Inchworm movement of two rings switching onto a thread by biased Brownian diffusion represent a three-body problem

Abstract

The coordinated motion of many individual components underpins the operation of all machines. However, despite generations of experience in engineering, understanding the motion of three or more coupled components remains a challenge, known since the time of Newton as the "three-body problem." Here, we describe, quantify, and simulate a molecular three-body problem of threading two molecular rings onto a linear molecular thread. Specifically, we use voltage-triggered reduction of a tetrazine-based thread to capture two cyanostar macrocycles and form a [3]pseudorotaxane product. As a consequence of the noncovalent coupling between the cyanostar rings, we find the threading occurs by an unexpected and rare inchworm-like motion where one ring follows the other. The mechanism was derived from controls, analysis of cyclic voltammetry (CV) traces, and Brownian dynamics simulations. CVs from two noncovalently interacting rings match that of two covalently linked rings designed to thread via the inchworm pathway, and they deviate considerably from the CV of a macrocycle designed to thread via a stepwise pathway. Time-dependent electrochemistry provides estimates of rate constants for threading. Experimentally derived parameters (energy wells, barriers, diffusion coefficients) helped determine likely pathways of motion with rate-kinetics and Brownian dynamics simulations. Simulations verified intercomponent coupling could be separated into ring-thread interactions for kinetics, and ring-ring interactions for thermodynamics to reduce the three-body problem to a two-body one. Our findings provide a basis for high-throughput design of molecular machinery with multiple components undergoing coupled motion.

Quantifying the barrier for the movement of cyclobis(paraquat-p-phenylene) over the dication of monopyrrolotetrathiafulvalene

“…21 These designs often rely on controlling 15,22–24 the mechanisms of stimuli-driven motion, and thus motivate studies of kinetics 25–29 and the underlying energy landscapes. 30,31 We do this here by measuring the impact of double oxidation on the barrier to the motion of a mobile ring (Scheme 1).…”

Individual‐Molecule Perspective Analysis of Chemical Reaction Networks: The Case of a Light‐Driven Supramolecular Pump

“…Such anew component, selected from the environment, then becomes an integral part of the whole system and must be included in the description of its dynamics.I nt his work we face such al evel of complexity which, to the best of our knowledge,h as not been considered yet. Indeed, the high significance of non-equilibrium self-assembly in natural [1][2][3] and synthetic [25] systems , and in the rapidly growing area of artificial molecular motors, [4,5,19,20] calls for the development of new tools that can enable ad eeper mechanistic understanding of these phenomena and, eventually,assist scientists in designing novel devices.…”

Individual‐Molecule Perspective Analysis of Chemical Reaction Networks: The Case of a Light‐Driven Supramolecular Pump

“…In this work we face such a level of complexity which, to the best of our knowledge, has not been considered yet. Indeed, the high significance of non‐equilibrium self‐assembly in natural and synthetic systems , and in the rapidly growing area of artificial molecular motors, calls for the development of new tools that can enable a deeper mechanistic understanding of these phenomena and, eventually, assist scientists in designing novel devices.…”