Shape Description of Macromolecular Folding

Molecular geometry and connectivity can be used to construct descriptors for other shape features. In this section, we introduce another aspect of macromolecular shape the complexity of self-entanglements in a polymer. The analysis is restricted to backbones that is, only main chain atoms are considered. 

The key idea is to use the pattern of crossings or double points that a curve in space exhibits when projected onto two dimensions. These points are obtained whenever we observe two bonds crossing over each other from a viewing direction in space. Because these points are crossings only by projection, we refer to them as over crossings. 

For a macromolecule, determine the center-of-mass coordinates of all the main chain atoms defining the backbone, and compute the span R. 

Consider an arbitrary point r on the sphere with radius R (which encloses the backbone completely), and determine the plane tangent to the sphere at r. 

Project the backbone coordinates onto the plane in step 2, and establish the number N of bond—bond crossings associated with this projection. 

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