# How much of a difference in a protein's radius of gyration can be considered significant?

In molecular dynamics simulations of proteins, the radius of gyration is often used to assess the compactness of a protein. When comparing two protein radius of gyration, what difference can be considered significant 1 Angstrom, 5 Angstroms, 10 angstroms? Significant meaning: yes it is definitely more compact or no it is definitely not more compact. I have been searching through but can't find any reference related to that.

• I think it depends on how is your data. Whether if you have a time series for the radii of gyration (that would mean a lot of data in time for both systems) or similar. You could then perform some statistical significance studies using the distribution of your data, for example I could think of a Kolmogorov-Smirnov test. Or, if you only have two sample (data points), then I would think it depends on how big is the radius itself (doing a relative difference). And all in-between. Sep 2 '20 at 3:36
• @IvanP As this question has remained unanswered for a while, would you consider turning your comment into an answer? Sep 6 '20 at 2:58
• @NikeDattani Sure, should I just do it and erase the comment? Or how does that work? Sep 7 '20 at 4:02
• @IvanP Yes please! It would be appreciated if you could expand the comment though, since answers that are short enough to go in a comment can be frowned upon. Sep 7 '20 at 17:54
• @IvanP would you have time to try to expand that comment into an answer now? It would be highly appreciated by many of us trying to maintain this site in good order! Sep 26 '20 at 20:50

It depends on your actual scenario. If we assume that you have two Molecular Dynamics (MD) replicas for the same protein (and their respective trajectories), then when you perform a Radius of Gyration ($$R_g$$) computation from a MD trajectory you commonly end up with a time series for the values for it, $$R_g(t)$$.
From $$R_g(t)$$ you can already plot the time series of the values (always good to visualize beforehand) and, once the simulation has converged for each replica, compute a histogram/distribution, so you should end up with something like the following for each MD trajectory (so, two of them in total).
Now, on the other hand, if what you have is just two individual values for $$R_g$$ then I suspect you can just directly use the relative error between them (surely one of the samples can be considered a reference) to have an idea how one deviates from another. Maybe something like $$>5$$ percent is significant, this is subjective.