The behavior of native cyclodextrins (CDs) in aqueous solution and at the air/water interface is much more complex than expected just considering their apparently simple molecular structure [1
]. Consequently, the correct prediction of their properties and skills such as their solubility, their ability to adsorb at interfaces, or to encapsulate a variety of molecules is not straightforward; not to mention their propensity to aggregate forming different patterns in the bulk solution and at the water/air interface [4
]. It is not a surprise then that the behavior of native and modified CDs, as well as that of the supramolecular complexes they form upon interacting with different types of molecules, is not trivial [7
In spite of their great potential for a large number of applications, atomic level information of CD molecules, which is key to understand how structure relates to function, is really scarce. It is also important to remember that, like most functional supramolecular systems, CDs are not static and that only by visualizing them in action it is possible to understand how structure and function are connected. Moreover, a detailed structural-dynamic description at atomic resolution that explicitly includes the surrounding molecules is crucial to fully understand the behavior of supramolecular complexes since such behavior is strongly correlated with the entire multi-component system where they are embedded. Without the ability to understand dynamic structural changes, the design, development, and optimization of applications using CDs has been traditionally based on empirical trial-and-error essays as well as a fair degree of serendipity.
Computational simulations are commonly employed to study a large variety of systems including proteins, peptides, DNA, lipids, surfactants, and heterogeneous mixtures of different molecules in different solvents [8
]. More specifically, molecular dynamics (MD) simulations are increasingly popular because they can provide structural, energetic, dynamic, and even mechanistic information. Computational studies of CDs are not so common, although a significant number of works based on MD simulations and docking of these molecules have already been published [10
]. The number of degrees of freedom of single (native or modified) CDs is much lower than that of typical macromolecules. So, computational studies of these cyclic oligosaccharides are expected to be able to easily sample their conformational space and so to provide a good understanding of their behavior at the atomic level, as well as the connection of such behavior with macroscopic properties. Single CDs and CD complexes can be computationally studied in aqueous solution using relatively small simulation boxes and explicit solvent: ~3000 water molecules at room temperature and atmospheric pressure are typically enough to exhibit negligible direct interaction of these molecules with their periodic images. Using last-generation computational resources, it is feasible to get atomistic trajectories of such systems in the microsecond timescale. However, CDs and CD complexes at concentrations employed in typical applications often aggregate, adsorb to interfaces, penetrate other media such as lipid bilayers, and acquire new levels of organization both in bulk solution and at interfaces. The study of such aggregates requires longer timescales and larger simulation boxes, and so, much more computational effort than that required for the study of single molecules. The implementation of methods to increase the sampling of the conformational space at lower computational cost is then convenient to better approach the convergence of the most important properties of the studied systems. A practical general solution to speed up MD simulations is to use the so called coarse-grained (CG) force fields, where groups of atoms are represented by single beads [13
], hence decreasing the number of degrees of freedom, mainly those that move faster. This also allows increasing the time step for the integration of the motion equations by more than one order of magnitude, as well as to smooth the energy landscape, avoiding kinetically trapped states and facilitating the evolution of the system towards the equilibrium. This method proved to work exceptionally well mainly for lipid membranes. Using this approach, it is more difficult to describe the behavior of other molecules -such as proteins or DNA- in a realistic way, so internal restraints are typically used to overcome obvious artifacts [14
]. In any case, the atomistic structure of the systems simulated at CG resolution can be recovered by applying different algorithms [15
]. CG parameterizations of CDs have been made in the past [17
] but they are not expected to be fully reliable since the larger van der Waals radius of CG beads significantly reduces the volume of the cavity, thus seriously affecting their ability to encapsulate molecules as well as the accessible conformational space of the system. An alternative to save computational time is the use of multiple time-step algorithms such as RESPA (Reference System Propagator Algorithm) [18
], but they have proved to introduce serious artifacts in some cases [20
]. A different and very simple general method to efficiently increase the sampling of MD simulations was proposed by Feenstra et al. 20 years ago [22
]. The method consists of transferring mass from heavy atoms to hydrogens (Hs) to slow their movement. This allows significantly increasing the time step for the integration of the motion equations. As a result, it is possible to reach longer trajectories as well as to smooth the energy landscape (as in CG simulations) by keeping the atomistic resolution of the system (in contrast to CG simulations). It is worth mentioning that the mass of the atoms is definitely much less critical for equilibrium properties than topological features (bond distances, angles, dihedrals, torsions, etc.), van der Waals, and electrostatic interactions. This can be experimentally demonstrated by the fact that structural and thermodynamic properties of many deuterated systems are indistinguishable from those of the equivalent hydrogenated structures (this has been specifically verified for CD systems) [23
]. The Feenstra method, also called the HMR (hydrogen mass repartitioning) method, has been tested for many systems providing good results [24
]. CD systems have also been simulated using this method for all-atom (AA) force fields with a mass transfer of 2 Da per H and a time step of 4 fs instead of the standard 2 fs [26
]. In general, AA force fields allow transferring a maximum of 2 Da from heavy to the bound H atoms due to the possible presence of methyl groups. A mass transfer of 2 Da from a single C atom to three H implies reducing the mass of such carbon atom from 12 to 6 Da. This makes it impossible to transfer more mass without leaving the carbon lighter than the Hs to which it is bound. In contrast to AA force fields, the HMR method applied to united atom (UA) force fields such as GROMOS allows transferring up to 3 Da from heavy atoms to the bound polar H atoms (non-polar H atoms are implicit in this force field and so not explicit methyl groups nor Hs in aliphatic chains are present in this case). Consequently, using the mass transfer approach, the time step in UA force fields could be increased up to 7 fs, instead of 4 fs. It is worth to test the effect of a direct mass increase in the explicit Hs of UA force fields, avoiding the repartition proposed by Feenstra to increase the time step. The application of this method would not have the limitation implicit in AA force fields due to the large number of explicit H atoms present in that representation, which would imply a significant increment of mass, thus making the movement of the total molecule too slow. As a consequence, the increase of mass in AA force fields could reduce the sampling even if the time step is increased. The mass increase of just polar Hs from 1 to 2 Da is justified based on the experimental fact that only the polar H atoms are spontaneously deuterated (thus doubling their mass) when they are solvated in deuterated water [1
]. In the present work, we propose to also test the mass increase of just the polar H up to 4 Da. This is expected to virtually mimic the behavior of the molecules with a heavier isotope of H (quadium) without the risk of subtracting too much mass to the bound carbon atoms, thus compromising the thermodynamic behavior of the global system. This last method will be named H2Q from here on. To our knowledge, the HMR method using UA force fields has not been tested yet for CD systems and the H2Q method has been marginally essayed (a literature revision is included in [22
]) but not analyzed in detail.
The validation of any new methodology implies the comparison to a recognizable reference method to demonstrate equivalence of the obtained results. The selection of a system sensitive enough to subtle and precise discrepancies among the different methodologies is also crucial. In the present paper, we will focus on the behavior of the supramolecular 2:1 complex formed by α-CD and sodium dodecyl sulfate (SDS) (see Figure 1
) in the bulk of aqueous solutions and also at water/air interfaces. CD-surfactant mixtures are especially interesting because they proved to exhibit interesting aggregation, mechanical, and adsorption properties under certain experimental conditions (concentration range and temperature) where the presence of 2:1 complexes dominate the solution [4
] but the molecular interactions leading to such behavior are unclear. This can be illustrated by an specific example: The adsorption of α-CD2
complexes at interfaces leading to a monolayer has been conclusively demonstrated by different methods including surface tension, rheology, ellipsometry, Brewster angle microscopy (BAM), atomic force microscopy (AFM), and neutron reflectometry (NR), [5
] although the adsorption driving force of those structures at the interface are still unknown. Additionally, preliminary work from our group indicates that this system is extremely sensitive to the parameterization, as will be shown in the present work. The selection of this highly sensitive system for which a lot of experimental information is available, and its study both in bulk and in the presence of an air/water interface, will allow testing several force field parameterizations as well as methods to speed up MD simulations of CD complexes at the time that the obtained information can be connected to the macroscopic properties of the system. The essayed methods could be later trustingly employed in larger and longer scale studies of similar systems. We will especially focus on the detailed analysis of the packing and structure of the solvent around the target complex, assuming that they have an important impact in its behavior, including their adsorption or penetration to media of different polarity, as well as to define their stoichiometry, topology, and also the stability of the corresponding structures. The role of the solvent structure for the aggregation and adsorption of different molecules has been discussed for many decades in the context of the hydrophobic effect [31
]. However, the organization of the solvent in the immediate environment of solutes is not commonly characterized in detail and so the impact of such organization is often implicitly ignored. The strong correlation between the order of the lipids induced by pore proteins or modified carbon nanotubes in a membrane and the toxicity of the systems [32
] has been recently reported. The structure of water around proteins has also been widely analyzed [33
]. In the case of CD systems, many interaction mechanisms are unknown, and they are simply ignored in benefit of experimentally improving formulations just based on trial-and-error essays. The order of the solvent around CD complexes is expected to be key to explain many of such mechanisms, including how they aggregate, adsorb and organize at interfaces, or sequester molecules from lipid membranes. Several studies have analyzed this behavior for native and modified CDs using different methods [35
] and some groups called the attention on the order of water around CD complexes [26
], but no detailed studies have been performed on this latter issue.
In what follows, we will describe a number of methods employed to simulate CD-based complexes in the water solution and at water/air interfaces. The α-CD2SDS1 structure will be taken as a reference system for the present study. Then, the obtained results will be analyzed in detail with specific strength in the local density and order of water molecules around the complex using different simulation methods.
The system selected for this study, a α-CD2
complex, proved to be extremely sensitive to different factors including temperature, concentration range, and the presence of water/air interface. A number of different experimental methods including calorimetry, surface tension, rheology, neutron reflectometry, ellipsometry, and several microscopies were employed to characterize its behavior under different conditions [1
]. Several studies were also performed by using β-CD2
instead of α-CD2
], as well as other similar structures that provide interesting self-assembly patterns in the bulk solution and at interfaces [29
]. However, the driving forces responsible for those events and arrangements are not clear. The connection between atomistic and macroscopic level information might be employed to design new applications as well as to optimize the already established employments of these systems. CDs are well suited for atomic resolution computational studies due to their small size and low number of degrees of freedom. A number of docking and computational studies involving CDs have been published [10
] but the use of these tools is much less extended for these molecules than in protein, peptide, or lipid systems. Thus, the proposal and validation of reliable and efficient computational methods for CD systems is expected to contribute to acquire a better knowledge able to complement the interpretation of wet-lab measurements.
Here, we performed MD simulations of α-CD2
complexes in the bulk aqueous solution as well as in the presence of water/air interfaces using five different parameterizations of the GROMOS force field and three different parameterizations of the AMBER/GAFF force field. The different parameterizations tested using GROMOS were aimed at optimizing the sampling, minimizing the use of computational resources. For this, we took advantage of manipulating the highest frequency motions, which in any molecule corresponds to the lightest atoms, i.e., the Hs. The time step employed in MD simulations for the integration of the motion equation is necessarily limited by these fastest degrees of freedom. For this reason, a time step of 2 fs is employed in most atomic force fields. Different methods have been proposed and tested to overcome this limitation. We decided to compare MD simulations using the standard GROMOS 54a7 force field (G_2), simulations transferring 3 Da of mass to the H atoms from the bound heavy atoms with 2 fs (HMR_2) and 7 fs (HMR_7) time steps, and simulations increasing the mass of H atoms from 1 to 4 Da with the same time steps (H2Q_2 and H2Q_7). Preliminary work performed in our lab indicated that simulations using AMBER behave significantly different from those using GROMOS for CD systems. Thus, we decided to test three different parameterizations of this force field, trying to explain the source of such discrepancy with experiments as well as with results using GROMOS. Simulations of the α-CD2
complex using the eight different parameterizations were performed in the bulk aqueous solution and also in the presence of water/air interfaces. As expected, the mass increase of H in the GROMACS parameterization using the H2Q method slows down the motion of these atoms, thus producing stable trajectories even with a time step of 7 fs. It has been said that the application of this method could negatively contribute to the sampling when applied to AA force fields, even if the time step is larger, due to slower diffusion that the resulting heavier molecules would exhibit [22
]. However, for UA force fields, the impact of the mass increase is much lower. This can be illustrated by a simple calculation: by increasing the mass of all H atoms of the α-CD molecules in 3 Da, the total mass increase of the molecule would be 18.5% in an AA representation and just 5.5% when using the GROMOS force field. The difference is even larger for the SDS molecule since the total mass increase using an AA force field would be 26% while the lack of polar H atoms in this molecule implies that the mass does not change at all upon the application of this method using the GROMOS force field. In addition to the latter argument, the mass increase just in the polar H atoms for the UA force fields can also be justified based on the experimental fact that only the polar H atoms are spontaneously deuterated (thus doubling their mass) when they are solvated in deuterated water [1
]. This experimental increase of mass just in the α-CD polar Hs maintains the stoichiometry, enthalpies, and equilibrium constants of the binding with SDS molecules, as revealed by ITC measurements performed using different isotopic contrasts, namely α-CD with hydrogenated and deuterated SDS in deuterated and non-deuterated water [23
]. Our proposal of increasing the H mass from 1 to 4 Da is based on the hypothesis that the use of quadium instead of deuterium (another mass increase by a factor of 2) also maintains the thermodynamic behavior of this system. Note that in this work, we did not change the parameterization of the water, which is equivalent to using one of the several possible isotopic contrasts. Our results provide almost indistinguishable results using the different GROMOS parameterizations, regardless of the mass of the H atoms. The highly specific density maps as well as the water dipole moment vector field were absolutely reproducible in all the details, both in the bulk solution and at the interface. It is worth to mention that the application of the mass increase just for the polar H atoms in AA force fields would not represent any advantage since the presence of nonpolar light H atoms would not make possible to increase the time step.
The simulations using the AMBER/GAFF force field provided completely different results, illustrating the high sensitivity of this system. In all the simulations performed in the presence of water/air interface using the different parameterizations of the GROMOS force field, the complex quickly adsorbed with the symmetry axis parallel to the surface. The perpendicular orientation was also observed in some marginal cases of this force field. Again, these results do not seem to depend on the method employed to deal with the mass of the H atoms nor on the time step. However, for the simulations performed using the AMBER force field, the affinity of the complex by the interface is negligible. In these simulations, the complex does not adsorb to the interface at all or, when it is adsorbed, the orientation is perpendicular to the surface (see Results section). The source of this discrepancy seems to be in the low number of intramolecular CD1-CD2 H-bonds in the complex for this force field, almost half the amount observed for all the parameterizations using GROMOS. Since the strength of the H-bonds critically depends on the partial charges, the three AMBER/GAFF parameterizations tested were performed in completely different ways, namely (i
) using the antechamber
tool with RESP charges for the whole CD; (ii
) using the antechamber tool with RESP charges to parameterize the methylated GPUs and then manually pasting them together to build the topology of the whole CD; and (iii
) same as (ii
) but using AM1-BCC charges. The first strategy introduces an artificial asymmetry in the charge distribution for chemically equivalent groups so the other two approaches, based on the building block strategy, could be considered as more reliable. The results coming from the three different AMBER/GAFF parameterizations are significantly different to each other but they match in the number of intramolecular CD1-CD2 H-bonds in the complex, approximately half of that observed for all the simulations using GROMOS, as well as in the larger number of H-bonds between the hydroxyls involving O2 and O3 with the solvent molecules. Thus, the differences between the two force fields rely on the intrinsic force field parameters (bond and angle constants) more than in the partial charges. The impact of this specific difference between both force fields is extremely serious for this system due to its high sensitivity to the presence of the water/air interface. As a result, the α-CD2
complexes exhibit no significant affinity to the interface with AMBER/GAFF, in contrast to experimental results and with the simulations using the different parameterizations of the GROMOS force field. These results indicate that the AMBER/GAFF force field does not describe the behavior of this system in a reliable way, regardless of the method employed to get the partial charges. Additionally, the simulations using GROMOS suggest a possible driving force for the adsorption of the CD-based complexes. The high specificity of the water distribution around the complex, like a well-fitted dress over the structure, with a relatively low number of H-bonds between the CDs and the water, play the role of a hydrophobic solvent shell that is partially released upon adsorption to the interface. This is expected to provide a favorable entropic contribution associated to this process. For the simulations using AMBER/GAFF, there is also a high-density water shell around the complex, but it is much less specific than in the case of GROMOS and the number of H-bonds with the CDs is significantly higher in the case of AMBER/GAFF. Thus, the force field parameters, providing a lower number of intermolecular CD1-CD2 H-bonds, lead to an important qualitative difference since they determine whether or not the structure adsorb to the interface. As stated above, there are conclusive experimental evidences on the adsorption of α-CD2
complexes at the water/air interface, but there is also an open discussion on its orientation with respect to the surface plane [23
]. A combination of atomic force microscopy, neutron reflectometry, and ellipsometry experiments suggests that the symmetry axis of the complex is parallel to such surface [6
] but there are not conclusive evidences for this. Our simulations using different parameterizations of GROMOS also indicate that the most probable orientation is the parallel one, but the perpendicular orientation also appeared marginally in some simulations. This suggests that both orientations might live together at the interface with different probability.
Some of our results could be extrapolated to other similar systems such as β-CD2
complexes, which exhibit an extremely interesting aggregation behavior in the bulk aqueous solution [4
]. The driving force for the self-aggregation of such complexes and for the stabilization of the resulting mesoscopic structures has been discussed [27
] but the arguments are not conclusive. Simulations of this complex in aqueous solution, using the H2Q_7 method, are expected to reproduce the aggregation pattern with atomic resolution, at least at a modest size scale of 10–15 nm. Additionally, the aggregation of α-CD2
complexes in the bulk solution has not been experimentally studied and it is expected to also produce interesting patterns with potential practical applications.
In the present work, we provide a detailed analysis of the behavior of the water around α-CD2SDS1 complexes in the bulk aqueous solution and at the water/air interface. For the simulations using different parameterizations of the GROMOS force field, highly specific density patterns and dipole moment vector fields are observed. The internal movement of the different groups within the complex are described and connected with the profile of specific regions with high water density. Especially interesting is the trajectory of the O6 atoms, showing an anisotropic petal-shaped profile probably due to the chirality of the GPU rings of the CD molecules. Such a movement seems to provoke a unidirectional rotation around the symmetry axis of the complex when it is adsorbed at the water/air interface. The adsorption of the complex is observed to be very quick (just a few ns) and the complex remains stable with its symmetry axis parallel to the water surface for the rest of the trajectory. However, a significant oscillation of the structure (~3 Å amplitude) with respect to the water surface is observed. The adsorption of the complex allows releasing of a significant number of highly packaged water molecules as well as a partial disorder of the solvent. This is translated in a decrease of the local sources and sinks of the dipolar moment vector field. Such release of packed water molecules and the associated decrease of solvent order could represent an entropic driving force for the adsorption of the complexes and also for self-assembly processes, since the aggregation of several 2:1 structures is also expected to allow releasing of neighboring water molecules.
In addition to illustrate the fanciful behavior of water molecules around the α-CD2
complex in water solution and at the water/air interface, the same highly specific analysis for different variations of the GROMOS force field that allow to significantly increase the sampling are tested, thus optimizing the use of computational resources. The HMR method was already proposed 20 years ago and it has been employed in a number of papers with reasonably good results. Here, we propose and test the use of what we call the H2Q method (hydrogen to quadium replacement) based on the experimental observation that deuterated CDs just in the polar Hs lead to the same stoichiometry and thermodynamic parameters than hydrogenated CDs [23
] and on the assumption that the replacement of deuterium by quadium also provides similar results. This allows significantly increasing the integration time step, thus speeding up MD simulations. The results obtained using both methods are found to be identical to those using the original force field, except in the lifetime of the H-bonds involving the modified H atoms.
In contrast to wet-lab experiments and to the results obtained using different variations of the GROMOS force field, the α-CD2SDS1 complex does not adsorb to the water/air interface when using different parameterizations of the α-CD for the AMBER/GAFF. This suggests that the latter force field is not well suited for simulations of the studied CD systems.
Overall, this paper is expected to contribute to the understanding of the behavior of supramolecular complexes based on CDs, revealing the importance of the solvent molecules as well as of the chirality of the glucopyranoside rings. Additionally, the HMR and the H2Q methods to optimize the sampling of the simulations provided exceptionally good results, while the AMBER/GAFF force field failed even at qualitative level. Our results provide an explanation for the formation and stability of several structures that have significant practical applications, including the design of smart films with specific mechanical properties for functional coatings, the synthesis of dielectric actuators based on cyclodextrin complexes (http://www.asmi.jp/en/tec
), artificial cell membranes, the so-called cyclodextrinosomes [29
], and other recently discovered compartmentalized structures that will eventually lead to new applications [4
]. All these new materials and structures were experimentally observed and characterized, but their behavior at atomic scale is still unknown. We aim to contribute to fill this gap between fundamental knowledge and practical applications. Additionally, the studied α-CD2
complex proved to be highly sensitive to the force field, so we propose to use it in order to test new parameters for computational simulations.