weired hmm.stationary_distribution

[yanhuaouyang]

Hi,
I met some problems when I was building MSMs following the pentapeptide tutorial. Firstly I build a MSM and next the MSM is coarse grained into a user-defined number of macrostates (n_sets=4). However, the results are weired as following:

hmm = M.coarse_grain(n_sets)

M.metastable_sets
[array([], dtype=int64),
array([ 0, 2, 3, 5, 6,..]),
array([ 1, 7, 10, 13, 14, ..]),
array([ 4, 11, 33, 36, ...,541])]

set(M.metastable_assignments)
{1, 2, 3}

hmm.stationary_distribution
array([ 0., 0., 0., 1.])

hmm.transition_matrix
array([[ 0.99195984, 0.00633326, 0.0017069 , 0. ],
[ 0.00732714, 0.98938238, 0.00197444, 0.00131605],
[ 0.00150973, 0.00150949, 0.99698078, 0. ],
[ 0. , 0. , 0. , 1. ]])

I am confused that why the MSM has only one macrostate and the other three macrostates have zero stationary_distribution. I changed the n_sets into 2 or 3, the results are the same. Does anyone know the problem?

[marscher]

Your system is non-reversible and one state absorbs all of the probability in the long term. Eg. you did not observe any transition escaping from that state.

[yanhuaouyang]

Thanks for your answer @marscher !
But I wonder that is it possible that the unreasonable MSMs parameters or the peptide sequence length lead to the system non-reversible? Because such non-reversible problem arise when I build MSMs on the middle segment of my peptide but not on the full length peptide.