Submitted to: Biophysical Chemistry
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 7/24/2012
Publication Date: N/A
Publication URL: http://handle.nal.usda.gov/10113/58562
Citation: Interpretive Summary: Many important biochemical and agricultural macromolecules (e.g., proteins, DNA) have a core backbone structure resembling a “cork screw”, referred to as an alpha-helix. The precise shape of the alpha-helix can vary depending on the radius, height and phase of the unit sized building block molecules (e.g., amino acids, nucleic acid bases). We developed a graphical model which allows for a more accurate prediction of the alpha-helix shape based on information about only three repeating atoms of the same atom type (e.g., N, C1, C2 ). This is comparable to a picture with higher resolution due to a greater number of pixels per unit area. This model should be valuable for other scientists and biomedical engineers in predicting the repeating sizes and shapes within important biological macromolecules and of the biophysical functions that correspond with these shape and sizes which may or may not be self-consistently repeatable.
Technical Abstract: Pitch is not a height but a ratio of rise/run. In an alpha-helix, run can be as the radius (r) from the center of the circle, as a diameter (d) measured across/bisecting a circumference, or as a distance (c) along a circumference; rise in each case can corresponds to same height (h) increase. For a representative standard peptide, dimensions are: r = 1.75 Å, d = 3.5 Å, pi d = 11 Å, and h = 5.4 Å. Thus empirically when 2 h = pi d, the rise/run around the circumference simplifies to h/(pi d) = 0.5000 = tan alpha(circumference) [and alpha (circumference)= 26.5651]. Every two steps in the XY-plane [each step = pi r/2] corresponds to one step [pi r/2] in the YZ plane. At alpha (circumference) = 26.56, because when h = r , h cannot be changed independently of r. Thus geometrically, the distance traveled per cycle (up the inclined plane) in an alpha-helix is 1.118 times longer the hypotenuse compared to distance without an inclined plane. The longer distance is evidence of every loop of a helix is higher in energy than the same period in the absence of an inclined plane.