TY - JOUR
T1 - Inchworm movement of two rings switching onto a thread by biased Brownian diffusion represent a three-body problem
AU - Benson, Christopher R.
AU - Maffeo, Christopher
AU - Fatila, Elisabeth M.
AU - Liu, Yun
AU - Sheetz, Edward G.
AU - Aksimentiev, Aleksei
AU - Singharoy, Abhishek
AU - Flood, Amar H.
N1 - Funding Information:
C.R.B., E.M.F., Y.L., E.G.S., and A.H.F. acknowledge support from the NSF Grant (CHE 1709909). C.M., A.A., and A.S. acknowledge support from the NIH Center for Macromolecular Modeling and Bioinformatics Grant (P41-GM104601) and the National Science Foundation (NSF) Center for the Physics of Living Cells Grant (PHY-1430124). A.S. acknowledges startup award funds from Arizona State University, NSF Grant (MCB1616590), and NIH Grant (R01-GM067887-11). This research used resources of the Oak Ridge Leadership Computing Facility, which is supported by the Office of Science, US Department of Energy (DE-AC05-00OR22725).
Funding Information:
ACKNOWLEDGMENTS. C.R.B., E.M.F., Y.L., E.G.S., and A.H.F. acknowledge support from the NSF Grant (CHE 1709909). C.M., A.A., and A.S. acknowledge support from the NIH Center for Macromolecular Modeling and Bioinformatics Grant (P41-GM104601) and the National Science Foundation (NSF) Center for the Physics of Living Cells Grant (PHY-1430124). A.S. acknowledges startup award funds from Arizona State University, NSF Grant (MCB1616590), and NIH Grant (R01-GM067887-11). This research used resources of the Oak Ridge Leadership Computing Facility, which is supported by the Office of Science, US Department of Energy (DE-AC05-00OR22725).
Publisher Copyright:
© 2018 National Academy of Sciences. All rights reserved.
PY - 2018/9/18
Y1 - 2018/9/18
N2 - 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.
AB - 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.
KW - Brownian dynamics
KW - Kinetic modeling
KW - Macrocycles
KW - Molecular machines
KW - Switching
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U2 - 10.1073/pnas.1719539115
DO - 10.1073/pnas.1719539115
M3 - Article
C2 - 29735677
AN - SCOPUS:85053498763
SN - 0027-8424
VL - 115
SP - 9391
EP - 9396
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 38
ER -