Programmable synthesis of organic cages with reduced symmetry

Integrating symmetry-reducing methods into self-assembly methodology is desirable to efficiently realise the full potential of molecular cages as hosts and catalysts. Although techniques have been explored for metal organic (coordination) cages, rational strategies to develop low symmetry organic cages remain limited. In this article, we describe rules to program the shape and symmetry of organic cage cavities by designing edge pieces that bias the orientation of the amide linkages. We apply the rules to synthesise cages with well-defined cavities, supported by evidence from crystallography, spectroscopy and modelling. Access to low-symmetry, self-assembled organic cages such as those presented, will widen the current bottleneck preventing study of organic enzyme mimics, and provide synthetic tools for novel functional material design.

For this reason, our approach has been to tune specic promising cage classes based on amide-linkages, which offer greater stability and post-functionalisation [58][59][60][61][62] options than the imine variants.To this end, we recently reported methodology to access robust, soluble and functional organic amide-linked cages 63 using an in situ Pinnick oxidation locking approach, 64,65 which advanced important work by Mastalerz. 61,66he resulting cages, which can be prepared on gram scale, are promising as sensors and catalysts as they feature a pair of endohedral antipodal carboxylic acid groups that resemble the enzyme motif found in a broad family of aspartyl proteases and glycoside hydrolases. 67,68The activity of these functional cages is expected to depend on cavity height, internal functionality, edge piece functionality, and edge piece steric presence, as well as symmetry.Towards our efforts to tune cavity properties, we now report a series of rational design principles that enable programable control of cavity shape, size, and symmetry (Fig. 1), supported by modelling, spectroscopy, crystallography, and exemplication of properties.Importantly, and unusually, we focus on the conformational preferences of the linking groups (amides) rather than the bonding vectors dened by the building block geometries.We rst decode the geometric rules underpinning the amide conformational preferences for a dynamic low-symmetry cage, 1.We then demonstrate how rational exploitation of these rules gives access to geometrically well-dened low symmetry cavities.

Results and discussion
2.1 Dening the geometric code underpinning symmetry of cage 1 2.1.1Symmetric cage 1 presents a reduced-symmetry conformation.In 2023, we reported the synthesis of the [2 + 3]  hexaamide cage 1 by the in situ trapping of metastable imine assemblies. 63We now report the single crystal X-ray structure of diacid cage 1 (Fig. 2d).Although symmetric in design, cage 1, like its dimethyl ester analogue 1e, 63 did not crystallise in the naively expected symmetric D 3h geometry that denes the trigonal prism cage topology 48 (oen termed [2 + 3] or Tri 2 Di 3 cages 48 ).In the crystal structures of both cages 1 and 1e, four of the six amide carbonyl groups are pointing out of the cage, with the remaining two, at the top and bottom of two separate edges, pointing inwards.This means both "symmetrical" achiral cages 1 and 1e display asymmetric chiral cavities in the solid state.We set out to understand this behaviour, believing it could underpin novel approaches to accessing reduced symmetry cages.
2.1.2The cavity of cage 1 is dynamic, but well-dened.In principle, any number of the six amide linkages could orient with the carbonyl oxygen pointing into or out of the cagethere are 13 unique permutations of six carbonyl orientations for planar 69 trans-amides, which we will refer to as conformations C1-C13 (Fig. 2a and Table S11 †).Three are chiral (C3, C8 and C9).
DFT models (Fig. 2b and Tables S12-S15 †) indicate C5 is predominant in solution (THF), with signicant amounts of C9 (as seen in the X-ray structures of 1 and 1e) accessible at 298 K. Cage 1 undergoes dynamic exchange between conformers, supported by variable temperature (Fig. S17 and S18 †) and NOESY 1 H-NMR data (Fig. S30 †), along with molecular dynamics simulations (nanosecond exchange) (Tables S17 and  S18 †).There are two crucial corollaries: rst, the different conformers have vastly different cavity heights/properties and so access of specic conformers would allow tuning of the cavity height and symmetry (Fig. 2c).Second, the population of cage 1 is acutely weighted towards a few key structures in solution (Fig. 2a and b), which suggests that control of the conformation and therefore the symmetry of the cages is highly achievable.Thus, we sought to understand the natural bias towards low symmetry in cage 1 as a means to access tuned cavities through rational design.
2.1.3Cavity symmetry is a function of predictable geometric rules.Analysis of the conformers C1-13 in Fig. 2 and their energies revealed three key observations, which we codi-ed as geometric rules underpinning cage behaviour (Fig. 1a).
(1) The low energy structures in Fig. 2 employ the amide conformational pattern 01-10-XX to maximally distribute strain.This is readily understood by noting that the amide bond linkages deviate from linearity: the CN^C angle opens to 129.5°, whilst the NC^(]O)C angle narrows to 114.8°(Fig.2a) 69,70 and so each terphenyl edge piece can project different bonding vectors depending on the conformation of the amide linkages (00, 01 and 11).Intuitively, "in-out" pairs of amides (01) cancel the angle deviations within an edge piece (Fig. 1a, centre).Likewise, up/down pairs of edges (01-10) cancel deviations between edges.Together, these allow the two triptycene caps to remain parallel, and accommodate a third edge piece.More generally, the sum of the internal angles of a convex 2D polygon with n sides (like benzene) must satisfy P n 2D q ¼ ðn À 2Þ180 : The anglepairing facilitated by conformers C5 and C9 satises this requirement, and so maximally distributes strain.
(2) Examining the DFT models, conformer C13 is axially twisted (25°) and energetically accessible, whilst C1 is untwisted (0°) and energetically inaccessible (Fig. 2, 2b).Geometry again explains this observation.Twisting a polygon into a third plane (e.g.benzene / cyclohexane), results in the inequality P n 3D q\ðn À 2Þ180 : This means planar polygon angle sum decits (but not excesses) can be accommodated without bond angle strain if low energy twisting (out of plane) is possible.In the case of conformer C13, the six "out" amide linkages result in an angle sum decit (−24°), which induces axial twisting (+25°) to relieve the bond angle strain.The angle excess in C1 cannot be accommodated, explaining its high energy.
Axial twisting bears its own cost: it requires a slight biaryl twisting in the terphenyl groups (Fig. 1a).This is tolerated, since the penalty for reducing conjugation within the terphenyl group by biaryl twisting from 34°(cage 1, C9) to 39°(cage 1, C13) is less costly than permitting bond angle strain from the angle decit. 71,72Since cage height can be controlled by setting the cage conformation (Fig. 2c), the cage height can be programmed by enforcing the amide conformations, which also controls twisting (Fig. 1B).
(3) A nal corollary is that the reverse process is possible: stabilising axial twisting can set the amide conformation.Since the strain from axial twisting can be dispersed in the edge-piece biaryl dihedral angles, it is possible to enforce biaryl twisting to reduce the cost of axial twisting, which alters the amide conformer preference and therefore the cage shape and size (Fig. 1D).We now exemplify these three rules to program cavity shape, size and symmetry.This new approach uses a dynamic system to solve geometric preferences, and then deploys rationally designed building blocks that reinforce the preferences to access stable cages with low symmetry.

Programming the cavity height using conformational rules
Use of hydrogen bonding to override geometric preferences has been applied widely, from helical peptides 73 and macromolecules 70,74 to organic cages. 75We wondered whether cages containing pyridyl bisaldehyde 6 (Fig. 3) would orient the amide NH groups internally due to hydrogen bonding (or by reducing N/ C]O dipole clashes). 70If so, then cage 2e would exist as C13, not C5, and the resulting angle decit would illicit twisting, and decrease the cavity height.Accordingly, we synthesised tetrapyridine hexaamide [2 + 3] cage 2e in up to 71% yield from 5 and 6 using our previously developed in situ Pinnick oxidation strategy 63 (Fig. 3).Cage 2e indeed crystallised in conformer C13, and shows a large twist angle of 34°(Fig.1B and S21 †) (cf.1e in C5 with no twist), and a signicantly reduced cavity height of 6.6 Å (cf.cage 1e = 8.8 Å). 63 NOE data shows exchange between the NH signal and the internal triptycene CH 5 , indicating that C13 predominates in solution for hexapyridine cages (Fig. S31 †).Control of this acid-acid distance is of high interest in tuning the cage as a lysozyme mimic; we will report studies to this end separately.The ability to reliably install helicity may also allow cage chirality by induction.

Programming symmetry using conformational rules
Recent work from Cooper, Jelfs, Slater, and Greenaway has focused on using computational screening to predict imine cage assembly. 53,55,76,77Using our geometry heuristics, we were able to design a low symmetry cage without further computation.Unsymmetric bisaldehyde 7, with one pyridyl aldehyde and one aryl aldehyde, can in theory form two [2 + 3] cages: all pyridine units can be adjacent to the same triptycene ("all up" = UUU: 1/4 chance), or one can be distal ("up-up-down" = UUD: 3/4 chance) (Fig. 4a). 50On the basis of our analysis of cage 1 (C5 preferred), and the observation that C13 is preferred for pyridyl cage 2e (pyridyl-directed amide orientation), we predicted formation of the cage with the UUD conguration and with cooperative matched pairs (C5 = 01-01-10) with "out carbonyls" adjacent to the pyridine units.The statistical (unbiased) probability of this outcome (UUD aligned with C5) is 1.2% across all possible congurations & conformations.When three equivalents of mixed bisaldehyde 7 were subjected to our assembly/oxidation cage protocol, 63 we observed a single cage species and conformer in the crude NMR.Purication by recycling GPC provided a pure sample of cage 3e in 34% yield, which could be unambiguously assigned by 1 H-NMR data as the expected UUD & C5 conguration and conformer.Notably, NMR data was consistent with the required C s symmetry for UUD (Fig. S3-S7 †) (2 : 1 signal ratios).Distinct and convincing ratios of NOE exchange between amide NH groups adjacent to the pyridine groups and either internal (5a, strong) or external (7a, weak) aryl-H environments were observed for both the UU  (Fig. 4b) and D (Fig. S6 and S32 †) environments, conrming that "N" environments were matched with "0" carbonyl out conformation.Additionally, the triptycene CH environments adjacent to a non-pyridyl aryl group showed reverse chemical shi trends compared to the analogous pyridyl-adjacent environments (Fig. 4c).Slight broadening of the environments near the non-pyridyl amide groups suggest amide rotation is limited to non-pyridyl amides, perhaps accessing minor amounts of C9 (and perhaps C12 & C13).We have been unable to obtain a suitable crystal for diffraction so far, as oen observed for lower symmetry cages. 53Crucially, no UUU conguration was detected in the crude NMR.This self-sorting synthesis exploits the theoretical dynamic conformational symmetry-reduction process and translates it into a stabilised congurational low symmetry cavity.

Programming the cavity size using modular synthesis and steric engineering
Tuning of cage windows 78 and cavity size and volume is a key technique for tuning cage properties. 77Modications at the periphery typically alter the window size, although they can also inuence cage topology. 79,80We sought to alter the cage cavity size by replacing the central aryl groups in the terphenyl edge pieces of cage 1 with 2,6-di-tert-butyl-anthracene groups.In solution (e.g.DMSO-d 6 , benzene-d 6 , d-chloroform), the anthracenyl bisaldehyde precursor 8 presented as syn/anti atropisomers (∼1 : 1) (Fig. S8 †) with a rotational Gibbs energy barrier of 87.7 kJ mol −1 , corresponding to a half-life on the order of minutes at 25 °C or milliseconds at 100 °C (Fig. S9 and Table S1 †), indicating the anti atropisomer would not hinder cage self-assembly reactions requiring the syn geometry.The anthracene cage 4 was assembled as for cages 1-3, but the hexaimine formation was performed at 100 °C for 4 h to aid isomerization (Fig. 5).In situ Pinnick oxidation conditions afforded dimethyl ester cage 4e in 61% yield.Unlike 1e, complete methyl ester hydrolysis of 4e to give 4 required heating at 60 °C over 3 days with NaOH with added THF for full solubility, indicative that the cavity environments are very different (cf. 2 h at ambient temperature to hydrolyse cage 1e). 63oluble anthracene cage 4 (>20 mg mL −1 , THF) exists as two pairs of enantiomeric interconvertible atropisomers (Fig. S11 †), accessed by 180°rotation of 1, 2, or 3 anthracenyl units from any starting point.Statistically, there are two equivalent congurations with D 3 symmetry, and six with C 1 . 1 H-NMR analysis indicates a roughly statistical mixture (2 : 6) of the two possibilities exists at equilibrium in THF at 298 K (Fig. S12 and S13 †).The crystal structure shows only one conformer; C13 with ∼D 3 symmetry, with a large axial twist angle of ∼32°, which appears to originate from the large dihedral angle between the anthracenyl groups and the anking aryl groups (average dihedral angle = 67°).This means that aryl-anthracene conjugation is already reduced in the edge pieces, and so the cage no longer pays a biaryl twisting cost.Since axial twisting can promote favourable symmetry lowering, C13 predominates (in the solid state at least; solution phase behaviour may be more complex, see Fig. S33 †).The axial twist may also be favoured due to a reduction in clashes between adjacent anthracene groups.In the crystal structure, the direction of the helical twist is determined by the axial atropisomeric conguration of the anthracenyl t Bu groups.This indicates another mode of cavity symmetry-lowering, although we have yet to realise control over it: cages formed with stable (M,M) or (P,P) enantiomers of bisaldehydes like 11 are predicted to translate their axial congurational chirality to a conformational helical chirality. 42,47Instead, we were able to demonstrate the sizeexclusion properties of cage 4 by observing a switch in binding preference for increasingly large bisamine guests (between the two carboxylic acids) at 298 K in THF relative to cage 1 (Fig. 5 and S14 †). 63Cage 4 therefore highlights programmable cavity size exploiting a sequence of heuristics, although we note that rational control becomes more difficult when the factors contributing to the energy become more numerous and less distinctive.In these cases, control over solution-state preferences becomes more challenging.

Discussion
Many current approaches to access low-symmetry cages use geometrically unsymmetric edge pieces. 53,80The aldehydes used in the current work are all geometrically symmetrictheir bonding vectors and steric requirements are equivalent.Yet, within the amide cages, they undergo a symmetry reduction.2][83][84] The observed symmetry-lowering here is a result of the linker design within the cage polymacrocycle system; the same preferences do not necessarily exist outside of the cage context.Inside a polymacrocycle, the angle sum requirements compel competing preferences to "rank themselves" to equally distribute strain. 85,86his can cause symmetry lowering in a way not available for xed bonding vectors.
"Self-sorting" describes the congurational assembly preference of components in a self-assembling mixture. 87,88lthough self-sorting inherently includes conformational biases, symmetry is usually dened by the conguration.In the current work, conformational preferences can affect the symmetry independently to conguration (e.g.cage 1).In our synthesis of cage 3e, we harness this conformational preference to drive congurational self-sorting.
We therefore emphasise that the technique discussed here should be viewed as a rational approach to achieve lowsymmetry assemblies using self-assembly synthesis, rather than merely an observation implying the symmetric structure is strained.Stated clearly, the concept is this: assemblies based on symmetric polyhedra can be biased to access non-symmetric conformational minima by incorporation of motifs in which strain cannot be symmetrically distributed (in the polymacrocycle environment).We tentatively term this, as yet unnamed, approach: "conformational autodesymmetrisation".

Conclusions
We have exemplied programmable cavity tuning and symmetry-lowering of amide-linked organic cages using heuristics derived from conformational analysis to access three new cage architectures.By subtle modication of the bisaldehyde edge-piece fragments in the three cages, we were able to tune the amide conformational preferences, which are intimately coupled to the cage axial twist and edge-piece biaryl twist angle.These parameters in turn dene the cage height, symmetry, and volume.In essence, we decoded the geometric preferences of a dynamic cage and applied them to access cages with well-dened geometries with reduced symmetry.Notably, we were able to reduce the symmetry of a D 3h [2 + 3] cage architecture to C s symmetry by using a conformational autodesymmetrisation approach, in which building blocks are selected to generate an assembly in which strain cannot be symmetrically distributed.The results are supported by crystallography data and NMR assignments, which demonstrate strong conformational preferences in solution for cages 2e and 3e.The protocols reported here represent important advances in tailored cage synthesis, and will lead to methods to access robust, chiral cages, with controllable exibility, and internal functionality mimicking enzyme motifs.

Fig. 1
Fig.1Programmable organic cage cavity tuning and symmetry lowering reported in this work.(a) Decoding the geometric rules underpinning the conformer landscape of cage 1 allows a set of codable rules to be defined.(b-d) Systematic exploitation of the conformational rules for programmable cage cavities with defined shape and reduced symmetry.

Fig. 2
Fig. 2 (a) The 13 conformers C1-C13 of cage 1 according to amide orientation [0 = carbonyl oxygen is oriented outwards; 1 = inwards] and their interconversion network.Their relative populations as calculated by MD simulations are shown as a percentage.Chiral conformers are marked with a star.(b) The table shows DFT energies (PBE0-D3BJ-def2-svp, CPCM(THF)) and Boltzmann weighted populations (298 K) for some of the conformers (see Tables S12-S15 †).(c) The graph shows calculated cavity heights measured between the two carboxylic acid carbon atoms (r CC ) for each conformer.Calculated axial twists are shown for C13 (left) and C1 (right), along with the internal macrocyclic angle sum, S, and the deviation (in brackets) from the ideal planar sum (540°).(d) Crystal structure data is shown for cage 1 (conformer C9).

Fig. 3
Fig. 3 Synthesis of cage 2e and crystal structure showing the expected C13 conformer (see also Fig. 1b for the axial twisting).

Fig. 4
Fig. 4 (a) Statistical permutations of configuration and conformation for [2 + 3] amide cages formed with an unsymmetric bisaldehyde.(b) Synthesis of cage 3e confirms the expected configuration and conformation according to the geometry heuristics discussed above.(c) 1 H-NMR data (CDCl 3 ) demonstrating the chemical shift effects of localised carbonyl orientation differences in cage 3e.

Fig. 5
Fig. 5 Synthesis of cage 4 depicting atropisomers and rotational barriers of bisaldehyde 8. Crystal structure of cage 4 (side view and top view, see also Fig. 1d) in conformer C13.Size exclusion properties of cage 4 compared to cage 1 demonstrated by comparison of 1 : 1 binding constants (298 K, THF) of bisamine guests.