I would like to know if there is a specific criteria to know when the energy of a simulation has converged. I was thinking something such as the ratio between the standard deviation and the slope of the linear regression as a wild guess.
Oh, that's a small question with a thousand possibilities to answer... what you can do is: You can take e.g. the last 10% of simulated time, and calculate the RMSD of the total system energy, or your energy term that you're interested in. Now check the forward average of the last 50% of simulated time. if this average converges into the average of the last 10% +/- RMSD, that's a pretty good sign your system is converged.
This is a very sensitive issue. Some researchers use correlation functions to determine the convergence of the simulation, others use techniques based on visual analysis of the RMSD, or more elaborate techniques based on principal component analysis. However, there is no consensus on this area. I've searched a lot in the literature and have not found an absolute test. What counts is the good sense and knowledge of the system.
It helps to also know which energy minimization algorithms you are executing. I couple steepest descent with conjugant gradient until there's a kcal/mol convergence within less of 1 order of magnitude in the Hamilton. (usually both in vacuo and aqueous just to make sure) The RMSD protein-atom_protein-atom is a good suggestion, but better yet try to implement a 2D-RMSD. There's lots of methods used, but you'd have to figure out why they did them for the specific system. For example, of you have a membrane protein, analysis for that would differ. So digging up the literature for that would be nice or you could get a bit creative.
The convergence in MD is, usually, defined by RMSD. When the curve comes to plateau, mean that MD is converged. For example, you can use the RMSD of Calpha of protein.
This is a good and interesting question. First if you are tolking about energy minimisation by molecular dynamic, rmsd or energy alone can not be adequate to study the convergence of the system. Some program use the relation between the two parmeter to study the convergence of the system. Second, if you are interesting to molecular dynamic simulation you can not understand this because it is depends on your protein.
I would like to add that RMSD is often a very poor metric of convergence, and energy is even poorer. Looking at multiple reaction coordinates is important to get the best sense of convergence. Also, comparing two completely independent simulations will give a better idea than just one simulation.
Thanks for pointing this out. So are you calculating the torsion angle as a function of MD frame? Would it be "better" in the statistical sense because of greater exploration in phase space?
I agree with K. Aurelia Ball which RMSD is a very poor metric of dynamics and that look at multiple reaction coordinates is important. You can try use the relaxation time of RMSD, for example. How Fakher Frikha pointed you should know what you want, becouse for example, total energy of system must be conserved during MD simulations. Like pointed out by K. Aurelia Ball, comparing two completely independent simulations will give a better idea than just one simulation. I do this in my lab, however you never know if your simulation converges because convergence is just a concept without theoretical basis and independent simulations tend to explorind different areas in the phase space. And like I say above, what counts is the good sense and a good knowledge of the system.
I agree with IC Baianu. However, the criterion 7 will be true only in very special situations. This is due to so-called Lyapunov instability that means that two trajectories that are initially very close will diverge exponentially as time progress.
I will quickly point out that what is often employed for convergence 'estimation' is the RMSD, and/or the potential energy neither of which is really very accurate in the real sense of it. However, one has to consider the particular requirement of the convergence since this will determine the acceptability of the convergence accuracy. What do I mean by this? If I am only interested in getting my system to an 'equilibrium' state with large forces from unphysical clashes removed in preparation for a production run, then RMSD (both of the coordinate and potential energy) is sufficiently accurate. On the other hand, if what I am interested in is the convergence of the trajectory, post-production run, then the measure of convergence must necessarily depend on the quantity of prime interest. Take for instance, in some studies I conducted sometime ago I had found it most relevant to employ the convergence of calculated chemical shift with respect to NMR chemical shift data in judging convergence. The important thing is to first decide the important quantity that best captures the aspect of the dynamics one is interested in, and to measure convergence based on that. One should also keep in mind that convergence is crucially dependent on the simulation length and sampling technique, especially when trying to obtain a perspective of the macroscopic state from the typically finite system simulated using MD.
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