Background
MD simulation is often used to investigate conformational changes caused by mutation. Consider a case where one has two ensembles of trajectories. We wish to see if there is a statistically significant difference between the ensembles by comparing the mean Calpha distance between specific residues. We require observations to be independent from each other.
Question
Within a single trajectory if the observations are taken far enough apart are they considered independent. For instance if we track the distance between Ser55 and Thr101 can we treat the distances at time point 10ns, 20ns, 30ns etc as independent observations.
The distance at various time points (10, 20, 30.....100 ns) can give a time series of that parameter for a trajectory (which could be consistently the same or change with time).
To achieve an independent observation, data-driven from the set of independent simulation runs is appropriate. A single trajectory must be ideally treated as an independent simulation from where one can interpret the result of that ensemble.
If you are concerned about your samples being drawn with enough time distance to be effectively independent, you can do the following:
1. Make a time series of potentially dependent samples with a high sample rate (e.g. use all your distance samples).
2. Find the time-correlation of this signal.
3. The time-correlation function should show an exponential decay, proportional to exp(-t/tau). The parameter tau is the correlation time in your time series.
4. Now sub-sample your time series with a time step of at least tau, or better, a multiple of it, and you can be more certain about the statistical independence of your samples.
The time correlation analysis as suggested by Mohsen Sadeghi is more appropriate.
I read somewhere (I forgot the name of book) that in MD simulation, the frames start to be decorrelated or independent after 50pico seconds. So, taking snapshots >50ps could be an alternative solution.
One more suggestion, you can also bin the data and then run some statistical tests.
Ayaz Anwar the decorrelation you mentioned sounds like the velocity decorrelation time, which tells you that after some time, particle momenta are practically independent of their starting values. The time itself depends on the system, and the tens of picoseconds sounds about right for all-atom models of liquid-phase and biomolecular simulations. But for another property of the system, especially a configuration-dependent one, the correlation time can actually be much larger, which is part of the general sampling problem with MD.
Hi Mohsen Sadeghi thank you for clarifying this, and I think this is more appropriate. And, yes the correlation time varies based on the property you are studying.
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