For a publication purpose what all analyses are crucial while carrying out the molecular dynamic simulation of only protein. What exactly each analysis represent i.e, what is their significance?
There is no general answer to this question, yet people often ask it. There is no recipe that says "do this analysis on a protein and get a paper out of it." The only answer to this question is: quantify whatever relevant properties are necessary to address the question of interest. One can do a whole host of trivial analysis and prove nothing, and the types of things you would look at while simulating polypeptide folding would be vastly different from what you would look at in the case of a protein-membrane interactions, ligand binding, transport properties, etc.
Generally people assess the protein structure stability and fold analysis using MD simulations. For this to be done, you can analyze the RMSD of the C-alpha coordinates from its reference structure and also the root mean square fluctuations of the specific residues over a particular time. I hope this helps.
I personally like to analyze the change of some physico-chemical properties of the protein along the simulation, like the exposed surface area of the molecule (hydrophobic, hydrophilic and total), the hydrodynamic radius, and others.
Taking into account just the biochemistry, it would be interesting to also look at some very specific items like the hydrogen and salt bonds, and also the secondary structure elements along the simulation. Changes in those parameters can be easily related for instance with a more "flexible" region in the molecule that can be involved in its function.
There are many things to look in the MD trajectories. The most important analysis is which reflects your research and helps you to answer the scientific goal of your MD simulation.
There are many things -
1) Primary analysis - RMSD and RMSF calculations to check the stability of protein
2) Effect of temp if you are interested in thermostability
3) in case of protein structure change do secondary structure analysis to check the change in secondary structure content of your protein of interest over the time
4) even for stability you can do H-bond network analysis
and there are many things to analyze just check the literature for more details and appropriate analysis will give you reasonable answers.
I think in Molecular Dynamic you can do different things and you can obtain a lot of results like RMDS, generate a new structures, the effect of temperature, the effect of the pressure, and ......