the best experts on this subject based on the ideXlab platform.

  • Theory of Active Particle penetration through a planar elastic membrane
    New Journal of Physics, 2019
    Co-Authors: Abdallah Daddi-moussa-ider, Benno Liebchen, Andreas M. Menzel, Hartmut Löwen
    Abstract:

    With the rapid advent of biomedical and biotechnological innovations, a deep understanding of the nature of interaction between nanomaterials and cell membranes, tissues, and organs, has become increasingly important. Active penetration of nanoParticles through cell membranes is a fascinating phenomenon that may have important implications in various biomedical and clinical applications. Using a fully analytical theory supplemented by Particle-based computer simulations, the penetration process of an Active Particle through a planar two-dimensional elastic membrane is studied. The membrane is modeled as a self-assembled sheet of Particles, uniformly arranged on a square lattice. A coarse-grained model is introduced to describe the mutual interactions between the membrane Particles. The Active penetrating Particle is assumed to interact sterically with the membrane Particles. State diagrams are presented to fully characterize the system behavior as functions of the relevant control parameters governing the transition between different dynamical states. Three distinct scenarios are identified. These compromise trapping of the Active Particle, penetration through the membrane with subsequent self-healing, in addition to penetration with permanent disruption of the membrane. The latter scenario is accompanied by a partial fragmentation of the membrane and creation of a hole of a size exceeding the interaction range of the membrane components. Our analytical theory is based on a combination of a perturbative expansion technique and a discrete-to-continuum formulation. Our approach might be helpful for the prediction of the transition threshold between the trapping and penetration in real-space experiments involving motile swimming bacteria or artificial Active Particles.

  • Membrane penetration and trapping of an Active Particle
    Journal of Chemical Physics, 2019
    Co-Authors: Abdallah Daddi-moussa-ider, Benno Liebchen, Christian Hoell, Arnold J. T. M. Mathijssen, Francisca Guzmán-lastra, Christian Schölz, Andreas M. Menzel, Hartmut Löwen
    Abstract:

    The interaction between nano- or micro-sized Particles and cell membranes is of crucial importance in many biological and biomedical applications such as drug and gene delivery to cells and tissues. During their cellular uptake, the Particles can pass through cell membranes via passive endocytosis or by Active penetration to reach a target cellular compartment or organelle. In this manuscript, we develop a simple model to describe the interaction of a self-driven spherical Particle (moving through an effective constant Active force) with a minimal membrane system, allowing for both penetration and trapping. We numerically calculate the state diagram of this system, the membrane shape, and its dynamics. In this context, we show that the Active Particle may either get trapped near the membrane or penetrate through it, where the membrane can either be permanently destroyed or recover its initial shape by self-healing. Additionally, we systematically derive a continuum description allowing us to accurately predict most of our results analytically. This analytical theory helps in identifying the generic aspects of our model, suggesting that most of its ingredients should apply to a broad range of membranes, from simple model systems composed of magnetic microParticles to lipid bilayers. Our results might be useful to predict the mechanical properties of synthetic minimal membranes.

  • membrane penetration and trapping of an Active Particle
    arXiv: Soft Condensed Matter, 2019
    Co-Authors: Abdallah Daddimoussaider, Benno Liebchen, Christian Hoell, Arnold J. T. M. Mathijssen, Christian Schölz, Andreas M. Menzel, Segun Goh, Francisca Guzmanlastra, Hartmut Löwen
    Abstract:

    The interaction between nano- or micro-sized Particles and cell membranes is of crucial importance in many biological and biomedical applications such as drug and gene delivery to cells and tissues. During their cellular uptake, the Particles can pass through cell membranes via passive endocytosis or by Active penetration to reach a target cellular compartment or organelle. In this manuscript, we develop a simple model to describe the interaction of a self-driven spherical Particle (moving through an effective constant Active force) with a minimal membrane system, allowing for both penetration and trapping. We numerically calculate the state diagram of this system, the membrane shape, and its dynamics. In this context, we show that the Active Particle may either get trapped near the membrane or penetrates through it, where the membrane can either be permanently destroyed or recover its initial shape by self-healing. Additionally, we systematically derive a continuum description allowing to accurately predict most of our results analytically. This analytical theory helps identifying the generic aspects of our model, suggesting that most of its ingredients should apply to a broad range of membranes, from simple model systems composed of magnetic microParticles to lipid bilayers. Our results might be useful to predict mechanical properties of synthetic minimal membranes.

Benno Liebchen – One of the best experts on this subject based on the ideXlab platform.

  • Theory of Active Particle penetration through a planar elastic membrane
    New Journal of Physics, 2019
    Co-Authors: Abdallah Daddi-moussa-ider, Benno Liebchen, Andreas M. Menzel, Hartmut Löwen
    Abstract:

    With the rapid advent of biomedical and biotechnological innovations, a deep understanding of the nature of interaction between nanomaterials and cell membranes, tissues, and organs, has become increasingly important. Active penetration of nanoParticles through cell membranes is a fascinating phenomenon that may have important implications in various biomedical and clinical applications. Using a fully analytical theory supplemented by Particle-based computer simulations, the penetration process of an Active Particle through a planar two-dimensional elastic membrane is studied. The membrane is modeled as a self-assembled sheet of Particles, uniformly arranged on a square lattice. A coarse-grained model is introduced to describe the mutual interactions between the membrane Particles. The Active penetrating Particle is assumed to interact sterically with the membrane Particles. State diagrams are presented to fully characterize the system behavior as functions of the relevant control parameters governing the transition between different dynamical states. Three distinct scenarios are identified. These compromise trapping of the Active Particle, penetration through the membrane with subsequent self-healing, in addition to penetration with permanent disruption of the membrane. The latter scenario is accompanied by a partial fragmentation of the membrane and creation of a hole of a size exceeding the interaction range of the membrane components. Our analytical theory is based on a combination of a perturbative expansion technique and a discrete-to-continuum formulation. Our approach might be helpful for the prediction of the transition threshold between the trapping and penetration in real-space experiments involving motile swimming bacteria or artificial Active Particles.

  • Membrane penetration and trapping of an Active Particle
    Journal of Chemical Physics, 2019
    Co-Authors: Abdallah Daddi-moussa-ider, Benno Liebchen, Christian Hoell, Arnold J. T. M. Mathijssen, Francisca Guzmán-lastra, Christian Schölz, Andreas M. Menzel, Hartmut Löwen
    Abstract:

    The interaction between nano- or micro-sized Particles and cell membranes is of crucial importance in many biological and biomedical applications such as drug and gene delivery to cells and tissues. During their cellular uptake, the Particles can pass through cell membranes via passive endocytosis or by Active penetration to reach a target cellular compartment or organelle. In this manuscript, we develop a simple model to describe the interaction of a self-driven spherical Particle (moving through an effective constant Active force) with a minimal membrane system, allowing for both penetration and trapping. We numerically calculate the state diagram of this system, the membrane shape, and its dynamics. In this context, we show that the Active Particle may either get trapped near the membrane or penetrate through it, where the membrane can either be permanently destroyed or recover its initial shape by self-healing. Additionally, we systematically derive a continuum description allowing us to accurately predict most of our results analytically. This analytical theory helps in identifying the generic aspects of our model, suggesting that most of its ingredients should apply to a broad range of membranes, from simple model systems composed of magnetic microParticles to lipid bilayers. Our results might be useful to predict the mechanical properties of synthetic minimal membranes.

  • membrane penetration and trapping of an Active Particle
    arXiv: Soft Condensed Matter, 2019
    Co-Authors: Abdallah Daddimoussaider, Benno Liebchen, Christian Hoell, Arnold J. T. M. Mathijssen, Christian Schölz, Andreas M. Menzel, Segun Goh, Francisca Guzmanlastra, Hartmut Löwen
    Abstract:

    The interaction between nano- or micro-sized Particles and cell membranes is of crucial importance in many biological and biomedical applications such as drug and gene delivery to cells and tissues. During their cellular uptake, the Particles can pass through cell membranes via passive endocytosis or by Active penetration to reach a target cellular compartment or organelle. In this manuscript, we develop a simple model to describe the interaction of a self-driven spherical Particle (moving through an effective constant Active force) with a minimal membrane system, allowing for both penetration and trapping. We numerically calculate the state diagram of this system, the membrane shape, and its dynamics. In this context, we show that the Active Particle may either get trapped near the membrane or penetrates through it, where the membrane can either be permanently destroyed or recover its initial shape by self-healing. Additionally, we systematically derive a continuum description allowing to accurately predict most of our results analytically. This analytical theory helps identifying the generic aspects of our model, suggesting that most of its ingredients should apply to a broad range of membranes, from simple model systems composed of magnetic microParticles to lipid bilayers. Our results might be useful to predict mechanical properties of synthetic minimal membranes.