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Proteins show rotational as well as lateral diffusion across the membrane. The lateral diffusion of proteins was confirmed through the cell fusion experiment where mouse and human cells were fused, resulting in hybrid cells. When the human and mouse cells fused, the specific membrane proteins on human and mouse cells were marked with the red and green-fluorescent markers, respectively. Initially, the red and green fluorescence was located on the respective hemisphere of the cell. As time...
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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Nonlinear diffusion and exclusion processes with contact interactions.

Anthony E Fernando1, Kerry A Landman, Matthew J Simpson

  • 1Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary
This summary is machine-generated.

Agent-based exclusion processes, when modeled using continuum equations, yield nonlinear diffusion. The accuracy of these models depends on interaction strength, with a new measure predicting continuum model validity for cell motility studies.

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Area of Science:

  • Mathematical Biology
  • Statistical Physics
  • Complex Systems

Background:

  • Exclusion processes model discrete systems like cell movement.
  • Continuum models, using partial differential equations, approximate average behavior.
  • Understanding agent-level interactions is crucial for accurate modeling.

Purpose of the Study:

  • To investigate how various contact interactions in exclusion processes affect continuum models.
  • To determine the conditions under which discrete and continuum models agree.
  • To develop a metric for assessing the validity of continuum descriptions for interacting agents.

Main Methods:

  • Combining a general class of contact interactions with lattice-based exclusion processes.
  • Deriving continuum models in the form of nonlinear diffusion equations.
  • Analyzing the dependence of diffusion functions on lattice structure and interaction neighborhoods.
  • Developing a measure to quantify the agreement between discrete and continuum models.

Main Results:

  • Diverse contact interactions consistently lead to nonlinear diffusion equations with varied diffusion functions D(C).
  • Diffusion function characteristics depend on lattice type and interaction neighborhood.
  • Mild to moderate interaction strengths show good agreement between discrete and continuum models.
  • Strong interactions can cause discrepancies, especially when D(C) becomes negative.

Conclusions:

  • Continuum diffusion equations effectively describe exclusion processes with contact interactions.
  • A predictive measure for model validity is established, crucial for interpreting cell motility data.
  • This framework enhances the modeling of cell motility by incorporating realistic cell-cell interactions.