Controlling kinetics within rugged energy landscapes using path reweighing and automatic differentiation

Biological molecular machines driven by ATP or other energy sources reliably undergo complex nanoscale dynamics in order to do work and perform tasks. While it is now possible to engineer complex nanostructures out of synthetic building blocks, we lack the ability to endow them with machine-like functionality in part because we do not have reliable tools to control their kinetics and therefore cannot directly tune their performance. In order to take full advantage of our engineering capabilities we need tools that let us connect the particle level design attributes to the dynamic target behavior of the assembled system.

I will show how to combine path reweighing, a tool for recovering the correct properties from a modified potential energy surface without having to re-simulate the model and automatic differentiation, a set of tools to compute derivatives of programs, in order to compute gradients of dynamical observables like transition rates without having to store and differentiate through the simulation trajectory. This makes it possible to formulate the task of achieving some desired functionality as the solution to an optimization problem, which can then be solved using gradient based optimizers.

I will go on to show, using a toy model, how this framework can be used to optimize the dynamics of a particle moving on a simple two dimensional rugged energy landscape with multiple meta-stable target states, thus shaping the landscape to target one or multiple target states with prescribed probabilities.