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. 2012 Apr 26;4(5):663–687. doi: 10.3390/v4050663

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© 2012 by the authors; licensee MDPI, Basel, Switzerland.

This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

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Shading of bacteria by bacteria. Shown is a progression starting with two “free” coccus-shaped bacteria (left) which is followed by a diplococcus displaying some degree of attachment (middle) that in turn is followed by a diplococcus displaying maximal attachment as well as minimized surface-to-volume ratio (right), i.e., existing as a combined-volume sphere of 2^1/3 -fold increased radius over an individual cell (see calculation, below). The left-hand lack of arrangement shows no shading whereas the right-hand arrangement shows an approximation of maximal shading for a combined spherical shape. The middle arrangement displays some intermediate degree of shading and therefore some intermediate overall target size between maximal and minimal (holding cell volumes constant). Note that the volume of a sphere, V₁, is equal to . Twice its volume (V₂) therefore is , which as a sphere is equal to . For , then r₂= 2^1/3r₁. With such shading, then, diameter increases by only 2^1/3 = 1.26 fold.

Inline graphic — Shading of bacteria by bacteria. Shown is a progression starting with two “free” coccus-shaped bacteria (left) which is followed by a diplococcus displaying some degree of attachment (middle) that in turn is followed by a diplococcus displaying maximal attachment as well as minimized surface-to-volume ratio (right), i.e., existing as a combined-volume sphere of 2^1/3 -fold increased radius over an individual cell (see calculation, below). The left-hand lack of arrangement shows no shading whereas the right-hand arrangement shows an approximation of maximal shading for a combined spherical shape. The middle arrangement displays some intermediate degree of shading and therefore some intermediate overall target size between maximal and minimal (holding cell volumes constant). Note that the volume of a sphere, V₁, is equal to . Twice its volume (V₂) therefore is , which as a sphere is equal to . For , then r₂= 2^1/3r₁. With such shading, then, diameter increases by only 2^1/3 = 1.26 fold.