Mechanical and Structural Tuning of Reversible Hydrogen Bonding in

May 9, 2019 - We present force probe molecular dynamics simulations of dimers of interlocked calixarene nanocapsules and study the impact of structura...
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Mechanical and Structural Tuning of Reversible Hydrogen Bonding in Interlocked Calixarene Nanocapsules Stefan Jaschonek, Ken Schäfer, and Gregor Diezemann J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.9b02676 • Publication Date (Web): 09 May 2019 Downloaded from http://pubs.acs.org on May 18, 2019

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Mechanical and Structural Tuning of Reversible Hydrogen Bonding in Interlocked Calixarene Nanocapsules Stefan Jaschonek, Ken Sch¨afer, and Gregor Diezemann∗ Institut f¨ ur Physikalische Chemie, Universit¨at Mainz, Duesbergweg 10-14, 55128 Mainz, FRG E-mail: [email protected]

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Abstract We present force probe molecular dynamics simulations of dimers of interlocked calixarene nanocapsules and study the impact of structural details and solvent properties on the mechanical unfolding pathways. The system consists of two calixarene ’cups’ that form a catenane structure via interlocked aliphatic loops of tuneable length. The dimer shows reversible rebinding and the kinetics of the system can be understood in terms of a two state model for shorter loops (≤ 14 CH2 units) and a three state model for longer loops (≥ 15 CH2 units). The various conformational states of the dimer are stabilized by networks of hydrogen bonds, the mechanical susceptibility of which can be altered by changing the polarity and proticity of the solvent. The variation of the loop length and the solvent properties in combination with changes in the pulling protocol allows to tune the reversibility of the conformational transitions.

I. Introduction The study of the mechanical unfolding of molecular complexes by experiments and molecular simulations allows to extract important information about the free energy landscape and the unfolding pathways. 1–4 In favourable situations it is possible to monitor the folding transition in addition to the forced unfolding. If this can be achieved, one is able to determine the force dependent kinetic equilibrium and to learn about a number of features of the free energy landscape like, e.g., transition state movements. 5,6 The observation of the hopping between the folded and an extended state of biomolecules can be used to understand the origin of force-induced free energy barriers. 7 Additionally, a number of experimental results that showed nonlinear dependences of the rupture forces on the pulling velocity have been reinterpreted in terms reversible binding. 8 The force dependent kinetics of reversibly bonding systems has been investigated using stochastic models 9,10 and also the counting statistics has been treated in terms of such models. 11–14 A commonly used method to induce the mechanical unfolding is provided by the force 2

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ramp (FR) protocol. Here, one pulls away part of the molecule from the remainder with a constant velocity and usually studies so-called force versus extension (FE) curves, i.e. one monitors the force at the pulling device as a function of the extension of the system. In the pull mode, the system is stretched until the relevant conformational unfolding transition takes place. Therefore, the force increases until the corresponding rupture force is reached. At this force, the molecular complex suddenly expands and the spring used to measure the force relaxes, giving rise to a force drop and a concomitant rip in the FE curve. If the pulling direction is inverted in the relax mode, the extension is reduced and at the rejoin force the system refolds again with an observable jump in the force. Since the system is driven out of equilibrium by the FR protocol, a hysteresis shows up between the FE curves in the pull and the relax mode. Such effects have been observed in pulling experiments 15,16 and also in molecular dynamics (MD) simulations of model systems. 17–19 The hysteresis depends on the deviation from thermal equilibrium and thus the amount of reversibility also does. For instance, if one pulls very fast, it is not expected that the system can rebind at all in the relax mode. Reversibility in the kinetics of conformational transitions plays an important role not only in the context of biomolecules but also for various applications of synthetic catenanes and rotaxanes. These systems consist of mechanically linked supramolecular structures that can act as switches, motors and sensors. 20,21 In the present paper, we investigate the impact of structural and environmental changes on the reversible transitions among the different conformational states of calix[4]arene dimers that we studied already earlier. 15,19,22 The system consists of two calix[4]arene monomers that are interlocked by four aliphatic loops consisting of methylene groups. The resulting dimer is well suited for our investigation because it exhibits different conformations that are stabilized by hydrogen bond (H-bond) networks, cf. Fig.1, and using force probe MD (FPMD) simulations one can force transitions among these states. Furthermore, some variants of calix[4]arene monomers and also catenanes are interesting systems for host-guest chemistry because they can capture guest molecules and

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have been discussed in the context of biomedical applications. 23,24 Here, we vary the number of methylene groups in the aliphatic loops systematically in a range from 12 CH2 units (termed T12 ) up to 20 CH2 (T20 ) units. This does not only alter the degree of reversibility but also the number of relevant conformational states of the system. In addition, we perform FPMD simulations on the T14 -system using various solvents as this might be of interest in the context of host-guest chemistry. In most experiments and our earlier simulations mesitylene was used. 15,19,22 Since this is an aprotic solvent there are no competing intermolecular H-bonds between calixarene and solvent molecules. The stability of the H-bond networks is likely to be altered when using polar solvents like tetrahydrofurane (THF) or protic ones like methanol (MeOH) and we will study this aspect in detail. The remainder of the paper is organized as follows. In the next section, we present the computational details and then in Section III we discuss the results of the variations in the loop length. After presenting the FPMD simulations in various solvents in Section IV we close with some conclusions.

II. Computational Details All simulations were performed using the GROMACS program package (versions 4.6.2 25 and version 5.1.2 26 ) with the OPLS (Optimized Potentials for Liquid Simulations) force field. 27 This force field was chosen because it was shown to yield reliable results in earlier FPMD simulations on the calixarene system. 19,22 The relevant parameters for the calix[4]arene system and mesitylene can be found in ref., 28 those for MeOH in ref. 29 and the ones for THF in ref. 30 All topologies were generated by hand. For the short-range interactions a cut-off of 1.4 nm was used, the long-range interactions were treated using the particle mesh Ewald summation method 31 and for the van der Waals interactions a dispersion correction 32 was applied. Periodic boundary conditions were used and the simulation time-step was 2 fs which is possible because the bonded interactions were constrained to their equilibrium values using

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the LINCS (Linear Constraint Solver) algorithm 33 and the neighbor list was updated every 10 fs. All production runs were prepared as follows: After an energy minimization for all molecules the solvation procedure was applied, followed by another energy minimization performed on the solvated system. Afterwards, the system was equilibrated for 1 ns using a velocity rescaling thermostat 34 with a time constant of 0.1 ps. The system was then coupled to a Parinello-Rahman barostat 35 with a time constant of 2 ps and compressibilities of 8.3 · 10−5 bar−1 for mesitylene, 9.7 · 10−5 bar−1 for THF and 12.0 · 10−5 bar−1 for MeOH. All production runs were performed using the NPT-ensemble at a pressure of 1 bar and a temperature of 300 K. For the FPMD simulations two different groups within the calix[4]arene are defined: a pulled group and a reference group as the respective center of mass of the methoxy carbons of the upper rim, c.f. Fig.1a. A time-dependent harmonic potential with a force constant K is applied to the pulled group along the vector connecting the two groups. The force experienced by the pulled group is

F = K(V · t − ∆q)

(1)

where ∆q is the displacement of the pulled group from its original position q0 , ∆q = q − q0 , V the pulling velocity and t the time. In the FPMD simulations, we used K = 0.8305 N/m and varied V to realize different values for the loading rate µ = K ·V . The following loop length were investigated: 12 CH2 units (T12 ) up to 17 CH2 (T17 ) units and 20 CH2 (T20 ) units. For the simulations with varying loop length of the calix[4]arene catenane dimer we used mesitylene as a solvent. The simulation boxes had dimensions 5.4nm×(4.4nm)2 and 435 mesitylene molecule (for the systems T12 , T13 , T14 ) and (5.5nm)3 and 746 mesitylene molecules (for the systems T15 , T16 , T17 , T20 ). For the T14 -system, additionally simulations using a box size of (5.8nm)3 and 827 mesitylene

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Figure 1: Upper panel: Stick models of the Calix[4]arene catenane with a loop length of 20 CH2 units (T20 ). The interlocked loops are shown transparent and for simplicity no hydrogen atoms are shown. Middle panel: Chemical structures. Lower panel: cartoons of the spatial structures indicating the calixarene ’cups’, the loops and the stabilizing H-bonds (colored dots). (a) The T20 -system. The pulled group and the reference group are indicated by the circles and the pulling direction is represented by the arrow. (b) Urea-Urea bonds (UUbonds) indicated in blue. (c) Urea-Ether bonds (UE-bonds) in green. (d) Structure devoid of H-bonds. molecules were performed with identical results. The simulations using THF as solvent were performed in a box of dimension (5.4nm)3 and 1062 THF molecules and for MeOH, we used a box size of (5.7nm)3 containing 2600 MeOH molecules.

III. Calixarene dimers with varying loop length Analysis of force versus extension curves For each of the calix[4]arene catenane systems we performed 500 FPMD simulations as described above and subsequently analyzed the resulting trajectories. In Fig.2, we present examples of FE curves for T14 and T17 , both in the pull mode (black) and the relax mode (red). In our simulations, the extention is completely determined by the pulling procedure and is given by x = V · t. The observed hysteresis is a clear signature of the non-equilibrium

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Figure 2: left: Examples of FE curves for T14 and T17 . The curves for T17 are shifted by 1500 pN; black: pull mode, red: relax mode; V = 1 m/s and K = 0.8305 N/m. right: number of UU-bonds (blue) and UE-bonds (green) nature of the FPMD simulations with a finite pulling velocity and the difference in the characteristic forces in the pull and the relax mode strongly increases with V . 19 For very large V , the system appears irreversible because the rebinding is not observable in the relax mode simulations. For vanishing pulling velocity, V → 0, an equilibrium FE curve without hysteresis will be observed resembling the behavior expected for a first order transition. 18 For T14 , a single transition from a starting conformation stabilized by roughly 16 UUbonds to a conformation stabilized by UE-bonds is observed. This is very similar to the findings in earlier studies on the T14 system. 15,19,22 In the FE curve, the transition is accompanied by a drop in the force at x '2.5 nm and when considering the number of closed H-bonds it is apparent that the network of UU-bonds opens and the UE-bonds form at the same extension, cf. the right panels in Fig.2. As discussed in detail earlier, the number of UU-bonds decreases gradually to a number of about 8 and then at the transition it rapidly drops to zero. 19,22 We defined an H-bond to be intact when the distance between the heavy atoms was smaller than 0.35 nm and the angle did not exceed 30o but the results do not depend sensitively on this choice. 19 An inspection of the FE curves in combination with the H-bond network dynamics reveals that for T17 one observes two transitions. In the pull mode, at x'2.3 nm, the transition from the ’UU-state’ to the ’UE-state’ takes place, followed by a transitions from the UE-state to a conformation with elongated loops and no residual 7

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H-bonds (NHb-state) at about 2.6 nm. A similar behavior has been observed earlier, when we considered a system that consisted of two loops only. 19 In that case, however, we were not able to observe the reverse transitions in the relax mode on the time scale of the MD simulations. To the best of our knowledge, the present example is the first observation of a reversible transition via a stable intermediate structure in all atom FPMD simulations. We found that for the systems with loop lengths T12 to T14 the FE curves represent a two-state behavior with transitions between the UU- and the UE-states. For the systems with longer loops, the additional transition to the NHb-state is observed. This behavior is schematically summarized in Fig.3. For a further analysis of each of the 500 individual FE

Figure 3: Schematic representation of the form of the FE curves in the pull (upper panels) and the relax mode (lower panels) for different loop lengths with the definition of the characteristic forces. curves, the values for the characteristic forces were extracted. Due to the stochastic nature of the concomitant transitions, these values fluctuate and the corresponding distributions were determined. As an example, in Fig.4 we present these distributions for the T20 system. From the distributions of rupture and rejoin forces, we determined the mean values and present the results in Fig.5. The following features are evident from that figure. In the pull mode the characteristic forces for the transition from the UU-state to the UE-state are almost independent of the loop length, indicating that these transitions are mainly determined by NHb the stability of the respective H-bond network. Only the force Frupt depends on the loop

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Figure 4: Distributions of the characteristic forces (not normalized) for T20 . The pulling parameters are V = 1 m/s and K = 0.8305 N/m.

Figure 5: Mean rupture and rejoin forces for the calixarenes ranging from T12 to T20 ; F UU : blue squares, F UE : green triangles, F NHb : grey circles. Full symbols: pull; open symbols: relax. The pulling parameters are V = 1 m/s and K = 0.8305 N/m. length and decreases with increasing number of methylene groups in the loop. For this transition the kinetics of the H-bond network appears to be of less relevance and the loop stiffness apparently is more important. Since this is expected to decrease with increasing NHb loop length, Frupt should decrease, as is observed.

In the relax mode, the situation is quite different. Here, all characteristic forces decrease with increasing loop length. This means, the hysteresis increases and systems with longer loops exhibit stronger non-equilibrium effects during the FPMD simulation. In Fig.5, the loading rate is µ = 0.8305 N/s and the hysteresis is known to depend strongly on the values of µ. 19,22

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Analysis of the H-bond network As has been pointed out above, the UU- and UE-states of the calixarene dimer systems are mainly stabilized by the formation of the H-bond networks. The evolution of the number of UU-bonds and UE-bonds as a function of the simulation time (or equivalently the extension V ·t) has been presented in Fig.2. In the pull mode, the number of UU-bonds decreases quite slowly until at an extension close to the rupture event it abruptly drops to zero and the UEbonds form. The kinetics of the H-bond networks reflect the hysteresis in the same manner as the FE curves. A quasi-equilibrium analysis of the H-bond network can be performed if one considers the dependence of the mean number of H-bonds on the mean end-to-end distance hqi, as has been discussed earlier for the T14 system. 22,28 In particular, it has been found that the non-equilibrium features induced by the fast pulling only play a very minor role because the results coincide with those obtained from calculations of the potential of mean force (PMF), i.e. the free energy as a function of the pulling coordinate. 28 Furthermore, we used the H-bond network characteristics for the definition of the mean positions of the minima and maxima of the PMF. It turned out that meaningful definitions of the various positions can be obtained using:

qUU = hqi(h#UUi = 8) ; qT = hqi(h#UUi = h#UEi) ; qUE = hqi(h#UUi = max).

(2)

Here, qUU and qUE denote the minima associated with the respective states and qT is an operational definition for the position of the transition state. 22 In Fig.6, we present the mean number of H-bonds, h#UUi and h#UEi, as a function of hqi for systems with different loop lengths obtained from pull mode simulations. The loading rate used was µ = 0.8305 N/s, but the results only very weakly depend on that value. For the T14 system this was already observed in ref. 22 and even for the systems with long loops (T17 and T20 ) we hardly found any dependence. The only quantity that shows a significant change with µ is the maximum number of UE-bonds formed during the pull mode simulation. This

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Figure 6: Mean number of H-bonds for T14 (full lines), T17 (dashed lines) and T20 (dotted lines) as a function of the mean end-to-end distance hqi for pull mode simulations using a loading rate of µ = 0.8305 N/s. h#UUi: blue; h#UEi: green. number decreases with increasing pulling velocity, which we view as a direct consequence of the imposed non-equilibrium conditions, cf. ref. 22 The faster the system is pulled the less time is available for the formation of UE-bonds before the end-to-end distance has increased beyond values around qUE . It is evident from Fig.6 that the characteristic positions do not vary much with the length of the loops of the system. This is quantified in Fig.7, where we present the positions as defined in eq.(2) as a function of the length of the aliphatic loops. This figure shows that

Figure 7: Positions of the minima X=UU (blue), UE (green) and the transition state (X=T, red) as defined in eq.(2) for different loop lengths. only for the shortest loops there is some shift of all three characteristic positions towards smaller values. For the systems with loop lengths larger than 13 the free energy landscape in the range of the two states UU and UE hardly changes. We conclude that the stiffness 11

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of the aliphatic loops only plays a minor role for the stability of the respective states. This is in accord with the finding that the harmonic force constants of the molecular free energy landscape as determined from the slopes of averaged FE curves do not depend on the loop (UU)

length. We find them to be given by the same value as for the T14 system, Km

' 13 N/m. 22

We can summarize our results for the PMF as shown schematically in Fig.8. If no force

Figure 8: Schematic free energy landscapes for two states (left, loop length smaller than 15) and three states (right). The upper curves are meant to represent the force free situation and the lower ones in the presence of a finite force. is applied, the PMF shows one or two shoulders at the positions that give rise to energy barriers in the presence of a finite external force. The minimum of the UU-state is located at qUU . The transition state position and the minimum of the UE-state of course are defined in a strict sense only in the presence of a finite force, where the observed shoulder turns into a barrier. Our analysis of the FE curves and the H-bond network does not allow to characterize the position of the transition state between the UE- and the NHb-state and also not the position of the NHb-state.

Reversibility of conformational transitions In the analysis of the H-bond network kinetics in the pull mode simulations discussed above, we always started from systems in the stable equilibrium configuration, the UU-state. At the end of the simulation, the extension has increased to x ' 3.5nm, cf. Fig.2. In the relax mode, the pulling direction is reversed and the same simulation is performed again. This means that the structure with the calixarene ’cups’ separated is returned into one with very small distance between them, cf. Fig.1. However, this does not mean that the UU-bond network

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is rebuilt reversibly in every case. For the systems with the shorter loop lengths, a reversible rebinding is observed in all simulations but this changes in particular when the NHb-state is observed. Additionally, the observation of reversible rebinding depends on the loading rate as can be anticipated from Fig.4 because for the chosen example the characteristic forces in the relax mode are nearly zero. Only about 70% of the relax trajectories returned to the initial configuration. For faster pulling, i.e. increased hysteresis, the system will only rebind with even smaller probability. For a working definition of the degree of reversibility we proceed as follows. Starting from the UU-state in the pull mode the transition to the UE-state - and for the longer loops additionally to the NHb-state - are induced and a reversible trajectory returns to the UU-state in the relax mode simulation. We define this condition to be met if more than 8 UU-bonds have been reformed at the end of the simulation. Of course, due to the stochastic nature of all conformational transitions, some of the systems will not always return to the starting UU-state. Therefore, it is useful to define the degree of reversibility as the fraction of the simulations that reach the UU-state, i.e. form more than 8 UU-bonds. We have calculated this fraction for each set of the FPMD simulations performed for three different values of the loading rate and the results are collected in Fig.9. It becomes evident that

Figure 9: Degree of reversibility, i.e. the fraction of relax simulations returning to the UUstate with more than 8 UU-bonds, for the various loop lengths. For each type of Calixarene, 500 simulations were performed with K = 0.8305 N/m. the degree of reversibility can be tuned by changing the loop length and thus alter the structure of the molecule and the free energy landscape of the system. As noted above, for the T12 · · · T14 systems, a two-state model is appropriate and the NHb-state becomes relevant for larger loop lengths. Alternatively, one can change the pulling velocity and expose the 13

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system with a given structure to different non-equilibrium situations.

IV. Calixarene dimer T14 in various solvents Sofar, we discussed the possibility of changing the degree of reversibility via changes in the structure of the calixarene dimers. All simulations were performed using mesitylene as a solvent. Because mesitylene is an aprotic solvent, the conformational transitions associated with changes in the H-bond network structure can be viewed as purely intramolecular. This situation is expected to change, when other, protic, solvents are used because then the H-bond network is affected by the competing formation of intermolecular H-bonds. In order to study the impact of the solvent on the conformational kinetics, we performed FPMD simulations using the T14 -system in THF and MeOH in addition to mesitylene. We chose these solvents because THF is polar but aprotic and MeOH is protic. This way, we can compare the results in quite different situations. We performed FPMD simulations for three different loading rates using a spring constant of K = 0.8305 N/m and pulling velocities V = (0.1, 1 and 10) m/s. In Fig.10, we present averaged FE curves for the three different solvents, where the average has been performed over 1000 simulations. The curves exhibit

Figure 10: Averaged FE curves for T14 in different solvents. Black curves represent pull mode and red curve relax mode simulations. The inset shows the mean number of H-bonds as a function of hqi, cf. Fig.6. The loading rate for all simulations was µ = 0.8305 N/s. the behavior typical for FE curves but without the sharp changes of the force at the rupture

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/ rejoin events, cf. Fig.2. This is because due to the stochastic nature of the transitions the steps in the averaged FE curves represent an average over the involved characteristic forces. It is obvious from Fig.10 that the pull mode curves (black lines) show a similar behavior for all three solvents with similar slopes in the UU-state and the UE-state. The main difference is that the average rupture force for MeOH is much smaller than for the other two solvents. In the relax mode (red curves), the situation is different. Only in mesitylene the system shows a fully reversible transition to the UU-state and the two curves for pull and relax coincide for small extensions. For THF a partial rebinding is observable and for MeOH on average no rebinding is observed at all. The inset in Fig.10 shows the averaged number of H-bonds as a function of the mean endto-end distance of the dimer. It is apparent that the overall behavior of the H-bond network is quite similar to that observed in Fig.6. For THF the differences to the results obtained for mesitylene are negligible. Using the same definition for the characteristic points in the free energy landscape as above, one conjectures that the polarity of THF has hardly any impact on the behavior of the system. This situation changes when MeOH is considered. While the curvature of the minima in the free energy landscape as determined from the slopes of the mean FE curves are similar to the other solvents, both the transition state position and the UE-state position change somewhat. The value of qT as defined in eq.(2) increases to about 1.75 nm and qUE ' 1.9 nm, to be compared with 1.7 nm and 2.0 nm, respectively. In addition, we note that the average number of UU-bonds in equilibrium is reduced from 15.5 to 14 in MeOH. In Fig.11, we present the mean characteristic forces as determined from their distributions for the T14 system in mesitylene and in MeOH. The values using THF as a solvent are very similar to those for mesitylene. This means that the polarity of THF does not significantly alter the stability of the H-bond network on average. This is quite different, when the protic MeOH is used as a solvent. Here, the competition between intra- and intermolecular Hbonds strongly reduces the stability and therefore the characteristic forces as compared to

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Figure 11: Mean characteristic forces for T14 in mesitylene (squares) and MeOH (circles) as a function of the loading rate. F UU : blue, F UE : green; the forces in the relax mode are represented by open squares. For MeOH all forces in the relax mode take on values around zero and are not shown. mesitylene. Of course, the discussion of the average values of various quantities does not tell much about the actual degree of reversibility. As is evident from the averaged FE curves in Fig.10, for a loading rate of µ = 0.8305 N/s, only the mesitylene relax simulations show a reversible behavior. For THF there is some reversibility and for MeOH, the UU-state appears not to be reached in most of the simulations. The actual degree of reversibility is determined using the same definition as above. For THF and MeOH, we used 1000 FPMD simulations and determined whether or not the UU-state was reached at the end of the relax simulations. The results are summarized in Fig.12. From this, it is evident that use of the protic solvent MeOH basically destroys the

Figure 12: Degree of reversibility in percent. For THF and MeOH, 1000 simulations were performed with K = 0.8305 N/m and the pulling velocity as given. reversible rebinding of the system for the loading rates used in the simulations. However, it is expected that the degree of reversibility will increase for smaller loading rates. This appears 16

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meaningful because in that case there is more time for the rebuilding of the UU-bond network also if intermittent intermolecular H-bonds have been formed between MeOH molecules and some urea groups. Interestingly, the use of the polar solvent THF hardly affects the structural properties of the H-bond networks, but has a strong impact on the kinetics in the sense that the degree of reversibility quite strongly depends on the loading rate in the range studied. Apparently, the electrostatic interactions partly inhibit the formation of the UU-bonds in the relax mode simulations.

V. Conclusions In the present study we investigated the impact of structural and environmental conditions on the mechanical opening and rebinding of a model system consisting of calixarene nanocapsules interlocked via aliphatic loops. For chemical and mechanical applications of such systems it is important to have the maximum possible control over the free energy landscape and to know the dependence of important structural and kinetic parameters on the external conditions. We have altered the length of the aliphatic loops intercalating the calix[4]arene dimers in a systematic manner and we have found that the free energy landscape ist changed in a qualitative manner for the longer loops (more than 16 methylene groups). For short loops, the properties of the system can be understood excellently in terms of a two-state model, i.e. a free energy landscape with two metastable states. At room temperature the stable UU-state can be transformed into the UE-state via pulling the system to an elongated structure. For longer loops, another state can be reached devoid of any stabilizing H-bond network. The reversible reconstruction of the UU-bond network after mechanically forcing its dissociation strongly depends on the non-equilibrium nature of the rupture process and on the loop length. For longer loops the degree of reversibility decreases even though for slow pulling reversible transformations via a stable intermediate can be observed. This fact might

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have interesting implications for the applicability of such systems in the field of mechanically induced molecular switches. In particular, the free energy landscape in the regime of the UU- and the UE-states is almost not altered by increasing the loop length meaning that the transition to a three-state system is achieved without significant perturbation of the original two-state system. For applications of calixarene systems in the field of host-guest chemistry, the properties of the solvent used can be of importance. We have studied three different solvents, namely the apolar and aprotic mesitylene, polar and aprotic THF and polar and protic MeOH. While the kinetic stability of the H-bond networks is almost not affected by the transition from an apolar to a polar solvent, the degree of reversibility changes considerably. The most prominent effect, however, is observed when the protic MeOH is used. Here, the competition between the formation of different kinds of H-bonds changes both, the free energy landscape parameters and the kinetic properties. In particular, the system appears irreversible on the time scale of the simulations performed. These properties might have an important effect on the capability of guest capture in such systems. In summary, we have presented a detailed study of the dependence of the kinetics of H-bond networks of a model calixarene catenane dimer and have shown that the free energy landscape of the system can be controlled via chemical manipulation and also via changes of the environment. These results might have interesting applications of such systems as molecular switches and as hosts for various guest molecules.

Acknowledgement Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) Project number 233630050 - TRR 146 and via Grant No. Di693/3-1. We gratefully acknowledge the computing time granted on the super-computer Mogon at Johannes Gutenberg University Mainz (hpc.uni-mainz.de). We thank Gerald Hinze for fruitful discussions.

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References (1) Ott, W.; Jobst, M. A.; Schoeler, C.; Gaub, H. E.; Nash, M. A. Single-Molecule Force Spectroscopy on Polyproteins and Receptor–Ligand Complexes: The Current Toolbox. J. Struct. Biol. 2017, 197, 3–12. (2) Dudko, O. K.; Hummer, G.; Szabo, A. Theory, Analysis, and Interpretation of SingleMolecule Force Spectroscopy Experiments. Proc. Nat. Acad. Sci. USA 2008, 105, 15755–15760. (3) Rico-Pasto, M.; Pastor, I.; Ritort, F. Force Feedback Effects on Single Molecule Hopping and Pulling Experiments. J. Chem. Phys. 2018, 148, 123327 1–9. (4) Lee, E. H.; Hsin, J.; Sotomayor, M.; Comellas, G.; Schulten, K. Discovery Through the Computational Microscope. Structure 2009, 17, 1295–1306. (5) Hyeon, C.; Morrison, G.; Thirumalai, D. Force-Dependent Hopping Rates of RNA Hairpins can be Estimated from Accurate Measurement of the Folding Landscapes. Proc. Natl. Acad. Sci. USA 2008, 105, 9604–9609. (6) Alemany, A.; Ritort, F. Force-Dependent Folding and Unfolding Kinetics in DNA Hairpins Reveals Transition-State Displacements along a Single Pathway. J. Phys. Chem. Lett. 2017, 8, 895–900. (7) Sch¨onfelder, J.; Sancho, D.; Berkovich, R.; Best, R. B.; Munoz, V.; Perez-Jimenez, R. Reversible Two-State Folding of the Ultrafast Protein gpW under Mechanical Force. Commun. Chem. 2018, 1–9. (8) Friddle, R. W.; Noy, A.; De Yoreo, J. J. Interpreting the Widespread Nonlinear Force Spectra of Intermolecular Bonds. Proc. Nat. Acad. Sci USA 2012, 109, 13573–13578. (9) Seifert, U. Dynamic Strength of Adhesion Molecules: Role of Rebinding and SelfConsistent Rates. Europhys. Lett. 2002, 58, 792–798. 19

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(10) Diezemann, G.; Janshoff, A. Dynamic Force Spectroscopy: Analysis of Reversible BondBreaking Dynamics. J. Chem. Phys. 2008, 129, 084904 1–10. (11) Manosas, M.; Ritort, F. Thermodynamic and Kinetic Aspects of RNA Pulling Experiments. Biophys. J. 2005, 88, 3224–3242. (12) Diezemann, G.; Janshoff, A. Force-Clamp Spectroscopy of Reversible Bond Breakage. J. Chem. Phys. 2009, 130, 041101 1–4. (13) Diezemann, G.; Schlesier, T.; Geil, B.; Janshoff, A. Statistics of Reversible Bond Dynamics Observed in Force-Clamp Spectroscopy. Phys. Rev. E 2010, 82, 051132 1–13. (14) Diezemann, G. Statistics of Reversible Transitions in Two-State Trajectories in ForceRamp Spectroscopy. J. Chem. Phys. 2014, 140, 184905 1–9. (15) Janke, M.; Y.Rudzevich,; Molokanova, O.; Metzroth, T.; Mey, I.; Diezemann, G.; Marszalek, P.; Gauss, J.; B¨ohmer, V.; Janshoff, A. Mechanically Interlocked Calix[4]arene Dimers Display Reversible Bond Breakage under Force. Nature Nanotech. 2009, 4, 225–229. (16) Alemany, A.; Ritort, F. Fluctuation Theorems in Small Systems: Extending Thermodynamics to the Nanoscale. Europhys. News 2010, 41, 27–30. (17) Lu, Z.; Hu, H.; Yang, W.; Marszaleky, P. E. Simulating Force-Induced Conformational Transitions in Polysaccharides with the SMD Replica Exchange Method. Biophys. J. 2006, 91, L57–L59. (18) Franco, I.; Schatz, G. C.; Ratner, M. A. Single-Molecule Pulling and the Folding of Donor-Acceptor Oligorotaxanes: Phenomenology and Interpretation. J. Chem. Phys. 2009, 131, 124902 1–13. (19) Schlesier, T.; Metzroth, T.; Janshoff, A.; Gauss, J.; Diezemann, G. Reversible Hydrogen

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Bond Network Dynamics: Molecular Dynamics Simulations of Calix[4]arene-Catenanes. J. Phys. Chem. B 2011, 115, 6445–6454. (20) Gil-Ramirez, G.; Leigh, D. A.; Stephens, A. J. Catenanes: Fifty Years of Molecular Links. Angew. Chem. Int. Ed. 2015, 54, 6110–6150. (21) Pezzato, C.; Cheng, C.; Stoddart, J. F.; Astumian, R. D. Mastering the NonEquilibrium Assembly and Operation of Molecular Machines. Chem. Soc. Rev. 2017, 46, 5491–5507. (22) Jaschonek, S.; Diezemann, G. Force Probe Simulations of a Reversibly Rebinding System: Impact of Pulling Device Stiffness. J. Chem. Phys. 2017, 146, 124901 1–9. (23) Rebek, J. Host-Guest Chemistry of Calixarene Capsules. Chem. Commun. 2000, 637– 643. (24) Yousaf, A., A.; Hamid, S.; Bunnori, N.; Ishola, A. Applications of Calixarenes in Cancer Chemotherapy: Facts and Perspectives. Drug Des. Dev. Ther. 2015, 9, 2831–2838. (25) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory Comput. 2008, 4, 435–447. (26) Abraham, M.; Murtola, T.; Schulz, R.; Pall, S.; Smith, J.; Hess, B.; Lindahl, E. GROMACS: High Performance Molecular Simulations through Multi-Level Parallelism from Laptops to Supercomputers. SoftwareX 2015, 1-2, 19–25. (27) Jorgensen, W. L.; Tirado-Rives, J. The OPLS [Optimized Potentials for Liquid Simulations] Potential Functions for Proteins, Energy Minimizations for Crystals of Cyclic Peptides and Crambin. J. Am. Chem. Soc. 1988, 110, 1657–1666. (28) Schlesier, T.; Diezemann, G. Performance of Different Force Fields in Force Probe Simulations. J. Phys. Chem. B 2013, 117, 1862–1871. 21

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(29) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids. J. Am. Chem. Soc. 1996, 118, 11225–11236. (30) Vasudevan, V.; Mushrif, S. H. Insights Into the Solvation of Glucose in Water, Dimethyl Sulfoxide (DMSO), Tetrahydrofuran (THF) and N,N-Dimethylformamide (DMF) and Its Possible Implications On the Conversion of Glucose to Platform Chemicals. RSC Adv. 2015, 5, 20756–20763. (31) Darden, T.; York, D.; Pedersen, L. Particle Mesh Ewald: A Nlog(N) Method for Ewald Sums in Large Systems. J. Chem. Phys. 1993, 98, 10089–10092. (32) Allen, M.; Tildesley, D. Computer Simulations of Liquids; Oxford, Oxford Science Publications, 1987. (33) Hess, B.; Bekker, H.; Berendsen, H. J. C.; Fraaije, J. G. E. M. LINCS: A Linear Constraint Solver for Molecular Simulations. J. Comput. Phys. 1997, 18, 1463–1472. (34) Bussi, G.; Donadio, D.; Parrinello, M. Canonical Sampling through Velocity Rescaling. J. Chem. Phys. 2007, 126, 014101 1–7. (35) Parrinello, M.; Rahman, A. Crystal Structure and Pair Potentials: A MolecularDynamics Study. Phys. Rev. Lett. 1980, 45, 1196–1199.

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Figure 13: Table of Contents Graphics

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