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Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
Gravity between Spherical Bodies01:27

Gravity between Spherical Bodies

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Spherical Coordinates01:23

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Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
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A 3D Spheroid Model as a More Physiological System for Cancer-Associated Fibroblasts Differentiation and Invasion In Vitro Studies
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Ficoll is not a rigid sphere.

William H Fissell1, Sargum Manley, Anna Dubnisheva

  • 1Department of Nephrology and Hypertension, The Cleveland Clinic, Cleveland, OH 44195, USA. whf@alum.mit.edu

American Journal of Physiology. Renal Physiology
|July 27, 2007
PubMed
Summary

Ficoll transport through kidney filtration membranes is complex. While smaller Ficoll molecules act like rigid spheres, larger ones show unexpected "hyperpermeability," challenging their use as ideal tracers.

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Published on: February 17, 2019

Area of Science:

  • Renal physiology
  • Membrane transport
  • Biomaterials science

Background:

  • Polydisperse Ficoll mixtures are used to study glomerular sieving.
  • Ficoll's renal handling is not fully understood, with contradictory literature on its behavior as a spherical solute.
  • Accurate interpretation of in vivo results requires a clearer definition of Ficoll transport dynamics.

Purpose of the Study:

  • To investigate Ficoll transport through well-defined slit-shaped pores.
  • To determine if Ficoll behaves as an idealized sphere across different molecular sizes.
  • To inform the interpretation of studies using Ficoll as a tracer molecule in renal research.

Main Methods:

  • Perfusion of flat-sheet membranes with slit pores (8 nm by 45 µm) using FITC-labeled Ficoll 70 and Bovine Serum Albumin (BSA).
  • Quantification of Ficoll and BSA concentrations using gel-permeation chromatography and Bradford assay, respectively.
  • Analysis of molecular transport rates relative to pore dimensions.

Main Results:

  • Ficoll and BSA molecules approximately half the slit pore width showed hindered transport, aligning with rigid sphere models.
  • Ficoll molecules larger than ~0.65 slit width exhibited transport rates exceeding predictions.
  • Ficoll molecules with diameters larger than the pore dimension were detected in permeate samples, indicating unexpected passage.

Conclusions:

  • Ficoll transport is accurately modeled as a sphere only within a specific size range.
  • The idealized sphere model for Ficoll breaks down as molecular diameter approaches pore size.
  • Apparent Ficoll hyperpermeability suggests the need for models incorporating molecular deformation for accurate membrane characterization.