# How to find the radius of gyration for a protein?

While going through the paper titled "GEOMETRIC ANALYSIS OF THE CONFORMATIONAL FEATURES OF PROTEIN STRUCTURES" by Manish Dutt, it talked about finding the radius of gyration of each protein structure. I am unable to understand how the radius of gyration has been obtained for the entire protein. I first find the root mean square distance between the centroid and the C alpha atom. Is the average of these distances the radius of gyration?

• Pretty sure that there are library methods to calculate this - otherwise the formula for the radius of gyration of a set of points is on wikipedia? in any case, more of a bioinformatics question than a biology one... – gilleain Sep 19 '16 at 16:24
• Radius of gyration (en.wikipedia.org/wiki/Radius_of_gyration) is a basic-physics concept. If we rotate freely a point-mass, we can quite easily derive various inter-related variables from other-such variables (like mass, speed, radius, etc); but if it is a complex object (say a wheel or stone), it is complicated, but we can imagin an EQUIVALENT point-mass in rotating; whose mass is same as whole object, and radius, speed, frequency-of rotation etc. all characteristics are exactly same to our object. – Always Confused Sep 19 '16 at 16:29
• there are square-roots in derivations for radius of gyration, and they are looking like (root (a. b. c. d... (r^2))) pattern. But I can't tell whether it is r.m.s. of that distance, or not. (from my H.S school physics textbook) – Always Confused Sep 19 '16 at 16:39
• @Rishika you could go-through the paper slowly, and mark statements and sketches which could be useful. Then add some more details to question. You could provide a link to the paper. Is it freely accessible paper? – Always Confused Sep 19 '16 at 16:44