  Markov state models represent a popular means to interpret molecular dynamics
trajectories in terms of memoryless transitions between metastable
conformational states. To provide a mechanistic understanding of the considered
biomolecular process, these states should reflect structurally distinct
conformations and ensure a timescale separation between fast intrastate and
slow interstate dynamics. Adopting the folding of villin headpiece (HP35) as a
well-established model problem, here we discuss the selection of suitable input
coordinates or `features', such as backbone dihedral angles and interresidue
distances. We show that dihedral angles account accurately for the structure of
the native energy basin of HP35, while the unfolded region of the free energy
landscape and the folding process are best described by tertiary contacts of
the protein. To construct a contact-based model, we consider various ways to
define and select contact distances, and introduce a low-pass filtering of the
feature trajectory as well as a correlation-based characterization of states.
Relying on input data that faithfully account for the mechanistic origin of the
studied process, the states of the resulting Markov model are clearly
discriminated by the features, describe consistently the hierarchical structure
of the free energy landscape, and$\unicode{0x2014}$as a
consequence$\unicode{0x2014}$correctly reproduce the slow timescales of the
process.
