[gmx-users] cosine content

jean-francois.gibrat jean-francois.gibrat at jouy.inra.fr
Sat Feb 11 13:18:10 CET 2006

Hi Gromacs users,

I carried out a 10 ns molecular dynamics simulation of a PrP mutant. To analyze the resulting 
trajectory I used principal component analysis. I divided the trajectory into overlapping intervals: 
the first 1 ns, the first 2 ns, the first 4 ns, the first 8 ns and the complete 10 ns trajectory and 
I computed the cosine content of the first principal components (pc) for each case.
I obtained the following results for the first 2 principal components:
1 ns trajectory: pc1=0.2 and pc2=0.1
2 ns trajectory: pc1=0.6 and pc2=0.6
4 ns trajectory: pc1=0.2 and pc2=0.3
8 ns trajectory: pc1=0.8 and pc2=0.7
10ns trajectory: pc1=0.7 and pc2=0.8

*If* one can trust the cosine content computation these results could be interpreted as follows:
during the first ns the protein has sufficient time to completely explore a local minimum basin (low 
values of pcs), then between 1 and 2 ns the protein overcomes an energy barrier and jumps to a new 
minimum basin. After 4 ns this basin has been completely explored by the protein (low values of 
pcs). Then between 4 ns and 8 ns the protein once again jumps into a new minimum well that it is 
still exploring even after 10 ns simulation (hight values of pcs).

However, looking at Berk Hess's paper in Phys. rev. E (2002), I noticed that the error bars on the 
computed values of the cosine content are huge (eg, in Fig. 8, for 1 ns trajectories of the HPr 
protein 90% of the values can be found between 0.1 and 0.8).

Therefore my question is: should I forget about the above interpretation of the cosine content on 
the ground that one cannot trust its computed value?

Another related question, more specifically addressed to B. Hess. In the same paper B. Hess states 
"When the cosine content is close to 1, one can be sure that the simulation is not converged".
Given the error bars, why should one trust a value of 1 more than any other value?



Jean-Francois Gibrat                    Tel: +33 (1) 34 65 28 97
Mathematique Informatique et Genome,    Fax: +33 (1) 34 65 29 01
Institut National de la Recherche       Email: jean-francois.gibrat at jouy.inra.fr
Agronomique, Domaine de Vilvert,        http://www-mig.jouy.inra.fr
78352, Jouy-en-Josas cedex, France


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