The Experts below are selected from a list of 9 Experts worldwide ranked by ideXlab platform

Peng Zhang - One of the best experts on this subject based on the ideXlab platform.

  • Uniqueness and traveling waves in a Cell motility model
    Discrete & Continuous Dynamical Systems - B, 2019
    Co-Authors: Matthew S. Mizuhara, Peng Zhang
    Abstract:

    We study a non-linear and non-local evolution equation for curves obtained as the sharp interface limit of a phase-field model for crawling motion of eukaryotic Cells on a substrate. We establish uniqueness of solutions to the sharp interface limit equation in the subcritical parameter regime. The proof relies on a Gronwall estimate for a specially chosen weighted \begin{document}$L^2$\end{document} norm. As persistent motion of crawling Cells is of central interest to biologists, we next study the existence of traveling wave solutions. We prove that traveling wave solutions exist in the supercritical parameter regime provided the non-linearity of the sharp interface limit equation possesses certain asymmetry (related, e.g., to myosin contractility). Finally, we numerically investigate traveling wave solutions and simulate their dynamics. Due to non-uniqueness of solutions of the sharp interface limit equation we numerically solve a related, singularly perturbed PDE system which is uniquely solvable. Our simulations predict instability of traveling wave solutions and capture both bipedal Wandering Cell motion as well as rotating Cell motion; these behaviors qualitatively agree with recent experimental and theoretical findings.

  • Uniqueness and traveling waves in a Cell motility model
    arXiv: Analysis of PDEs, 2017
    Co-Authors: Matthew S. Mizuhara, Peng Zhang
    Abstract:

    We study a non-linear and non-local evolution equation for curves obtained as the sharp interface limit of a phase-field model for crawling motion of eukaryotic Cells on a substrate. We establish uniqueness of solutions to the sharp interface limit equation in the so-called subcritical parameter regime. The proof relies on a Gr\"{o}nwall estimate for a specially chosen weighted $L^2$ norm. Next, as persistent motion of crawling Cells is of central interest to biologists we study the existence of traveling wave solutions. We prove that traveling wave solutions exist in the supercritical parameter regime provided the non-linear term of the sharp interface limit equation possesses certain asymmetry (related, e.g., to myosin contractility). Finally, we numerically investigate traveling wave solutions and simulate their dynamics. Due to non-uniqueness of solutions of the sharp interface limit equation we simulate a related, singularly perturbed PDE system which is uniquely solvable. Our simulations predict instability of traveling wave solutions and capture both bipedal Wandering Cell motion as well as rotating Cell motion; these behaviors qualitatively agree with recent experimental and theoretical fidings.

Matthew S. Mizuhara - One of the best experts on this subject based on the ideXlab platform.

  • Uniqueness and traveling waves in a Cell motility model
    Discrete & Continuous Dynamical Systems - B, 2019
    Co-Authors: Matthew S. Mizuhara, Peng Zhang
    Abstract:

    We study a non-linear and non-local evolution equation for curves obtained as the sharp interface limit of a phase-field model for crawling motion of eukaryotic Cells on a substrate. We establish uniqueness of solutions to the sharp interface limit equation in the subcritical parameter regime. The proof relies on a Gronwall estimate for a specially chosen weighted \begin{document}$L^2$\end{document} norm. As persistent motion of crawling Cells is of central interest to biologists, we next study the existence of traveling wave solutions. We prove that traveling wave solutions exist in the supercritical parameter regime provided the non-linearity of the sharp interface limit equation possesses certain asymmetry (related, e.g., to myosin contractility). Finally, we numerically investigate traveling wave solutions and simulate their dynamics. Due to non-uniqueness of solutions of the sharp interface limit equation we numerically solve a related, singularly perturbed PDE system which is uniquely solvable. Our simulations predict instability of traveling wave solutions and capture both bipedal Wandering Cell motion as well as rotating Cell motion; these behaviors qualitatively agree with recent experimental and theoretical findings.

  • Uniqueness and traveling waves in a Cell motility model
    arXiv: Analysis of PDEs, 2017
    Co-Authors: Matthew S. Mizuhara, Peng Zhang
    Abstract:

    We study a non-linear and non-local evolution equation for curves obtained as the sharp interface limit of a phase-field model for crawling motion of eukaryotic Cells on a substrate. We establish uniqueness of solutions to the sharp interface limit equation in the so-called subcritical parameter regime. The proof relies on a Gr\"{o}nwall estimate for a specially chosen weighted $L^2$ norm. Next, as persistent motion of crawling Cells is of central interest to biologists we study the existence of traveling wave solutions. We prove that traveling wave solutions exist in the supercritical parameter regime provided the non-linear term of the sharp interface limit equation possesses certain asymmetry (related, e.g., to myosin contractility). Finally, we numerically investigate traveling wave solutions and simulate their dynamics. Due to non-uniqueness of solutions of the sharp interface limit equation we simulate a related, singularly perturbed PDE system which is uniquely solvable. Our simulations predict instability of traveling wave solutions and capture both bipedal Wandering Cell motion as well as rotating Cell motion; these behaviors qualitatively agree with recent experimental and theoretical fidings.

Mark W. Lingen - One of the best experts on this subject based on the ideXlab platform.

  • Role of Leukocytes and Endothelial Cells in the Development of Angiogenesis in Inflammation and Wound Healing
    Archives of Pathology & Laboratory Medicine, 2001
    Co-Authors: Mark W. Lingen
    Abstract:

    Abstract The basic signs and symptoms of inflammation and wound healing have been appreciated for thousands of years. However, the specific Cells involved and their roles in this complex environment are still being elucidated today. In 1926, the origin of the phagocytic mononuclear ameboid Wandering Cell (macrophage) had not been determined. One popular theory was that the Cells were differentiated from the endothelial Cells of the nearby blood vessels, whereas others believed that the Cells came from the peripheral blood or resting Wandering Cells. The purpose of this article is to review the seminal article published by Lang regarding this topic nearly 75 years ago. In addition, this article will review what is now known with regard to the role of the macrophage and endothelial Cells in the development of angiogenesis, which is arguably the most critical component of successful inflammatory process or wound healing.