1. Most likely your energy conservation is just not fully correct, leading to a linear drift in the temperature and therefore also in the total energy.

1-3.Generally a molecular dynamics simulation in a canonical ensemble will always lead to a boltzmann weigthed ensemble (so the overall configurational space distribution that is natural for the molecule at the given temperatue) if running for long enoug. But for most systems this requires more time to simulate than the earth already exists in years, This means that such simulations usually relax from their initial bad starting structure to the next local minimum structure in the free energy and won't be easily able to ever escape from there within reasoanble real time. So the total energy variation is likely only a snapchot of the configurational space of your molecule and can hardly be interpreted.

To obtain the free energy of a protein conformation, you need to explore the overall conformationional space using e.g. REMD. Later you need a reaction coordinate to distinquish different states of the protein e.g. PCA. Afterwards you can create a histogram for the density of states along the selected reaction coordinates. This can finally be recomputed into the gibbs free energy as dG = RTln(P/Pmax) [J/mol]

If you simulate in an ensemble other than microcanonical, then it would be totally fine to observe total energy fluctuation. Also, if you have not performed a pre-equilibration MD run before starting the production run, then the energy may rise compared to the initial configuration because the latter presumably represents an energy-minimized state, while in the middle of a simulation one always has a significant fraction of atoms displaced from their minimum-energy positions.

Depending on the ensemble you performing the simulations, the energy fluctuations can be related to other macroscopic properties of the system.

In canonical ensemble, NVT simulations, these fluctuations are related to the heat capacity:

_NVT = k_B T^2 C_V

k_B Boltzmann's constant, T temperature and C_V heat capacity at constant volume V.

In NPT ensemble the fluctuations are different, however, the both can be related:

_NPT  = k_B T^2 C_V - k_B T [T(\partial P/\partial T)_N,V - P]^2 (\partial V\partial P)_N,T

where P is pressure.

By comparing the two expressions, it can be seen that the energy fluctuations in canonical ensemble (with N , V and T constant) differ from the fluctuations in isothermal-isobaric ensemble (with N , p and T constant) by a term which includes the change of pressure with temperature (at constant N and V ) and change of volume with pressure (at constant N and T ).

Therefore, depending on the behavior with temperature and/or pressure of these terms (either C_V or second term in NPT ensemble) you can interpret the fluctuations of energy. For constant temperature T, relative fluctuations of energy decreases as 1/N^{0.5}. Thus, I would suggest to monitor the temperature variations (and pressure) during the simulations.

Dear All,

Thank you for your answers and clarifications.

More details about the parameters that I used:

I'm working in an NPT ensemble.

I relaxed and equilibrate my system before the simulation (1.2ns)

During the MD, my temperature and pressure remained globally stables (300K and 1 bar).

My potential energy was also stable!

Maybe there is a bug in the software! It doesn't make sens to have such variations in total energy whereas potential energy and the temperature are stable!?

People often blame the program (""a bug in the software") only to later find out that the problem was not in the program's code. It is extremely unlikely that your case is an exception . . .

Dear Martin, 

Thank you for your answer. 

I detailed my protocol and I really don't know where is the problem.

Maybe I'm missing something and this is why I asked my question.