# Supramolecular rotaxanes and polyrotaxanes as potential MRI contrast agents: a comprehensive 17O NMR and relaxometric study

Jean Wilfried Fredy, Jérémy Scelle, Bernold Hasenknopf, Éva Tóth, Guillaume Vives, Célia S Bonnet

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## ► To cite this version:

Jean Wilfried Fredy, Jérémy Scelle, Bernold Hasenknopf, Éva Tóth, Guillaume Vives, et al. "Supramolecular rotaxanes and polyrotaxanes as potential MRI contrast agents: a comprehensive 17O NMR and relaxometric study." Inorganica Chimica Acta, 2026, 589, pp.122947. 10.1016/j.ica.2025.122947. hal-05362359

HAL Id: hal-05362359

https://hal.science/hal-05362359v1

Submitted on 13 Nov 2025

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# Supramolecular rotaxanes and polyrotaxanes as potential MRI contrast agents: a comprehensive ¹⁷O NMR and relaxometric study☆

Jean Wilfried Fredy<sup>a</sup>, Jérémy Scelle<sup>a</sup>, Bernold Hasenknopf<sup>a</sup>, Éva Tóth<sup>b</sup>, Guillaume Vives<sup>a, *,</sup>
Célia S. Bonnet<sup>b, *</sup>

ARTICLE INFO

Keywords:

Rotaxanes

Lanthanides

Contrast agents

Cyclodextrins

Water exchange rate

Relaxivity

A B S T R A C T

Rotaxanes and polyrotaxanes made of substituted cyclodextrins (CDs) were designed as potential MRI contrast agents or bimodal optical and MRI probes. After characterization of the threading kinetics and the exact composition of the polyrotaxanes, their MRI properties have been investigated by ¹H relaxometry and ¹⁷O NMR. We demonstrated that the relaxivity of these systems is increasing with increasing size (modified CDs, rotaxanes, and polyrotaxanes). ¹⁷O NMR studies show that the various systems have similar water exchange rates, in the same range as that of Gd-DOTA-monoamide complexes. Interestingly, NMRD data of the smaller systems can be only analyzed by considering both local and global motions via Lipari-Szabo approach, underlining the importance of internal flexibility. On the other hand, the disubstituted rotaxane and the polyrotaxanes are highly rigid and can be characterized with a single rotational correlation time. Their relaxivity is considerably enhanced by a second sphere contribution which is strongly dependent on the structure. It increases from the rotaxane to the mono- and the disubstituted polyrotaxanes, and as expected, it diminishes with decreasing coverage of the axle. The fundamental understanding provided by this comprehensive study will help the design of versatile and more efficient supramolecular interlocked systems such as rotaxanes and polyrotaxanes for MRI applications.

1. Introduction

Magnetic Resonance Imaging (MRI) is a powerful technique that allows the visualization of the whole body based on the measurement of water proton relaxation times. MRI is endowed with high spatial and temporal resolution, but suffers from low selectivity. To overcome this problem, paramagnetic contrast agents can be used which decrease the relaxation times of water protons in their vicinity. Nowadays, nearly 50 % of clinical MRI examinations are performed after administration of a contrast agent, which is a molecular complex of Gd³⁺ [1]. Indeed, with its high electron spin (7/2), and slow electronic relaxation, Gd³⁺ is the most efficient relaxation agent. To prevent toxicity of the free ion, Gd³⁺ is complexed by polyamino-polycarboxylate ligands forming kinetically inert and thermodynamically stable complexes [2]. The most studied complexes are derived from DTPA and DOTA. The MRI efficacy of such complexes is given by their relaxivity, and arises from three different mechanisms: (1) the inner-sphere (IS) mechanism which originates from

water molecules directly coordinated to Gd³⁺ in exchange with the bulk: (2) the outer-sphere (OS) mechanism, which concerns water molecules diffusing in the vicinity of the paramagnetic centre; and (3) the second sphere (SS) mechanism related to water molecules that are not directly bound to Gd³⁺, but retained in its vicinity through H-bonding, for example [3]. The inner sphere mechanism is the most efficient mechanism, explaining why all commercial contrast agents have one or two water molecules directly coordinated to Gd³⁺.

The use of supramolecular assemblies is particularly attractive in the development of MRI contrast agents as these systems rotate slowly compared to small molecular complexes. Hence, the relaxivity will be optimized at intermediate magnetic fields (20–80 MHz), where the MRI resolution is better than at lower fields [4]. Attaining higher relaxivity offers several practical advantages: (1) the possibility to reduce the injected dose; (2) in molecular imaging where biomarkers of interest are detected, this allows to lower the detection threshold [1]. In addition, supramolecular systems also offer versatile ways for the development of

<footnote><sup>a</sup> Sorbonne Université, CNRS, Institut Parisien de Chimie Moléculaire, IPCM, 75005 Paris, France</footnote>

<footnote><sup>b</sup> Centre de Biophysique Moléculaire, CNRS UPR4301, Université d'Orléans, Rue Charles Sadron, 45071 Cedex 2, Orléans, France</footnote>

<footnote>* This article is part of a Special issue entitled: 'Glen Deacon' published in Inorganica Chimica Acta.</footnote>

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: guillaume.vives@sorbonne-universite.fr (G. Vives), celia.bonnet@cnrs-orleans.fr (C.S. Bonnet).</footnote>
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Schematic representation of the supramolecular systems discussed in this work. The macrocycle is α-CD and the axle, poly((N,N-dimethylammonio)undecamethylene chloride. The chemical structures are depicted Figs. 2 and 3.</figcaption></figure>

multimodal imaging agents.

The development of multimodal approaches is gaining increasing interest as none of the imaging techniques available fulfill all the criteria for optimal diagnosis, i.e. sensitivity, high spatial resolution, or whole body imaging. Therefore, to combine the advantages of different techniques, recent efforts have focused both on instrument and on chemical probe development. The synthesis of molecular systems combining detection capabilities for different modalities is very tedious and it is often difficult to account for the different sensitivity of each technique. In such a context, the use of supramolecular assemblies combining several molecular entities should be attractive.

Interlocked molecules such as rotaxanes and polyrotaxanes represent a class of supramolecular assemblies in which one or more macrocycles are threaded onto an axle and held in place by bulky stoppers that prevent their spontaneous dissociation. These architectures are particularly attractive due to their inherent modularity which allows for the optimization of the imaging properties by functionalizing the macro-cycle and to precisely control the assembly of individual molecular components through a final self-assembly step. They have gained growing attention for applications in biology and medicine [5,6], particularly in the context of imaging, with the design of MRI contrast agents [7,8] and radiolabeled probes [9–11]. We have previously demonstrated the successful development of bimodal fluorescent and MRI imaging agents by threading functionalized cyclodextrins (CDs) with MRI contrast agents or fluorescent probes onto short or polymeric axles, resulting in the formation of rotaxanes [12] and polyrotaxanes [13], respectively. CDs were chosen as the macrocyclic platform owing to their natural origin, biocompatibility, and well-established use in polyrotaxane formation, as originally demonstrated by Harada and Wenz [14,15]. The relaxivity of these interlocked systems is significantly enhanced as compared to the clinical standard GdDOTA. Moreover, rotaxanes have been successfully administered in vivo, and they exhibited superior image contrast and prolonged retention relative to GdDOTA [12].

Thus, these supramolecular systems offer considerable versatility, combining the structural and analytical advantages of small molecular complexes with the enhanced relaxometric properties characteristic of

macromolecular assemblies. However, to fully realize their potential and further optimize their performance, it is essential to rationalize their composition and understand the microscopic parameters governing relaxivity. We have therefore performed kinetic studies on the threading of functionalized CDs onto a model axle to better understand their behavior on the polymeric axle. Additionally, we have carried out a systematic study combining ¹⁷O NMR and NMRD (Nuclear Magnetic Relaxation Dispersion) measurements at different temperatures to decipher the different mechanisms and important parameters governing the relaxivity. A schematic representation of the different structures discussed here is given in Fig. 1.

## 2. Experimental section

### 2.1. Synthesis

Functionalized cyclodextrins [13] CD-La, CD-Gd, CD-La₂, CD-Gd₂, CD-Bod, axles 1 [16] and 3 [17], rotaxanes [12] RotGd₂ and RotGd₄ and polyrotaxanes [13] PR-CD-Ln, PR-CD-Ln₂, PR-Bod-CD-Ln were synthesized according to literature.

PR-Bod-CD-Gd₂ was synthesized using the same procedure as the other polyrotaxanes. A solution of poly((N,N-dimethylammonio)undecamethylene chloride) (10.0 mg) and CD-Gd₂ (95 mg, 0.043 mmol) in H₂O (3 mL) was stirred at 80 °C for 24 h. Methanol (0.3 ml) and CD-Bod (17 mg, 0.013 mmol) were added. The reaction mixture was stirred at 60 °C for 3 days. The product was washed by a solution of methanol and distilled water (1:9) and purified by ultrafiltration to yield a solid (27 mg, 22 %).

### 2.2. Preparation of the stock solutions

Functionalized cyclodextrins, rotaxanes, and polyrotaxanes were dissolved in water and the pH was adjusted to 7.4. The Gd content in each solution was determined by ICP-OES and/or BMS (Bulk Magnetic Shift) measurements.
<figure><img src="image_4.png" /><figcaption>Fig. 2. Schematic representation of the synthetic pathways to obtain modified CDs and polyrotaxanes.</figcaption></figure>

## 2.3. General procedure for kinetic studies on model axle

In an NMR tube, permethylated diaminododecane was dissolved in 0.5 mL of D₂O with a concentration of 2.8 mM. Then the CD was added

(1 equiv) and the mixture was monitored by ¹H NMR at 300 K for 10 h. The threading was determined from the integration of their characteristic methyl signals. The data were fitted with an exponential model (y = A(1 - exp. (-kt))) giving the rate constant of the threading process.
## 2.4. General procedure for kinetic studies on model polymer axle

In an NMR tube, poly((N,N-dimethylammonio)undecamethylene chloride) and CD (1 equiv. by monomer) were dissolved in 0.5 mL of D₂O and the mixture was heated at 60 °C for 35 days with regular acquisition of ¹H NMR spectrum on an Avance BRUKER® 600 MHz. The coverage was determined from the integration of characteristic methyl signals.

## 2.5. General procedure for the optical measurements

The fluorescence emission spectra were recorded on a JASCO J-815 CD instruments and the UV-visible absorption spectra on a JASCO V670 spectrometer. Solutions were prepared in 1:1 H₂O: MeOH.

## 2.6. Temperature-dependent ¹⁷O NMR measurements

The transverse ¹⁷O relaxation rates (1/T₂, 1/T₁) and chemical shifts were measured in aqueous solutions of CD-Gd and RotGd₄ (11.82 mM and 10.15 mM) over a temperature range of 5–75 °C using a Bruker Avance 500 spectrometer (11.7 T, 67.8 MHz). Temperature measurements were performed based on prior calibrations with ethylene glycol and methanol [18]. An acidified water solution (HClO₄, pH 3.3) served as external reference. Longitudinal relaxation times (T₁) were determined using the inversion-recovery method, while transverse relaxation times (T₂) were obtained via the Carr-Purcell-Meiboom-Gill spin-echo technique [19]. The methodology for ¹⁷O NMR measurements on Gd³⁺ complexes has been previously described [20]. Samples were sealed in glass spheres fitted into 10 mm NMR tubes to avoid susceptibility corrections of the chemical shifts [21]. To enhance sensitivity, ¹⁷O-enriched water (10 % H₂¹⁷O) was added to the solutions to achieve approximately 1 % enrichment. The ¹⁷O NMR data were analyzed according to the Solomon-Bloembergen-Morgan theory of paramagnetic relaxation. The least-squares fitting of the ¹⁷O NMR data was performed using Visualizeur/Optimiseur software [22,23] running on a MATLAB 8.3.0 (R2014a) platform.

## 2.7. Relaxometric measurements

Proton NMRD profiles were recorded for CD-Gd ([Gd] = 1.84 mM), CD-Gd₂ ([Gd] = 3.29 mM), RotGd₂ ([Gd] = 3.46 mM), RotGd₄ ([Gd] = 2.89 mM), PR-CD-Gd ([Gd] = 1.03 mM), PR-CD-Gd₂ ([Gd] = 1.86 mM), PR-CD-Bod-Gd ([Gd] = 0.72 mM), and PR-CD-Bod-Gd₂ ([Gd] = 2.56 mM) on a Stelar SMARTracer fast field cycling relaxometer (0.01–10 MHz) and a Bruker WP80 NMR electromagnet adapted to variable field measurements (20–80 MHz) and controlled by a SMAR-Tracer PC-NMR console. The temperature was monitored by a VTC91 temperature control unit and maintained by a gas flow. The temperature was determined by previous calibration with a Pt resistance temperature probe. The least-squares fit of the ¹H NMRD data was performed using Visualizeur/Optimiseur software [22,23] running on a MATLAB 8.3.0 (R2014a) platform.

# 3. Results and discussion

## 3.1. Synthesis

The synthesis of functionalized cyclodextrins CD-Gd, CD-Gd₂, CD-Bod was achieved by Copper-catalyzed Azide-Alkyne Cycloaddition (CuAAC) between mono or bis-azido-α-cyclodextrin and alkyne-substituted Gd-DOTA or Bodipy probes as reported previously [13]. Briefly, when mixed in water, the CD and the diazidododecane axle first form an inclusion complex through the threading of two CDs onto the axle due to the hydrophobic effect. Then, the alkyne-terminated stoppers and the click catalyst are added to form the triazole rings and obtain the interlocked [3]rotaxane architecture. The [3]rotaxanes RotGd₂ and

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Schematic representation of the synthesis of bimodal polyrotaxanes with partial occupation of the alkyl chains of the polymer.</figcaption></figure>

RotGd₄ were selectively obtained in a one-pot five-component synthesis using Copper-catalyzed Azide-Alkyne Cycloaddition (CuAAC) between CD-Gd and CD-Gd₂ diazidododecane axle and alkyne substituted isophththalic acid moieties as previously reported [12]. The phthalic groups act as stoppers to prevent the dethreading of the CD and to maintain the interlocked architecture of the rotaxanes. The general procedure is reported Fig. 2.

Polyrotaxanes (PR-CD-Ln, PR-CD-Ln₂, PR-Bod-CD-Ln) were previously synthesized using poly((N,N-dimethylammonio)undecamethylene chloride) (3) as polymeric axle (Fig. 3). In order to compare the influence of the bis-substituted CD, Pr-Bod-CD-Gd₂ was synthesized using the previously developed methodology. (See Fig. 3)

# 4. Characterization of the polyrotaxanes

While the rotaxanes are well defined structures containing two substituted CDs, an alkyl chain and stoppers at the end, polyrotaxanes are made of polymers covered with the substituted CDs (Fig. 3). To rationalize the self-assembly of the functionalized CDs on the polyrotaxanes, it is important to evaluate their threading kinetics and affinity. To do this, we started on a simpler system using permethylated diaminododecane (1) as model of the polymer unit since it presents two hydrophilic heads allowing water solubility and a hydrophobic C₁₂ alkyl chain which allows the formation of an inclusion complex with the cavity of the CD (Fig. 4) [16,24].

The threading of CD-La, the diamagnetic counterpart of CD-Gd, is slow enough to be monitored by ¹H NMR in an aqueous solution. As previously described for native CD [24], the appearance of a new set of peaks for the axle and the CD is observed over time (Fig. 4) indicating a slow exchange between the free species and the inclusion complex (IC) compared to the NMR acquisition time. The methyl groups on the two amine functions act as a pseudo-stopper slowing down the dynamic exchange of the IC and enabling the monitoring of the threading by NMR. In the IC, the peaks of the axle methyl groups are split into two singlets at 3.12 and 3.14 ppm due to the dissymmetry induced by the
<figure><img src="image_6.png" /><figcaption>Fig. 4. ¹H NMR (D₂O, 600 MHz, 300 K) monitoring of the threading of CD-La on model axle 1 (1:1 eq, 2.8 mM).</figcaption></figure>

threaded CD-La. One end of the axle is close to the primary rim of the CD, the other is close to the secondary rim. The protons of the CD are also affected by threading, for example, the signals of anomeric protons (H¹) are shifted downfield, while the triazole proton is shifted upfield due to inclusion of 1. Over time, the peaks attributed to free CD-La disappear and the peaks attributed to the CD-La in the IC appear progressively. The peaks of the methyl groups of the axle are well suited to quantify the inclusion with the signal at 3.14 ppm corresponding to 3 CH₃ of the threaded axle and the signal at 3.12 ppm corresponding to an overlap between the 6 CH₃ of the free axle and the remaining 3 CH₃ of the inclusion complex. The threading percentage is calculated from the integrals of both signals and fitted with a monoexponential evolution as function of time (eq. 1)

$$y = A(1 - \exp(-kt)) \quad (1)$$

The same experiments were performed with the other functionalized CDs (CD-La₂, and CD-Bod) and the kinetics (t₁/₂) and thermodynamic data (log Kₐeq) for each CD could be determined (Fig. 5 and Table 1).

Table 1 summarizes the threading data and shows that the mono-functionalized CD-La and CD-Bod have a similar association constant with the model axle 1. The thermodynamic association constants for the mono- and difunctionalized CDs are slightly lower than that for native α-CD. This decrease is in agreement with the increase of steric hindrance

on the primary rim that should destabilize the formation of the inclusion complex. The association constants are similar to the ones we previously obtained with diaminododecane as axle [13] (log K = 3.4 and 3.0 for CD-La and CD-La₂ respectively) indicating that the thermodynamic stability is governed by the hydrophobicity of the C₁₂ alkyl chain with little influence of the end-chains. On the contrary, these end-chains have an influence on the kinetics of the threading. Indeed, threading was fast on the NMR time scale and the equilibrium was reached immediately after mixing with diaminododecane [13], while slow threading allowing NMR monitoring was observed for 1 due to its charged and bulky ammonium end-chains. The threading half-times with 1 are less than one hour for native CD and CD-Bod, but slightly higher with CD-La and CD-La₂. This suggests that the threading should be fast enough to obtain polyrotaxanes by threading on a polymeric axle. Thus, due to the close affinity and similar threading rates of the functionalized CDs for the monomer, we are able to control the ratio of each CD on the polymer directly via their initial proportion [13].

The syntheses of the polyrotaxanes were performed by heating a solution of the components (CD and polymer 3) in pure water. The necessity to warm the mixture results from the presence of intermediate bulky ammonium moieties. While the first energy barrier is low enough to be overcome at room temperature as observed on the model study, the successive barriers encountered to diffuse along the polymer axle are
<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Percentage of the threading of α-CD, CD-Bod, CD-La, and CD-La₂ as function as time (based on the integration of methyl groups of the axle) and their mono-exponential fit.</figcaption></figure>

<caption>**Table 1**</caption>

Association constants, percentages of maximum inclusion complex and half times for threading a 1:1 (2.8 mM, 300 K) mixture of CDs and monomer in pure water.

<table><thead><tr><th>Compounds</th><th>IC (%)</th><th>log K<sub>eq</sub></th><th>t<sub>1/2</sub> (min)</th></tr></thead><tbody><tr><td>α-CD</td><td>88</td><td>4.3</td><td>43</td></tr><tr><td>CD-Bod</td><td>64</td><td>3.2</td><td>48</td></tr><tr><td>CD-La</td><td>71</td><td>3.5</td><td>84</td></tr><tr><td>CD-La<sub>2</sub></td><td>53</td><td>2.9</td><td>85</td></tr></tbody></table>

much higher and require a higher thermal energy. The threading of α-CD on the polymer was performed at 60 °C and monitored by ¹H NMR over 5 weeks (Fig. 6). Like in the model system, the appearance of a new set of signals corresponding to the polyrotaxanes is observed. Upon threading, the anomeric proton of α-CD is deshielded and the methyl groups of the polymer split into two signals indicating the formation of the inclusion complex. The formation of the polyrotaxanes can be easily monitored by the integration of the anomeric proton at 5.13 ppm and can be empirically [17] fitted by an exponential function, using the square root of time according to Eq. 2.

$$y = A(1 - \exp(-\sqrt{kt})) \qquad (2)$$

The ¹H NMR spectrum of the final stage showed a coverage of around 50 % of the polymer after 35 days, meaning that one polymer segment out of two is occupied. This coverage is similar to the one described by Wenz [17,24] on comparable polyalkylammonium chains (~50 %). The threading presents a t₁/₂ of 10 days at 60 °C. At room temperature, the dethreading is extremely slow making the polyrotaxane kinetically stable in aqueous solution over weeks. PR-CD was thus easily purified from free CDs still present in the mixture by dialysis or ultrafiltration to reach pure PR at 46 % yield. Similar results were obtained with CD-La (Fig. S1) with a coverage of 25 % and a t₁/₂ of 6 days at 60 °C, showing that the substitution on the CD has little influence on the threading kinetic, even if the percentage of coverage is significantly lower.

The percentage of coverage of each PR studied is described in Table 2. The total coverage of PR-CD-La₂ with di-functionalized CD-La₂ (20 %) is lower than that of PR-Bod and PR-CD-La with mono-functionalized CDs (~25 %). These coverage values are consistent with the affinities observed for the monomeric axle, as CD-La₂ exhibits a lower affinity than CD-La. Importantly, the same ratio of coverage on

the mixed polyrotaxanes PR-Bod-CD-La as the initial ratio in solution (1:4) of mono-functionalized CD was obtained, demonstrating the absence of segregation or selectivity of the threading reaction for CD with similar affinities. However, when the affinities are different as it is the case for PR-Bod-CD-Ln₂, a strong decrease in the coverage of CD-Gd₂ is observed.

The optical properties of PR-Bod-CD-Gd₂ were also investigated by absorption and emission spectroscopy. PR-Bod-CD-Gd₂ exhibits a strong absorption maximum in the visible region at 499 nm and an emission maximum at 511 nm, characteristic for Bodipy derivatives (Fig. S2). Upon threading onto the bimodal polyrotaxanes, the optical properties of the BODIPY dye were maintained, with no significant band shift or quenching, as was previously observed for the other polyrotaxanes [13]. Indeed, the low coverage of CD-Bod makes the dyes well separated along the polymeric thread, thereby avoiding potential self-quenching. The high absorption and emission in the visible range, combined with the strong photostability of the BODIPY dyes, make the PR particularly suitable for bioimaging studies.

In the end, the coverage is low enough to avoid quenching, but high enough for the polyrotaxanes to be relevant as potential MRI contrast agents.

### 4.1. Relaxation properties

To characterize the relaxation properties of the rotaxanes and polyrotaxanes, ¹H Nuclear Magnetic Relaxation Dispersion (NMRD) profiles were measured in water at 25 °C in the field range 10 kHz-500 MHz (Fig. 7).

These profiles show high relaxivities compared to the commercial GdDOTA complex ($r_1 = 4.74 \text{ mM}^{-1} \text{ s}^{-1}$ at 20 MHz, 25 °C [22]), and humps at intermediate fields (20–80 MHz), which are typical of slowly rotating species. As previously observed, slow rotation is confirmed by the temperature dependence of the relaxivities indicating that the water exchange rate is limiting the relaxivity rather than the rotation [12,13]. In general, relaxivities increase from modified cyclodextrins to rotaxanes and then further to the polyrotaxane family (Fig. 7 and Table S1). Interestingly, this is consistent with the size of the supramolecular adducts even if rotation is not the limiting factor.

The relaxivity of CD-Gd is 7.87 mM⁻¹ s⁻¹ at 25 °C, 20 MHz, lower than that of a previously reported β-CD (9.67 mM⁻¹ s⁻¹, 25 MHz, 25 °C) [25], which can be explained by the size of the CD (α vs. β) and the longer linker between the CD and the Gd complex due to the presence of the triazole ring that adds additional flexibility. The addition of a second Gd³⁺ complex on the CD results in higher relaxivities per Gd for the CD adducts, the rotaxanes and the monomodal PR. In the case of the bimodal PR, the effect of the addition of a second Gd³⁺ complex is negligible, which could be related to the lower % of CD covering the polyrotaxane.

In order to gain better insight into the microscopic parameters governing the relaxivity of the different systems, NMRD profiles were also recorded at 37 °C for all the complexes, and at 50 °C for CD-Gd₂, RotGd₄, and PR-CD-Gd₂ (Figs. 8–10, S5–7). Relaxivity is determined by many microscopic parameters of the complex, such as the water exchange rate, rotational correlation times, electronic relaxation, it is therefore important to independently assess the maximum of these parameters. To this end, NMRD measurements are usually combined with ¹⁷O NMR spectroscopy.

Variable temperature ¹⁷O T₂ measurements give access to the water exchange rate, $k_{ex}$. The ¹⁷O T₁ data are determined by dipole-dipole and quadrupolar relaxation mechanisms and provide information about the rotational correlation time, $\tau_R$. The ¹⁷O chemical shifts give indication of the number of water molecules directly coordinated to Gd³⁺, q [3]. Longitudinal, transverse ¹⁷O relaxation rates and chemical shifts were measured as a function of the temperature on aqueous solution of CD-Gd and RotGd₄, and on a diamagnetic reference (HClO₄, pH 3.3) at 11.7 T. The ¹⁷O longitudinal relaxation rates of the complexes and the reference
<figure><img src="image_8.png" /><figcaption>Fig. 6. a) $^1$H NMR monitoring of the threading of α-CD on the permethylated polyalkylammonium 3 at 60 °C over 5 weeks in deuterium oxide; b) evolution of the polymer coverage obtained by integration of the anomeric peak and best fit to Eq. 2.</figcaption></figure>

<table><caption>**Table 2**

Threading coverage of CDs on the PRs (% of alkyl chains of the polymer covered with CD).</caption><thead><tr><th></th><th>α-CD</th><th>CD-BODIPY</th><th>CD-Ln</th><th>CD-Ln<sub>2</sub></th><th>t<sub>1/2</sub> (days)</th></tr></thead><tbody><tr><td>PR-CD</td><td>50</td><td>–</td><td>–</td><td>–</td><td>10</td></tr><tr><td>PR-Bod</td><td>–</td><td>25</td><td>–</td><td>–</td><td>n.d.</td></tr><tr><td>PR-CD-Ln</td><td>–</td><td>–</td><td>25</td><td>–</td><td>6</td></tr><tr><td>PR-CD-Ln<sub>2</sub></td><td>–</td><td>–</td><td>–</td><td>20</td><td>n.d.</td></tr><tr><td>PR-Bod-CD-Ln</td><td>–</td><td>4</td><td>21</td><td>–</td><td>n.d.</td></tr><tr><td>PR-Bod-CD-Ln<sub>2</sub></td><td>–</td><td>6.5</td><td>–</td><td>5.5</td><td>n.d.</td></tr></tbody></table>

were too close to yield reliable data, and were therefore not considered. The reduced $^{17}$O transverse relaxation rates and chemical shifts are presented in Figs. 8 and S2–3. The values found for CD-Gd and RotGd4 are the same within experimental error, demonstrating that the addition of a Gd$^{3+}$ complex on the CD, or the formation of a supramolecular assembly such as the rotaxanes do not influence the exchange rate of the coordinated water molecule.

The experimental $^{17}$O chemical shifts evidence monohydration of the complex, as expected. The reduced $^{17}$O transverse relaxation rates first increase (up to ca. 328 K), then decrease with increasing temperature indicating that the complex is in the slow kinetic region at low temperatures and in the fast exchange region at higher temperatures. In the slow kinetic region, $1/T_{2r}$ is directly determined by the exchange rate constant $k_{ex}$, which enables a reliable and direct assessment of $k_{ex}$.

The transverse $^{17}$O relaxation rates, the $^{17}$O chemical shifts, and the NMRD profiles of CD-Gd, were simultaneously analyzed with the Solomon-Bloembergen and Morgan (SBM) theory including the Lipari-Szabo approach to yield the microscopic parameters characterizing water exchange and rotation. This Lipari-Szabo approach considers both local and global motions, characterized by a local rotational correlation time $\tau_{i}^{298}$ of the Gd$^{3+}$ complex, and a global rotational correlation time

$\tau_{g}^{298}$ of the whole system. The model-independent order parameter $S^2$ reflects the degree of spatial restriction of the local motion with respect to the global motion. Its value ranges from 0 to 1, referring respectively to an isotropic and a completely restricted internal motion. The fitting of the NMRD data has been restricted to frequencies above 4 MHz as at lower magnetic fields the SBM theory fails in describing electronic parameters and rotational dynamics of slowly rotating species. Despite this, we were unable to fit the $^{17}$O data and NMRD profiles using similar electronic parameters, therefore different electronic parameters were used. In the fitting process, the number of inner sphere water molecules has been fixed to 1, and the diffusion coefficient $D_{GdH}^{298}$ to $2.60 \times 10^{-9} \text{ m}^2 \cdot \text{s}^{-1}$. Several distances have been fixed to common values. First, based on crystal structures and ENDOR results [26], the Gd-water oxygen distance $r_{GdO}$ has been fixed to 2.5 Å, and the Gd-water proton distance to $r_{GdH}$ to 3.1 Å. Finally, the closest approach between the Gd$^{3+}$ ion and the outer sphere protons $a_{GdH}$ was fixed to 3.6 Å. The parameters resulting from the best fit are presented in Tables 3 and S2.

The fit yielded a value of $k_{ex}$ of $0.80 \times 10^6 \text{ s}^{-1}$ for the water exchange rate, which lies perfectly between the values of DOTA ($4.1 \times 10^6 \text{ s}^{-1}$) and DOTAM ($0.05 \times 10^6 \text{ s}^{-1}$) [3], and is consistent with other GdDOTA-monoamide systems [28]. Nine-coordinated GdDOTA-type complexes generally undergo a dissociatively activated exchange of the coordinated water molecule. In the case of a dissociative mechanism, the replacement of a negatively charged carboxylate function in the ligand by a neutral amide function decreases the water exchange rate of the Gd$^{3+}$ complex by a factor around 4 [3], as it is observed here. Finally, the activation entropy has a large positive value, similar to that of GdDOTA, suggesting a dissociative mechanism for the exchange of the water molecule.

Given the similarity in the $^{17}$O data of RotGd4 and CD-Gd (Fig. S3–4), we made the reasonable assumption that the $k_{ex}$ values were similar for all the complexes, and fixed the values of the activation enthalpy and the water exchange rate to those of CD-Gd.
<figure><img src="image_9.png" /><figcaption>Fig. 7. ¹H NMRD profiles of aqueous solutions of CD-Gd (♦), CD-Gd₂ (▲), RotGd₂ (●), RotGd₄ (♦), PR-CD-Gd (■), PR-Bod-CD-Gd (▲), PR-Bod-CD-Gd₂ (♦), PR-CD-Gd₂ (●) in water at pH 7 and 25 °C.</figcaption></figure>

Like for CD-Gd, the relaxivities for CD-Gd₂ and RotGd₂ could be well fitted using the Lipari-Szabo approach (Fig. 9). The global and local correlation times of CD-Gd and CD-Gd₂ are very similar, while S² increased from 0.26 to 0.57 indicating higher rigidity in the case of CD-Gd₂. This can be likely explained by intramolecular H-bonding between the two substituents on the CD. For RotGd₂, an increase in both τg and S² is observed, which is consistent with the formation of the supramolecular adduct and possible π-π stacking interactions between the triazole on each CD and the triazole of one axle, leading to a bigger and more rigid system.

Surprisingly, for RotGd₄ and all the polyrotaxanes, the NMRD data could not be analyzed using the Lipari-Szabo approach. These data could be satisfactorily fitted using a single rotational correlation time, and introducing a contribution from second sphere water molecules. The results are presented in Fig. S4, Tables 4 and S2. A single rotational correlation time implies that the systems are rotating in a rigid manner. In the case of RotGd₄, this can be explained by the presence of some π-π stacking between the three triazole rings and some H-bonding and/or steric hindrance between the two GdDOTA-monoamide complexes on each side of the rotaxane which contribute to the rigidity of the system. It should be noted that RotGd₂, which has only two triazole rings and one Gd³⁺ complex on each side of the rotaxane, could not be satisfactorily fitted with this model.

As for the polyrotaxanes, this rigidity is certainly due to the formation of the supramolecular assemblies, and the possibility of H-bonding between the CDs on the same axle, as previously observed for similar system [29]. The introduction of second-sphere water molecules is also consistent with the presence of a high number of hydroxyl groups which can retain water molecules in the vicinity of Gd³⁺ through H-bonding interaction.

The contribution of second sphere water molecules to relaxivity is governed by the same relaxation mechanism as that of inner sphere water molecules. In the fitting procedure, we fixed the water exchange rate of those second sphere water molecules to common values used in the literature: $k_{ex}^{298 \text{ SS}} = 2000 \times 10^6 \text{ s}^{-1}$ [30,31]. In practice, the exact value has no impact on the fitting, we can simply assume that second sphere water exchange is fast enough not to have any influence on the

relaxivity. The corresponding activation enthalpy, $\Delta H^{\text{‡SS}}$, was fitted. The values of $q^{\text{SS}}$ and $r_{\text{GdH}}^{\text{SS}}$ are strongly correlated and their simultaneous calculation is often not reliable. In order to have a comparison of the second sphere relaxivity contributions for the different systems, we used the following approach: in a first step, for RotGd₄ we fixed $q^{\text{SS}}$ to 1 and fitted the distance between Gd³⁺ and this water molecule, $r_{\text{GdH}}^{\text{SS}}$. Then for the polyrotaxanes, we fixed $r_{\text{GdH}}^{\text{SS}}$ to the value found for RotGd₄ and calculated the number of second sphere water molecules present at this distance. While the absolute $q^{\text{SS}}$ and $r_{\text{GdH}}^{\text{SS}}$ values estimated in this way might not be precise, this approach allows a direct comparison of the importance of second sphere effects between the different systems by comparing the number of second sphere water molecules calculated. The results are presented in Figs. 10, S5-S7, Tables 3 and S2.

For RotGd₄, a value of $r_{\text{GdH}}^{\text{SS}} = 4.7 \AA$ was found, which is comparable with other data found in the literature for DOTA-based complexes [32]. This distance remains compatible with the size of these objects. The rotational correlation time ($\tau_R$ = 1350 ps) is in the same order of magnitude as the global rotational correlation time calculated for RotGd₂, which is altogether consistent with their similar size.

Concerning the polyrotaxanes, their rotational correlation times lie in the range of 1200–1700 ps. Except for PR-Bod-CD-Gd₂, all the other systems have a similar percentage of threading on the axle of CD-Gd, or CD-Gd₂, and can therefore be compared. The PR containing CD-Gd has a $\tau_R$ = 1200 ps, while the one containing CD-Gd₂ has a higher $\tau_R$ of ca. 1700 ps.

Using this approach for the fitting of the data, the second sphere contribution for the different systems is directly comparable by comparing the number of second sphere water molecules located at 4.8 Å distance from the Gd³⁺ centre. $q^{\text{SS}}$ values of 4.4, 5.9, and 6.4 were found for PR-CD-Gd, PR-Bod-CDGd, and PR-CD-Gd₂, respectively. Interestingly, this shows that the replacement of 4 % of CD-Gd on the axle by CD-Bodipy increases the second sphere contribution to the relaxivity. Using a polyrotaxane with CD-Gd₂ remains the most efficient way to increase relaxivity.

Finally, the values found for PR-Bod-CD-Gd₂ are very similar to those of PR-Bod-CD-Gd, and the positive effect of CD-Gd₂ is lost, which
<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Temperature dependence of reduced ¹⁷O (a) transverse relaxation rates and (b) chemical shifts of CD-Gd at 11.7 T; c) ¹H NMRD profile of CD-Gd at 25 °C (●) and 37 °C (▲). The lines represent the fit to the SBM theory using the parameters of Table 3 and S2.</figcaption></figure>

can be explained by the lower threading percentage on the axle (5.5 % for PR-Bod-CD-Gd₂ vs 21 % for PR-Bod-CD-Gd).

## 5. Conclusion

We have synthesized a new bimodal polyrotaxane PR-CD-Bod-Gd₂ following a previously described protocol. We have studied the kinetics of threading of the different polyrotaxanes on a model axle, and showed that the end-chains of the polymer influence the kinetics of the threading. Importantly, dethreading is a very slow process making it possible to maintain the polyrotaxanes intact for several weeks. The percentage of coverage of each polyrotaxane has also been determined to fully characterize those supramolecular assemblies.

A comprehensive relaxometric and ¹⁷O NMR study has been performed on the rotaxanes and polyrotaxanes, and the parameters determining their relaxivity have been compared to those of the monomeric substituted cyclodextrins. We have shown that the water exchange rate remains unaffected, and is consistent with a Gd³⁺-DOTA-monoamide complex. The coordinated water molecule undergoes dissociatively activated exchange mechanism.

These supramolecular systems have very interesting relaxivities as compared to commercial contrast agents, including at high magnetic fields. For the best PR-CD-Gd₂, r₁ amounts to 19.7 mM⁻¹.s⁻¹ at 60 MHz, 37 °C, nearly seven times higher than the corresponding value for GdDOTA. As expected, their rotational dynamics is very different depending on the size and the structure. The NMRD profiles of the functionalized CDs and RotGd₂ evidence internal flexibility, as they could only be fitted by separating local and global motions using the Lipari Szabo approach. This analysis, and in particular the values of the S² parameter, evidence increasing rigidity when going from CD-Gd to CD-Gd₂ and RotGd₂. In contrast, RotGd₄ is completely rigid. The ¹H relaxation data do not reflect any internal motions and could be fitted with a single rotational correlation time. This could be ascribed to the presence of H-bonding and π-π stacking interactions involving the three triazole rings on each side of the rotaxane.

The polyrotaxane systems are also very rigid without detectable internal flexibility. Their relaxivity is strongly influenced by the percentage of CD threading on the axle, a higher percentage promoting relaxivity increase. PR substituted with CD-Gd₂ have slower rotation, thus higher relaxivity. Second sphere relaxivity contributions are significant, and essentially, they account for the differences observed between the different systems.

In overall, this detailed and systematic analysis is important to rationalize the relaxation behavior, thus the MRI efficacy of these supramolecular constructs, as a function of their structure. The conclusions will not only help further structural optimization towards more efficient rotaxane- or polyrotaxane-based contrast agents, but can be also useful for the design of other supramolecular MRI probes. They point out the importance of second sphere contributions promoted by the cyclodextrins, and the role of steric crowding, hydrogen bonds or π-π stacking to freeze out internal motions.

<figure><img src="image_11.png" /><figcaption>**Fig. 9.** ¹H NMRD profiles of (left) CD-Gd₂ at 25 °C(●), 37 °C(▲), and 50 °C (◆), and (right) RotGd₂ at 25 °C(●), 37 °C(▲).</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Fig. 10. ¹H NMRD profiles of (left) PR-CD-Gd and (right) PR-Bod-CD-Gd at 25 °C(●) and 37 °C(▲). The lines represent the best-fit to the SBM theory introducing second-sphere contribution.</figcaption></figure>

Table 3

Best-fit parameters obtained from the fitting of the ¹H NMRD profiles and the ¹⁷O data to the SBM theory including the Lipari-Szabo approach.

<table><thead><tr><th>Parameters</th><th>CD-Gd</th><th>CD-Gd<sub>2</sub></th><th>RotGd<sub>2</sub></th><th>GdDOTA<sup>b</sup></th></tr></thead><tbody><tr><td>q<sup>a</sup></td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>r<sub>1</sub> 25 °C, 60 MHz (mM<sup>-1</sup>.s<sup>-1</sup>)</td><td>7.56</td><td>8.99</td><td>11.5</td><td>4.25</td></tr><tr><td>k<sup>298</sup><sub>ex</sub> (10<sup>6</sup> s<sup>-1</sup>)</td><td>0.80 (1)</td><td>0.80<sup>a</sup></td><td>0.80<sup>a</sup></td><td>4.1</td></tr><tr><td>ΔH<sup>‡</sup> (kJ mol<sup>-1</sup>)</td><td>54 (2)</td><td>54<sup>a</sup></td><td>54<sup>a</sup></td><td>49.8</td></tr><tr><td>ΔS<sup>‡</sup> (kJ mol<sup>-1</sup>)</td><td>+ 49 (6)</td><td></td><td></td><td>+ 49</td></tr><tr><td>E<sub>g</sub> (kJ mol<sup>-1</sup>)</td><td>27 (2)</td><td>25 (1)</td><td>50 (1)</td><td></td></tr><tr><td>τ<sup>298</sup><sub>g</sub> (ps)</td><td>715 (20)</td><td>650 (20)</td><td>1780 (20)</td><td>77</td></tr><tr><td>E<sub>1</sub> (kJ mol<sup>-1</sup>)</td><td>25 (2)</td><td>80 (4)</td><td>80 (5)</td><td></td></tr><tr><td>τ<sup>298</sup><sub>R</sub> (ps)</td><td>207 (7)</td><td>213 (15)</td><td>340 (20)</td><td></td></tr><tr><td>S<sup>2</sup></td><td>0.26 (1)</td><td>0.57 (1)</td><td>0.60 (2)</td><td></td></tr></tbody></table>

Table 4

Best-fit parameters obtained from the fitting of the ¹H NMRD profiles to the SBM theory including second sphere (SS) water molecules.

<table><thead><tr><th>Parameters</th><th>RotGd<sub>4</sub></th><th>PR-CD-Gd</th><th>PR-CD-Gd<sub>2</sub></th><th>PR-Bod-CD-Gd</th><th>PR-Bod-CD-Gd<sub>2</sub></th></tr></thead><tbody><tr><td>q<sup>a</sup></td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>r<sub>1</sub> 25 °C, 60 MHz (mM<sup>-1</sup>.s<sup>-1</sup>)</td><td>13.6</td><td>15.4</td><td>18.1</td><td>16.8</td><td>16.5</td></tr><tr><td>k<sup>298</sup><sub>ex</sub> (10<sup>6</sup> s<sup>-1</sup>)</td><td>0.80<sup>a</sup></td><td>0.80<sup>a</sup></td><td>0.80<sup>a</sup></td><td>0.80<sup>a</sup></td><td>0.80<sup>a</sup></td></tr><tr><td>ΔH<sup>‡</sup> (kJ mol<sup>-1</sup>)</td><td>54<sup>a</sup></td><td>54<sup>a</sup></td><td>54<sup>a</sup></td><td>54<sup>a</sup></td><td>54<sup>a</sup></td></tr><tr><td>q<sup>SS</sup></td><td>1<sup>a</sup></td><td>3.9 (2)</td><td>5.6 (2)</td><td>5.2 (2)</td><td>4.5 (2)</td></tr><tr><td>k<sup>SS298</sup><sub>ex</sub> (10<sup>6</sup> s<sup>-1</sup>)<sup>a</sup></td><td>2000</td><td>2000</td><td>2000</td><td>2000</td><td>2000</td></tr><tr><td>ΔH<sup>‡SS</sup> (kJ mol<sup>-1</sup>)</td><td>25</td><td>80 (7)</td><td>52 (3)</td><td>50 (5)</td><td>80 (8)</td></tr><tr><td>τ<sup>SS</sup><sub>GdH</sub> (Å)</td><td>4.7 (2)</td><td>4.7<sup>a</sup></td><td>4.7<sup>a</sup></td><td>4.7<sup>a</sup></td><td>4.7<sup>a</sup></td></tr><tr><td>E<sub>R</sub> (kJ mol<sup>-1</sup>)</td><td>30 (1)</td><td>25 (2)</td><td>33 (1)</td><td>28 (10)</td><td>27 (2)</td></tr><tr><td>τ<sup>298</sup><sub>R</sub> (ps)</td><td>1300 (25)</td><td>1170 (20)</td><td>1730 (20)</td><td>1220 (20)</td><td>1400 (30)</td></tr></tbody></table>

Acknowledgement

We thank Agnès Pallier for performing ICP measurements on the Gd³⁺-containing samples. We thank the LabEx MiChem programme under reference ANR-11-IDEX-0004-02 and the Rotaximage project, grant ANR-16-09-0018CE, for support.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have influenced the work reported in this paper.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.ica.2025.122947.

Data availability

The data used are available in the Supplementary Information of the article

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<footnote>a Fixed during the fitting process; b. From ref. [27].</footnote>

<footnote>a Fixed during the fitting procedure.</footnote>