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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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Crystal Field Theory
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Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
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Scientists identified the plasma membrane in the 1890s and its principal chemical components (lipids and proteins) by 1915. The model for plasma membrane structure, proposed in 1935 by Hugh Davson and James Danielli, was the first model to be widely accepted in the scientific community. The model was based on the plasma membrane's "railroad track" appearance in early electron micrographs. Davson and Danielli theorized that the plasma membrane's structure resembled a sandwich...
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The cellular Potts model on disordered lattices.

Hossein Nemati1, J de Graaf1

  • 1Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands. h.nemati@uu.nl.

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|September 16, 2024
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Summary
This summary is machine-generated.

This study introduces an irregular lattice variant of the cellular Potts model (CPM) to reduce simulation artifacts. The new model reveals a distinct first-order phase transition in cell tissue organization, differing from jamming transitions.

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Area of Science:

  • Computational biology
  • Biophysics
  • Cellular modeling

Background:

  • The cellular Potts model (CPM), or Glazier-Graner-Hogeweg model, is a key numerical tool for studying biological tissues at the cellular level.
  • Traditional 2D CPMs use regular square or hexagonal lattices, which can introduce artifacts affecting cell shape and tissue dynamics.

Purpose of the Study:

  • To develop a flexible CPM variant applicable to irregular lattices, thereby mitigating known simulation artifacts.
  • To investigate the fluid-disordered to solid-ordered phase transition in confluent cell tissues using this new model.

Main Methods:

  • Developed a novel CPM variant capable of utilizing a broad range of irregular lattice structures.
  • Simulated monodisperse confluent cells on an irregular lattice derived from a fluid-like configuration.
  • Analyzed cell shape parameters to characterize phase transitions as a function of surface tension.

Main Results:

  • The irregular lattice CPM successfully removed artifacts related to lattice symmetry, particularly on fluid-like configurations.
  • Observed a distinct first-order phase transition between fluid-like disordered and solid-like hexagonal phases in cell tissues.
  • This transition differs significantly from the glass/jamming transitions typically seen in vertex and active Voronoi models.

Conclusions:

  • The irregular lattice CPM offers a more realistic simulation environment for biological tissues by reducing lattice-induced artifacts.
  • The identified first-order phase transition provides new insights into tissue morphogenesis and collective cell behavior.
  • This model serves as a valuable reference for future research on epithelial tissues.