Markovian milestoning with Voronoi tessellations

Area of Science:

• Computational Chemistry
• Biophysics
• Statistical Mechanics

Background:

• Traditional milestoning methods approximate trajectory reinitialization distributions.
• Efficient computation of kinetic properties from molecular dynamics (MD) simulations is crucial.
• Understanding protein-lipid interactions requires accurate kinetic modeling.

Purpose of the Study:

• To introduce a new milestoning procedure utilizing Voronoi tessellations.
• To overcome limitations of traditional milestoning, specifically the reinitialization approximation.
• To provide a robust framework for calculating transition rates and kinetic properties.

Main Methods:

• Employing Voronoi cell edges as milestones in MD simulations.
• Restricting MD simulations within Voronoi cells to gather kinetic information.
• Estimating the transition rate matrix from MD trajectory data within cells.
• Validating Markovian milestoning under specific assumptions.

Main Results:

• The proposed method avoids approximations associated with reinitializing trajectories from milestones.
• Successfully computes kinetic information and transition rates between milestones.
• Demonstrates accuracy on 2D test cases.
• Applies the method to model protein insertion kinetics into lipid bilayers.

Conclusions:

• The Voronoi tessellation-based milestoning offers a more accurate and efficient approach to studying molecular dynamics.
• This method provides a reduced description of dynamics, enabling efficient computation of key kinetic quantities.
• The technique is applicable to complex biological processes, such as protein-membrane interactions.