Note: MSM lag time cannot be used for variational model selection

Area of Science:

• Computational chemistry
• Statistical mechanics
• Biophysics

Background:

• The variational principle is a key method for constructing Markov state models (MSMs) in conformational dynamics.
• MSMs are essential for understanding molecular processes by analyzing transition pathways.
• Hyperparameter optimization is crucial for accurate MSM construction.

Purpose of the Study:

• To elucidate the necessity of a constant lag time in the variational approach for approximating the transfer operator.
• To provide a theoretical basis for the correct application of the variational principle in MSM construction.

Main Methods:

• Theoretical analysis of the variational principle for conformational dynamics.
• Examination of the transfer operator approximation within the variational framework.
• Discussion on the role of lag time in the optimization process.

Main Results:

• The lag time used for approximating the transfer operator must be invariant within the variational approach.
• Deviations from a constant lag time can lead to inaccuracies in the resulting Markov state models.

Conclusions:

• Maintaining a constant lag time is a critical requirement for the valid application of the variational principle.
• This finding ensures the reliability of Markov state models derived using this method for studying molecular dynamics.