Complex Movements in Rotaxanes: Shuttling Coupled with

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Complex Movements in Rotaxanes — Shuttling Coupled with Conformational Transition of Cyclodextrins Shuangshuang Wang, Tanfeng Zhao, Xueguang Shao, Christophe Chipot, and Wensheng Cai J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b06948 • Publication Date (Web): 03 Aug 2016 Downloaded from http://pubs.acs.org on August 8, 2016

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The Journal of Physical Chemistry

Complex Movements in Rotaxanes — Shuttling Coupled with Conformational Transition of Cyclodextrins Shuangshuang Wang,a Tanfeng Zhao,a Xueguang Shao,a,b,c,d Christophe Chipot,e,f,g and Wensheng Cai*,a,b,d

a

Research Center for Analytical Sciences, College of Chemistry, Nankai University, Tianjin, 300071,

China

b

Tianjin Key Laboratory of Biosensing and Molecular Recognition, Tianjin, 300071, China

c

State Key Laboratory of Medicinal Chemical Biology, Tianjin, 300071, China

d

Collaborative Innovation Center of Chemical Science and Engineering, Tianjin, 300071, China

e

Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at

Urbana−Champaign, Unité Mixte de Recherche No. 7565, Université de Lorraine, B.P. 70239, 54506 Vandoeuvre−lès−Nancy cedex, France

f

Theoretical and Computational Biophysics Group, Beckman Institute, University of Illinois at

Urbana−Champaign, Urbana, Illinois 61801, United States

g

Department of Physics, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United

States

1

ACS Paragon Plus Environment


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ABSTRACT In cyclodextrin(CD)-based rotaxanes, the shuttling rate of the macrocycle along the thread is crucial to characterize their function as molecular machines. In general, the composition of the thread and the environment are considered to be important factors affecting the nature of the movement. Yet, the role of ancillary motions on the shuttling rate remains unclear. In the present contribution, two rotaxanes having the same components, yet significantly different shuttling rates between two stable states in an aqueous environment, have been investigated at the atomic level using numerical simulations. These two rotaxanes consist of an axle with two stations linked by a 2-methylpyridinium group and an α-CD sliding on the axle and assuming two different orientations. We found that a number of cyclodextrin glucopyranose units (GLUs) isomerized during shuttling, which we anticipate to affect the shuttling rate. The two-dimensional free-energy landscapes characterizing the isomerization of the GLUs and the shuttling along the thread were mapped, and revealed that the energetic barriers hampering spontaneous transition between the two stations significantly differ for the two rotaxanes. Structural analysis shows that this difference mainly arises from steric hindrances caused by the methyl substituent of the pyridinium group, which leads to different number of the GLUs experiencing conformational change during shuttling. Moreover, the thermodynamic stability of the complex is found to be distinct between the two rotaxanes. This discrepancy may be ascribed to the dipole moment of the complex, which is sensitive to the orientation of CD. It can be concluded that shuttling in the rotaxanes is not only highly coupled with isomerization of GLUs, but it is also affected by thermodynamic stability, resulting in a shuttling rate sensitive to the orientation of the CD. The present results help understand the complex molecular motion in CD-based molecular shuttles, and are expected to serve in the design of molecular filters for selectively screening molecules with a specific orientation. 2


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INTRODUCTION Much

attention

has

been

directed

in

recent

years

to

the

potential

applications

of

mechanically-interlocked molecules, notably as nanoscale devices.1-5 Rotaxanes, which are composed of a linear molecular axle flanked with stoppers at both termini and a macrocycle threaded onto it, are a paradigm of such interlocked molecules. A characteristic feature of rotaxanes is that the macrocycles can shuttle between two or more stations along the axle, which makes them being key materials for the construction of molecular shuttles and motors. Many types of macrocyclic molecules are available for the ring components of rotaxanes, e.g., crown ethers,6,7 cucurbiturils,8 pillararenes9-11 and cyclodextrins (CDs).12 CDs are commonly-used macrocyclic molecules in rotaxanes — they are cyclic oligomers of α-D-glucopyranose units bearing a well-defined, non-symmetric ring structure and hydrophobic cavities combined with their hydrophilic hydroxyl rims.13-15 Because of their intrinsic flexibility, CDs can undergo guest-induced conformational changes upon inclusion of guest molecules. Over the past decades, a lot of CD-based rotaxanes have been constructed, synthesized and studied.16-19 Most of current experimental and theoretical research focuses on the shuttling of CD in these rotaxanes, usually disregarding other movements, like the conformational transition of the glucopyranose units (GLU) during shuttling. Such isomerization often modifies the speed of the ring as it moves relative to the thread. Among CD-based rotaxanes, two similar molecular architectures composed of the same dumbbell-shaped thread formed by two decamethylenes as stations and three pyridiniums units with methyl branches as the linker or stoppers and a threaded α-CD16 (rotaxane 1A and 1B in Scheme 1) have attracted our attention. The only difference between these two rotaxanes is the orientation of the CD — they, therefore, correspond to two distinct isomers. Interestingly enough, it was observed experimentally that the shuttling 3



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speeds of the α-CD between the two stations are significantly different — the rate constant of S21 (defined in Scheme 1) is not only lower than that of S22, but it is also much lower than that of S11. These results suggest that translocation of the α-CD is sensitive to its orientation and is kinetically controlled by the linker, i.e., the 2-methylpyridinium group (MPY).

Scheme 1. Structures of the rotaxanes. Translocation of the CD between the two stations in rotaxane 1A are denoted as S11 (from station 1 to station 2) and S12 (from station 2 to station 1), and accordingly, S21 and S22 in rotaxane 1B. Two model rotaxanes, 2A and 2B, are constructed for the purpose of investigating the role played by the methyl substituent on the central pyridinium unit by comparing with 1A and 1B.

It would appear that the methyl substituent on the MPY gives rise to steric hindrances for the shuttling 4


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in rotaxane 1A and 1B. However, the answer to the following questions still remains unclear. Why can such steric hindrances lead to different shuttling rates of the α-CD in the two rotaxanes? Why are forward and backward translocations, even in the same rotaxane, so different? Is shuttling entangled with other movements of different nature, e.g., the conformational transition of the GLUs of the α-CD? If the latter conformational transition does, indeed, exist, how can this motion affect the kinetics of shuttling? Last, is the thermodynamic stability of the rotaxanes at different metastabilities sensitive to the orientation of the α-CD? To answer these questions cogently, the two rotaxanes, namely rotaxane 1A and 1B, were investigated by all-atom molecular dynamics (MD) simulations combined with microsecond-timescale free-energy calculations. The two-dimensional free-energy landscapes characterizing the shuttling in the rotaxanes coupled with the isomerization of the GLUs in the macrocycle were determined, and the least free energy pathways20 were identified. The factors at play contributing to the free-energy barriers, such as the orientation difference of the α-CD and the isomerization of the GLUs, were analyzed to shed new light onto the discrepant shuttling rate constants for the CD in the rotaxanes. Following the free-energy pathways, the most likely conformational transition of the α-CD during shuttling was inferred. The present contribution not only explains the atomic-level mechanism responsible for the orientation-selective shuttling of the CD in the rotaxanes, but also lays the groundwork for designing molecular filters used for discriminating between molecules with a specific orientation.

SIMULATION DETAILS

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Molecular Models. Scheme 1 shows the structures of rotaxanes 1A and 1B. In order to assess the effect of the methyl substituent on shuttling, two similar model rotaxanes, namely 2A and 2B, were built, wherein the methyl branch on the pyridinium linker was removed. The initial coordinates of the α-CD were extracted from the available three-dimensional crystal structure.21 The four molecular assemblies were constructed and energy-minimized, and then immersed independently in a periodic box of water using the Solvate module of the visualization program VMD,22 with a headspace of at least 20 Å from each edge of the box to any atom of the complexes. During the MD simulations, the backbone of the rotaxane was softly restrained to its extended conformation to avoid spurious folding of the alkyl chains. Three chloride ions were placed in the solvent boxes, 15 Å away from the rotaxanes, to ensure electric neutrality. A soft harmonic potential was used to restrain the position of the counter-ions. For each solvated system, a 20-ns equilibrium MD simulation was performed prior to the free-energy calculations. Molecular Dynamics Simulations. All the atomistic MD simulations described here were performed using the parallel, scalable MD program NAMD,23 with the CHARMM36 carbohydrate force field,24,25 the CHARMM general force field (CGenFF)26 and the TIP3P water model.27 Langevin dynamics was used to control the temperature at 343 K and the Langevin piston method was applied to maintain the pressure at 1 atm.28 Covalent bonds involving hydrogen atoms were constrained to their equilibrium length employing the SHAKE/RATTLE algorithms,29,30 except for water, for which the SETTLE algorithm was applied.29 The r-RESPA multiple time step algorithm31 was employed to integrate the equations of motion with a time step of 2 and 4 fs for short- and long-range interactions, respectively. Short-range van der Waals and electrostatic interactions were calculated using a smoothed 12.0 Å spherical cutoff. Long-range

6


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electrostatic forces were evaluated by means of the Particle Mesh Ewald method.32 Visualization and analysis of the MD trajectories were performed with the VMD program. Free-Energy Calculations. The two-dimensional free-energy landscapes characterizing shuttling in rotaxanes 1A and 1B were generated using the multiple-walker adaptive biasing force (MW-ABF) algorithm,33,34 an improved, importance-sampling approach aimed at achieving ergodic sampling on the basis of the ABF algorithm,35-39 implemented within the collective variables module (Colvar)40 of NAMD. No isomerization of the GLUs of the α-CD was observed in rotaxane 2A and 2B. For this reason, only one-dimensional free-energy calculations were performed to characterize the shuttling processes. The model reaction coordinate, either one- or two-dimensional, was formed by collective variables ξ and ϕ, respectively, the distance separating the centroid of the glycosidic oxygen atoms of the α-CD and that of the left pyridine group, and the dihedral angle C4-C5-O5-C1 in a GLU to describe the conformational change of this sugar unit (see Scheme 1 and 2). A detailed discussion on the choice of the collective variable ϕ can be found in the Supporting Information. The transition pathway being explored spanned -70º ≤ ϕ ≤ 70º, and 6 Å ≤ ξ ≤ 26 Å. Instantaneous values of the force were accrued in bins 5º and 0.1 Å wide. The variation of the free energy, ∆G(ξ), was determined by integrating the average force acting on ξ. The variation of the free energy, ∆G(ξ,ϕ), was determined by integrating the average force acting concomitantly on ξ and ϕ. All the MW-ABF simulations were carried out in water at 343 K. The simulation time was extended incrementally to probe the convergence of the free energy in those regions featuring a barrier, leading to a total simulation time amounting to 1.30, 1.09, 0.56, and 0.48 µs for rotaxane 1A, 1B, 2A, and 2B, respectively. The least free-energy pathways connecting the minima of the two-dimensional free-energy landscapes were identified using the LFEP algorithm.2 0 The free-energy 7



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profiles of the rotaxanes as a function of the position (s) along the least free energy pathways were generated using the method described by Branduardi et al.4 1

4

2

C1:

1

SO:

C4:

Scheme 2. Schematic representation of the GLU in the 4C1, 2SO and 1C4 conformations. The stability of these three isomers is ranked as 4C1 > 1C4 > 2SO. Dihedral angle ϕ : C4-C5-O5-C1, 4C1: ϕ = +60°, 2SO: ϕ = 0°, 1C4: ϕ = −60°.

RESULTS AND DISCUSSION Free-Energy Profiles. We will show that collective variable ξ is not sufficient to describe the shuttling process. The one-dimension free-energy profiles for rotaxanes 1A and 1B featuring the translational movement of the α-CD along the thread were determined (see Figure S2 in the Supporting Information). The two resulting free-energy barriers, however, appear to be almost identical, which is in blatant disagreement with the experimental measurements. This disagreement suggests that shuttling is necessarily entangled with other movements of different nature. Analysis of the MD trajectories shows that some GLUs in the α-CD isomerized during shuttling due to steric hindrance of the methyl substituent on the MPY. This result implies that there are hidden barriers in the space orthogonal to the transition coordinate, resulting in quasi non-ergodic sampling, and, consequently, in a poor estimation of the underlying free energy. In order to improve the ergodicity of the sampling, additional collective variables ought to be introduced to characterize the process controlling the conformational change of the α-CD.

8


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Figure 1. Free-energy landscapes characterizing the shuttling of rotaxane 1A (a) and 1B (b). The black lines depict the least free-energy pathways. Free-energy profiles for rotaxane 1A (c) and 1B (d) as a function of the position (s) along the least free-energy pathways.

The two-dimensional free-energy landscapes, characterizing the shuttling motion and isomerization of the α-CD along ξ and a dihedral angle C4-C5-O5-C1 of the GLU, ϕ (see Scheme 1), are depicted in Figure 1a and 1b for rotaxanes 1A and 1B, respectively. Each map features two basins separated by one ridge. In addition, the least free-energy pathways from one minimum (ξ = 6, ϕ = 55°) to the other (ξ = 26, ϕ = 55°) were determined using the LFEP algorithm.20 In each path, the two regions, namely, 6 ≤ ξ ≤ 13 Å and 21 ≤ ξ ≤ 26 Å, correspond to the global minimum of the free-energy landscapes, i.e. stable states, where ϕ is

9



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about 55°. The transition region spanning 13 ≤ ξ ≤ 21 Å reflects the isomerization of GLU. As shuttling proceeds, dihedral angle ϕ rapidly decays from 55° to 0° to -55°, before swiftly returning to 55°, which illuminates that the conformation of GLU undergoes a transition from 4C1 to 1C4 through 2SO, and then goes back to 4C1, i.e. 4C1 ⇌ 2SO ⇌ 1C4 ⇌ 2SO ⇌ 4C1 (see Scheme 2). The free-energy change for rotaxanes 1A and 1B along the least free-energy pathways as a function of the position (s) is reported in Figure 1c and 1d, respectively. s is the order parameter of the pathway. s = 0.0 and s = 1.0 correspond to the locations ξ = 6, ϕ = 55° and ξ = 26, ϕ = 55° on the pathway, respectively. The two profiles possess a similar shape, but different barriers. ∆G‡ represents the free-energy barrier between the linker and the station. For rotaxane 1A, ∆G‡ of S11 (18.3 kcal/mol) approximates to ∆G‡ of S12 (18.2 kcal/mol), while for rotaxane 1B, ∆G‡ of S21 (24.8 kcal/mol) is higher than ∆G‡ of S21 (20.6 kcal/mol). Although the shuttling velocities estimated from the Eyring equation4 2 on the basis of the estimate of ∆G‡ are slightly different from those determined experimentally,16 the overall trend inferred from the free-energy calculations agrees well with the experimental results. The pronounced difference in ∆G‡ between processes S11 and S21 rationalizes the experimental observation that the former (characterized by a rate constant of k = 1.7×10-5 s-1) is much faster than the latter (k = 5.0×10-7 s-1). The Effect of the Methyl Branch on the Linker to the Free-Energy Barriers. It is reasonable to deduce that steric hindrances caused by the methyl branch on the MPY constitute the main contribution to the free-energy barriers in the four processes S11, S12, S21, and S22. Does it mean that the methyl branch is the cause of the difference in the barriers for S11 and S21, and that for S21 and S22? To investigate its effect on the free-energy barriers, the free-energy profiles featuring the shuttling of the α-CD in rotaxanes 2A and 2B were determined, as shown in Figure 2. Compared to Figure 1, the free-energy barriers significantly 10


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decrease, and the difference between the barriers for the forward translocations (S11 and S21) decreases from 6.5 to 3.2 kcal/mol, indicating that the methyl branch on the linker amplifies the difference in the free-energy barriers between the same rotaxanes, yet with different orientations of their threaded α-CD. Quite unexpectedly, the difference in the barriers between the forward and backward translocations highlighted in Figure 2b persists and appears to be identical to that in Figure 1d, suggesting that the asymmetric free-energy barriers in rotaxane 1B do not arise from methyl substitution on the MPY.

Figure 2. One-dimensional free-energy profiles of rotaxanes 2A (a) and 2B (b) characterizing shuttling along ξ.

To delve deeper into the structural origin of the difference in the sterical hindrances entailed by the methyl branch in the shuttling of the CD in its two orientations, the conformational deformation of the six GLUs was analyzed during shuttling in rotaxanes 1A and 1B. Cremer and Pople43 have defined a spherical-coordinate system for describing the puckering conformation of general monocyclic rings, allowing their conformations to be mapped on a sphere. This method can describe the critical 11



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conformations of the GLU more accurately than the dihedral angle, φ, defined above possibly would. Here, we used the set of spherical coordinates (Q, θ, φ) to analyze the conformations of the GLUs extracted from the ABF trajectories. The distribution of the puckering conformations of each GLU in the region corresponding to the free-energy minima and maximum along the least free-energy pathway on the Cremer−Pople sphere was determined and is provided in the supporting information (see Figure S3 in the Supporting Information). This distribution shows that most of the GLUs undergo interconversion between three conformations, namely 4C1, 2SO and 1C4. In order to display the overall conformational changes of all GLUs during shuttling, the evolution of one of the spherical coordinates, θ, was monitored as a function of ξ for each GLU, as depicted in Figure 3. At the free-energy barrier (i) in rotaxane 1A, four GLUs in the 4C1 conformation isomerized to two 2SO and two 1C4 conformations, and (ii) in rotaxane 1B, five GLUs in the 4C1 conformation interconverted to four 2

SO and one 1C4 conformations. It is apparent that when the α-CD passes through the MPY with different

orientations, the methyl group borne by the latter induces various degrees of conformation isomerization of the former. This result partly rationalizes the barrier of rotaxane 1B being higher than that of rotaxane 1A. It should be noted that although the Cremer-Pople spherical coordinates can describe the puckering conformations of a GLU with appropriate accuracy, they cannot be selected as collective variables in the Colvars module of the current version of NAMD 2.11 for practical algorithmic reasons.

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Figure 3. Conformational change of the six GLUs of α-CD in rotaxanes 1A (a) and 1B (b) along ξ. 4C1: θ = 0°, 2SO: θ = 90°, 1C4: θ = 180°.

Effect of the Orientation of α-CD on the Thermodynamic Stability of the Rotaxanes. From the PMFs of rotaxane 1A in Figure 1c, it can be observed that the stability of the complex at the two thermodynamically favored states, wherein the CD resides at station 1 (state 1) and station 2 (state 2), is nearly identical, which is also mirrored in Figure 2a. Conversely, for rotaxane 1B, the complex at state 1 is more stable than that at state 2, whether the methyl group on the linker exists or not (see Figure 1d and 2b). It follows that the orientation of the α-CD affects the relative stability of the two thermodynamically favored states of the complex, which may be rooted in the polarity of the complexes. On the basis of the point charges utilized in the present work, the dipole moments for the four optimized structures, corresponding to rotaxane 1A at state 1 and 2, and rotaxane 1B at state 1 and 2, were computed and are equal to 711.8, 704.8, 882.4 and 726.2 D, respectively. It is manifest that inasmuch as their dipole moment is concerned, there is no obvious difference between the two states of rotaxane 1A, whereas for rotaxane

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1B, the polarity of the complex at state 1 is appreciably greater due to the alignment of the dipole moment of the α-CD. It should be mentioned that in an aqueous solution, the larger dipole moment will lead to the more favorable electrostatic interaction of the complex with the solvent.44 Therefore, the configuration of rotaxane 1B with the α-CD located at station 1 is expected to be energetically favored, leading to an increase of the free-energy barrier for translocation of the α-CD from station 1 to station 2, compared to the backward process, i.e., from station 2 to station 1. Put together, the steric hindrances induced by the methyl branch on the MPY and the energetically favored station for the α-CD result in an increase of the free-energy barriers for the translocation from station 1 to station 2 in rotaxane 1B. This pronounced free-energy barrier leads to a shuttling rate significantly different between rotaxane 1A and 1B. In other words, shuttling is sensitive to the orientation of the CD. Multifaceted Motion in the Rotaxanes. To delve further into the analysis of the conformation of the α-CD during shuttling, we will now discuss the three other movements coupled to the translocation in rotaxane 1. Isomerization of the Sugar Units of the α-CD during Shuttling. The representative structures corresponding to the inflection points in Figure 1c and 1d are shown in Figure 4. For rotaxane 1A, as the α-CD approaches the MPY, one GLU first isomerizes from 4C1 to 2SO, leading to an increase of the free energy to a local maximum at point I in Figure 1c. As the α-CD moves further, more GLUs isomerize gradually. When the free energy reaches the maximum at point II in Figure 1c, four GLUs undergo isomerization and the cavity of the α-CD deforms significantly to match the MPY. Here, the methyl branch of the MPY is located at the secondary side of the α-CD, while the flat pyridinium ring is encapsulated 14


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near its primary side. As the pyridinium ring moves out of the cavity, leaving the methyl branch at the primary rim, most of the isomerized GLUs revert rapidly to the 4C1 conformation (see Figure 4d), resulting in the local maximum at point III in Figure 1c. Finally, when the α-CD resides at station 2, all the GLUs return to the 4C1 conformation. For rotaxane 1B, the shuttling process resembles that of rotaxane 1A. The only difference lies in that five GLUs experience isomerization at the maximum of the free-energy profile (see Figure 4h). At this point, the methyl branch of the MPY resides in the primary side of the α-CD, while the flat pyridinium ring is located at its secondary rim.

Figure 4. Snapshots of rotaxane 1A (panels a to e) and rotaxane 1B (panels f to j) at the inflection points

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along the free- energy profiles of Figure 1c and 1d. Panels a to e correspond to the structures at ξ = 7.0, 14.3, 17.3, 20.2 and 23.5 Å in Figure 1c, respectively. Panels f to j correspond to the structures at ξ = 6.6, 13.2, 16.5, 19.8 and 24.3 Å in Figure 1d, respectively. On the right side of each panel, a snapshot of the α-CD in inserted, wherein the isomerized GLUs are marked with tan color.

Tilt of the Macrocycle. From Figure 4c, the tilt of the macrocycle with respect to the axle can be observed as the α-CD passes through the MPY. This movement was monitored in the course of the translocation by measuring the tilt angle between the axle and the plane formed by the six glucosidic oxygen atoms of the α-CD, as depicted in Figure 5a. The curves possess a valley spanning 14 ≤ ξ ≤ 19 Å, where the MPY is encapsulated within the α-CD cavity, which indicates that upon surmounting the MPY moiety, the α-CD not only changes its conformation, but also adjusts its tilt to a suitable direction to match this large steric group, MPY. Furthermore, it can be seen that the degree of inclination of the α-CD is higher in rotaxane 1B than in rotaxane 1A in the range of 14 ≤ ξ ≤ 19 Å.

Figure 5. Fluctuation along the model reaction coordinate ξ of (a) the tilt angle between the axle and the

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plane formed by the six glucosidic oxygen atoms of the α-CD, and (b) the longest distances separating the center of mass of two opposite GLUs in the α-CD.

Deformation of the Macrocycle. In Figure 4c and 4h, deformation of the α-CD is shown to result from the isomerization of the GLUs. To monitor the degree of deformation of the macrocycle in the course of shuttling, the longest distance separating the center of mass of two opposite GLUs in the α-CD was measured (Figure 5b). In an ideal α-CD, this distance is about 10.85 Å, but its maximal value reaches to 10.99 Å and 11.18 Å for rotaxane 1A and rotaxane 1B, respectively. These larger separations imply that the macrocycle experiences greater deformation in rotaxane 1B than in rotaxane 1A. Put together, shuttling of the CD in rotaxane 1A and 1B is accompanied with the isomerization of the GLUs, as well as a tilt and deformation of the macrocycle. The latter three motions are engendered by steric hindrances. Moreover, the difference in the steric hindrances between rotaxanes 1A and 1B originates from the asymmetry of the α-CD. Therefore, the shuttling rate of the α-CD varies with its orientation.

CONCLUSION In this contribution, the shuttling in two rotaxanes has been investigated by means of one- and two-dimensional free-energy calculations. The two rotaxanes are isomers, differing only in the orientation of the α-CD. Comparing the one- and the two-dimensional results, shuttling is found to be highly coupled with the conformational transition of the GLUs in the α-CD. The two-dimensional free-energy landscapes underlying the concomitant shuttling and isomerization processes reveal that the free-energy barriers hampering the α-CD from moving from station 1 to station 2 significantly differ, in line with the

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experimental rate constants for translation. This prominent difference can be mainly ascribed to the contribution of steric hindrances, which are sensitive to the orientation of the α-CD and the difference in the stability of the complexes corresponding to different thermodynamically favored states. The steric hindrances arising from the bulky MPY induce the conformational change of GLUs in the α-CD, and the degree of isomerization of the latter in rotaxane 1B is higher than that in rotaxane 1A. The structure of rotaxane 1B corresponding to the state wherein the α-CD resides at station 1 is found to be more stable compared to another metastability (α-CD at station 2), owing to its larger dipole moment in aqueous solution. Steric hindrances caused by the methyl substituent of the linker give rise to a difference in the free-energy barriers for the shuttling in the two rotaxanes. Furthermore, the free-energy difference is magnified by the relative thermodynamic stability of the complex at the two states. Consequently, the shuttling rate of α-CD is much faster in the orientation where the secondary rim faces station 1 than that with an opposite orientation. The present results provide a complete understanding of the orientation-selective shuttling in the CD-based rotaxanes, which is crucial for rational design of new molecular machines, notably for the design of molecular filters based on rotaxanes that can screen molecules with a specific orientation and allow ones with the opposite orientation to pass through. Such molecular filters can be designed via introducing a steric group sensitive to the orientation of the target molecule, and/or selecting a target molecule such that its relative stability at different states varies as a function of its orientation. The suggested prototypical molecular filter can be further optimized using the strategy outlined in the present study.

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ASSOCIATED CONTENT Supporting Information. The detailed discussion of choozing the collective variable ϕ. The 1D free-energy profiles of rotaxane 1A and rotaxane 1B featuring the shuttling process of the α-CD along the thread. Distribution of the puckering conformations of each GLU on the three-dimensional Cremer−Pople sphere. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author * (W.C.) Email: [email protected]. Tel: +86-22-23503430 Notes The authors declare no competing financial interests. ACKNOWLEDGMENT This study is supported by National Natural Science Foundation of China (No. 21373117). The CINES, Montpellier, France, and the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase) are gratefully acknowledged for provision of generous amounts of CPU time. The Cai Yuanpei program is also appreciatively acknowledged for its support of the international collaboration between the research groups of C.C. and W.C.

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Complex Movements in Rotaxanes: Shuttling Coupled with

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