Efficient Conditional Path Sampling of Rare Events

Proteins consist of chains of amino acids that fold themselves into specific shapes that determine their effects. An amino acid chain is a large collection of molecules that is constantly pushed about by the water molecules in which it is dissolved. The useful, folded shapes are metastable states - they are states that the protein tends to stay in despite random noise. However, the protein may have other metastable states corresponding to unfolded or partially folded. We would like to understand the ways in which a large protein chain transitions from one metastable state to another.

Simulating these protein chains is a daunting task due to their size and the relevance of molecular noise. It might take many hours of computing time before even a single transition spontaneously occurs, much less many transitions allowing us to understand the distribution of transition types. We would like to sample paths from a conditional distribution of paths, conditioned on starting in one metastable state and ending in another.

We developed an algorithm to draw samples from just such a conditional distribution using Hamiltonian Monte Carlo methods. At present, this is a proof-of-concept that we hope to develop into a usable tool for sampling high-dimensional rare events. This work was developed as part of the Washington Experimental Mathematics Lab, an undergraduate research experience at the University of Washington.

Collaborators:

• Jesse Rivera (University of Washington)
• Landon Shorack (University of Washington)
• Qingtong Zeng (University of Washington)
• Panos Stinis (Pacific Northwest National Laboratory)
• Jayadev Athreya (University of Washington)

Future Projects:

• Generalize the algorithm to higher dimensions
• Improve code efficiency
• Develop visualization and statistical summary tools to understand the resulting paths