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Mathematical and Computational Modeling of Amoeboid Cell Crawling

Sergio Alonso, Carsten Beta

Abstract

Amoeboid motion is a dynamic mode of cell motility essential for processes such as the immune response and wound healing. This review examines recent developments in the mathematical and computational modeling of amoeboid crawling, focusing on the interplay between intracellular biochemical signaling and the physical mechanics of the cell membrane. We discuss the core components of cell motility and the integration of chemical and mechanical guidance cues suchg as chemotaxis and curvotaxis. We evaluate a range of modeling frameworks, from simple stochastic descriptions of center of mass motion to more complicated phase-field, finite-element methods and Potts models that capture complex cell shape deformations. Finally, we highlight emerging challenges, such as modeling interactions with complex topographies and large-scale multicellular coordination, as important steps toward a better understanding of cell locomotion.

Mathematical and Computational Modeling of Amoeboid Cell Crawling

Abstract

Amoeboid motion is a dynamic mode of cell motility essential for processes such as the immune response and wound healing. This review examines recent developments in the mathematical and computational modeling of amoeboid crawling, focusing on the interplay between intracellular biochemical signaling and the physical mechanics of the cell membrane. We discuss the core components of cell motility and the integration of chemical and mechanical guidance cues suchg as chemotaxis and curvotaxis. We evaluate a range of modeling frameworks, from simple stochastic descriptions of center of mass motion to more complicated phase-field, finite-element methods and Potts models that capture complex cell shape deformations. Finally, we highlight emerging challenges, such as modeling interactions with complex topographies and large-scale multicellular coordination, as important steps toward a better understanding of cell locomotion.
Paper Structure (18 sections, 5 equations, 3 figures, 1 table)

This paper contains 18 sections, 5 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Cells in motion
  3. Actin-driven motility
  4. Eukaryotic chemotaxis
  5. Other forms of taxis
  6. Models of cell crawling
  7. Modeling pattern formation at the membrane
  8. Pattern formation at the cell border
  9. Influence of mass conservation
  10. Pattern formation at the basal membrane
  11. Modeling cell shape dynamics
  12. Phase field model
  13. Mechanical interface descriptions
  14. Cellular Potts Model
  15. Modeling the center-of-mass motion of the cell
  16. ...and 3 more sections

Figures (3)

  • Figure 1: Types of cells and motion strategies (A): slow and large mesenchymal cells ($1 \mu m /min$, $50 \mu m$), fast and large keratocytes ($30 \mu m /min$, $40 \mu m$), and fast and small amoeboid cells ($15 \mu m /min$, $20 \mu m$). Chemotactic (B) and random (C) motions of amoeboid cells.
  • Figure 2: Modeling approaches to cell motion: (A) evolution of one dimensional pattern formation at the cell membrane, see Section \ref{['subsec3.1']}, (B) two dimensional pattern formation including shape deformation of the borders and the internal pattern formation, see Section \ref{['subsec3.2']}, (C) center of mass, see Section \ref{['subsec3.3']}.
  • Figure 3: Types of cell motion strategies for Dictyostelium discoideum: Amoeboid (A) and fan-type (B) motions, where color corresponds with the expression of Lifeact-GFP as a marker for filamentous actin; and for numerical simulations with phase field: Amoeboid (C) and fan-type (D) motions, where color corresponds with the internal field from a stochastic reaction-diffusion process. Time is color coded from red, orange and yellow to green.