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Diamagnetic Shielding of Nuclei: Local Diamagnetic Current01:14

Diamagnetic Shielding of Nuclei: Local Diamagnetic Current

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Updated: May 9, 2026

Nutrient Regulation by Continuous Feeding for Large-scale Expansion of Mammalian Cells in Spheroids
11:01

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Published on: September 25, 2016

Nutrient shielding in clusters of cells.

Maxim O Lavrentovich1, John H Koschwanez, David R Nelson

  • 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 16, 2013
PubMed
Summary

Cellular nutrient shielding in colonies limits growth. A new theory predicts the nutrient-rich outer shell thickness (ℓ) based on cell absorption strength (ν), volume fraction (φ), and nutrient concentration (ψ(∞)).

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09:06

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Published on: May 20, 2014

Area of Science:

  • Cellular and Molecular Biology
  • Biophysics
  • Mathematical Biology

Background:

  • Cellular nutrient consumption depends on uptake kinetics and spatial arrangement.
  • Large cell clusters exhibit inhibited growth at the center due to nutrient shielding by outer cells.

Purpose of the Study:

  • To develop an effective medium theory predicting the thickness of the nutrient-receiving outer shell of cell clusters.
  • To identify key parameters influencing nutrient penetration and growth within cell colonies.

Main Methods:

  • Developed an effective medium theory treating cells as partially absorbing spherical nutrient sinks.
  • Introduced a dimensionless parameter (ν) for cell absorption strength.
  • Compared theoretical predictions with numerical simulations and experimental data from yeast colonies.

Main Results:

  • The theory predicts a nutrient-receiving shell thickness (ℓ) within cell clusters.
  • Shell thickness (ℓ) decreases with increasing cell absorption strength (ν), cell volume fraction (φ), and decreasing ambient nutrient concentration (ψ(∞)).
  • Experimental validation using Saccharomyces cerevisiae colonies showed good agreement with theoretical predictions.

Conclusions:

  • The effective medium theory provides a robust framework for understanding nutrient diffusion and growth limitations in cell colonies.
  • The study quantifies the relationship between cellular properties, colony architecture, and nutrient availability.
  • Findings are applicable across diverse cell types, from microbes to human tissues.