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In mechanical engineering, a three-dimensional force system is a system of forces acting in three dimensions, with forces applied along the x, y, and z coordinate axes. The three-dimensional force system is an important concept in mechanical engineering, as it allows engineers to understand and analyze the behavior of objects and structures in three dimensions. By understanding the forces acting on a system, engineers can design more efficient and effective mechanical systems that can withstand...
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Solving problems related to two-dimensional force systems is an essential aspect of mechanics and engineering. By applying the principles of vector analysis and force equilibrium, one can determine the effect of multiple forces acting on an object in a two-dimensional space.
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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Force-based three-dimensional model predicts mechanical drivers of cell sorting.

Christopher Revell1, Raphael Blumenfeld1,2, Kevin J Chalut1,3

  • 11 Cavendish Laboratory, Department of Physics, University of Cambridge , Cambridge CB3 0HE , UK.

Proceedings. Biological Sciences
|April 10, 2019
PubMed
Summary
This summary is machine-generated.

Researchers developed a new computational model to study cell sorting in multicellular aggregates (MCAs). This model predicts the minimum cell adhesion and tension asymmetry required for robust tissue self-organization and sorting.

Keywords:
biological physicscell sortingcortical tensiondifferential interfacial tensionmodellingself-organization

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Area of Science:

  • Computational biology
  • Developmental biology
  • Biophysics

Background:

  • Cell sorting is crucial for tissue morphogenesis.
  • Mechanical drivers of cell sorting in multicellular aggregates (MCAs) are not well understood.
  • Lack of appropriate computational models hinders investigation of cell-cell mechanical interactions.

Purpose of the Study:

  • To develop a novel computational model for simulating mechanical interactions in MCAs.
  • To investigate the effects of cell-cell adhesion and tension on cell sorting.
  • To provide insights into the mechanisms driving tissue self-organization.

Main Methods:

  • Developed a three-dimensional, local force-based simulation using the subcellular element method.
  • Modeled cells as collections of locally interacting force-bearing elements.
  • Investigated the influence of tension and cell-cell adhesion on MCA sorting dynamics.

Main Results:

  • Predicted a minimum adhesion level necessary for inside-out sorting of two cell types, aligning with developmental observations.
  • Quantified the tension asymmetry required for robust cell sorting.
  • Demonstrated the model's ability to simulate key aspects of tissue self-organization.

Conclusions:

  • The developed computational model offers a powerful tool for studying cell sorting and tissue self-organization.
  • Cell-cell adhesion and tension asymmetry are critical mechanical factors governing sorting in MCAs.
  • The model's flexibility makes it applicable to diverse biological processes like embryogenesis and tumorigenesis.