This article describes a molecular realization of the classical three-body problem, where the motion of three or more bodies is directed by a set of pairwise forces. Surprisingly, motion of the components of the three-body molecular systems is found to be highly choreographed by differences in strength of intercomponent interactions, promoting a rare inchworm-like loading of molecular rings onto a molecular thread. Our work demonstrates the utility of an integrative approach to design and develop functional molecular machines.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 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.
Biological molecular machines perform the work of supporting life at the smallest of scales, including the work of shuttling ions across cell boundaries and against chemical gradients. Systems of artifi cial channels at the nanoscale can likewise control ionic concentration by way of ionic current rectifi cation, species selectivity, and voltage gating mechanisms. Here, we theoretically show that a voltagegated, ion species-selective, and rectifying ion channel can be built using the components of a biological water channel aquaporin. Through all-atom molecular dynamics simulations, we show that the ionic conductance of a truncated aquaporin channel nonlinearly increases with the bias magnitude, depends on the channel’ s orientation, and is highly cation specific but only for one polarity of the transmembrane bias. Further, we show that such an unusually complex response of the channel to transmembrane bias arises from mechanical motion of a positively charged gate that blocks cation transport. By combining two truncated aquaporins, we demonstrate a molecular system that pumps ions against their chemical gradients when subject to an alternating transmembrane bias. Our work sets the stage for future biomimicry eff orts directed toward reproducing the function of biological ion pumps using synthetic components.
Porous polyoxometalate nanocapsules of Keplerate type are known to exhibit the functionality of biological ion channels; however, their use as an artificial ion channel is tempered by the high negative charge of the capsules, which renders their spontaneous incorporation into a lipid bilayer membrane unlikely. In this Letter we report coarse-grained molecular dynamics simulations that demonstrate a route for embedding negatively charged nanocapsules into lipid bilayer membranes via self-assembly. A homogeneous mixture of water, cationic detergent, and phospholipid was observed to spontaneously self-assemble around the nanocapsule into a layered, liposome-like structure, where the nanocapsule was enveloped by a layer of cationic detergent followed by a layer of phospholipid. Fusion of such a layered liposome with a lipid bilayer membrane was observed to embed the nanocapsule into the lipid bilayer. The resulting assembly was found to remain stable even after the surface of the capsule was exposed to electrolyte. In the latter conformation, water was observed to flow into and out of the capsule as Na(+) cations entered, suggesting that a polyoxometalate nanocapsule can form a functional synthetic ion channel in a lipid bilayer membrane.