The lubricating role of water in the shuttling of rotaxanes

The special properties of water make it an effective lubricant in rotaxanes to enhance their shuttling.


Molecular dynamics simulations.
All the atomistic MD simulations presented herein were performed using the parallel, scalable program NAMD 2.11. 1 Water was described by the TIP3P model 2 while other molecules in this study were modeled by the CHARMM General Force Field (CGenFF). 3 The temperature and the pressure were maintained at 300 K and 1 atm, respectively, employing Langevin dynamics and the Langevin piston method. 4 Chemical bonds involving hydrogen atoms were constrained to their experimental lengths by means of the SHAKE/RATTLE 5-6 and SETTLE algorithms. 7 The r-RESPA multiple-time-stepping algorithm 8 was applied to integrate the equations of motion with a time step of 2 and 4 fs for short-and long-range interactions, respectively. A smoothed 12 A spherical cutoff was applied to truncate van der Waals and short-range electrostatic interactions. Periodic boundary conditions (PBCs) were applied in the three directions of Cartesian space. Long-range electrostatic forces were taken into account by the particle-mesh Ewald scheme. 9 Visualization and analysis of the MD trajectories were performed with VMD 1.9.2. 10 Free-energy calculations. The free-energy calculations reported herein were carried out utilizing the multiple-walker extended adaptive biasing force (MW-eABF) algorithm. [11][12][13] To increase the efficiency of the calculations, the free-energy surface was broken down into six consecutive, non-overlapping windows. Instantaneous values of the force were accrued in bins, with 0.1 Å × 2° wide. The sampling time required to determine each PMF was 2.2 μs. The least free-energy pathway connecting the minima of the two-dimensional free-energy landscapes was located using the LFEP algorithm. 14 The concept of committor 15,16 was utilized to demonstrate that the  Figure S3). For each structure, 100 5000-step equilibrium simulations were carried out with different initial velocities. The frequency characterizing the molecular assembly tending to relax to state B before reaching state A, p B , was calculated for each structure. The distribution of p B for the 100 distinct structures is provided in Fig. S7. This distribution is Gaussian-like, with a peak at p B = 0.5, which suggests that the chosen coarse variables are suitable for studying the movement of the macrocycle in the rotaxane.

Comparison between classical ABF and eABF
In the classical ABF method, the biasing force is added to the groups of atoms at play, whereas in extended ABF, the bias is applied onto a fictitious particle coupled to the coarse variable of interest by means of a stiff spring. In most cases, classical ABF is appropriate for multidimensional free-energy calculations in the limit of low dimensionality problemstypically n ≤ 3. However, extended ABF must be employed in the following cases, i) The second derivative of the coarse variable is not available in the free-energy calculation engine.
ii) The chosen coarse variables are not independent from each other.
iii) The chosen coarse variables are coupled to geometric restraints or holonomic constraints.
In this study, the variable describing the conformational change of the macrocycle, φ=(φ 1 +φ 2 +φ 3 )/3, consists of three coarse variables coupled to each other. Extended ABF must, therefore, be used in the free-energy calculations.
Moreover, the eABF method possesses also a much higher convergence rate compared with the original algorithm. See ref.
12 and 17 for more information.

Lubrication effect by water on the motion of abiological and biological molecular machines
Water can greatly weaken hydrogen bonds and stabilize transition states due to its high polarity, ability to act as both a hydrogen donor and acceptor, and very small molecular volume.
Lubrication by water, therefore, is universal for all the hydrogen-bonding driven molecular S13 machines, including the wheel-and-axle machine reported by Panman et al. 18 The ability of changing the driving force from hydrogen bonding to hydrophobic interaction is, however, specific for those complexes possessing large hydrophobic groups. The wheel-and-axle machine only features succinamide moieties as stoppers, which are not large enough to help water convert the driving force from hydrogen bonding to hydrophobic interaction, as can be inferred from structure D1 and D2 in Fig. 5.
In addition to its role in abiological, artificially designed molecular machines, water also plays a key role in biological machines. For example, the rotation of the motor protein ATPase is generally believed to be controlled by electrostatic interactions. Water can, however, help hydrophobic residues induce local deformations prior to electrostatically driven rotation, thereby reducing the barriers of side-chain dissociation and association that drive stalk rotation. 19