Addressing the Embeddability Problem in Transition Rate Estimation

Abstract

Markov State Models (MSM) and related techniques have gained significant traction as a tool for analyzing and guiding molecular dynamics simulations due to their ability to extract structural, thermodynamic, and kinetic information on proteins using computationally feasible simulations. Here, we revisit the common practice in extracting the thermodynamic and kinetic information from the empirical transition matrix. We propose to build a rate/generator matrix from the empirical transition matrix to provide an alternative approach for estimating both thermodynamic and kinetic quantities. We also discuss a fundamental issue with this approach, known as the embeddability problem and the ways to address this issue. We use a one-dimensional toy model to show the workings of the proposed methods. We also show that the common method of estimating the rates based on the eigendecomposition and our proposed method based on the rate matrix are complementary in that they can potentially provide an upper and a lower limit for transition rates.

Elucidating the Molecular Basis of pH Activation of an Engineered Mechanosensitive Channel

“…The methodology described in Goolsbyet. al., 70 is used to quantify EM and free energy. The calculation of average free energies are done using first 10 T reported at low lag time.…”

“…Following the SMwST simulation, unbiased MD simulations are conducted for ∼2 ns, starting with the last snapshot of each image copy (1000 simulations) of SMwST simulations. Then post SMwST MD trajectories are used to build an empirical transition matrices 70 using a given lag time. Using a novel approach developed by Goolsby et .al., 70 this transition matrices were used to estimate both the free energy profile and the activation rate.…”

“…Then post SMwST MD trajectories are used to build an empirical transition matrices 70 using a given lag time. Using a novel approach developed by Goolsby et .al., 70 this transition matrices were used to estimate both the free energy profile and the activation rate.…”

Artificial intelligence techniques for integrative structural biology of intrinsically disordered proteins

“…Current AI/ML applications (barring a few like [44,39]) tend to use fitting procedures in a blind manner, without much physical bearing, or paying attention to the underlying statistical physics of the system of interest. The resulting fitting procedure can end up overfitting and may not generalize to fully leverage the power of ML/AI in other domains [43,21]. In particular, transferring a ML/AI model learned across simulations can be challenging.…”