Hello
I have a very hard question.
Let's consider a two molecular dynamics simulations with small-sized protein in the water solvent.
1. Simulation is performed with a crystallographic structure from PDB database.
2. Simulation is performed with the same crystallographic structure from PDB database; the difference is that the position of several atom coordinates of the structure was moved by 0.01Å.
After the, i.e., 1ns simulation of both systems, trajectory and resulted structure are different.
Then a question arises: If the crystallographic resolution is, i.e., 2Å, how reliable it is if a very small change of 0.01Å has changed so much.
I don't want anything to suggest; thus I don't provide my point of view.
This is the key aspect of chaos theory: an infinitesimally small deviation in boundary conditions will yield exponentially divergent trajectories. Hence, it is sufficient to change slightly e.g. the initial velocity or position of a single atom to obtain two different structures after some time.
This is also why it is fundamental to get a good grasp of statistical mechanics, as what you typically want to measure is *averages* over many non-identical replicas of the same system (or over long time intervals), and in case of equilibrium systems these should converge to a well-defined quantity.
This is the key aspect of chaos theory: an infinitesimally small deviation in boundary conditions will yield exponentially divergent trajectories. Hence, it is sufficient to change slightly e.g. the initial velocity or position of a single atom to obtain two different structures after some time.
This is also why it is fundamental to get a good grasp of statistical mechanics, as what you typically want to measure is *averages* over many non-identical replicas of the same system (or over long time intervals), and in case of equilibrium systems these should converge to a well-defined quantity.
Yes, Miłosz is right. A small change in the initial configuration may result in different output, but that doesn't mean the crystal structure is incorrect. The system is just exploring different regions of the phase space.
So, It is not useful to check the end structure for the correctness of the initial model, instead you can compute the physical properties (such as Energy, Temperature, Pressure, RMSD, RDF etc) of the system. The averages of these quantities will be same for both, if not, at least they will be within the error bar.
Yes, problem is in covering all the space possible vs. the available space in complex protein structure within 1ns simulation. Trajectory provides average structure with fluctuations but not worth to check final structure(s). Depending on protein some caveat in the structure also may take the trajectory to a different phase space than near the crystal structure space, hence suggested that to be near the crystal structure space and compare the real-space correlation.
You didn't cover the entire phase space. Of course it depends on the size of your system, but I don't think your system can be converged after 1 ns. Let both trajectories run for enough time (maybe hundreds of ns or even us) and they should yield similar results unless the systems get trapped in local minimas. If that happens you have to used some enhanced sampling techniques. Well, it all depends on the question you are trying to answer.
Generate an ensemble of structures and energies by running many short MD simulations started from different initial conditions (e.g., initial velocities). Compare MD structures and (free) energies with relevant experimental data.
I agree with everyone about the initial coordinates before starting which determine all the forces exerted on all the atoms. This is why most MD simulations perform an energy minimization step before the MD. The minimization increases the reproduciblity of the results because it brings the structures to closer initial coordinates.
Why the two structure should be same after 1ns in the first place. Even if the initial structure as exactly similar, there is always randomness in MD. It is like saying that we both start a journey with similar average speed over the course of the journey. Does this means we both should be at point place at time t?
What you should do is to compare crystal parameters after 1ns to see how different they are. If you starting with reasonably good structure, regardless of initial structure the force field would relax your crystal parameters to the those that predicted by the force field.
Do not compare the frames, rather compare the properties (like crystal parameters, density and so on) to see if the initial structure had any impact on your result.
And how you compare trajectories over 1ns? That is a volume of 6N dimensional points.
Javad, if the initial structures, initial conditions, and simulation parameters are exactly the same, the trajectories will be identical as well.
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