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

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          Abstract

          <p id="d8725162e278">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. </p><p class="first" id="d8725162e281">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. </p>

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          Most cited references45

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          Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization.

          Myosin V is a dimeric molecular motor that moves processively on actin, with the center of mass moving approximately 37 nanometers for each adenosine triphosphate hydrolyzed. We have labeled myosin V with a single fluorophore at different positions in the light-chain domain and measured the step size with a standard deviation of <1.5 nanometers, with 0.5-second temporal resolution, and observation times of minutes. The step size alternates between 37 + 2x nm and 37 - 2x, where x is the distance along the direction of motion between the dye and the midpoint between the two heads. These results strongly support a hand-over-hand model of motility, not an inchworm model.
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            Kinesin walks hand-over-hand.

            Kinesin is a processive motor that takes 8.3-nm center-of-mass steps along microtubules for each adenosine triphosphate hydrolyzed. Whether kinesin moves by a "hand-over-hand" or an "inchworm" model has been controversial. We have labeled a single head of the kinesin dimer with a Cy3 fluorophore and localized the position of the dye to within 2 nm before and after a step. We observed that single kinesin heads take steps of 17.3 +/- 3.3 nm. A kinetic analysis of the dwell times between steps shows that the 17-nm steps alternate with 0-nm steps. These results strongly support a hand-over-hand mechanism, and not an inchworm mechanism. In addition, our results suggest that kinesin is bound by both heads to the microtubule while it waits for adenosine triphosphate in between steps.
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              First passage time approach to diffusion controlled reactions

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                Author and article information

                Journal
                Proceedings of the National Academy of Sciences
                Proc Natl Acad Sci USA
                Proceedings of the National Academy of Sciences
                0027-8424
                1091-6490
                September 18 2018
                September 18 2018
                September 18 2018
                May 07 2018
                : 115
                : 38
                : 9391-9396
                Article
                10.1073/pnas.1719539115
                6156619
                29735677
                55b8367d-0a96-4862-a57c-0ed69b33d9fe
                © 2018

                Free to read

                http://www.pnas.org/site/misc/userlicense.xhtml


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