Introduction

Treosulfan (TREO; Fig. 1) was first synthesized in the early 1960 s by Feit1,2 as a more water-soluble analogue of busulfan, a widely used anticancer drug3. Its enhanced solubility in water is due to the presence of two hydroxyl groups located at positions 2 and 3 of the aliphatic chain (Fig. 1)4. Like busulfan, TREO was found to possess antitumor activity5,6. Studies on its mechanism of action revealed that TREO is a prodrug, meaning it lacks biological activity in its current form. This activity emerges after TREO converts into two epoxide derivatives: (2 S,3 S)−1,2-epoxy-3,4-butanediol 4-methanesulfonate and (2 S,3 S)-diepoxybutane. This transformation occurs in the presence of water at 310.15 K and a pH of 7.5, through a two-step, non-enzymatic intramolecular nucleophilic substitution reaction7,8. These derivatives are responsible for DNA alkylation, exhibiting a mechanism of action similar to that of nitrogen mustards4.

Initially approved for the treatment of ovarian cancer9,10, TREO is currently marketed under the trade name Ovastat4,11,12 and is used to treat a broad spectrum of cancers, including lymphoma, acute and chronic leukemias, and various solid tumors13. At the recommended dosage of 5–8 g/m² per day, treosulfan is characterized by low organ toxicity, which has led to its application in pediatric hematopoietic stem cell transplantation (HCT)13,14. It is most often used in combination with other drugs in so-called conditioning regimens. The combination of TREO and fludarabine is particularly common in the treatment of severe combined immune deficiency (SCID)15,16,17,18,19. However, in the literature, treosulfan is reported to be administered with various other anticancer drugs, such as gemcitabine, during chemotherapy20.

Despite TREO’s relatively low toxicity, certain adverse effects have been observed during treatment. The most serious include myelosuppression, anemia, alopecia, neutropenic fever, and grade III/IV hematological side effects. Milder side effects include fatigue, transient fever, pain, and headache21,22,23,24,25,26,27,28.

Another issue arose when TREO was tested against glioblastoma, as the treatment produced no positive results. The primary reason was that TREO does not sufficiently penetrate the brain11. The most common indicator of a drug’s ability to cross the blood-brain barrier is the partition coefficient n-octanol/water (logP). Drugs with a logP higher than 2 are typically capable of crossing the blood-brain barrier, but treosulfan and its epoxide derivatives have logP values below 229.

To better understand and potentially modify the molecular interactions of treosulfan in solution, it is important to explore its complexation behavior with other molecules capable of forming stable supramolecular assemblies.

Cryptands and related macrocyclic compounds are well-known for their ability to form stable host-guest complexes with ions and neutral molecules30,31. In particular, diazacrown cryptands functionalized with ureido-sugar moieties exhibit enhanced hydrogen bonding capabilities due to the presence of hydroxyl and amide groups32,33. An example of such compound is 1,10-N, N’-bis-(β-d-ureidocellobiosyl)−4,7,13,16-tetraoxa-1,10-diazacyclooctadecane (TN; Fig. 1). TN was previously studied in complexation with the anticancer drug carmustine, where experimental and theoretical analyses confirmed the formation of a stable 1:1 non-inclusion complex. The theoretically predicted structure of the complex was confirmed using various spectroscopic methods34.

Prompted by these results and the fact that, to date, neither TN nor its complex has been investigated thermodynamically, we decided to conduct such a study. For this analysis, we selected treosulfan. A literature review indicates that TREO has not been crystallized, and no recent theoretical studies describing its ground state have been found. Consequently, knowledge about its spatial geometry remains limited. Therefore, in this work, computational studies aimed at identifying the most energetically favorable conformer were conducted using different theoretical methods.

The TN:TREO complex was studied in water, and its formation was confirmed through experimental analyses, including spectroscopic methods and thermodynamic evaluation. Our results indicate that TN is highly soluble in water, while its complex with treosulfan remains thermodynamically stable in aqueous solution over a temperature range of 293.15 to 313.15 K. The experimental findings were also compared with theoretical models. Additionally, our results were evaluated in relation to existing literature data.

Fig. 1
figure 1

The structures of cryptand 1,10-N, N’-bis-(β-d-ureidocellobiosyl)−4,7,13,16-tetraoxa-1,10-diazacyclooctadecane (TN) and treosulfan (TREO) with the atom numbers used in the NMR analysis.

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Materials and methods

Computational studies

The initial models of the TN: TREO complex were built in the HyperChem program35 using the most stable conformers of TN (TN-1 in Fig. 2 in34 and TREO (TREO-1; see Fig. 2). They were obtained from the final stage of the conformational search performed in water, described by the polarizable continuum model of solvent (PCM), at the M06–2X–GD3/6–31G(d, p) theory level (details of this method are provided below). It should be noted that the results of the theoretical investigation aimed at finding the most stable structure of TN were presented in our previous work34. For treosulfan, we conducted a conformational search, which details are described in Text S1 of Electronic Supplementary Information (ESI). As shown in Fig. 3, we created seven initial configurations (LS; RS; AS; US; FS; BS; IS), in which various possible orientations of TREO relative to TN were considered.

Fig. 2
figure 2

The most stable conformer of treosulfan (TREO-1) obtained from the M06–2X–GD3/6–31G(d, p) calculations performed in water (PCM). The dotted line with letter represents HB. Atom colors: carbon – cyan, oxygen – red, hydrogen – grey, sulfur–yellow.

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Next, for these seven structures, a three-stage configurational search was performed, using different and increasingly advanced levels of theory. The first stage involved a comprehensive exploration of the configuration space of the complex by generating a large number of energetically stable structures. New molecules were obtained by systematically rotating TREO-1 around each of the X, Y, and Z axes, incrementally varying the angle by 20°. As a result, 40,830 complexes were generated and subsequently optimized in vacuo using the AMBER99 force field36 available in HyperChem. We chose AMBER99 because it had been successfully applied in our previous works34,37,38, which investigated a similar system, and also as it provides suitable parametrization for molecules containing sugars36.

All structures obtained from the first step were re-optimized in vacuo at the semiempirical theory level using the PM7 method39 and the MOPAC2016 program40. The PM7 optimized complexes were ranked according to increasing heats of formation (ΔHf).

The final stage involved density functional theory (DFT) calculations, which were performed using the Gaussian16 program (revision C.02)41. Ten of the most stable structures from each configuration of the TN:TREO complex were selected (a total of 70 different molecules) and re-optimized in water (PCM) at the M06–2X–GD3/6–31G(d,p) theory level. The M06–2X–GD3 is a meta exchange-correlation functional (M06–2X)42 that includes Grimme’s empirical dispersion corrections (GD3)43. This dispersion-corrected functional was combined with the Pople basis set 6-31G(d, p)44. The choice of this method was motivated by its good performance in thermochemistry and in the description of noncovalent interactions42,45,46,47,48,49. Furthermore, this method was employed in our previous study34, where TN was investigated as a drug carrier for carmustine. The M06-2X-GD3/6-31G(d, p) method has been widely applied in the study of supramolecular complexes involving cyclodextrins50,51, nanovehicles52,53, and calix[n]arenes54. Since the basis set used for optimization is relatively small, the 6–31G(d, p) results were further validated by performing single point (SP) calculations using the same functional (M06–2X–GD3) but larger basis sets: 6–31 + + G(d, p), 6–311 + + G(d, p) and def2-TZVP. Although attempts were made to perform optimizations with these larger basis sets, they were unsuccessful due to convergence issues. Information about complexation energies and spectroscopic calculations is provided in Text S2.

Fig. 3
figure 3

The graphical representation of the seven orientations (Fig. 3a: LS; RS; AS; US; BS; Fig. 3b: FS and IS) of treosulfan (TREO; presented as circle) towards 1,10-N, N’-bis-(β-d-ureidocellobiosyl)−4,7,13,16-tetraoxa-1,10-diazacyclooctadecane (TN). In order to correctly show the IS and FS configurations, in (b) TN is rotated by 90° about X axis.

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Synthesis of the cryptand

In anhydrous toluene (15 mL), the mixture of 2,3,6,2’,3’,4’,6’-hepta-O-acetylazido-β-d-cellobiose (0.699 g, 1.0 mmol) and triphenylphosphine (3.3 mmol) was stirred at room temperature for 30 minutes. Subsequently, 4,7,13,16-tetraoxa-1,10-diazacyclooctadecane (0.130 g, 0.5 mmol) was added, and the solution was stirred under a continuous flow of CO₂ for 24 hours. The solvent was then removed, and the residue was purified via silica gel column chromatography (eluent AcOEt/MeOH 8:1) to yield a 99% recovery (0.784 g, 0.495 mmol) of the 1,10-N, N’-bis-(2,3,4,6,2’,3’,4’,6’-hexa-O-acetyl-β-d-ureidocellobiosyl)−4,7,13,16-tetraoxa-1,10-diazacyclooctadecane (white powder; acetylated form of TN). Next, this compound (0.784 g, 0.495 mmol) was dissolved in anhydrous methanol (15 mL) and cooled to 0 °C in an ice bath. A 1 M solution of sodium methoxide in methanol was added dropwise, and the reaction was stirred under an argon atmosphere for 1 hour at 0 °C, followed by an additional hour at room temperature. To neutralize the mixture (pH = 7.0), small amounts of IRN77® ion exchange resin were added. The suspension was filtered, and the filtrate was evaporated to dryness. The resulting solid was dissolved in distilled water (20 mL) and lyophilized to yield a 99% recovery (0.776 g, 0.778 mmol) of 1,10-N, N’-bis-(β-d-ureidocellobiosyl)−4,7,13,16-tetraoxa-1,10-diazacyclooctadecane (TN) as a pure white amorphous powder30.

Sytnthesis of cryptand: treosulfan complex

Treosulfan was purchased from Sigma-Aldrich. TN and treosulfan were then added to 1 mL of deuterated dimethyl sulfoxide (DMSO-d6) in a 1:1 molar ratio and stirred for 24 h. Afterward, the NMR spectra were recorded. The complex was transferred from the NMR tube to a flask, and 25 mL of water was added. In the final stage, the solution was lyophilized. The synthesis of the complex was carried out at room temperature. The product of the synthesis was not precipitated after the reaction was completed.

Measurement of conductivity

Conductivity measurement is a technique used to determine the ability of a solution to conduct an electric current. This is primarily influenced by the concentration of ions in the solution, their mobility, and the temperature.

Conductance measurements were performed using a Wayne-Kerr 6430B RLC conductivity metre, featuring an uncertainty of 0.02%, within a three-electrode cell configuration similar to the one described in previous studies55. For the calibration of all measurements, an UB 20 F thermostat (Lauda, Germany) was used, ensuring temperature stability better than 0.005 K. The temperature regulation was achieved using an Amarell 3000TH AD thermometer (Germany), and the thermostat was connected to a DLK 25 throughflow cooler (Lauda, Germany). The glass cell was calibrated using an aqueous potassium chloride solution with a high purity level (0.99999, Merck)56. Throughout all experiments, an inert gas was supplied to the measuring vessel to maintain an inert atmosphere. To ensure maximum precision, test salt solutions were prepared gravimetrically using a Sartorius RC 210D analytical balance with an uncertainty of ± 1∙10⁻⁵ g. Conductance measurements were taken at various frequencies, specifically: 0.2, 0.5, 1, 1.5, 2, 3, 5, 10, and 20 kHz. All conductance values (Λ = 1/R∞) were derived by extrapolating the cell resistance, R∞(ν), to infinite frequency, using the empirical function R(ν) = R∞ + A/ν, where A is a cell-specific parameter. The general uncertainty in the measured conductivity values, taking into account calibration, sample purity, and measurement accuracy, was estimated to be ± 0.05%.

The gravimetric method

The gravimetric method is one of the oldest and most accurate analytical methods used for the quantitative determination of chemical components in a sample. It involves precipitating the component that is being measured in the form of a poorly soluble precipitate, washing it, drying it, and then weighing it. Below is a detailed description of the steps and principles of this method.

The tested sample of a specific mass was added to a precisely measured mass of solvent, which was water. The temperature was maintained within a range of 0.003 K using a calibrated UltraUB 20 F with a DLK 25 circulatory cooler, Lauda, Germany. The sample was then left aside for a certain period to allow equilibrium between the solution and the precipitate. After this time, the solution was filtered, and the remaining precipitate was dried to a constant mass to remove the solvent. The difference between the initial mass of the tested substance, m0, and the mass of the undissolved substance, m1, provided the mass of the tested substance in a precisely measured mass of solvent.

A specific amount of the tested substance was carefully weighed using a precise analytical balance. All solutions were prepared using an analytical balance (Sartorius RC 210D) with an accuracy of ± 1·10− 5g.

The value obtained was then converted to solubility, that is, the mass of the substance in 100 g of solvent. The gravimetric method is highly accurate and is often used in chemical laboratories to determine exact solubility values. The measurement was repeated several times for a given temperature to verify the obtained results. A similar research procedure was provided in the following article57.

Results and discussion

Conformational search of treosulfan

Many articles in the literature describe investigations on treosulfan, particularly its therapeutic effects. However, there are surprisingly no recent theoretical studies reporting its structural and energetic parameters. We also searched the Cambridge Structural Database (CCDC), but no crystallographic data for treosulfan were found. Therefore, we conducted a very detailed conformational search to identify the most stable conformer (see Text S1). The most energetically favorable structure (TREO-1) obtained from the M06–2X–GD3/6–31G(d, p) calculations is shown in Fig. 2, while less stable molecules are presented in Figure S2. TREO-1 is characterized by a specific geometry (resembling an “inverted-U” shape), where the methanesulfonate groups are oriented toward each other, with the distance between the two sulfur atoms being approximately 4 Å. This geometry likely results from intramolecular interactions within the molecule. For instance, TREO forms moderate hydrogen bonds (HB) (as classified in58 based on the dX···A distance) between the hydroxyl groups and oxygens from the methanesulfonate groups. The geometrical parameters of HB are listed in Table S1. It is worth noting that in other, less stable conformers (Figure S2), the “inverted-U” shape of geometry still predominates, although TREO-5 exhibits a more open geometry, with the distance between the two sulfur atoms being approximately 7 Å.

In the final stage of the conformational search for TREO (see Text S1), optimizations in water (PCM) were performed not only with M06–2X–GD3/6–31G(d, p) but also with other methods: CAM–B3LYP–GD3/aug–cc–pVDZ, MN15–L/aug–cc–pVDZ, and MP2/aug–cc–pVDZ. The rationale for selecting these methods is explained in Text S1. The results of these calculations are presented in Figure S3, which shows the relative energy differences (ΔE) for the fifteen most stable conformers. As seen, all methods identify TREO–1 as the most energetically favorable structure.

The theoretical results were compared to experimental studies, specifically 1H nuclear magnetic resonance (NMR) analysis of the TREO structure. The experimental chemical shifts (δ) were obtained in DMSO-d6. Consequently, the structure of TREO–1 was re–optimized in DMSO (PCM) using the M06–2X–GD3/6–31G(d, p) method, while NMR calculations were performed in DMSO at the M06–2X/6–31 + + G(d, p) theory level. Further details regarding the NMR calculations are provided in Text S2. Figure S4 presents the comparison of δ values obtained from both experimental and theoretical methods, while the experimental spectra are shown in Figures S5–S6. The theoretical chemical shifts for each atom of treosulfan are listed in Table S2. As can be seen in Figure S4, there is good agreement between the two techniques, indicating that the theoretical analysis accurately predicts the geometry that treosulfan can adopt. The small differences observed in the chemical shift values obtained from calculations and measurements may result from differences in the environment. NMR calculations were performed in DMSO, whereas the experiment was conducted in DMSO-d6.

Configurational search of the most stable TN: TREO complex–analysis of energetic and structural properties

TN was theoretically studied in our previous work34, where we analyzed its complexation abilities toward the anticancer drug carmustine. From those studies, we know that TN is capable of forming a very stable non-inclusion complex with carmustine. Therefore, we decided to investigate its complexation abilities with treosulfan and examine whether any energetic and structural similarities could be observed in this case.

The most stable complexes from each configuration (AS; US; LS; RS; FS; BS), obtained from the M06–2X–GD3/6–31G(d, p) calculations in water (PCM), are shown in Fig. 4, while their energetic parameters are listed in Table S3. As illustrated in Fig. 4, TN forms only a non-inclusion complex with TREO, as the latter is positioned on the exterior of the TN structure. More specifically, TREO preferably interacts with the cellobiose units. This arrangement is observed in all presented complexes, except for LS, where the drug interacts exclusively with the diazacrown ether. In Fig. 4, the IS structure (see Fig. 3), which represents the inclusion complex formation (with TREO located between two ureidocellobiosyl units), is not shown, as this type of complex is not stable due to its positive complexation energy. This phenomenon was also observed in the case of the complex with carmustine34. It may result from the specific geometry of TN. The latter forms numerous intramolecular hydrogen bonds, which are disrupted during the inclusion process of complexation. While this disruption can also occur during the formation of a non-inclusion complex, most hydrogen bonds remain intact. For instance, in the most stable AS complex, TN retains seven intramolecular HBs, whereas in TN–1 (the most stable conformer of TN34, eight HBs were observed. Another reason may be related to the fact that TN does not form a so-called cavity, like those observed in cyclodextrins59 or nanotubes60. This is particularly evident in Figure S7, where the structure of TN–134 is shown. The distance between the two oxygens belonging to the β−1,4-glycosidic bond is 3.9 Å (Figure S7 A). For comparison, the distance between two opposite oxygen atoms (belonging to the α−1,4-glycosidic bond) in the crystalline structure of β-CD61 is approximately 9.74 Å. It should be noted that this trend (formation of the non-inclusion complex) was also observed in our previous work37, in which a very similar cryptand (L2) was investigated along with its complexes with paracetamol. The main differences between L2 and TN lie in the size of the crown ether.

Fig. 4
figure 4

The most stable non-inclusion complexes (treosulfan is bound to the external part of TN, specifically to the diazacrown ether and the cellobiose units) selected from each configuration (Fig. 3) and obtained from the M06–2X–GD3 optimizations. For better visualization, FS and BS were additionally rotated around the X-axis by approximately 90°. Treosulfan is colored pink. The coordinates are listed in Table S4.

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In Fig. 5 are presented the BSSE-corrected complexation energies (EBSSEcompl) calculated for the structures shown in Fig. 4. Additionally, in Figure S8, we show the EBSSEcompl values for the twenty most stable complexes. The most energetically favorable configuration is AS, with a complexation energy of approximately − 23 kcal/mol. Notably, among the 20 most stable complexes, this configuration is dominant (see Figure S8). It is worth mentioning that this type of configuration was also the most energetically preferable in the case of the earlier analyzed complexes with carmustine34. Nevertheless, the complex with TREO is approximately 3 kcal/mol more stable. This raises the question of why this geometry (AS) is so energetically preferable. One possible reason is that it allows for the formation of the largest number of hydrogen bonds. This is particularly evident when comparing AS and BS, which are the most and least stable complexes, respectively. In the AS configuration, TN forms three hydrogen bonds, the highest number, whereas in BS, no moderate hydrogen bonds are observed. The geometrical parameters of HB are collected in Table 1. According to Jeffrey’s categorization based on the dX···A distance58, where X denotes the hydrogen bond donor and A the acceptor, these interactions are considered moderate. It is worth noting that the formation of the BS configuration is associated with significant deformation of TREO (Edef_TREO; see Table S5). The lowest deformation and weakest interactions are observed for FS.

Fig. 5
figure 5

The BSSE-corrected complexation energies presented for the most stable complexes (Fig. 4) obtained from the M06–2X–GD3/6–31G(d, p) calculations in water (PCM).

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In the context of molecular interactions, it is relevant to compare dipole moments. These values were obtained from calculations performed for isolated TREO and TN at the M06-2X-GD3/6-31G(d, p) theory level. The computed dipole moment of treosulfan is approximately 10.5 D. For TN, dipole moments were determined separately for its structural components: cellobiose units and the diazacrown ether. The sugar moieties exhibit greater polarity, with a dipole moment of 3.6 D, whereas the diazacrown ether has the lowest dipole moment (1.5 D). This finding further supports the preferential interaction of TREO with cellobiose rather than with the ether.

Table 1 The geometrical parameters of moderatea hydrogen bonds O–H···O formed in the most stable complexes of TN:TREO.
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It should be noted that the results obtained from the M06–2X–GD3/6–31G(d, p) optimizations were further validated by the single point (SP) calculations. These were performed in water (PCM) using the same functional (M06–2X–GD3) but larger basis sets: 6–31 + + G(d, p), 6–311 + + G(d, p) and def2-TZVP. Although attempts were made to perform optimizations with these larger basis sets, convergence issues were encountered. The single-point approach, however, enables the incorporation of higher-level electronic structure effects, thereby providing a more accurate electronic description of the system. Figure S9 presents the relative energy differences between the most energetically favorable complex (AS, shown in Fig. 4) and the remaining complexes. As shown, AS is identified as the most stable complex across all methods.

It is worth comparing the complexation abilities of TN with the literature data. The complexation of TN with busulfan and two protein amino acids was studied using spectroscopic methods30. From the obtained results, it was determined that TN forms stable complexes with a 1:1 stoichiometry. The complex with busulfan was examined in D2O, and it was found that during the complexation process, both cellobiose units are positioned on the same side of the crown ether. This effect is also observed in the theoretical prediction of the TN:TREO geometry (Fig. 4). The formation of non-inclusion complexes was also confirmed in the case of two other diazacrown cryptands, L38 and L237. These cryptands feature smaller diazacrown ethers than TN, with L containing glucose units instead of cellobiose. L and L2 exhibit the same geometric properties as TN, which facilitates the formation of a large number of intramolecular hydrogen bonds. Both cryptands form non-inclusion complexes, where the drug is primarily bound by the sugar units.

For the TN:TREO complex, both theoretical and experimental NMR analyses were conducted. The strategy followed is the same as described in Text S2 and in the discussion of the treosulfan NMR studies mentioned above. Experimental NMR was carried out in DMSO-d6, while the NMR calculations for AS were performed at the M06–2X–GD3/6–31 + + G(d, p)//DMSO theory level.

The experimental 1H NMR spectra showing the overlap of the three spectra obtained for the complex, TN, and TREO are presented in Fig. 6. The signals in the spectrum of the complex are shifted compared to those of the isolated cryptand and treosulfan, indicating that complex formation has occurred. The largest changes are observed for the urea moiety of TN (Fig. 7), which is linked to the diazacrown ether, and for the OH groups present in the cellobiose units of TN (Figure S10).

Fig. 6
figure 6

Overlapping the 1H NMR spectra of: TN: TREO complex (blue line); treosulfan (red line) and TN (green line). The measurement was conducted in DMSO-d6. Atom numbering is shown in Fig. 1.

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Fig. 7
figure 7

1H NMR spectra of NH proton belonging to the urea linker present in TN. Blue line indicates complex; red – treosulfan; green -TN. The measurement was conducted in DMSO-d6.

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A comparison between the theoretical values ((CAL) - obtained for the AS complex) and the experimental ones (EXP) is presented in Fig. 8. In the latter, the changes in the chemical shifts of the unbound protons (Fig. 8a) and the protons belonging to the OH groups (Fig. 8b), which are located in the sugar fragments of TN in the complex, are shown. A full description of the theoretical chemical shifts (δ) is provided in Tables S6–S9.

As depicted in Fig. 8, the formation of the TN:TREO complex is also confirmed by theoretical calculations. Although the Δδ values obtained from the two approaches (CAL and EXP) differ in magnitude and sign, a consistent trend can be observed. Specifically, larger chemical shift changes are noted for the protons belonging to the hydroxyl groups in the cellobiose units of TN. This observation supports the non-inclusion geometry of the complex, as suggested by the theoretical results, which indicate that the OH groups are oriented outward. As we have mentioned many times in this work, hydrogen bonds are crucial interactions that stabilize the complex. Their significance is also reflected in the changes in chemical shifts, as the largest changes within the OH set are observed for protons belonging to 2OH. The total Δδ value for 2OH originates from two protons located in two cellobiose units (see Fig. 1). Both protons participate in the formation of hydrogen bonds with TREO. In contrast, the protons from 6OH are oriented towards the interior of the carrier, preventing them from forming hydrogen bonds with TREO.

As shown in the experimental spectrum presented in Fig. 7, the urea moiety—particularly the oxygen atom—interacts with TREO. It is important to note that this type of interaction was observed only in the AS complex. The experimental chemical shifts (δ) and their changes obtained for treosulfan are listed in Table S10.

For the unbound protons, experimental data indicates that the changes in chemical shifts are minimal, with the exceptions of H–5’ and H–6b’. In the AS complex, H–5’ is oriented toward treosulfan, while H–6b’ forms an intramolecular HB with the OH group of TN.

As the final remark, we would like to mention that the final NMR spectrum is also influenced by the presence of different conformers in the solution. Such a situation is observed in our case and is discussed in detail below in the section “Thermodynamical description of the TN:TREO complex in water”.

Fig. 8
figure 8

The changes in the chemical shifts Δδ [ppm] of unbound protons (a) and protons belonging to the OH groups (b), present in the cellobiose units of TN within the TN: TREO complex. Δδ are obtained from the M06–2X/6–31 + + G(d, p)//DMSO calculations (CAL) and experimental measurements (EXP) conducted in DMSO-d6. They are calculated as: Δδ = δTN in complex – δTN. Theoretical results are presented for the most stable complex AS. H-6a and H-6’a indicate higher values, while H-6b and H-6’b –lower values of H-6 and H–6’ chemical shifts.

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Thermodynamical description of the TN: TREO complex in water

To gain insights into the thermodynamic properties of the TN: TREO complex, conductometric studies were performed in water. Some of the experimental results were compared to the computed values. Additionally, since the solubility of TN in water had not been investigated in our previous work34, such studies were conducted here. At 298.15 K, the solubility of TN in water was found to be 16.50 g/100 mL, indicating very good water solubility. For comparison, one of the most used cyclodextrin, beta-cyclodextrin (β-CD), has water solubility value of 1.85 g/100 mL62.

Table 2 presents the thermodynamic quantities characterizing the TN: TREO complex, obtained from both experimental measurements and theoretical calculations. The thermodynamic parameters were studied in water over a temperature range of 293.15 to 313.15 K. The values of experimental thermodynamic functions were calculated based on the measurements of molar conductivity of the studied objects using the equations given below.

The temperature dependence of the association constant was used to calculate the free energy of Gibbs (ΔGo).

$$\Delta {G^{\text{o}}}\left( T \right)\,=\, - \,R{\text{ }}T{\text{ln}}{K_{\text{A}}}\left( T \right)$$
(1)
$$\Delta {G^{\text{o}}}\left( T \right)\,=\,A\,+\,B{\text{ }}T\,+\,C{\text{ }}{T^{\text{2}}}$$
(2)

The entropy and enthalpy of ion association are defined as:

$$\Delta {S^\text{o}}(T)= - {\left( {\updelta \Delta {G^\text{o}}/\updelta T} \right)_p}= - B - 2 C T$$
(3)
$$\Delta {H^{\text{o}}}\,=\,\Delta {G^{\text{o}}}+T\Delta {S^{\text{o}}}$$
(4)

In general, we observed agreement between both approaches, as they indicate that complex formation is an exothermic and spontaneous process, regardless of temperature, due to the negative values of enthalpy (ΔH) and Gibbs free energy (ΔG). The spontaneity of the process is primarily driven by the negative enthalpy change (ΔH), indicating that the TN: TREO binding process is enthalpy-controlled. The negative entropy contribution suggests that this phenomenon is associated with an increase in system order, such as the reduction of molecular freedom upon binding. While entropy plays a lesser role in this case, its contribution remains significant for a comprehensive understanding of the interaction mechanism. The negative ΔS reflects the increased ordering of the system, particularly the formation of a stable TN:TREO complex in solution. The dominance of ΔH in determining ΔG highlights that the binding is primarily governed by enthalpic factors, consistent with interactions such as hydrogen bonding.

The theoretical values are presented for two complexes: the most stable, AS, and the least stable, BS. For the latter, the convergence between the experimental ΔG and the computed values is quite good. This can be explained by the fact that, in real solutions, not only the energetically preferred configuration is present but also other less stable structures. Therefore, the experimental outcomes reflect the combined effect of various molecules. The experimental NMR results were compared with theoretical predictions for BS (Figure S11). While the overall agreement is small, it appears slightly better for H-1, H-4, and H-crown (O) compared to the results observed for AS (see Fig. S8a). The discrepancies in enthalpy may primarily result from the fact that the theoretical values are uncorrected. It should also be emphasized that theoretical modeling cannot fully replicate the experimental conditions. Many factors influence the final results, including the choice of solvent models, functional, and basis set. For instance, calculations for AS were also performed using the SMD solvent model (AS was re–optimized). At room temperature, the values of ΔH and ΔG are − 26.0297 kcal/mol (−108.9083 kJ/mol) and − 19.2143 kcal/mol (−80.3926 kJ/mol), respectively. Thus, the differences between the SMD and PCM models are minor, although the results for enthalpy are improved in the case of the SMD model.

As a final remark, it should be highlighted that the solvent models used in this work do not account for the possibility of specific solute–solvent interactions, such as hydrogen bonding. These interactions can significantly impact the thermochemical results.

Table 2 Thermodynamic quantities: enthalpy (ΔH) [kcal/mol], Gibbs energy (ΔG) [kcal/mol], and entropy (ΔS) [kcal/mol·K] of the TN: TREOcomplex in water, obtained over the temperature range of 293.15 to 313.15 K from conductometric measurements (EXP) and theoretical calculations (CAL). The values in kJ/mol or kJ/(mol·K) (for ΔS) are given in parentheses.
Full size table

Molonite values were converted to molar concentrations (c) using Eq. 5, based on independently determined density gradient values (b):

$$\:c/\stackrel{\sim}{m}=q={q}_{0}+b\stackrel{\sim}{m}$$
(5)

where ρ is the density of the solution. Molarity (c) was required for the conductivity equation. The concentrations and molar conductivities of the TN: TREO (Λ) are shown in Table S11 as functions of the TN: TREO molarity (m-moles of electrolyte per kilogram of solvent). The relationship between m̃ and c is given by:

$$\:\stackrel{\sim}{m}=c/p=m/(1+m\bullet\:M)$$
(6)

Conductivity was analysed using equations cited in works63,64 based on the low concentration chemical model (lcCM)57,65. This model employs the following set of equations:

$$\Lambda =\alpha \left[ {{\Lambda _o} - S{{(\alpha c)}^{1/2}}+E(\alpha c)\ln (\alpha c)+J(\alpha c)+{J_{3/2}}{{(\alpha c)}^{3/2}}} \right]$$
(7)

together with

$${{\text{K}}_{\text{A}}}=\frac{{1 - \alpha }}{{{\alpha ^2}cy_{ \pm }^{2}}}$$
(8)

and

$$\ln {y_ \pm }= - \frac{{A{\alpha ^{1/2}}{c^{1/2}}}}{{1+BR{\alpha ^{1/2}}{c^{1/2}}}}$$
(9)

The values of Λ for the compound, in the examined temperature range, were obtained using the Fuoss method63,64. These calculations assumed R = q (q representing the Bjerrum distance65. As observed, the molar conductivities as a function of temperature exhibit linear behavior, decreasing with increasing concentration and increasing with higher temperatures. This is in agreement with conductivity theory. The high linear correlation of the results underscores the precision of the measurements, as presented in Table S12. Values of Λ0 increase with rising temperature, which is in agreement with the general trend that higher temperatures increase the mobility of ions by reducing the viscosity of the solvent. For a given solvent and solute, an increase in Λ0 with temperature may indicate a greater ability of the ions to move in the liquid.

The association constant values KA, which also show a very good linear correlation, particularly for lnKA, are well confirmed by the inverse of temperature 1/T. The association constant KA (also known as the equilibrium constant of the complex) describes the ability to form a complex between a ligand and a molecule. In the study of complexes such as sugar cryptand with treosulfan, KA reflects how strong the binding between them is, as presented in Table S12. In theoretical analysis, the change of KA values as a function of temperature can be interpreted in the context of thermal effects on the strength of the intermolecular interaction. Typically, for many chemical systems, the value of KA decreases with increasing temperature, which can be attributed to the higher kinetic energy of molecules leading to weakened intermolecular interactions. The natural logarithm lnKA is used to analyze data related to chemical equilibria and can be useful in calculations involving the enthalpy and entropy of association. The decreasing value of lnKA with increasing temperature suggests that the strength of the interactions between the complex components decreases with temperature.

Conclusions

In this study, a combination of experimental and theoretical techniques was employed to investigate the complexation abilities of a cryptand, 1,10–N, N’–bis–(β–d–ureidocellobiosyl)–4,7,13,16-tetraoxa–1,10-diazacyclooctadecane (TN), with the anticancer drug treosulfan (TREO) in a 1:1 stoichiometry. NMR analysis confirmed the successful formation of a complex and suggested non-inclusion geometry. This conclusion is supported by theoretical investigations, which reveal that in the most stable configurations, treosulfan is adsorbed onto the external surface of TN. Theoretical analysis further indicates that an inclusion complex is unlikely to form due to TN geometry, which is stabilized by numerous intramolecular hydrogen bonds.

The most stable configuration is AS, in which treosulfan interacts with all TN moieties (cellobiose units and the diazacrown ether). The complexation energy of this structure, estimated from the M06–2X–GD3/6–31G(d, p) calculations, is − 23.27 kcal/mol, which is about 3 kcal/mol lower than that of the complex with carmustine studied in our previous work34. Although both drugs are relatively small in size (with molecular masses under 300 g/mol), treosulfan contains two hydroxyl groups that readily interact with the sugar units of TN.

Conductometric studies indicate that TN is highly soluble in water (16.50 g/100 mL H2O). Furthermore, thermodynamic parameters suggest that the formation of the TN complex is spontaneous and exothermic (negative values of Gibbs energy (ΔG) and enthalpy (ΔH)), with this trend persisting even at temperatures as high as 313.15 K. A good convergence between thermodynamic measurements and theoretical predictions (regarding ΔG) is achieved only for the BS structure. According to DFT predictions, this structure is the least stable complex. This may suggest that, in the real solution, not only the most energetically favorable structures are present but also other less stable ones. This is particularly evident in the NMR spectrum, as the BS structure shows better agreement with the experimental data for three protons than the most stable complex, AS.