Unveiling the Underlying Mechanism for Compression and

Article pubs.acs.org/JPCC

Unveiling the Underlying Mechanism for Compression and Decompression Strokes of a Molecular Engine Peng Liu,† Christophe Chipot,‡,§,⊥ Wensheng Cai,*,† and Xueguang Shao*,† †

State Key Laboratory of Medicinal Chemical Biology (Nankai University), Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Research Center for Analytical Sciences, College of Chemistry, Nankai University, Tianjin, 300071, People’s Republic of China ‡ Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana−Champaign, Unité Mixte de Recherche N° 7565, Université de Lorraine, B.P. 70239, 54506 Vandoeuvre-lès-Nancy cedex, France § Theoretical and Computational Biophysics Group, Beckman Institute, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States ⊥ Department of Physics, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States S Supporting Information *

ABSTRACT: Manufacturing at the molecular level engines to power nanocars represents a challenge in the development of nanomachines. A molecular engine formed of βcyclodextrin (β-CD), aryl, and amide moiety has been studied by means of molecular dynamics simulations combined with free-energy calculations. The compression and decompression strokes involving the binding processes of the (Z)- and (E)-isomers of this engine with 1-adamantanol (AD) have been elucidated by determining the underlying potentials of mean force (PMFs). The difference in the binding-free energies, considered as the work generated by and stored within this engine, is calculated to be +1.5 kcal/mol, in remarkable agreement with the experimentally measured quantity. Partitioning the PMFs into physically meaningful free-energy components suggests that the two binding processes are primarily controlled by the favorable inclusion of AD by the β-CD. The work generated by the engine is harnessed to push the alkyl moiety from the hydrophobic cavity of the CD to water, to modify a dihedral angle by a twisting motion about the C−Cα bond, and to increase the tilt angle between the mean plane of the sugar unit, which connects the amide moiety, and the mean plane of the CD. By deciphering the intricate mechanism whereby the present molecular engine operates, our understanding of how similar nanomachines work is expected to be improved significantly, helping in turn the design of novel, more effective ones.

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INTRODUCTION Human life has been greatly facilitated by the invention and generalization of cars powered by engines. The counterpart of cars at the molecular level is envisioned to hold great potential as nanomanipulators,1 which can transport molecules at the nanolevel.2 In the last 20 years, an increasing number of nanocars3−5 have been designed, synthesized, and characterized. The protocol to build the framework of nanocars is well established and has been thoroughly tested,6 whereas the design and construction of the heart of nanocars, the molecular engine, is just unfolding.7−9 A cylinder is the central working part of an engine, which provides the space for the piston to travel. Possessing a shape similar to that of a cylinder, macrocyclic molecules, such as cyclodextrin (CD),10 cyclophane,11 and other hollow molecular architectures,12 have been introduced into the structure of the molecular engine. Molecular engines perform the core function of their analogue in the macroscopic world, namely, converting energy to mechanical work. Yet, their low-converting efficiency13 admittedly requires further improvement. A sine qua noncondition for this improvement is the complete © 2014 American Chemical Society

understanding at the molecular level of the underlying mechanism that governs how such nanoengines operate. The cyclodextrin derivative designed by Coulston et al.10 can be considered as a paradigm for molecular engines. This engine comprises an aryl substituent connected to a β-CD by an Nmethyl-3-propionamido moiety and is fueled by 1-adamantanol (AD), as shown in Scheme 1. The amide (Z)-isomer of this engine (mZ) binding with AD is considered as the compression stroke. The decompression stroke involves the binding process of the amide (E)-isomer (mE) with AD in a reverse sequence. Interconversions of two isomers before and after binding with AD constitute two other processes, corresponding to the two vertical legs depicted in the scheme. Put together, these four processes compose the operation cycle of the molecular engine. The two interconversion processes have been studied experimentally. With the aid of the thermodynamic cycle shown in Scheme 1, the difference in the binding-free energies Received: April 1, 2014 Revised: May 15, 2014 Published: May 16, 2014 12562

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(CGenFF)27 parameters were utilized to describe the β-CD and AD, respectively. The temperature and pressure were maintained at 303.15 K and 1 bar, respectively, employing Langevin dynamics and the Langevin piston method.28 The length of the covalent bonds involving a hydrogen atom was frozen to its equilibrium value by means of the Shake/Rattle and Settle algorithms.29 The r-RESPA multiple-time-stepping algorithm was applied 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 (VDW) and electrostatic interactions were truncated smoothly by means of a 12 Å spherical cutoff with a switching function applied beyond 10 Å. Long-range electrostatic forces were taken into account by the particle-mesh Ewald30 scheme. Visualization and analysis of the MD trajectories were performed with VMD.31 Free-Energy Calculations. The free-energy profiles delineating the inclusion of AD in the cavity of the molecular engine were generated using the ABF algorithm implemented within the collective-variables module32 of NAMD. Projection of the vector joining the COM of the β-CD and the AD on the z-direction of Cartesian space was selected as the transition coordinate, ξ, as shown in Figure 1A and B. The length of the

Scheme 1. Synoptic Representation of How Molecular Engine 6A-Deoxy-6A-(N-Methyl-3-Phenylpropionamido)-βCD Operatesa

a The amide (Z)- and (E)-isomers of the molecular engine are denoted mZ and mE, respectively.

between the compression and decompression strokes has been determined. Both the thermodynamics, specifically how the free energy varies, and the underlying mechanism of the two strokes are, however, still largely undocumented. The main thrust of the present contribution is to explore the molecular detail of the compression and decompression strokes of the molecular engine, quantifying with unprecedented accuracy its thermodynamic features. A preferential-sampling algorithm,14−16 coined adaptive biasing force (ABF),17−20 was utilized to map the free-energy landscape that underlies the compression and decompression strokes of the molecular engine. To reveal the molecular mechanism whereby the engine operates, the different physical contributions extracted from the potentials of mean force (PMFs) were analyzed to shed light on the intimate structure− function relationship of the nanomachines.

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SIMULATION DETAILS Molecular Models. The initial coordinates of the β-CD were taken from the available three-dimensional crystal structure.21 The structure of N-methyl-3-phenylpropionamido (PPA) and AD was constructed using Insight II22 and was used to build the molecular machine. The geometry of these individual molecules was optimized using a conjugate-gradient algorithm. In the subsequent molecular dynamics (MD) simulations, the center of the glycosidic oxygen atoms of the β-CD was placed at the origin of Cartesian space. The longitudinal axis of the cavity of the β-CD was arbitrarily collinear with the z-direction of the coordinate system. Two possible isomers for the molecular engine, namely, mZ and mE, were considered. Each isomer was immersed in a water bath. The initial size of the water box was 48.7 × 48.7 × 58.4 Å3 for mZ, with 4613 water molecules, and 48.6 × 48.6 × 58.3 Å3 for mE, with 4607 water molecules. To improve the convergence of the freeenergy calculations, the movement of the center of mass (COM) of AD in the (x, y)-plane was restrained by means of a harmonic potential with a force constant of 0.5 kcal/mol/Å2. Molecular Dynamics Simulations. All the MD simulations reported here were conducted employing the NAMD program23 with the CHARMM force field.24 The TIP3P25 model was used to describe the water molecules. The carbohydrate solution force field (CSFF)26 parameters and the CHARMM general force field for organic molecule

Figure 1. Definition of the transition coordinate, ξ, characterizing the binding of (A) mZ with AD and (B) mE with AD. (C) Free-energy profiles delineating the binding processes of mZ and mE with AD along the transition coordinate, ξ. The error bars correspond to the statistical error of the free-energy calculation, i.e., the precision.

reaction pathway is equal to 13.0 Å. For numerical efficiency, this pathway was broken down into 13 consecutive, 1.0 Å wide windows. Instantaneous values of the force were accrued in bins, 0.1 Å wide. The variation of the free energy, ΔG(ξ), was determined by integrating the average force acting on ξ. In each window, a trajectory of at least 8 ns was generated. The total simulation time amounted to 144 and 120 ns for mZ and mE binding with AD, respectively. Block average regression17,18,33 was applied to estimate the standard error of the free-energy change.

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RESULTS AND DISCUSSION Free-Energy Profiles. The free-energy profiles characterizing the binding processes of mZ and mE with AD are depicted in Figure 1C. These profiles reveal that (1) each PMF possesses an appreciably deep minimum and (2) the minimum of the free-energy landscape underlying the binding of AD to mE is deeper than that for mZ. 12563

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For each binding process, a relatively flat region, namely, −13.0 ≤ ξ ≤ −10.0 Å, prefaces a broad and deep valley spanning −8.0 ≤ ξ ≤ +1.0 Å. This flat region corresponds to the free state of the molecular engine with AD, wherein the two molecules are well separated. Under these premises, AD can rotate freely in all directions. The aryl moiety in mZ is included in the cavity of the β-CD (see Figure 2A), whereas the same

forces independently. The resulting free-energy components are gathered in Figure 3.

Figure 2. Typical configurations of the molecular engine mZ with AD (A) in the free state and (B) in the bound state and of the molecular engine mE with AD (C) in the free state and (D) in the bound state.

Figure 3. Decomposition of the total free-energy profile into AD−CD, AD−water, and AD−PPA contributions for the binding process of (A) mZ with AD and (B) mE with AD.

AD−CD Interactions. The AD−CD contributions for the binding processes of molecular engines mZ and mE with AD are similar. The free-energy components possess a broad and deep valley, indicating that the AD−CD term favors binding and represents the primary contribution to the complete PMFs (see Figure 3A and B). To understand the detail of the AD−CD interaction, this term was further decomposed into van der Waals and electrostatic contributions, as depicted in Figure 4A. A glance at the graph immediately reveals that the molecular engine−AD complexes are primarily stabilized by AD−CD van der Waals interactions. It can be concluded that van der Waals contact between AD and β-CD plays a predominant role on the emergence of the valley observed for the AD−CD term and has a marginal influence on the deeper valley witnessed in the binding of mE with AD. AD−Water Interactions. The free-energy profile for the AD−water term in both cases possesses a barrier when AD and CD are in contact. It indicates that the AD−water interaction hampers the binding of molecular engines with AD. Additional analysis was carried out by partitioning AD−water interactions into meaningful contributions from the hydroxyl group and the alkyl moiety. The corresponding free-energy components are depicted in Figure 4B. Within the region spanning ca. −6.0 ≤ ξ ≤ 0.0 Å, a slight barrier emerges for the AD OH−water term, alongside with a deep valley for the AD alk-water counterpart. The height of the barrier represents the free energy needed to desolvate partially the hydroxyl group. The depth of the valley is the free energy gained by the desolvation of the alkyl moiety.34 For the two binding processes, the free energy needed to disrupt the solvent shell of the hydroxyl group is similar. Compared to mZ, however, the energetic gain to desolvate the

moiety in mE is extended into water (see Figure 2C). The valley in the PMFs reflects a stable state of the nanomachine, wherein AD resides in the cavity of the β-CD within the engine. The hydroxyl moiety in AD points out of the cavity of the βCD, conducive to a hydrogen-bonding interaction with the hydroxyl groups located in the secondary rim of the β-CD. The aryl moiety in mZ covers the primary face of the β-CD (see Figure 2B), whereas the same moiety in mE still extends in water (see Figure 2D). The work generated by the molecular engine can be considered as the difference, δΔG, between the binding free energies characterizing the compression and decompression strokes. On the basis of the assumption that the effect of the geometrical restraints on the free-energy profiles is nearly identical for mZ and mE, δΔG may be recovered through the following formula 1 ∫ dξ ξ exp[−β ΔGmE(ξ)] δ ΔG = − 1n β ∫ dξ ξ exp[−β ΔGmZ(ξ)]

Here, β = (kBT)−1, where kB is the Boltzmann constant and T is the temperature. From this expression, δΔG has been estimated to be equal to 1.5 kcal/mol, which is in excellent agreement with the experimental value, 1.4 kcal/mol.10 Driving Force Responsible for Binding. To identify the free-energy components that contribute to the deeper valley observed in the binding process of mE with AD, variation of the constituent intermolecular interactions of different nature was examined as a function of ξ. This was achieved by (1) partitioning the instantaneous force acting along the transition coordinate into AD−CD, AD−water, and AD−PPA contributions, (2) binning the latter and inferring the average force for each contribution, and (3) integrating the different average 12564

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Figure 4. (A) Partitioning of AD−CD contributions into van der Waals and electrostatic contributions. (B) Partitioning of AD−water contributions into AD alk(the alkyl moiety)−water and AD OH(the hydroxyl group)−water contributions.

Figure 5. Fluctuation of (A) the solvent-accessible surface area for the aryl moiety, (B) the dihedral angle (C7−C8−C9−N12) about the C−Cα bond, and (C) the tilt angle between the mean plane of the sugar unit bearing PPA and the mean plane of the β-CD.

Figure 6. Typical configurations of the mZ molecular assembly in the inclusion process. (A) ξ = −6.0 Å, (B) ξ = −3.0 Å, and (C) ξ = −1.0 Å. The atoms involved in the dihedral angle, C7−C8−C9−N12, are shown in an opaque licorice representation.

shallow valley, indicating that the AD−PPA interaction slightly favors the binding of AD to mE. To interpret the different roles played by the AD−PPA term in the two binding processes, the geometric changes of PPA, composed of an aryl moiety and an N-methyl-3-propionamido moiety, were investigated in further detail. The solventaccessible surface area (SASA) for the aryl moiety was examined using the Shrake and Rupley algorithm,35 as depicted in Figure 5A. When mZ with AD is well separated, the SASA for the aryl moiety of mZ remains small (∼45 Å2), because this moiety is included in the cavity of the β-CD. As the two molecules are brought together, the SASA decreases owing to the contact between AD and the aryl moiety. As AD penetrates deeper into the cavity, the SASA increases, suggesting the aryl moiety is pushed out of the cavity of the β-CD by AD and makes additional contact with water. In stark contrast with mZ, the corresponding SASA oscillates around a large value (∼130 Å2) in the binding process of mE with AD. This result can be

alkyl moiety in the binding of mE with AD is greater. With the aid of Figure 2, the observed difference in AD alk-water terms can be explained as follows. The aryl moiety of mE directly extends in water with a marginal influence on the interaction of AD and water. Conversely, the aryl moiety of mZ acts as a lid, thwarting partially the contact of water molecules with AD. The lesser contact between water and the hydrophobic alkyl moiety of AD results in additional energy gained by the desolvation of the alkyl moiety of AD, thus rationalizing that the AD−water term in the binding of AD to mZ is more favorable than that in the binding of AD to mE. AD−PPA Interactions. As illustrated in Figure 3, the AD− PPA contributions contrast sharply between mZ and mE, which constitutes the main difference between the two PMFs. In Figure 3A, the AD−PPA component possesses a barrier, demonstrating that AD−PPA interaction hampers the binding of AD to mZ. In Figure 3B, the AD−PPA term features a 12565

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molecular engine and eliminates the rotation about the C−Cα bond, hence, increasing the work performed on the amide bond. Another possible approach would consist in employing rigid architectures within the molecular machines, which could enhance the harvesting efficiency of the mechanical energy arising from the binding process. This inference has been demonstrated cogently in the shuttling of rotaxanes by Stoddart and co-workers.36,37 Put together, these results deepen our understanding of the mechanism whereby molecular engines like the one presented here are envisioned to help the design at the atomic level of novel, more efficient engines.

rationalized by the former observation that the aryl moiety in mE remains exposed to water during the entire binding process. The four dihedral angles about the chemical bonds of the Nmethyl-3-propionamido moiety have been measured in mZ and mE. Evolution of these dihedral angles with respect to ξ is shown in Figure S1 of the Supporting Information. Six out of the eight angles in mE and mZ are almost constant. The remaining two angles, which characterize the dihedral angle (C7−C8−C9−N12) about the C−Cα bond in the two isomers, are plotted in Figure 5B. In the binding process of mZ with AD, the dihedral angle C7−C8−C9−N12 increases, whereas in that of mE with AD, it oscillates around the initial value. These results suggest that the inclusion of mZ with AD is accompanied by a twist around the C−Cα bond, as highlighted in Figure 6, and this twist does not occur in the binding of mE with AD. To quantify the impact of the movement of PPA on the conformation of the β-CD, the tilt angle, φ, between the mean plane of the sugar unit bearing PPA and the mean plane of the β-CD has been measured, as shown in Figure 5C. The tilt angle increases in the binding of mZ with AD, which can be ascribed to the coupled motion of the sugar unit with the extrusion of the aryl moiety of AD from the cavity of the β-CD. Binding of mE with AD is accompanied by a slight decrease in the tilt angle, which can be considered as a conformational perturbation of the β-CD caused by its inclusion with AD. In the light of the above arguments, it can be inferred that the conformation of the amide moiety within the molecular engine has a significant impact on the binding of AD to the engine. The amide (Z)-isomer of the molecular engine (mZ) induces a conformation, wherein the aryl moiety is included in the cavity of the β-CD. Inclusion with AD displaces the aryl moiety out of the cavity of the β-CD, twists the dihedral angle about the C−Cα bond, and results in an obvious increase of the tilt angle between the mean plane of the sugar unit bearing PPA and the mean plane of the CD. For the amide (E)-isomer of the molecular engine (mE), the aryl moiety extends into water. Binding with AD has a marginal influence on the relative position of the aryl moiety and the conformation of the β-CD.

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ASSOCIATED CONTENT

S Supporting Information *

Discussion of the force field parameters. Evolution of four dihedral angles about chemical bonds of the N-methyl-3propionamido moiety in mZ and mE with respect to ξ. The complete refs 4, 24, 27, and 36. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected] Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The study was supported by National Natural Science Foundation of China (No. 21373117), Natural Science Foundation of Tianjin, China (No. 13JCYBJC18800), MOE Innovation Team (IRT13022) of China. The CINES, Montpellier, France, and NSCC, Tianjin, China, are gratefully acknowledged for provision of generous amounts of CPU time on their SGI Origin Altix and TH-1. 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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CONCLUSION In this contribution, the influence of amide bond isomerization on the binding process of AD to β-CD derivatives has been explored. The binding of two isomers of a molecular engine, namely, mE and mZ, with AD has been studied by means of free-energy calculations. The difference of binding free energies agrees remarkably well with the quantity determined experimentally. Partitioning the PMFs into different components reveals that favorable van der Waals contacts between AD and the cavity of the CD represent the primary driving force in the binding processes. The AD−PPA interaction contributes predominantly to the difference in the depth of the free-energy valleys, which reflects the work performed on the molecular engine. This work is harnessed to push the alkyl moiety from the hydrophobic cavity of the CD to water, to rotate the dihedral angle around the C−Cα bond, and to increase the tilt angle between the mean plane of the sugar unit bearing PPA and the mean plane of the CD. In the light of the newly deciphered mechanism, improvement of the efficiency of the molecular engine could be considered from two perspectives. As has been proven by Coulston et al.,10 incorporating a double bond between the aryl moiety and the amide bond increases the rigidity of the

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