Requirements of Constrictive Binding and Dynamic Systems on Molecular Cages for Drug Delivery

1. Introduction

Molecular cages are supramolecular structures that can isolate guest molecules from the surrounding media by encapsulation in their central cavity, mimicking the encapsulation processes found in biological systems [1,2,3]. In fact, in biology compartmentalization has a vital importance in keeping the living organisms away from equilibrium, resulting in a complex network of non-equilibrium chemical systems [4]. Molecular cages are therefore suitable systems for mimicking these complex functions. The three-dimensional shape of their cavity gives a unique preorganization with enhanced affinity for guests in comparison to related supramolecular architectures such as macrocycles [5,6]. This property makes cages unique species for diverse applications such as catalysis [7,8,9,10,11], sensing of diverse chemical species [12,13,14,15,16,17,18,19], separation of chemicals [20,21,22,23,24], removal of pollutants from water [25,26,27,28], stabilization of chemical species [29,30], biological applications [31,32,33,34,35,36,37,38,39,40], and many others [1,2]. In addition to these properties, molecular cages can be engineered to transport cargo molecules [41] with stimuli-responsive properties to pH [34,42,43] and light [44,45,46,47], among others [48,49,50,51,52,53,54]. Typically, cages are prepared by the thermodynamically controlled self-assembly of metals and ligands to yield metallo-cages or by the self-assembly of only organic ligands to yield pure organic cages [1,2,55,56,57]. To facilitate the design of cages with specific geometries and properties, computational modelling has been extensively used. This allows reducing trial-and-error attempts or predict host-guest properties [58,59,60,61,62,63,64].

Focusing on therapeutic applications of molecular cages, cages are capable of encapsulating drugs, forming inactive guest⊂cage complexes, in which the activity of the drug is restored upon their release from the cage [31,32]. In this area, it is crucial to design cages that efficiently encapsulate drugs and respond to selective stimuli for controlled drug release [34,65,66]. Various systems have been developed for this purpose, most of which rely on equilibrium processes, which present limitations related to dynamic equilibria and drug dissociation when applied in a physiological environment [1,2]. Achieving systems where drugs are kinetically trapped inside the cage, is a challenging task. To accomplish this, the constrictive binding strategy has been proposed in simple host–guest systems, where the guest in–out activation barrier prevents rapid equilibrium between the drug inside the cavity and the external environment. The in-and-out passage of the guest molecule requires heating to widen the portals to create sufficient space [67].

Cram, back in 1991, reported an example of constrictive binding of a 1,1,2,2-tetrachloroethane guest molecule using a fully organic hemicarcerand host [68]. This guest⊂cage complex is stable at room temperature in the solid state or in solution, but slowly decomplexes by heating it at 100–134 °C. The van’t Hoff analysis provided an activation barrier of 24.6 kcal/mol, with a t_1/2 value of 18 h at 100 ^oC. Further studies by Cram showed that the in–out activation barriers are guest-dependent for a series of hemicarcerands, with the larger guests found to have lower activation energies for decomplexing. This is likely due to an increased compression of the cage to accommodate them, which are released upon decomplexation [69]. The relative size of the guest regarding the size of the portals of the cage is a key parameter for successful constrictive binding. If the guests are too small, constrictive binding is ineffective as the guest molecules pass through the portals; if the guests are too large, the energy barrier becomes too high, preventing complexation from occurring [70,71]. Both guest shape and size influence the observed constrictive binding [72]. As a result, the in-and-out kinetics of the guest depend on the cage’s conformation and are also correlated with the cage–guest affinity, where stronger affinity leads to slower kinetics [73]. The binding properties in these guest⊂cage complexes can be described as the combination of intrinsic binding (i.e., free energy difference between the complex and free cage and guest) and the constrictive binding as the additional free energy barrier associated with the guest passing through the portals of the cage (Figure 1) [75]. These systems, in which the guest molecule is trapped inside the cage, and it is only released from it under specific conditions, act as a gating mechanism as described by Houk [74,75,76,77,78].

Metallo-organic cages have the same host–guest behaviour as organic cages. Fujita and his team have shown a “ship in a bottle” entrapment-type synthesis showing that a large labile cyclic silanol, that fits tightly to the cage cavity, prevents its hydrolysis for more than one month [79]. This shows the feasibility of using molecular cages to effectively isolate the encapsulated guest from the surrounding media, highlighting the importance of having a large enough sized guest that cannot pass through the portals of the host. If the size of the guest is smaller than the portal, Raymond showed that the partial dissociation of the host structure can create a portal for in–out guest passage, and the deformation of the host structure can create a dilated aperture for guest passage without any host rupture [80].

Nitschke and his team measured the rate constant for guest uptake (k_in) and the association constant (K_Ass) for Nitschke’s water-soluble Fe₄L₆ metal–organic cage. We have carefully reanalyzed this data and determined guest release rate constants (k_out) as k_out= k_in/K_Ass, showing a guest release decrease with guest size. On one side, the guest must have a smaller size than the cavity size (150 ų) as guests with a size of 135 ų or larger do not bind. For smaller guests, the k_out decreases with the size of the guest, from 5 ×10^–2 s^–1 for acetone (73 ų) to 5 ×10^–8 s^–1 for cyclohexane (111 ų). These results show an impressive change of 6 orders of magnitude in the out-rate, changing the release timescale from seconds to months, from the smaller to the larger guest [81].

In this work, we study the thermodynamic and kinetic requirements of guest⊂cage complexes for drug delivery applications. We focus on both, dynamic and constrictive binding systems, analyzing the effects of dilution, binding constant strength, and the activation energy required for the encapsulated guest to escape the cavity of the cage in operational systems.

2. Materials and Methods

The molecular encapsulation kinetics and thermodynamics have been obtained using standard 1:1 host–guest binding isotherms. Simulations were performed using the R software [82] and the RStudio software interface [83]. Differential equations, corresponding to the host–guest kinetic models, were solved with the library deSolve using the standard parameters [84]. The Eyring equation was used to convert activation free energy barriers into kinetic constants [85].

3. Results and Discussion

To explore the effects of dilution, binding constant strength, and the guest in–out activation energy, we modelled the host–guest encapsulation process considering the in-and-out processes involved in the encapsulation equilibrium (Figure 2). The in-step of guest encapsulation involves the reaction between a guest molecule and a host molecule; while the step of guest release involves a dissociative mechanism creating an empty cavity. This is a reasonable assumption considering the large host cavity occupancy required by the guest [86,87,88]. The cage formation step is, therefore, a second-order reaction, while the dissociative mechanism for the decomplexation step is a first-order reaction with the corresponding equations described in Figure 2.

3.1. Effects of Dilution in Guest⊂Cage Complexes

A large number of the reported cage structures in literature have sufficiently large portals that allow the fast entry and exit of guests from the cavity, allowing these systems to operate under equilibrium conditions at room temperature. These systems result in labile guest⊂cage complexes, where the guest can rapidly pass in–out of the cage. When the guest⊂cage complex is diluted, a re-equilibration takes place as dictated by the equilibrium constant, resulting in the guest escaping from the cage cavity. As the required concentrations for biological experiments are usually in the micromolar range, this produces practically no significant binding, unless the binding constant is as high as 10⁶ or 10⁸ M^–1. Figure 3a shows the effect of the binding constant on the encapsulation equilibrium, for example, when K_Ass = 10⁸ M^–1 a 4% of the guest is released from the cage at 5 µM concentration, and nearly 40% if K_Ass = 10⁶ M^–1. The amount of encapsulated guest can be increased by using an excess concentration of the cage. According to Le Chatelier principle, the excess of cage shifts the equilibrium towards the formation of the host–guest complex (Figure 3b). For example, when the association constant is 10⁶ M^–1 and the concentration of the guest is 5 µM, an increase of cage concentration from 5 µM to 25 µM rises the amount of encapsulated guest from 60% to 95% (from Figure 3a to Figure 3b). Thus, cages with a good affinity towards the guests may be suitable for biological applications by using either equimolar amounts, if the association constant is as high as 10⁸ M^–1, or using an excess of the cage to favor encapsulation. Note that, these systems may be suitable for in vitro studies, as it is possible to set up the concentration in the well, but not suitable for in vivo studies, where additional dilution effects will occur. Therefore, to preserve the encapsulated guest in the guest⊂cage complex after dilution, it is necessary to develop systems with constrictive binding.

3.2. Energy Barrier for Guest Escaping the Cavity in Guest⊂Cage Complexes

To overcome the limitations of the guest⊂cage complexes that operate under equilibrium conditions, it is necessary to develop kinetically locked guest⊂cage systems, i.e., systems under constrictive binding. We have simulated the guest release from a guest⊂cage complex at different energy barriers and association constants considering an initial guest⊂cage concentration of 1 µM (Figure 4). When the association constant is as low as 10³ M^–1 and the guest out activation barrier is 23 kcal/mol or lower, a complete release of the guest is achieved in less than 20 h (Figure 4a). If the association constant is 10⁶ M^–1, a similar release kinetics dependency with the guest out activation barrier is observed (Figure 4b), but with a significant difference, in this case, the larger affinity results in a significant amount of encapsulated guest when the equilibrium is reached. These results show that guest⊂cage systems with a guest-out activation barrier of at least 25 kcal/mol are suitable to keep 95% of the encapsulated guest for at least 10 h. These inert systems are ideal for achieving the required performance in biological applications, as they will not suffer from the re-equilibration by dilution effects, making them suitable for in vivo studies.

The results from the simulations of Figure 4 demonstrate that guest⊂cage systems with an activation barrier of at least 25 kcal/mol for guest exit are ideal “gate closed” systems, effectively keeping the guest inside the cage. Engineering the structure of cages with stimuli-responsive motifs results in a “gate closed”–“gate open” system for on-command guest release. In these systems, the encapsulated guest is not able to escape from the cavity of the cage in the “gate closed” (i.e., large guest out activation barrier) until a certain stimulus is present that activates the “gate open” state (i.e., low guest-out activation barrier). We have simulated the release of the guest from a guest⊂cage at the concentration of 1 µM with a guest-out activation barrier of 26 kcal/mol. A minimal guest release is observed until the gate opening occurs in response to a specific stimulus that reduces the barrier to 23 kcal/mol (Figure 5). This change in the activation barrier leads to complete guest release when the association constant is 10³ M^–1 (Figure 5a), and 60% release when the association constant is 10⁶ M^–1, due to the equilibrium reached between the host and guest (Figure 5b).

The “gate closed”–“gate open” systems are, therefore, ideal for biological applications due to their release properties. A last aspect to consider is the feasibility of preparing the guest⊂cage complex under chemical synthetic conditions. An effective guest⊂cage synthesis requires a high association constant to drive the formation of the host–guest complex. Therefore, from the synthetic point of view, an association constant of 10⁶ M^–1 would be preferred. However, as described in Figure 5b the high guest–cage affinity does not allow the complete release of the guest due to encapsulation equilibrium. Developing a more sophisticated guest⊂cage system that simultaneously produces gate opening and affinity reduction in response to stimuli would be ideal. This can be achieved for example by partial or full cage disassembly. We have simulated using the same conditions described in Figure 5, but adding to the reduction of the guest-out barrier in the “gate open” event a reduction of the association constant (Figure 6). This system has the ideal properties from the synthetic point of view, i.e., a high association constant that facilitates the guest⊂cage formation with a high out activation barrier that prevents the guest from escaping the cavity. Note that synthesis may require heating to achieve a suitable guest rate or to self-assemble the cage around the guest molecule. Then, when the gate is open, a reduction in both, guest-out energy barrier and cage–guest affinity, resulting in a complete guest release. These guest⊂cage have, therefore, ideal properties for in vivo studies.

4. Conclusions

Molecular cages have excellent host–guest properties for drug delivery applications. We have shown that dynamic systems, in which the guest can rapidly pass in–out, can result in a guest⊂cage complex suitable for drug delivery in vitro, with limitations for in vivo experiments due to guest release by dilution effects. These limitations are overcome with constrictive binding guest⊂cage complexes, where the guest is trapped in the cavity of the cage in a “gate closed” state. On-command guest release is therefore achieved by “gate open”, which produces a reduction of the guest-out energy barrier allowing the release of the guest. A complete guest release is achieved when the gate-opening event also produces a reduction in the cage–guest affinity. As a result, this study shows that overall guest⊂cage complexes might have suitable properties for drug delivery in biological environments, yet to achieve this goal molecular cages with the necessary structures and properties to meet the required thermodynamic and kinetic criteria need to be designed. Future work in the field of molecular cages will soon enable the synthesis of molecular cages with constrictive binding of drug molecules with optimal properties for in vivo drug delivery.