Alexander
Saltzman
a,
Du
Tang
a,
Bruce C.
Gibb
b and
Henry S.
Ashbaugh
*a
aDepartment of Chemical and Biomolecular Engineering, Tulane University, New Orleans, LA 70118, USA. E-mail: hanka@tulane.edu
bDepartment of Chemistry, Tulane University, New Orleans, LA 70118, USA
First published on 27th September 2019
Octa-acid (OA) and tetra-endo-methyl octa-acid (TEMOA) are deep cavity cavitands that readily form multimeric complexes with hydrophobic guests, like n-alkanes, in aqueous solution. Experimentally, OA displays a monotonic progression from monomeric to dimeric complexes with n-alkanes of increasing length, while TEMOA exhibits a non-monotonic progression from monomeric, to dimeric, to monomeric, to dimeric complexes over the same range of guest sizes. Previously we have conducted simulations demonstrating this curious behavior arises from the methyl units ringing TEMOA's portal to its hydrophobic pocket barring the possibility for two alkane chains to simultaneously bridge between two hosts in a dimer. Here we expand our prior simulation study to consider the partially methylated hosts mono-endo-methyl octa-acid, 1,3-di-endo-methyl octa-acid, and tri-endo-methyl octa-acid to examine the emergence of non-monotonic assembly behavior. Our simulations demonstrate a systematic progression of non-monotonic assembly with increasing portal methylation. This behavior is traced to the progressive destabilization of 2:2 complexes (two hosts assembled with two guests) rather than stabilizing other potential host/guest complexes that could be formed.
Design, System, ApplicationThe programming of aqueous phase assembly processes constitutes a grand challenge in soft matter physics. Deep-cavity cavitands, a class of water-soluble, bowl-like supramolecular hosts, readily bind non-polar guests via hydrophobic interactions to build well-defined complexes. Here we report a molecular simulation study of the impact of methylation about the rim of cavitand host pockets on the stoichiometry of their assemblies with n-alkanes. While non-methylated hosts exhibit a monotonic assembly pattern with increasing n-alkane size from monomeric to dimeric host complexes, increasing rim methylation progressively leads to the onset of non-monotonic assembly patterns, where the monomeric complex is reemergent for intermediate guest chain lengths. The effective use of a “throttle” between dimerized hosts hints at a novel route for manipulating host/guest assembly, forcing guests to thread constrictions that stabilize/destabilize specific complex structures. |
Motivated by these challenges, Gibb has explored the relationship between the functionalization of water-soluble deep cavity cavitand hosts and the complexes formed with n-alkane guests.5–8 Specifically, his group has examined octa-acid (host 0 in Fig. 1) and tetra-methyl-endo-octa-acid (host 4 in Fig. 1), which differ only by the presence of four methyl units that ring the portal to the hydrophobic, guest binding pocket of the cavitand. The n-alkane complexes of host 0 display a straightforward progression of assembly states with increasing guest length: methane (C1, where the subscript indicates the number of carbons in the n-alkane) does not bind the host; ethane (C2) forms a monomeric 1:1 complex (denoted i:j, where i and j indicate the number of host and guest molecules in a complex. Complexes with one host are referred to as simple, monomeric host–guest complexes, while those with two hosts are referred to as dimeric capsular complexes. These host/guest complexes are illustrated in Fig. 2); propane (C3) through octane (C8) form dimeric 2:2 complexes; while larger guests form dimeric 2:1 complexes. This progression from monomeric to dimeric assemblies is a monotonic assembly pattern. Host 4, on the other hand, exhibits a decidedly non-monotonic progression of assemblies with increasing guest length: C1 and C2 form monomeric 1:1 complexes; C3 through C6 form dimeric 2:2 complexes; C7 and C8 form monomeric 1:1 complexes; while C9 and longer guests form dimeric 2:1 complexes. In difference to host 0, that at most only forms dimeric complexes, host 4 can also form tetrameric and hexameric complexes with alkanes C17 and longer.8
Ashbaugh and Gibb reported molecular simulation studies of cavitand assembly with n-alkanes in water,9 breaking down the association process into elementary steps to understand the factors stabilizing distinct host/guest complexes. These simulations accurately captured the distinct monotonic versus non-monotonic assembly patterns of hosts 0 and 4. The non-monotonic assembly of 4 was found to arise from destabilization of the 2:2 complex. This destabilization was shown to result from the added methyl groups choking the portal region at the equator of the complex dimer, and limiting the ability of two alkane guests to thread between the hosts. 2:2 complex destabilization begins with guest C6, which is comparable in length to the depth of an individual host pocket. The 1:1 complex subsequently reemerges over the 2:1 complex since the 2:1 complex requires alkanes C9 and longer to bridge between two hosts. Within host 0, guests longer than ∼C15 must adopt a J-shaped conformational motif with a reverse turn in their main-chain. Interestingly however, simulations demonstrated that due to the portal narrowing within dimers of 4, alkanes cannot adopt such motifs.10,11 As a result, 2:1 complexes with guests C16 or larger are destabilized relative to the corresponding capsular complex with 0. A follow up simulation study of the transfer of alkanes into tetrameric and hexameric complexes of host 4 demonstrated that guest packing preferences can tilt the assembly equilibrium towards those larger assemblies,12 in agreement with experiment. These molecular simulations subsequently highlighted guest packing within confined host/guest complexes as a useful strategy for directing the stabilization of distinct assembly morphologies.
A question that follows from our previous studies is: what is the impact of partial methylation of the cavitand portal on their assemblies with n-alkanes? To address this question, we have performed a theoretical study of mono-endo-methyl-octa-acid (1), 1,3-di-endo-methyl-octa-acid (2), and tri-endo-methyl-octa-acid (3) (Fig. 1) complexed with n-alkanes from C1 to C14 to form 1:1, 2:1, and 2:2 complexes in aqueous solution. Molecular dynamics simulations were conducted to evaluate free energies for forming 1:1, 2:1, and 2:2 host/guest complexes along the association pathways illustrated in Fig. 2. These association free energies are subsequently utilized by a reaction network model we previously developed to predict the distribution for host/guest complexes formed as a function of the host methylation and guest length. While hosts 1 through 3 can in principle be synthesized, the cavitands would be formed in statistical yields and could not be readily purified. Here then, theory offers insight into the origin of the non-monotonic assembly in this interesting class of supramolecular complexes that cannot be met by synthetic means.
Complex stability was characterized by evaluating potentials-of-mean force (PMF) between hosts and guests. A PMF quantifies the interaction free energy between components along a designated reaction trajectory, which here lies along the host's four-fold (C4) rotational axis of symmetry.9 We consider three distinct PMFs (Fig. 2): the interaction between a single alkane and cavitand to form a 1:1 complex; the interaction between an empty cavitand (1:0) and a 1:1 alkane/cavitand complex to form a 2:1 complex; and the interaction between two 1:1 alkane/cavitand complexes to form the corresponding 2:2 complex. In the first set of simulations, we determined the PMF between a host and guest (C1 to C14) from bulk water. In these simulations the cavitand and guest were solvated by 2600 water molecules in a cubic simulation box. Restraint potentials were applied to two dummy atoms along the C4-axis of each host to align the cavitand along the z-axis of the simulation box. The first “bottom” dummy atom was determined by the average position of the four atoms connecting the four feet of the cavitand to the bottom row of aromatic rings, while the second “top” dummy atom was determined by the average positions of the four carbon atoms on the second row of aromatic rings closest to the cavitand portal (see ESI† Fig. S1). The dummy atom at the bottom of the binding pocket was spatially restrained with a harmonic force constant of 100000 kJ mol−1 nm−2, while the vector connecting the bottom atom to the top was fixed along the z-axis using a harmonic constraint of 50000 kJ mol−1 nm−2. The PMF was determined over a series of overlapping windows spanning from bulk water into the host pocket using umbrella sampling.25 The guest center was restrained to the C4-axis of the host using a harmonic potential acting normal to the symmetry axis with a force constant of 100000 kJ mol−1 nm−2. In the case of guests with an odd number of carbon atoms, the center was taken as the middle carbon along the chain backbone (i.e., carbon number (n + 1)/2). For guests with an even number of carbons, a dummy atom was placed between the n/2 and n/2 + 1 carbons to serve as the restraint center. Sample windows were simulated from 5 Å deep-inside the cavitand pocket, measured from the center of the top plane defined by the four carbon atoms on the second row of aromatic rings closest to the cavitand mouth, to 15 Å out into bulk solvent. Forty overlapping windows were used along the z-axis with the harmonic umbrella potential minimum separated in 0.5 Å increments and a force constant of 15000 kJ (mol−1 nm−2).25 Each simulation window was equilibrated for 1 ns, followed by a 15 ns production run. We have found in our previous simulations of cavitand/alkane interactions that this simulation time is sufficient to obtain reproducible, converged results,9,10,12 suggesting the guest conformational landscape has been well explored. System configurations were saved every 0.2 ps for post-simulation analysis. The PMF for forming the 1:1 complex was reconstructed from the overlapping windows using the weighted histogram analysis method.26
In the second set of simulations, we evaluated the PMF between an empty cavitand (1:0) and a second cavitand in a 1:1 complex with a C1 to C14 guest in water. The two cavitands were oriented with their binding pockets facing one another aligned along their C4-axes to form a dimeric 2:1 host/guest assembly. Both hosts were aligned with the simulation box's z-axis, using the same restraints as in the 1:1 complexation simulations. No restraint was applied to the guest, however, which was held within its host pocket via hydrophobic interactions. Sample windows were simulated from distances ranging from the center of the two cavitand faces, which established a separation of zero, to 13 Å into the bulk water. Twenty-seven overlapping windows were simulated, with the harmonic umbrella potential minimum separated in 0.5 Å increments and a force constant of 15000 kJ (mol−1 nm−2). The same simulation procedures and PMF reconstruction methods were used here as for the 1:1 complexation study. In addition, we considered the PMF between two empty hosts devoid of guests to form a 2:0 dimer. Approximately 3000 TIP4P/EW water molecules were used to solvate these complexes.
In the third set of simulations, we evaluated the PMF between two 1:1 host/guest complexes to form a 2:2 complex (Fig. 2). As in the 2:1 complexation simulations, the cavitands were oriented with their binding pockets facing one another aligned along their C4-axes. For host 1, 2, and 3 we simulated alkane guests up to C11, C10, and C10 in length, respectively. Longer guests exhibited increasingly destabilizing repulsive interactions. As above, no restraints were placed on the guests. The same simulation procedures, PMF reconstruction methods, and numbers of hydration waters were used here as for the 2:1 complexation study.
1:0 + G ⇌ 1:1, | (1a) |
1:0 + 1:0 ⇌ 2:0, | (1b) |
1:1 + 1:0 ⇌ 2:1, | (1c) |
1:1 + 1:1 ⇌ 2:2. | (1d) |
The equilibrium constants for these reactions, K1:1, K2:0, K2:1, and K2:2, are evaluated as a Boltzmann weighting of the minima in the PMFs (ωi:j) evaluated from the corresponding simulations described above. The equilibrium constants for the monomeric and dimeric host/guest assembly reactions subsequently are
K1:1 = αexp(−ω1:1/RT) and K2:j = βexp(−ω2:j/RT), | (2) |
The free host concentration, [1:0], is determined from the solution of a quadratic equation (see ESI† for full derivation)
2(K2:0 + K2:1K1:1[G] + K2:1K21:1[G]2)[1:0]2 + (1 + K1:1[G])[1:0] − [1]total = 0. | (3) |
The total host concentration, [1]total, corresponds to the amount of host added to solution distributed amongst all potential assembly states, i.e., [1]total = [1:0] + [1:1] + 2([2:0] + [2:1] + [2:2]). We assume [1]total = 3 mM, which corresponds to a typical experimental concentration. The alkane guest concentration was assumed to be saturated as described by the relationship
(4) |
As previously demonstrated, the relative stability of the distinct host/guest assembly states is dominated by the free energy minima of the PMFs, denoted ω1:1, ω2:1, and ω2:2, respectively. The 1:1, 2:1, and 2:2 PMF minima for hosts 0 through 4 as a function of the alkane guest chain length are compared in Fig. 4. The PMF minima for 1:1 complex formation for all the hosts exhibit an increasing attraction with guest chain length beginning with methane that plateaus for guests approximately longer than pentane (Fig. 4a). The PMF minima for the shorter guests (∼C4 and shorter) examined are comparable for all the hosts simulated. The plateau begins roughly for guests longer than the depth of the binding pocket. Longer guests subsequently are unable to stuff more methylene units within the pocket away from water and thereby do not gain any additional benefit for forming a 1:1 complex. Interestingly, the plateau for the methyl functionalized hosts (1 through 4) is more attractive than that for host 0, but are approximately the same as one another. Previously, we attributed the greater attraction between host 4 for longer guests compared to host 0 to increased van der Waals interactions between the methyl units of host 4 and the guests.9 We might then expect the plateau for hosts 1 through 3 to systematically deepen with increasing methylation between the host 0 and 4 limits, which we do not observe. This interpretation, however, does not consider the solvent's role on directing hydrophobic host/guest interactions. Moreover, we do not observe systematic variations with host methylation for the PMF minima of the short guests despite the systematic chains in host/guest van der Waals interactions. A definitive conclusion regarding the dependence of the 1:1 complexation plateau on host methylation is thus not immediately apparent.
The 2:1 PMF minima are attractive for all guest/host combinations considered (Fig. 4b). For guests up to C8, ω2:1 weakly decreases with increasing alkane chain length with little distinction between the free energies for any of the hosts within the simulation noise. Beginning with C9, ω2:1 drops precipitously with increasing chain length further stabilizing the 2:1 complexes. This guest size corresponds to the point at which a guest readily spans between the two hosts to gain additional favorable van der Waals interactions to stabilize the complex. Similar to the 1:1 free energies, ω2:1 drops to lower levels with increasing chain lengths for the methylated hosts (1 through 4) compared to that for host 0. While ω2:1 for hosts 1 through 3 are practically indistinguishable, ω2:1 for host 4 exhibits a minimum at C12 after which the complexation free energy increases with increasing guest length. In our previous work considering guests up to C16 the 2:1 complex of host 4 ultimately becomes unstable.9 Experimentally8 and from simulation12 this host transitions from a dimeric 2:1 complex to a tetrameric 4:2 complex for sufficiently long guests. Host 0, on the other hand, only forms dimeric complexes with increasing guest length. Based on these observations, we may anticipate that ω2:1 for hosts 1, 2, or 3 may exhibit a free energy minimum with increasing alkane chain length that destabilizes the dimer in favor of a tetramer. That lies beyond the scope of the present study, however.
The most significant assembly PMF changes are observed for 2:2 complexation (Fig. 4c). Generally, ω2:2 for all hosts is attractive for shorter chains and then dramatically diverges towards more positive free energies beyond a characteristic alkane chain length. This divergence was previously demonstrated to be correlated with constriction of the portal region at the dimeric complex equator by the endo-methyl rim groups. That is the endo-methyls choke the portal region between hosts blocking guests in opposing hosts threading through the portal. The divergence begins for guests C6 and longer for the host 4 dimer, which has the narrowest portal. This guest length corresponds to the depth of an individual host pocket as inferred from the ω1:1 plateau (Fig. 4a). While the divergence length for hosts 0 and 1 are similar, the divergence systematically shifts to increasingly shorter guest lengths for 2, 3, and 4. This observation agrees with the interpretation of the portal region becoming progressively constricted as more endo-methyls are added. We may anticipate then that the 2:2 complexes will become increasingly unstable with increasing methylation, tipping the balance towards other assemblies.
The PMF minima reported in Fig. 4 can be utilized within the host/guest assembly model described above to predict the distribution of complexes between 1:0, 1:1, 2:0, 2:1, and 2:2 for a given guest. The predicted population of assemblies for host 3 as a function of the alkane chain length is reported in Fig. 5. This host/guest system exhibits non-monotonic assembly characteristics with increasing guest chain length. Specifically, the dimeric 2:2 complex dominates for guests from C2 to C5, the monomeric 1:1 complex dominates for guests C6 to C8, and the dimeric 2:1 complex dominates for guests C9 and longer. Interestingly, even in the absence of any guest (C0), the dimeric 2:0 complex is predicted to exhibit a population comparable to the free 1:0 host within the simulation error. Guest free dimers are not observed experimentally. Moreover, our previous study of hosts 0 and 4 predicted a negligible population of 2:0 complexes. Based on the expectation that the guest is a necessary element of the assembly to draw the two hosts together, it is likely that that the predicted population of 2:0 complexes is erroneous. Indeed, no 2:0 complexes are predicted for guests longer than C1. We attribute this prediction to the fact that small errors on the order of RT are sufficient to shift the populations of complexes observed, especially for the shorter guests. Examining the 2:0 PMF minimum for hosts 2 and 3 we observe predicted free energies ∼10 kJ mol−1 (4 RT) more stable than those for hosts 0, 1, and 4 (Fig. 4c). Given the lack of systematic variation in the PMF minimum with increasing hosts methylation, it appears the predicted overstabilization may be diminished with increasing simulation run times. Another potential source of error may result from the simplified reaction coordinate along the principle axis of host symmetry assumed to evaluate the equilibrium constants within the host/guest assembly model (eqn (2)). To alleviate this difficulty here after we assume K2:0 = 0 within the host guest assembly model, eliminating the potential for forming 2:0 complexes. The impact of this assumption is to redistribute the population of assembly states amongst the 1:0, 1:1, 2:1, and 2:2 complexes for C0 (no guest) and C1. No complex population differences were observed for longer alkanes. Thus, this assumption has no impact on the onset of non-monotonic dimer-to-monomeric-to dimeric complex assembly patterns for longer guests.
Fig. 5 Population of 1:0, 1:1, 2:0, 2:1, and 2:2 complexes for host 3 as a function of the alkane guest chain length predicted from the host/guest assembly model using the free energies reported in Fig. 4. The symbols for each complex are defined in the legend. The error bars indicate one standard error. |
The predicted distributions of 1:0, 1:1, 2:1, and 2:2 complexes as a function of the alkane guest chain length are reported in Fig. 6 for hosts 0 through 4. As previously documented, the dominant (most populous) complexes observed for host 0 progresses from 1:0 for C1; to 1:1 for C2 and C3; to 2:2 for C4 through C8; to 2:1 for C9 and longer guests (Fig. 6a). Thus host 0 is predicted to exhibit monotonic assembly from monomeric to dimeric complexes with increasing alkane chain length, as observed experimentally. Similar monotonic assembly is observed for host 1, although the population of 1:1 assemblies is suppressed for the shortest guests (Fig. 6b). Interestingly, a small (∼10%) population of 1:1 complex is observed for C9 near the transition between 2:2 and 2:1 assemblies, hinting at the potential of a reemergent population of monomeric complex. This population of 1:1 complex near the 2:2 to 2:1 transition grows to ∼40% of the total for 2 (Fig. 6c), albeit with its peak maximum shifted to C8. This population of 1:1 complex finally becomes dominant for guests from C6 through C8 complexed with 3 (Fig. 6d). The host subsequently exhibits full non-monotonic assembly from monomeric, to dimeric, to monomeric, then back to dimeric complexation with increasing alkane chain length. Interestingly, the reemergence of the 1:1 population for longer guests is accompanied with growth in the 1:1 population for shorter guests as well, with a minimum between the short and long chain peaks. This trend continues for host 4, which exhibits a progression from 1:1 complexes for C1 and C2; to 2:2 complexes for C3 through C5, to 1:1 complexes for C6–C8; to 2:1 complexes for C9 and longer guests (Fig. 6e). The 1:1 population minimum between the short and long chain guests is more clearly defined for host 4 than for host 3, continuing the systematic trends observed with increasing host methylation.
Fig. 6 Population of 1:0, 1:1, 2:1, and 2:2 complexes as a function of the alkane guest chain length predicted from the host/guest assembly model using the free energies reported in Fig. 4. Figures a, b, c, d, and e report results for hosts 0, 1, 2, 3, and 4, respectively. The symbols for each complex are defined in the legend in a. Error bars, which are comparable to those reported in Fig. 4, are neglected for clarity. |
The emergence of the non-monotonic assembly pattern can be more directly visualized by evaluating the mean host aggregation number as
〈N〉 = p1:0 + p1:1 + 2(p2:1 + p2:2), | (5) |
Fig. 7 Host aggregation number, 〈N〉, as a function of the alkane guest chain length predicted from the probabilities reported in Fig. 6. Graphs for each host are identified by the text at the top right-hand side. |
Footnote |
† Electronic supplementary information (ESI) available: Full derivation of eqn (3); dummy atom placement to align cavitands and guests along their reaction coordinate; GROMACS topology files for simulating hosts 0–4. See DOI: 10.1039/c9me00076c |
This journal is © The Royal Society of Chemistry 2020 |