Direct Measurement of Intermolecular Mechanical Force for Non-specific Interactions between Small Molecules

Abstract

Mechanical force can evaluate intramolecular interactions in macromolecules. Due to rapid motion of small molecules, it is extremely challenging to measure mechanical forces of non-specific intermolecular interactions. Here, we used optical tweezers to directly examine the intermolecular mechanical force (IMMF) of nonspecific interactions between two cholesterols. We found that IMMFs of dimeric cholesterol complexes were dependent on the orientation of the interaction. The surprisingly high IMMF in cholesterol dimers (~30 pN) is comparable to the mechanical stability of DNA secondary structures. Using Hess-like cycles, we quantified that changes in free energy of solubilizing cholesterol (ΔG_solubility) by β-cyclodextrin (βCD) and methylated βCD (Me-βCD) were as low as −16 and −27 kcal/mol, respectively. Compared to the ΔG_solubility of cholesterols in water (5.1 kcal/mol), these values indicated that cyclodextrins can easily solubilize cholesterols. Our results demonstrated that the IMMF can serve as a generic and multi-purpose variable to dissect nonspecific intermolecular interactions among small molecules into orientational components.

Graphical Abstract

When two molecules interact with each other, intermolecular force (IMF)² is used to evaluate the strength of the interaction. IMF can be quantified by chemical energy, which offers a convenient way to directly compare different types of IMF. However, as a thermodynamic variable, chemical energy is pathway independent and cannot probe the directionality of molecular interactions. Both pathway and directionality, however, are essential factors to render a full picture of kinetic intermolecular interactions. For example, folding or unfolding energy trajectories of proteins are dependent on the direction of a process in which intermediates with different local energy minima are located.

Mechanical force is a kinetic variable that is dependent on both pathway and direction of a process^{3, 4}. Recent technical advances on the application and measurement of picoNewton forces⁵ are instrumental to the development of interdisciplinary fields, such as mechanobiology^6–8 and mechanochemistry^{9, 10}, in which mechanical forces participate in biology and chemistry processes, respectively. Many mechanical properties of polymers and biomacromolecules, such as proteins and nucleic acids, have been portrayed by single molecule force spectroscopy (SMFS)^11–13 in optical tweezers, magnetic tweezers, or AFM instrument.¹¹ However, almost all measurements are focused on the intramolecular interactions inside a particular molecule. It is rare to follow intermolecular interactions from a mechanical perspective.¹⁴ It is even more challenging to investigate the mechanochemistry between two small molecules which have large freedom of motions. One reason for this difficulty is the low throughput of the SMFS. It is difficult to repeatedly probe the interaction between two small molecules. Upon dissociation of the two interacting molecules, it is time consuming to locate and track next pair of molecules for measurement. In addition, once two molecules are forced apart, it is almost impossible to evaluate the same molecule pair again, which increases the measurement noise due to the stochastic variation in consecutive sampling practice.

Our recent success in the investigation of individual host-guest pairs has provided a solution to increase the throughput of SMFS and to address the issue of the variation in stochastic sampling. This has been achieved by introducing a linker between two interacting molecules so that the two components do not escape to the surroundings after mechanical dissociation. As a result, the same molecular pair can repeatedly form an interacting complex for next round of measurement on a single-molecule platform.

In this work, this strategy has been catapulted to probe the intermolecular mechanical force (IMMF)¹⁵ during the interaction of two cholesterol molecules. As a small molecule, cholesterol is an essential constituent of cell membrane and a precursor for many important biomolecules like corticosteroids hormone, sex hormones, and vitamin D.^{16, 17} Cholesterol contains a large hydrophobic motif (central planar fused rings and a flexible hydrocarbon tail, see Figure 1) and a small hydrophilic motif (the hydroxyl head group). The central hydrophobic rings have two faces: a flat and smooth face that has no substituents (the α face) and a rough face with methyl groups (the β face). Due to its structural complexity, cholesterol may form a dimer in which two α faces interact with each other.¹⁸ Cholesterol dimers play a fundamental role in many functions such as those occur in the cell membrane.^19–24 When cholesterol molecules aggregate, dimer is the simplest unit based on which cholesterol crystal may form in artery plaques, which can cause atherosclerosis conditions.²⁵

Figure 1:

Schematic diagram for single molecular mechanical unfolding of cholesterol dimers with different orientations (bottom insets). The self-assembled construct is sandwiched between two dsDNA handles, which are tethered between two optically trapped polystyrene beads by Streptavidin (Strep)/Biotin and Digoxigenin (Dig)/Anti-digoxigenin (Anti-Dig) interactions. Cholesterol structure is shown in the top inset.

Given the importance of cholesterol molecules in various physiological and pathological processes, here, we directly measured the IMMF between two interacting cholesterols (dimer) in aqueous buffer by a single-molecule mechanochemical assay in optical tweezers instrument (Figure 1). Unlike the IMF which is a thermodynamic variable, IMMF provides a mechanical information between cholesterol molecules. This produces an unprecedented perspective on the kinetic aspect of small molecule interactions. Surprisingly, we found that the IMMFs between two nonspecifically interacting cholesterol molecules are comparable to the unfolding force of DNA tetraplexes^26–28 while higher than the unzipping force of DNA duplexes.²⁹ By uniquely manipulating orientations of individual cholesterol molecules, we further evaluated the mechanical anisotropy in the interaction of the cholesterol dimers. Finally, the changes in free energy of dissociation of cholesterol dimers were compared with those of cholesterol-cyclodextrin complexes. This allowed us to determine, for the first time, the change in free energy of solubility of cholesterol in β-cyclodextrin (βCD) or methylated βCD (Me-βCD), two compounds widely used to extract cholesterols from cell membranes or artery plaques. This IMMF measurement therefore provides convenient and direct quantification of the fundamental nonspecific intermolecular processes among small molecules.

Based on different cholesterol alignments, a cholesterol dimer can have three possible orientations, head-to-head, head-to-tail, and tail-to-tail (Figure 1). To evaluate IMMF of cholesterol dimers with these three orientations, we modified cholesterols either at the alkyl tail with an alkyne group or the hydroxyl head extended with an azide group. The modified cholesterol was conjugated to a single-stranded DNA by copper (I) catalyzed cycloaddition reaction (Figure S1–S11)^{15, 30}. The conjugate was finally incorporated in our single-molecule platform by self-assembly of DNA strands (Figure 1). The platform contained a poly-thymidine (T₄₀) ssDNA linker which helps to keep two cholesterols in close proximity even after the dimer is dissociated. This linker facilitated repeated inter-cholesterol association and dissociation events. The entire molecular setup was anchored to two optically trapped beads by using affinity linkages of streptavidin/biotin and digoxigenin/antibody, respectively (Figure 1).

Using this setup, we first evaluated the mechanical stability of the cholesterol dimer with a misaligned orientation. This was achieved by pulling one cholesterol from the hydroxy head and the other cholesterol from the alkyl tail end (Figure 1, inset). Mechanical dissociation and association of cholesterol dimers were carried out by moving one trapped bead away from the other. This process increased tension in the DNA tether, leading to the dissociation of the cholesterol dimer, which was manifested by a sudden rupture event in a force-extension (F-X) curve (Figure 2A, left). After mechanical breaking of the cholesterol dimer, one bead was moved towards another, relaxing the tension in the DNA tether. Since two dissociated cholesterol molecules were still in proximity due to the presence of the T₄₀ linker, the cholesterol pair would interact again for another cycle of dissociation-association experiment. From these repetitive force ramping experiments, we constructed a rupture force histogram (Figure 2A, middle), which revealed an average IMMF of 24 pN for this type of cholesterol dimer orientation. After the cholesterol dimer is dissociated at 24 pN, the T40 linker will be fully stretched, which leads to an extended molecular construct. By calculating the change in the contour length (ΔL) due to this extension (Figure 2A, right), we found the ΔL value was close to that expected from the release of the T40 linker after breakage of the cholesterol dimer (see SI and Figure S12 for detailed calculation). This suggested that observed rupture events were due to the dissociation of cholesterol dimers at a specific IMMF.

Figure 2:

Mechanical dissociation of cholesterol dimers with different orientations. A typical stretching (red) and relaxing (black) force-extension curve, rupture force (IMMF) histogram, and change-in-contour-length (ΔL) histogram for a cholesterol dimer pulled from (A) head-to-tail direction, (B) head-to-head direction, and (C) tail-to-tail direction. The dotted line in the middle panel depicts 24 pN. N and n represent the total numbers of data points and molecules, respectively, for each experiment. The histograms are fitted by Gaussian curves. See SI Figure S15 for fitting based on the equation proposed by Dudko¹.

To confirm that the observed IMMF was indeed due to the dissociation of two cholesterols, we performed two control experiments. In the first control, we incorporated only one tail-modified cholesterol in the single-molecule platform. In the second control, we integrated a head-modified cholesterol in our DNA platform. In each control, we did not observe any rupture event, suggesting there should be no interaction between cholesterol and the DNA template used in the IMMF measurement platform. Thereby, the rupture events observed in the F-X curves in Figure 2 were indeed dissociations of cholesterol dimers.

Next, we changed the association/dissociation of the cholesterol dimer from the head-tail to the head-head orientation. This was achieved by attaching both cholesterols to the IMMF measurement platform via their hydroxy heads (head-to-head) (Figure 1). The rupture force histogram showed an IMMF of 29 pN (Figure 2B), a value higher than the head-to-tail pulling (24 pN). This can be attributed to a better match in molecular shape between two cholesterols for this head-to-head orientation, which increased the interfacial area of the cholesterol dimer associated via hydrophobic interactions. To test this hypothesis, we prepared another construct in which cholesterol dimers are associated and dissociated from the alkyl tails (tail-to-tail) (Figure 1). We found that the average IMMF for this orientation was 31 pN (Figure 2C). This IMMF was again higher than that of the head-to-tail orientation, suggesting that tail-to-tail orientation also had more contact area between two interacting cholesterol molecules than that in the head-to-tail orientation. Such an orientational effect is of high clinical importance since interaction strength among cholesterol molecules can decide how well cholesterol crystals in the artery plaques are dissolved by chemical agents.

To understand the molecular mechanisms of the cholesterol-cholesterol interactions, we performed molecular dynamic (MD) simulations (see SI for details) on the mechanical dissociation of the three different dimer conformations studied in single-molecule force measurements. All simulations of dimer dissociation were set to be along either in-plane or out-of-plane of the cholesterol α faces. However, the final rupture conformation shows the strong tendency of dimer dissociation along the in-plane trajectory, except the misaligned case, signaling this is most likely the lowest energy pathway of the dimer rupture. MD simulations gave two different values of dissociation force, ~97 pN and ~82 pN for the head-to-head/tail-to-tail and the head-to-tail orientations, respectively (Figure S16 for the in-plane and Figure S17 for the out-of-plane dissociations). In Figure S16, we showed that the head-to-head/tail-to-tail dissociation forces were larger than that of head-to-tail misaligned contact conformation with statistical significance. These results were consistent with the trend of force histograms shown in Figure 2. However, because of the long flexible DNA handles connected to cholesterol dimers, we could not completely exclude the possible misaligned orientations. But it was clear that the majority of dimer conformations upon association followed the aligned orientation. It is noteworthy that MD simulation gave higher force values due to the requirement of a much higher pulling rate (0.002 Å/ps here) used in the field.^{15, 31–33}

To quantify the contact area in the cholesterol dimer, we counted the number of C and O atoms within 5Å between the two cholesterol molecules (blue and orange atoms in Figure S17). For the head-to-head/tail-to-tail contact, we counted 40 ± 2 atoms, while in the head-to-tail, we only found 33 ± 4 atoms in their contact plane. This result signifies that the contact area in the head-to-tail dimer is smaller than that in the head-to-head or tail-to-tail dimer, while the latter two clearly have more stable α-α face-to-face contact conformation (Figure S16A). Such a finding explains why the head-to-tail contact often cannot maintain the face-to-face separation (flip/rolling separation) during the pulling, leading to lower dissociation force which is in accordance with the experimental findings.

After measurements of IMMFs in all three cholesterol dimers with different orientations, we further evaluated the stability of cholesterol dimers from free energy perspectives. To this end, we calculated the dissociation works of these three cholesterol dimers, from which changes in free energy of dissociation (ΔG_dissociation) were retrieved by using Jarzynski non-equilibrium equation (See Supplementary Section).^{27, 34, 35} We found ΔG_dissociation of 9.2 ± 1.6, 11.6 ± 0.7, and 13.4 ± 0.9 kcal/mol, respectively, for the head-to-tail, head-to-head, and tail-to-tail orientations (Supplementary Table S2 and Supplementary Figure S13 for the dissociation work histograms). It is noteworthy that each ΔG_dissociation represents the combination of the ΔG to break a cholesterol dimer and that to stretch the T40 loop (Figure 1), the latter of which remains the same for all intermolecular systems using the T40 loop. It is clear that thermodynamic stability of the tail-to-tail cholesterol dimer is significantly different from that of the head-to-tail or the head-to-head dimers at the confidence level of 99.9% (Student’s t-test), which is consistent with different inter-cholesterol contact areas revealed by MD simulations above.

With this set of ΔG_dissociation for different cholesterol dimers, we proceeded to calculate the change in free energy of solubilization (ΔG_solubility) of cholesterol in β-cyclodextrins (β-CD) or methylated β-CD, two well-known biomolecules for cholesterol extractions.^36–39 By using the Hess like cycle (Figure 3), ΔG_solubility can be calculated in eqn 1,

$$\Delta G_{\text{solubility}}=\Delta G_{\text{cholesterol dimer}}-\Delta G_{\text{host-cholesterol}}$$ (1)

where ΔG_{cholesterol dimer} is the change in free energy of dissociating cholesterol dimers (either the head-tail, head-head, or tail-tail orientation) and ΔG_{host-cholesterol} is the free energy change to dissociate host-cholesterol complex (host: Me-βCD or βCD). By obtaining the ΔG_{host-cholesterol} from our recent work (Figure 4A and Supplementary Figure S14, here ΔG_{host-cholesterol} contains the ΔG to break a host-cholesterol complex and that to stretch the T40 loop, the latter of which remains the same for all the systems using the T40 loops),¹⁵ we found that all ΔG_solubility’s of cholesterol inside βCD’s are negative. In contrast, the ΔG_solubility of cholesterol in water was found to be positive in literature (5.1 kcal/mol).⁴⁰ These data indicate that solubilization of cholesterols in βCD or Me-βCD is a spontaneous process. In addition, ΔG_solubility of cholesterol in Me-βCD (−16.05 kcal/mol) is more negative than βCD (−8.9 kcal/mol), which is in full agreement with the finding that Me-βCD is more effective with respect to βCD to solubilize cholesterol due to its increased size of the hydrophobic cavity.¹⁵ Similarly, we discovered that ΔG_solubility of the cholesterol in misaligned cholesterol dimers is more negative than that in aligned cholesterol dimers (Figure 4B). This result indicated that fully aligned cholesterol molecules are more difficult to dissolve, which is in agreement with increased IMMF for these dimers. Finally, when cholesterols enter cyclodextrins with a head(hydroxyl)-on fashion, the cholesterol solubility becomes larger (Figure 4B). This result has been rationalized by simulations in which stronger interactions persist between hydroxy head of a cholesterol and the wide opening of the cyclodextrin.¹⁵

Figure 3:

A schematic diagram to determine the change in free energy of solubilization (ΔG_solubility) of cholesterol in Me-βCD or βCD molecule (green barrel) by using a process analogous to the Hess cycle.

Figure 4:

Summary diagram for changes in the free energy of solubilization of cholesterols in βCD or Me-βCD with different interaction directions. A) Left: Change in free energy (ΔG) associated with the dissociation of βCD-cholesterol complex pulled from the head (top) and tail (bottom) of the cholesterol (chol). Middle: Change in free energy (ΔG) associated with the dissociation of the cholesterol dimer pulled from the head-to-head (top), head-to-tail (middle), and tail-to-tail (bottom) orientations. Right: Change in free energy (ΔG) associated with the dissociation of Me-βCD-cholesterol complex pulled from the head (top) and the tail (bottom) of the cholesterol. B) Changes in free energy of solubilization (ΔG_solubility) of cholesterols are dependent on the disruption orientations of cholesterol-cholesterol dimers (top) as well as on the orientation of a cholesterol (bottom notation) entering either β-CD (green) or Me-β-CD (brown). Slanted arrowheads depict increasing magnitudes of ΔG_solubility.

Bulk methods such as Isothermal Titration Calorimetry (ITC) and Surface Plasmon Resonance (SPR) have been used to investigate affinity complexes of biological molecules with defined interaction orientations. However, in small molecules such as cholesterols discussed here, the interactions are often nonspecific without a predominant binding mode. For these cases, the ensemble average approaches can only give an average description of overall nonspecific interactions. Our IMMF allows to precisely dissect specific interactions among many nonspecific binding modes, such as the head-to-head/tail-to-tail and the head-to-tail interacted cholesterol dimers. This offers an unprecedented opportunity to understand molecular interactions, e.g., solubilities, from a perspective of defined orientations (Figure 4).

In conclusion, we demonstrated that intermolecular mechanical force (IMMF) can be directly measured for interactions between small molecules. Such IMMF indicated that fully aligned cholesterol dimers have a stronger interaction than misaligned dimers. Solubility of cholesterol in βCD has been rationalized by the magnitude of IMMF, which represents a new and generic variable to describe solubility of chemicals beyond the cholesterols studied here. Given the importance of the cholesterol in various cellular and biological processes, the mechanisms of and the insights on the cholesterol dimer interaction revealed here are expected to understand a range of physiological and pathological processes involving cholesterols.