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. Author manuscript; available in PMC: 2012 Jan 27.
Published in final edited form as: J Phys Chem B. 2010 Dec 30;115(3):487–499. doi: 10.1021/jp109545v

Molecular Simulations of Dodecyl-β-maltoside Micelles in Water: Influence of the Headgroup Conformation and Force field Parameters

Stéphane Abel §, François-Yves Dupradeau , E Prabhu Raman , Alexander D MacKerell Jr , Massimo Marchi §
PMCID: PMC3076730  NIHMSID: NIHMS261577  PMID: 21192681

Abstract

This paper deals with the development and validation of new potential parameter sets, based on the CHARMM36 and GLYCAM06 force fields, to simulate micelles of the two anomeric forms (α and β) of N-Dodecyl-ß-maltoside (C12G2), a surfactant widely used in the extraction and purification of membrane proteins. In this context, properties such as size, shape, internal structure and hydration of the C12G2 anomer micelles were thoroughly investigated by molecular dynamics simulations and the results compared with experiments. Additional simulations were also performed with the older CHARMM22 force field for carbohydrates (Kuttel, M. et al. J. Comp. Chem. 2002, 23, 1236-1243). We find that our CHARMM and GLYCAM parameter sets yields similar results in case of properties related to the micelle structure, but differ for other properties such as the headgroup conformation or the micelle hydration. In agreement with experiments, our results show that for all model potentials the β-C12G2 micelles have a more pronounced ellipsoidal shape than those containing α anomers. The computed radius of gyration is 20.2 Å and 25.4 Å for the α- and β-anomer micelles, respectively. Finally, we show that depending on the potential the water translational diffusion of the interfacial water is 7 - 11.5 times slower than that of bulk water due to the entrapment of the water in the micelle crevices. This retardation is independent of the headgroup in α- or β- anomers.

I. Introduction

Glycolipids (GLs) are glycosyl derivatives of lipids that belong to a large family of molecules known as glycoconjugates.1 From a chemical point of view, GLs designate any molecule with surfactant properties containing a carbohydrate headgroup (with one or more monosaccharide unit) attached to a lipophilic tail. In particular, alkyl-glycosides are simple glycolipid molecules obtained, for instance, by condensation such as “Fischer glycosidation” of a sugar with a fatty alcohol.2 Their tension-active properties depend on the length of the alkyl chain.3,4 Because they are highly effective, ecologic and non toxic, this class of surfactants has a wide range of applications in food, cosmetic and pharmaceutical industries.5-7 Similar to other surfactants, GLs can form different mesophases in water, such as micelles, lamellae, vesicles, etc; depending on experimental conditions (see for instance refs.3,8-15).

During the last decades, alkyl-glucosides have also attracted a great deal of interest in the context of membrane protein extraction16,17 given that they have a low critical micellar concentration (cmc) around 10 -3-10-4 mol.1-1 (see Table 2 of ref.7 for data and references), form large aggregates and keep the protein structure and its activity intact.18,19 In particular, alkyl-glucosides have been successfully used for solubilization of large membrane protein complexes, such as rhodopsin20, cytochrome c oxydase21,22 and protein channel.23,24

Among these detergents, N-Dodecyl-ß-maltoside (C12G2) (Figure 1) is one of the most used alkyl-glucosides in membrane protein extraction experiments.17 Two anomers, α- and β-, exist for C12G2 due to two possible connectivities of the dodecane chain (DOD) and of the anomeric carbon (C1′) linking DOD to the maltose head. The β-isomer is in a linear conformation, whereas the α-isomer is in a right-angle bent formed between the maltose headgroup and the alkyl tail. The α-anomer is less soluble than the β7,25 and is not commonly used in membrane protein studies, albeit with some notable exceptions. For instance, in the bacterial E.Coli Na+/H+ antiporter, it was reported recently 24 that the α-C12G2 surfactant is needed to obtain a crystallized protein in its native state. To explain this feature, it is generally assumed that the orientation of the maltose head in the surfactant leads to differences in sterical constraints (i.e. due to different packing parameters) and, possibly, in hydration behaviors. SANS and SAXS scattering experiments have shown that the α-anomer of C12G2 forms small quasi-spherical micelle, while the β- conformation forms large oblate aggregates.13,26

Figure 1.

Figure 1

The α- (a) and β-anomers (b) of C12G2 surfactants with the atom numbering scheme used in the paper. The anomeric center C1′ of the molecule is underlined with a star.

In the past few years, molecular dynamics simulations (MD) have been extensively used to study the structure and hydration of mono- and di-saccharides, in aqueous solutions (e.g., refs 27,28,29,30,31,32,33,34,35, 36,37,38,39,40). MD with alkyl-glycosides (such as alkyl-β-O-glucoside (C8Glc1) or alkyl-β-O-galactoside (C8Gal)) have been also performed in the past, involving bilayers,41, 42, 43 micelles 44,45, 46, 47 or interacting with a plant protein.48 In the studies of Bogusz et al. 44 and Chong et al. 47, the influence of the surfactant headgroup conformation on the micelle structure and hydration has been thoroughly examined. It was reported that despite the conformational changes in the headgroup, several properties remain nearly unchanged for the aggregates, in particular micelle shape, surfactant tail length and conformation. In contrast, other properties directly related to the interaction between the solvent and the headgroup (i.e. solvent accessible surface area, headgroup cluster structure, number of isolated water at the micelle surface) are significantly modified by the stereochemistry of the carbohydrate head.44,47 It was also noted that the sugar counterpart is responsible for strong perturbations of the water structure at the micelle surface and it affects the formation of a large hydrogen bond (HB) network at the micelle surface between water and the headgroups, and within the headgroups themselves (inter- and intra- HBs, respectively).41,47,49 This HB network may also explain the good thermal stability of the surfactants49 and cryoprotective effects.36,50

Despite their crucial role in membrane protein extractions, C12G2 micelles have been rarely studied by computational methods, and to our knowledge, only a single MD study has been performed on these systems in the past.51 That investigation was mainly focused on the hydration properties of the micelles and used a thermodynamical approach to examine the micellisation behavior of surfactants with different chemical nature, and was compared with experiments. To simplify the calculations, the simulations were carried out starting from a spherical aggregate of 45 β-C12G2. This aggregation number is far from that of 130, commonly accepted in the literature.13,14,26 Moreover, the authors used the OPLS-AA force field not fully optimized for glycolipid molecules.52 In absence of optimized parameters for the two C12G2 anomers for the widely used CHARMM and GLYCAM06 force fields, we have developed two sets of parameters compatible with these force fields for condensed-phase MD simulation studies. We expect that these new parameters will allow us to examine the influence of the headgroup stereochemistry in C12G2 micelle structures under experimental conditions. Our endeavour included the calculations of new RESP atomic charges for the current GLYCAM06 potential and an optimization of the dihedral angles for the acetal linkage between the maltose headgroup and the alkyl chain for both the α- and β-anomers compatible with the CHARMM36 force field (see next sections). These new CHARMM and GLYCAM parameters (named GLYCAM06 and CHARMM-Opt, respectively) have been tested and validated by performing different MD simulations of two realistic models of C12G2 micelles in explicit water. To compare our results with previous MD studies of glycolipid micelles,44-46 we have also performed two simulations with the old CHARMM22 parameters taken from Kuttel et al.53 and Reiling et al.54, named throughout the paper with the acronym CHARMM-K.

This paper is organized as follows: in the next sections, we describe the procedures followed to derive RESP atomic charges as well as the optimization of the dihedral angles for the acetal linkage for the α-and β-anomers for the GLYCAM and CHARMM force fields. This is followed by sections covering MD simulations, the results, as well as the interpretations of these results.

II. Methods

1. RESP charge derivation for the α- and β-anomers of C12G2 for GLYCAM

RESP charge derivation for C12G2 GL for the GLYCAM force field was carried out using standard methods.55-57 For this purpose, we have followed a similar approach than that described by Gouin et al.39 Three molecules i.e. methyl α-D-glucopyranoside (AMG), methyl β-D-glucopyranoside (BMG) and 1-dodecanol (OH-DOD) were involved in charge derivation. For each glucose unit, two rotamers were selected for the ω (i.e. represented by the O6C6C5C4 and O6C6C5O5 rotational angles) in the gauche-gauche (gg, ω = -60°) and gauche-trans (gt, ω = +60°) conformations (see Figure S1 in the supplementary material) considering that they are the most populated in solution.58 Optimized geometries presenting intramolecular HB were excluded from charge derivation to avoid over-polarization effect.56 As a consequence, geometry optimization was carried out with dihedral angle constraints. The HO4′O4′C4H′4 dihedral angle of the glucosides AMG and BMG was constrained to 180°, whereas the HO3-O3-C3-H3 and HO2-O2-C2-H2 dihedrals of AMG and BMG were constrained to 180°, respectively. A single conformation for 1-dodecanol was considered in charge derivation, and the selected geometry was optimized in its extended conformation (i. e. “all trans dihedrals”). Indeed, it has been previously shown that the surfactant alkyl chain adopts mainly this conformation in the micelle core (see for instance refs.44,59,60). Frequencies were calculated for all the molecules, and transition state structures were excluded from the charge derivation procedure. Geometry optimization, frequency calculation and molecular electrostatic potential (MEP) computation were carried out using the Gaussian03 quantum mechanics (QM) package in the gas phase,61 whereas charge fitting was performed using the RESP program.55,56 The HF/6-31G** level of theory was used in the geometry optimization and frequency calculations62, while MEP computation was based on HF/6-31G* leading to implicit polarization required in condensed phase simulations when using the non-additive AMBER force field model.55,56 The CHELPG algorithm was used to compute the grid of points involved in MEP computation.63 The molecular orientation of each optimized geometries was controlled using the rigid-body reorientation algorithm implemented in the R.E.D. program.63 Four molecular orientations for each optimized geometry of AMG and BMG (based on the glucose atom names C1C3C5, C5C3C1, C2C4O5 and O5C4C2, see Figure S1) and for the alkyl chain (based on the 1-dodecanol atom names C1C2C3,C3C2C1, C1C3C5 and C5C3C1, see Figure S1) were generated before MEP computation, and involved in the charge fitting procedure to yield reproducible atomic charges. Charge fitting was performed using a single RESP stage with a hyperbolic constraint value of 0.01. Intra-molecular charge constraints between the methyl and the C4 hydroxyl groups of AMG and BMG and inter-molecular charge constraints between the methyl group of each methyl glucoside and the hydroxyl group of OH-DOD (Figure S1) were set to a value of zero during charge fitting allowing the definition of the molecular fragments and force field libraries required to build C12G2 GL. Each hydrogen atom bound to a sp3 carbon was also constrained to a target value of zero during charge fitting to ensure a compatibility with the GLYCAM force field.64 The charge derivation procedure was automatically carried out using version IV of the R.E.D program.63 RESP charges for the α– and β–anomers of C12G2 are reported in the supplementary information, and are freely available from R.E.DD.B. server (http://q4md-forcefieldtools.org/REDDB/)65 with the accession code “F-72”.

2. Optimization of the dihedral angle potentials for the acetal linkage in α- and β- C12G2 for CHARMM

Ethoxy tetrahydropyran (Et-THP) was used as a model compound to parameterize the acetal linkage in C12G2 GL. α- and β- substituted anomers were involved in the study (Figure S2). Tetrahydropyran (THP) parameters were those previously developed in the context of hexopyranoses.66 The bond, angle, dihedral, Lennard-Jones, and partial charge parameters involving the acetal group were transferred by analogy to methoxy-THP (Met-THP) parameters developed previously67 and existing linear ether parameters (Listing S1).68 The optimization of these transferred parameters was undertaken as follows. QM MP2/cc-pVTZ//MP2/6-31G* Φ/Ψ scans for both α- and β-anomers were performed (Φ = OR-C1-OE-C6, Ψ = C1-OE-C6-C7) at 15 degree increments, thus giving rise to 576 conformations as target data. Figure S3 shows that the transferred parameters serve as a good initial guess as they reproduce the QM energy surface satisfactorily. The dihedral parameters involving the exocyclic heavy atoms were directly fit using the MCSA automated dihedral fitting procedure 69 to the QM Φ/Ψ data, resulting in a marked improvement in the root mean square error (RMSE) from 2.01 (1.23) to 0.81 (0.83) kcal/mol for both α- and β- anomer. Figure S3 shows that the fit parameters reproduce well the QM Φ/Ψ potential energy surface for both anomers. Additionally, Figure S4 shows that the fit parameters reproduce the 1-D QM energy as a function of Ψ (Φ is kept constant at +/- 60 for α and β-anomer) much better than the transferred ones. Unconstrained MP2/6-31G* optimization of the molecules revealed the QM global minima for the α- anomer at values of (61.5°, 175.1°) and for the β-anomer at values of (-63.2°, -172°). These QM minima are correctly reproduced by our optimized dihedral parameters as seen in Table S2. We also notice that they also reproduce well the energy difference between the two anomers global minima, ΔEα−β (ΔEα-β= -1.52 kcal/mol for QM and ΔEα−β= -1.85kcal/molforMM).

The transferred partial charge on the ether oxygen atom (OE) was validated by performing water pair interaction energy calculation as performed in previous studies.66 This consists of optimizing the solute/water interaction distance at the HF/6-31G* level theory, with constraints on all other degrees of freedom. Table S3 shows that our parameters reproduce well the scaled QM interaction energies and adjusted distances,66 thus validating the transfer of charges. These new sets of parameters are provided in the supplementary information in the CHARMM readable format (Listing S1).

3. Simulation Methods

To be consistent with the force fields developed in this study, we used an “all-atom” approach to model all micellar systems. RESP charges derived in the section II. 1 were involved in GLYCAM-based MD simulations with the bonded and non-bonded parameters taken from the GLYCAM06 force field version f.64 The 1-4 van der Waals and electrostatic scaling factors were set to 1.0, in agreement with the developer recommendations.64 In the case of the CHARMM-K simulations, we used two sets of parameters to model the sugar headgroup and the exocyclic atom connecting the maltose head and the alkyl chain. For the maltose head we used the parameters of Kuttel et al.53 (a revision of the CHARMM22 force field for sugars of Ha et al.)70 and for the acetal atom those of Reiling et al.54, which is assigned to an ether oxygen atom type with a partial charge of -0.30 e. These two sets of parameters were previously employed by Bogusz et al.44,45 and Konidala et al. 46 in MD simulations of C8G1 micelle in water. For the CHARMM-Opt simulations, we used the new set of parameters for hexopyranose66 with optimized parameters for the ΦHH glycosidic dihedral angles which significantly improves the CHARMM force field for simulations of polysaccharides.67 For the connection between the maltose head and the alkyl chain, we adopted the optimized parameter set for ethers by Lee et al.71 combined with the optimized torsion parameters developed for Et-THP described in the previous section II.2. For all MDs performed with the CHARMM force fields, the alkyl chain of the surfactant was modeled with parameters developed by Klauda et al. for alkanes.72 This contrasts with previous investigations44,45 and the work of Konidala et al.46 where for alkyl chain the parameters73 were used. Finally, the TIP3P water model73 was adopted to model the solvent for all the simulations.

4. Construction of the Micelles and Simulation Techniques

In this paper, we made the choice of using two preassembled micelles with 75 and 132 monomers of α- and β-C12G2 respectively. For the three different force fields studied in this work, the same approach was used to construct the six micelles and an identical protocol was applied in MD simulations. The aggregation numbers (Ndet) was obtained by Dupuy et al.13 by fitting the scattering curves from SAXS and SANS experiments at a temperature of 297 K and a concentration range between 20 and 100 mM for monodispersed micelles. We should emphasize that the Ndet values may depend on the experimental methods and on the concentration. For example, the Ndet value for the β-C12G2 micelle used here is higher than the value of 98 found by Rosevear et al.74 using gel filtration method, the value of 82 to 120 obtained by SAXS measurements26 at 310 K, and the value of 111 ± 10 derived by Time Resolved Fluorescence Quenching (TRFQ) spectroscopy.75 On the other hand, our Ndet is well within the findings of others experiments, e.g. Ndet = 125 ± 10 was reported using others TRFQ results at 4.89 - 19.6 mM, at 289 K - 333 K,14 whereas Ndet = 135-145 was found by Lipfert et al.76 by SAXS at 298 K. In case of α-C12G2 micelle, only one aggregation number has been reported in the literature, Ndet= 75.13

The starting configurations of the two aggregates were constructed using the Packmol program.77 This program created an initial starting point for MD by packing in the sphere Ndet C12G2 molecules in their extended conformation, with the first carbon atom (C7) of the alkyl chain, near the headgroup at ∼17 Å from the center of the micelle. This is larger than the total length (∼14.0 Å) of the DOD chain in an extended conformation obtained with the DS Visualizer v2.0 (Accelrys Inc., San Diego) modeling program. In this way, the number of ‘steric clashes’ for the terminal ethyl groups of the C12G2 alkyl chain is reduced. To remove other inter- and intra-molecular overlaps, additional stages of conjugate gradient minimization followed by MD equilibration in vacuum with a small time step were carried out. Following this step, the headgroups were randomized by running MD simulation of the aggregates at 450 K for 300 ps, with the surfactant tail kept fixed to their minimized conformation. From this point on, in all cases the systems were solvated by adding TIP3P water at standard density in a truncated octahedron cell, corresponding to a simple cubic primitive cell unit with parameters a=b=c and α=β=γ=109.472°. Given the two different Ndet used in our study, we chose a=85 Å and a=95 Å for the simulations of the α- and β- anomers, respectively. These box sizes were chosen to ensure that all the molecular systems were within the experimental L1 phase (i.e. < 45% in weight concentration),75 and that there was a sufficient distance (∼15 Å) between the micelle surface and the edge of the box to minimize interactions with periodic images.78 As shown in Table 1, where we provide the composition of the two simulated systems, the simulated concentrations of the detergent are near 0.3 M and 0.40 M for the α- and β-C12G2 anomers, respectively. This is higher than the surfactant concentration used in the experimental study of Dupuy et al. 13 (0.02 - 0.04 mol·L-1) and higher than the critical micelle concentration (cmc) for the α- and for β-C12G2 (∼1.5.10-4 mol.L-1 and ∼2.0.10-4 mol.L-1, respectively) 13,75 at temperature 298 K. Indeed, simulations near the cmc would require about 2000 times more water in the simulation system leading to a dramatic increase of the calculation time. Furthermore, in order to equilibrate the solvent molecules, the systems were run for 300 ps at 450 K, with the ensemble of the micelles atoms fixed to their initial positions. Then, the constrained micelle atoms were released and the system slowly heated from 0 K to 297 K in 300 ps as described in ref.79 Finally, the resulting conformations were simulated in the NPT ensemble (T = 297 K and P = 0.1 MPa) for 14 ns after discarding the initial 300 ps. MD snapshots were saved every 240 fs for subsequent analysis.

Table 1. Simulations parameters for the micelle simulations.

NC12G2, NH2O, and Natm are the numbers of N-dodecyl-ß-D-maltopyranoside monomers (C12G2), water and atoms composing the simulated systems. mC12G2/mTot is the weight concentration (in %) of C12G2 in each system. tsim is the simulation time (the 300 ps equilibration period was excluded from the analysis).

System α-C12G2 β-C12G2
NC12G2 75 132
NH2O 13771 18389
Natm 47388 65859
mC12G2/mTot 13.4 16.9
T (K) 297 297
tsim (ns) 14.0 14.0
ρ (g/cm3) 1.02 ± 0.01 1.03 ± 0.01

5. Molecular Dynamics

For all the simulations and analysis performed in this study, a serial and parallel versions of the ORAC code were used.80 To simulate in the NPT ensemble, ORAC uses a method based on the extended system approach by adding extra (virtual) coordinates and momenta in the system to control the temperature and the pressure.81-85 To integrate the equation of motion, a five time step r-RESPA integration scheme with a Liouvillean separation in three non-bonded shells, was used.86 The procedure combines a Smooth Particle Mesh Ewald (SPME) to handle electrostatic interactions,87 and the method of constraints to keep the covalent bonds involving hydrogen's at their equilibrium length.88 The SPME parameters were chosen to maintain a relative error of less than 0.1 % on the electrostatic interactions for all the micelles. For this purpose, a convergence parameter α = 0.43 Å-1, a fifth-order B-spline and a 96 grid point in each cartesian direction to take care of the SPME charge interpolation for each simulated system was used.

III. Results

First, we consider the general structure of the α- and β-C12G2 aggregates at different simulation times: tsim≈ 0 fs, tsim= 7.0 ns and tsim=14.0 ns of the production period. Figure 2 (a-f) provides three snapshots for each type of C12G2 micelles taken from the CHARMM-Opt simulations; these results are representative of the other simulations described in this paper. Visual inspection of the figures shows that at the beginning of the run, the micelles have rougher surfaces with some glycolipid protrusions (see Figures 2(a) and 2(d)). Thus, the micelles present large solvent-exposed surfaces where the alkyl chains of the surfactant are exposed to the solvent (see below). However, after typically 2-3 ns of production, Figs. 2(b-c) and 2(d-e), the surfactants arrange themselves to form compact aggregates where a major part of the alkyl tails are buried and the surface is covered with the glycolipid headgroups. These pictures also show that the α- and β-C12G2 micelles are not perfectly spherical and that β-C12G2 micelle is more ellipsoidal than α-one (see below). This finding has been observed in the various MD simulations performed in this study, regardless of the force field. Finally, in contrast with previous simulations 46,47 of octyl-β-glucoside micelles, the integrity of the micelles studied with the GLYCAM and CHARMM force fields is maintained all along our simulation time window (14 ns), and no surfactant molecules escaped from the micelle. This is consistent with previous experimental results obtained for alkyl-maltoside micelles where it was found that monomer exchange between micelle and the solvent is in the order of 0.1 to 1.2 μs.89

Figure 2.

Figure 2

Representative MD Snapshots of the α- (a-c) and β-anomers (d-f) of C12G2 micelles simulated with the CHARMM-Opt force field at t≈240 fs (a, d), t≈7.0 ns (b, e) and (c, f) and t ≈14 ns of the production period. Oxygen and hydrogen are in red, and white colors. Carbons in GlcA, GlcB and in the alkyl chain are blue, cyan and gray respectively. Water molecules are removed for visual clarity. Figures were produced with the PyMOL program.122

A. Size of the micelles

To examine the stability and to measure the dimensions of the micelle in the six runs, we have computed their instantaneous radii of gyration, Rg, over the course of the simulations (Fig. 3) using the following expression:

Figure 3.

Figure 3

Time evolution of the radius of gyration, Rg, for α- (a) and β-anomers (b) of C12G2 micelles.

Rg2=imi(rircm)2/imi (1)

Where mi is the mass of the atom i of the micelle at the distance ri from the center of mass rcm. For all the micelles studied here, the Rg values are stable after typically ∼3 ns of production. As indicated previously, during the beginning of the productive run (i.e. between ∼ 0 and 3 ns time period), local arrangements and compaction of the surfactants on the micelle surfaces are observed. This feature was also observed in previous glycolipid micelle simulations.47

The instantaneous Rg values for the α-C12G2 micelle in the three runs stabilizes after ∼ 3 ns around ∼20 -21 Å until the end of the trajectory. The average Rg values, 〈Rg〉, of the α-C12G2 micelles, computed from the last 11 ns of CHARMM-K, CHARMM-Opt and GLYCAM06 runs (20.5 ± 0.1 Å, 20.2 + 0.1 Å and Rg= 20.0 ± 0.1 Å, respectively) are close to the Rg experimental value (18.6 ± 0.6 Å13 calculated from the semi-axis lengths of the micelle aM, bM and cM and the expression Rg2=(aM2+bM2+cM2)/5 for an ellipsoid with an uniform density.79 In the case of the β-C12G2 micelles, Rg reached stable values after ∼2.5–3 ns depending the force field used. In contrast to the α-C12G2 simulations, the three force fields lead to significant differences (up to 1.0 Å) for the instantaneous and averaged Rg, especially for the two CHARMM force fields versions. For β-C12G2, the 〈Rg〉 's are equal to 26.4 ± 0.1 Å, 25.4 ± 0.1 Å and 25.1 ± 0.1 Å, for the aggregates simulated with the CHARMM-K, CHARMM-Opt and GLYCAM06, respectively. The 〈Rg〉's obtained with the CHARMM-Opt and GLYCAM06 parameters are closer to the experimental value of 23.3 ± 0.6 Å.13

B. Shape of the Micelles

The micelle shape can be characterized by computing the instantaneous ellipsoidal axis ratio between the micelle major (aM) and minor (cM) semi-axis lengths, or aM/cM, obtained from the inertia tensors (see ref.79 for details). As shown in Figure 4, the six micelles present a stable ellipsoidal shape (i.e. aM/cM > 1.0) after typically ∼4.0 ns. For the α-C12G2 micelles, their shapes do not depend significantly on the force field. This contrasts with the behaviors of the β-C12G2 micelles where the ratio aM/cM shows a much larger fluctuations. To be consistent with the calculation of the Rg, the initial 3 ns of each trajectory were discarded in the calculation of aM/cM. The average values of the ratio, 〈aM/cM〉, are reported in the 7th column of Table 2 for the different micelles studied. In our calculation, both α- and β-C12G2 are ellipsoidal, but α-C12G2 is the closest to the shape of a sphere. In the case of β-C12G2 aggregates, the instantaneous aM/cM values stabilize around ∼1.40 at the end of the simulations independently of the considered force field and the 〈aM/cM〉 values are close for the three micelles: 1.38 ± 0.03, 1.43 ± 0.01 and 1.38 ± 0.04 for CHARMM-K, CHARMM-Opt and GLYCAM06, respectively. In contrast, β-C12G2 micelles have a pronounced oblate shape (aM>bM≈cM), which agrees well with the experimental observations.13,26,75

Figure 4.

Figure 4

Time evolution of the major and minor semi-axis of inertia ratio for α- (a) and β-anomers (b) of C12G2 micelles.

Table 2. Average dimensions and shapes of the six micelles.

〈…〉 stands for the ensemble average. Values with M and HC subscripts were computed by including all the micelle atoms and those of the hydrophobic core, respectively. The radii of gyration and the semi-axis lengths were computed using the inertia tensor (e.g. see ref.79) and the main text for details. 〈lpl〉 is the average polar layer thickness of the micelle in Å. The statistical errors (maximum errors) are always lower than 0.1 Å, 0.8 Å and 0.3 Å for the Rg, semi-axis lengths and polar layer thickness, respectively.

Force field Micelle 〈Rg 〈aM 〈bM 〈cM 〈aM/cM 〈aHC 〈bHC 〈cHC 〈lpl
CHARMM-K α-C12G2 20.5 28.4 25.6 23.8 1.20 22.1 19.1 16.5 6.7
β-C12G2 26.4 38.8 34.7 28.1 1.38 33.1 27.3 20.0 7.2
CHARMM-Opt α-C12G2 20.2 27.8 26.1 24.3 1.14 21.5 19.1 16.7 7.0
β-C12G2 25.4 38.1 33.0 26.5 1.43 30.6 24.8 19.3 7.7
GLYCAM06 α-C12G2 20.0 28.4 25.5 23.1 1.23 22.3 18.6 16.5 6.5
β-C12G2 25.2 37.2 32.0 30.1 1.38 30.1 24.4 19.2 7.2

However, we can underline that the 〈aM/cM〉 values for the β-C12G2 micelles remain, depending the force field between lower than the estimated experimental values (i.e. aM/cM =1.70 from Dupuy et al.).13 The instantaneous length values of the semi-axis of each micelle hydrophobic core (i.e. aHC, bHC and cHC) have been also computed by including only the contributions from the surfactant hydrophobic chain in the calculations of the inertia tensors. The average values of the three semi-axes, (〈aHC〉,〈bHC〉 and 〈cHC〉), are reported in the 8th, 9th and 10th columns of Table 2. We find that the average major and minor semi-axis lengths 〈aHC〉 and 〈cHC〉 are in relative agreement with experimental values for α-C12G2 and β-C12G2 (i.e. 〈aHC〉 =〈cHC〉 = 18.6 Å ± 1.0 Å) and 〈aHC〉 = 28.2 ± 1.0 Å and 〈cHC〈 = 14.1 ± 1.0 Å, respectively).13 The average thickness of the polar outer layer, or 〈1pl〉, computed by subtracting the semi-axis length of the hydrophobic core from those of the whole micelle (〈aM〉,〈bM〉 and 〈cM〉), does not change significantly with the force field and is 6.7 ± 0.3 Å for the α-anomer of the C12G2 and increase up to 7.3 ± 0.4 Å for the β-anomer. Due to the partial folding of the maltose head, these values are 39.1 % and 33.4 % smaller than the calculated length of the maltose in its extended configuration (∼11.0 Å). The larger 〈1pl〉 value for β-C12G2 is consistent with the fact that the β- anomer is linear and extends in the solvent, whereas α- is more folded, hence constrained on the micelle surface. In all cases, the 〈1pl〉 values are within 1 Å of the experimental values estimated from SAXS and SANS experiments, i.e. 5.4 ± 0.1 Å and 6.2 ± 0.1 Å for α-C12G2 and β-C12G2, respectively.13,76

C. Density profiles of the Micelles

To compare the spatial extent of the most relevant atomic group components of the micelles, we have computed their average radial mass density profiles ρ(r) as a function of the distance, r, of the group from center of mass (COM) of the micelle.79 We discuss here the ρ(r) values obtained for the entire micelle (Micelle), the maltose headgroup (Maltose), the dodecane tail (DOD), the two maltose glucose rings (GlcA and GlcB), and the hydration water (H2O). As previously discussed,79 the non-spherical nature of the micelles will affect ρ(r) value to a certain extent, causing the broadening of these functions. ρ(r) values, averaged over the last 11 ns of each trajectory, are shown in Figure 5(a-b). The hydrophobic core ρ(r) profiles extend from 0 to ∼19.0 Å from the micelle COM, and present similar shapes regardless of the force field. For the hydrophilic maltose head, the ρ(r)'s present a strong peak with density maxima at 21.0 ± 0.5 Å and 25.0 ± 0.5 Å for the α- and β-C12G2 micelles, respectively. These values are close to those obtained previously for 〈Rg〉. We notice that the position of the main peaks for the GlcA and GlcB density profiles depend more strongly on the force field than that of the other groups studied here. Considering all the results, GlcA ρ(r)'s extend from 15.0 Å to 25.0 Å and from 18.0 Å to 28.0 Å for α- and β-C12G2 micelles, respectively. Larger values, of 1 to 2 Å, are found for all GlcB ρ(r) values. The water density profile in Fig. 5 shows that water molecules deeply penetrate into the micelle headgroup and solvates the maltose heads to a different degree with a preference for the outermost glucose ring (GlcA). We can also emphasize that water shares significant contact with the micelle hydrophobic core as seen by the intercepts of the water and DOD ρ(r) curves. Finally, the water ρ(r) curves reach their bulk density value (∼1.0 g/cm3) near the edge of the box at 35 Å (α-C12G2) and 38 Å (β-C12G2) from the micelle COM.

Figure 5.

Figure 5

Average radial density profiles with respect to the center of mass (r = 0 Å) for simulations performed with CHARMM-K (continuous line), CHARMM-Opt (dotted lines) and GLYCAM06 force fields (dashed line) for micelles α- (a) and β-anomers (b) of C12G2 micelles. In the inset, the radial profiles for the micelle hydrophobic core (maroon), the maltose headgroup (orange) and water (blue) are plotted. A 0.5 Å bin width was used for both figures.

D. Hydration of the headgroup

As discussed in the previous section, radial mass density profiles show significant interaction between water and the C12G2 surfactant headgroups. To gain insights on this aspect, we provide in the Table 3 some surface area (SA) properties of the micelles computed from the last 11 ns of the simulations. We first compare the instantaneous value of the SA per surfactant headgroup (SAHGC12G2) with the results of Dupuy et al.13 obtained from SAXS and SANS experiments assuming that the α- and β-micelles are spherical. As described by these authors SAHCC12G2, the surface of the hydrophobic core of a sphere of radius R̄HC was calculated. The average ellipsoid semi-axis of the micelle hydrophobic core 〈aHC〉, 〈bHC〉 and 〈cHC〉 were used to calculate R̄HCwith the expression: R̄HC =(〈aHC〉〈bHC〉〈cHC〉)1/3. The average values of SAHGC12G2 ( SAHGC12G2 are reported in the third column of the Table 3. We found that the SAHGC12G2 values are in the range of 60.3 to 61.1 Å2 and 55.5 to 65.1 Å2 for the C12G2 α- and β-anomers, respectively. Values obtained with CHARMM-Opt and GLYCAM06 agree well with the experimental values (58 Å2 and 52 Å2 for the C12G2 α- and β-anomers, respectively), whereas the CHARMM-K results are further away.

Table 3. Surface properties of the micelles.

〈…〉 stands for the ensemble average. SAHGC12G2 (in Å2) are the average surface area per headgroup computed using the micelle oil core radius. SAvC12G2 and SAeC12G2 are the average micelle surfaces computed with the Voronoi polyhedron, 90 assuming an ellipsoid-like geometry for the micelle. 〈ftail〉 is the average surface fraction shared between the water and the C12G2 alkyl chain. The statistical errors (maximum errors) are always lower than 3.0 % and 0.2 % for the surfaces and 〈ftail〉 values.

Force field Micelle
SAHGC12G2
SAVC12G2
SAeC12G2
ftail
CHARMM-K α-C12G2 61.1 19425.0 9244.5 11.0
β-C12G2 65.1 33237.6 16581.5 10.0
CHARMM-Opt α-C12G2 60.4 17625.0 9013.2 10.9
β-C12G2 56.8 29422.8 15894.6 9.3
GLYCAM06 α-C12G2 60.3 15675.0 9146.6 9.8
β-C12G2 55.5 25726.8 15666.0 9.3

In the 4th and 5th columns of the Table 3 are reported the average surface areas (SA) for the whole micelles SAVC12G2 and SAeC12G2, respectively. The SAvC12G2 values were obtained from the Voronoi construction90 by adding up the surface area of each Voronoi polyhedron shared between all surfactant atoms and water.91 Instead, SAeC12G2 was the ellipsoidal surface of the micelle obtained from the average semi-axis lengths (〈aM〉,〈bM〉 and〈cM〉) computed in section II.B. Comparison of the two values confirms that the micelle interfaces are corrugated (as also shown in Figure 1). Indeed, the surface rugosity factors fs = SAvC12G2/SAeC12G2 was calculated between 1.7 and 2.1 and between 1.64 and 2.0 for the α- and β-anomers, respectively.

In the 6th column of Table 3, we also provide the average C12G2 surface alkyl chain ratio of the micelles, 〈ftail〉 in contact with the solvent. The 〈ftail〉 values were calculated with the SAvC12G2 and the surface area of the alkyl chain atoms, SAvC12. 〈ftail〉 values for all the micelles decrease by ∼1.0 % when the surfactant head changes from the α- to the β-anomer and are calculated between 9.8 and 11.1 % and between 9.3 and 10 % for the α- and β-anomers, respectively. The lower 〈ftail〉 values of GLYCAM06 indicate that for those micelles the surfactant alkyl chains of the micelle are more protected from the solvent than those obtained in the simulations with the CHARMM force fields. In comparison, the 〈ftail〉 values reported in this work are lower than those found by Stephenson et al.51 for a micelle with 45 β-C12G2 (∼17.0 %), and also lower than for micelles with 27 octyl-β-galactose47 (∼30%) and 92 octyl-β-glucose monomers (20%).46 The latter is probably due to the smaller size of the headgroup in those micelles, which shields less the micelle hydrophobic core from water.

The average number of water molecules, 〈n w〉, in the first solvation shell of each surfactant, or hydration number, were also computed during the last 11 ns of each run. They are presented in Table 4. For each configuration, the hydration water molecules were selected using a simple cutoff radius criterion, as described in ref.92. Briefly, a water molecule is considered near the micelle surface if its distance with any of the detergent atoms is less than Rcut =f(Rw + RC12G2), where Rw and RC12G2 are the force field van der Waals radii of the water and of the C12G2 atoms, respectively, f is a parameter set arbitrarily to 1.1 in our calculations.92 Five hydration numbers were calculated here: for the whole C12G2 molecule (nwC12G2), for the headgroup (nwG2), for the GlcA (nwGlcA) and GlcB (nwGlcB) units and for the alkyl chain (nwC12). For all 〈nw〉 's, higher values are found for the simulations obtained with CHARMM-K, whereas the〈nw〉's of CHARMM-Opt and GLYCAM06 simulations are close to one another. The nwG2 value for CHARMM-Opt and GLYCAM06 are computed around 8.2 - 7.2, respectively, and compare well with the estimation of nwC12G2 obtained from SANS, SAXS (8.0)13 or TRFQ experiments for β-C12G2 micelle (7.9).75 The bent conformation of the α-C12G2 slightly increases the headgroup hydration by 0.4 - 0.6 waters for the micelles simulated with the CHARMM-Opt and GLYCAM06 parameters, whereas for CHARMM-K the nwG2 decreases by 0.3 units. For maltose molecules in water, hydration numbers between 5.7 and 22.6 are estimated by experimental studies, whereas values within 6.5 - 14.5 are obtained from computer simulations (see Table 3 of ref.33 and references therein). The validity of these results depends on the experimental techniques or the force field considered. Comparison of the hydration of the glucose rings GlcA and GlcB show that the number of water molecule around GlcB, connected to the alkyl chain, is, on average, ∼2.6 units lower than for GlcA. This is independent of the force field employed and the conformation of the headgroup. Finally, the low values for nwC12 (< 1.0 water) confirm that the micelle hydrophobic core have only sporadic contacts with the solvent consistently with the 〈ftail〉 value calculated in this work.

Table 4. Hydration numbers.

〈…〉 stands for the ensemble average. nwG2, nwGlcA, nwGlcB, nwC12 and nwC12G2 give the average number of water molecule at 4.0 Å of the maltose head, the outermost and innermost glucose rings and the alkyl chain, respectively. The statistical errors (maximum errors) are always lower than 0.1 %.

Force field CHARMM-K CHARMM-Opt GLYCAM06
System α-C12G2 β-C12G2 α-C12G2 β-C12G2 α-C12G2 β-C12G2
nwG2
8.3 8.6 8.2 7.6 7.6 7.2
nwGlcA
5.2 5.6 5.2 5.1 4.7 4.9
nwGlcB
3.1 3.0 3.0 2.5 2.9 2.3
nwC12
0.8 0.8 0.8 0.7 0.6 0.6
nwC12G2
9.1 9.4 9.0 8.3 8.2 7.8

To further examine the headgroup hydration, in Table 5 we provide the average number of nearest water for each maltose-oxygen, or 〈nOx−Ow〉, obtained from the computed radial pair density functions (RDF) of the maltose-oxygen (O1-10) and water-oxygen (Ow) atoms. To obtain 〈nOx−Ow〉 the RDF functions were integrated until the first minimum at r ≈ 3.5 Å after the first peak. The 〈nOx−Ow〉 results indicate that water molecules solvate primarily the hydroxyl oxygen atoms (O1, O2, O3, O4,O6, O8, O9 and O11) of the maltose headgroup. This is consistent with previous simulation studies performed on other glycolipid micelles.44,46,47 The number of water molecules in the first shell of these atoms are found between 1.9 and 3.7 as a function of the oxygen localization on the headgroup. These values vary little with the force field employed and the surfactant conformation. In general, the higher 〈nOx−Ow〉 values are obtained for the oxygen atoms O3 (2.9 - 3.4) and for O6 (3.2 - 2.4), the most the atoms are exposed to the solvent in GlcA. As an example, the hydroxyl oxygen O11 in GlcB has about one water molecule in its first shell that the equivalent atom O6 in GlcA. The hydration of the ring oxygen atoms O5 and O10 of GlcA and GlcB does not change much (∼0.3 water) when the surfactant conformation changes from the α- to β-anomer. Finally, for the oxygen atoms involved in the glycosidic bond (O1) and the link between the headgroup and alkyl chain (O7), present low〈nOx−Ow〉 values (< 0.8 and < 0.5) indicating that these oxygens are shielded from the solvent. This result is also consistent with another study, 46 where a 〈nOx−Ow〉 value close to 0.2 – 0.3 for O7 was observed.

Table 5. Nearest neighbors for the micelle oxygens.

The micelle oxygen atoms are labeled as it followed: O1 and O7 are the acetalic oxygens, O5 and O10 are the maltose ring oxygens and all the remaining are hydroxyl oxygens (see Figure 1). Also, Δβ-α is the difference in the average number of nearest neighbors between the β- and α-anomers. The values have been obtained by integrating the Ox-Ow pair correlation functions g(r) up to the first minimum at around r≈3.5 Å. Total GlcA and Total GlcB give the average nearest neighbors for the outermost and innermost glucose unit of the molecule, respectively.

Force field CHARMM-K CHARMM-Opt GLYCAM06
〈nOx−Ow α-C12G2 β-C12G2 Δα→β α-C12G2 β-C12G2 Δα→β α-C12G2 β-C12G2 Δα→β
O1-Ow 0.7 0.8 0.1 0.5 0.5 0.0 0.5 0.4 -0.1
O2-Ow 2.3 2.7 0.4 2.5 2.3 -0.2 2.1 2.6 0.5
O3-Ow 3.6 3.7 0.1 2.9 3.2 0.3 3.0 3.4 0.4
O4-Ow 2.0 2.6 0.6 2.3 2.6 0.3 1.9 2.4 0.5
O5-Ow 1.1 1.3 0.2 1.3 1.0 -0.3 1.3 1.0 -0.3
O6-Ow 3.1 2.5 -0.6 2.6 2.3 -0.3 3.2 2.4 -0.8

Total GlcA 12.8 13.6 0.8 12.1 11.9 -0.2 12.0 12.2 +0.2

O7-Ow 0.2 0.5 0.3 0.3 0.3 0.0 0.2 0.4 0.2
O8-Ow 2.4 1.9 -0.5 1.9 1.6 -0.3 1.7 1.5 -0.2
O9-Ow 2.4 2.0 -0.4 2.2 1.8 -0.4 2.2 1.6 -0.6
O10-Ow 0.8 0.9 0.1 0.7 0.6 -0.1 0.6 0.8 0.2
O11-Ow 2.0 1.7 -0.3 1.7 1.6 -0.1 1.8 1.3 -0.5

Total GlcB 7.8 7.0 -0.8 6.8 5.9 -0.9 6.5 5.6 -0.9

Considering the strong interaction between the C12G2 headgroup atoms and water, it is clear that the headgroup oxygen atoms will form an extended network of hydrogen bonds with water molecules and with donor groups of the detergent themselves.93 The average number of HB between water molecules and the maltose headgroup (WHB) and within the surfactant headgroups (HHB), were computed for the last 11 ns of the simulations, using the following geometrical criterion: a HB was considered if the oxygen-oxygen distance equals or is smaller than 3.5 Å and the angle O-H…O was between 120 and 180°.94 These values are reported in Tables S4, S5 and S6 of the supplementary information. We observed that each α-C12G2 molecule presents 0.5 - 1.0 more WHB than the β-anomer. These values vary only slightly with the force fields, CHARMM-K having the largest number of HB in α-C12G2 followed by CHARMM-Opt and GLYCAM06. This result is in agreement with small variations of hydration water in the first shell of the C12G2 headgroup and the decrease of 〈nOx−Ow〉 reported in the previous paragraph. We found that each C12G2 headgroup makes, on average, ∼1.5 times more in the establishment of HB as an acceptor (∼7.0) than as a donor (∼5). This is consistent with previous computer simulations studies of C8G1 and C8Gal in water.47 As also expected the total number of WHB obtained in this work is lower than the total WHB found for maltose in TIP3P water where the number of WHB (∼15.9 and 22.4).27,32 Further analysis of the individual HB donors and acceptors shows that the O3 and O6 (GlcA) and O8 and O9 (GlcB) hydroxyl oxygens make about one additional HB with water than the other oxygens. For these same oxygens, the number of WHB decreases by ∼0.2 when the headgroup changes from the α- to the β-anomer. Finally, due to the strong entanglement of the maltose head at the micelle surface and to the low hydration of some of the hydroxyl oxygen atoms, it is expected that a large network of inter- and intra- headgroup donor/acceptor HB (INHB and INTHB, respectively) will be favored. Several inter-headgroup HB have been computed (among these previously examined by Chong et al.47) and are reported in the 5th to 9th columns in Tables S4, S5 and S6 in the supplementary information. The number of INHB is found to be much lower than the number of solvent-headgroup HB. On average, there are ∼0.10 and ∼0.25 HB per lipid for structures obtained from the CHARMM and GLYCAM force field simulations, respectively. The number of INHB is greater in β-C12G2 micelles and is due to the O6-H…O4, O8-H…O10 and O8-H…O9 HB. Furthermore, three other INTHB were previously observed (O6H6…O5 and O11H11…O10 in the first and second glucose rings and O2H2…O9 between GlcA and GlcB).27,28,94 These HB are correlated with the rotational freedom of the ω torsion angles and the α(l→4) glycosidic linkage flexibility. Our calculations indicate that these HB types exist during all of the simulations. In particular, O2H2…O9 is present during approximately 70 - 80 % of the simulation times, whereas the two others INTHB only ∼30 - 40 % of the time.

E. Conformation of the Surfactant

To examine in more detail the hydration differences of the micelles, we have studied the surfactant conformation by computing the main peak of the average end-to-end distance probability distributions P(r). Specifically, we have computed the dC12 and dG2 by collecting from the trajectories the distances between the atoms C7 and C19 of the alkyl chain and between the O4 and O12 of the maltose head, respectively. Since the dC12 and dG2 end-to-end distances are strongly related to the conformations of the alkyl tail and headgroup of the surfactant, respectively, we have examined the conformation of several characteristics torsion angles of the tail (such as all the CCCC dihedral angles, the first C7C8C9C10, and last C15C16C17C18 dihedrals)44, the torsion angles involved in the connection of the alkyl chain and the maltose head (i.e. O7C7C8C9 44, O10C1O7C727,95, C′1O7C7C828,96) and ω1 and ω2 angles (i.e. O6C6C5O595 and O11C6C5O1064) by computing the corresponding normalized dihedral angle distribution P(ϕ). These functions were computed and averaged over the last 11 ns of each run. The relative gauche+- (pg+-) and trans (pt) populations were also extracted and are presented in Table 6. P(r) functions for the two CHARMM simulations (not shown here) display similar shapes with a strong peak at dC12 ≈12.3 Å for all the micelles regardless of the surfactant headgroup anomer. This is ∼10.9 % smaller than the value (∼14.0 Å) calculated for an extended dodecane chain with the modeling program Discovery Studio Visualizer. In contrast to the CHARMM results, the alkyl tail P(r) functions for the two micelles simulated with GLYCAM06 parameters present two peaks at dC12 ≈ Å and dC12 ≈ 13.8 Å (figures not shown) indicating a coexistence of two populations for the alkyl chain length. In the literature, a smaller value for dC12 is strongly related to the partial folding of the hydrophobic chain in the micelle core and existence of “gauche defaults”.97,98 In this context, we found that the CCCC dihedral angles of the alkyl chain are mostly in their trans state with relative populations pt close to 72.0 % and 84.6 % for the CHARMM and GLYCAM06 force fields, respectively. These results are consistent with previous simulations of micelles containing surfactant with a dodecane chain (see for instance refs 99, 100, 59). As for the CHARMM simulations, the peaks in P(r) peaks do not change much (< 1 %) when going from an axial (α-) to an equatorial (β-) conformation of the surfactant headgroup (see Table 6). Further investigation shows that the outermost and innermost CCCC dihedral angles (i.e. C7C8C9C10 and C15C16C17C18) have a larger gauche+- population, pg+-≈ 27 %, than the others dihedrals in the alkyl chain, pg+-≈15 %. Similar results were found in previous MD simulations of octyl-β-glucoside micelles44, where the lower steric conflicts found at the extremities of the alkyl chains decrease the gauche conformation of the chain. Finally, we find only small differences, less than 12 % in pt, in the CCCC angles between the CHARMM and GLYCAM06 simulations. Similar behaviors were obtained in simulations of LDAO micelles simulated with the CHARMM27 and AMBER94 force fields, pt ≈ 71.0 % and pt≈ 82.8 %, respectively.101

Table 6. Trans and Gauche populations.

Dihedral angles between -180° and -120°, between -120° and +120° and between +120° and +180° are defined as gauche+ (pg+), trans (pt) and gauche- (pg-), respectively. The exponents a, b and c are for agauche+-, bgauche+ and cgauche-, respectively. The statistical errors (maximum errors) are always lower than 0.3 %. See the main text for details.

Force field CHARMM-K CHARMM-Opt GLYCAM06
Micelle α-C12G2 β-C12G2 α-C12G2 β-C12G2 α-C12G2 β-C12G2
CCCC 71.8, 28.2a 72.0, 28.0a 71.4, 28.6a 72.1, 27.9a 84.6, 15.4a 84.7, 15.3a
C7C8C9C10 67.4, 32.6a 70.9, 28.1a 66.7, 33.3a 67.7, 32.3a 82.0, 18.0a 80.0, 20.0a
C15C16C17C18 73.3, 26.7a 75.4, 24.6a 70.8, 29.2a 68.5, 31.5a 81.0, 19.0a 82.8, 17.2a
O7C7C8C9 80.5, 20.5a 80.6, 20.4a 54.4, 46.6a 53.3, 47.7a 61.8, 38.2a) 63.0, 37.0a
O10C′1O7C7 2.3, 97.7b 0.1, 99.9c 0.5, 99.5b 4.9, 95.1c 2.4, 97.6b 6.7, 93.3c
C′1O7C7C8 90.1, 8.9a 89.1, 10.9a 71.7, 28.3a 76.4, 23.6a 81.7, 18.3a 78.1, 11.9a
O6C6C5O5 (ω1) 59.0b, 43.7c 59.3 b, 39.4c 60.9b 35.0c 51.6b, 39.3c 51.7b, 44.7c 50.9b, 44.5c
O11C6C5O10 (ω2) 24.5c, 75.3c 37.0 b, 54.4c 36.7b, 60.0c 29.9b, 26.7c 30.9b, 65.9c 37.1b, 53.9c

In our simulations, the O7C7C8C9 dihedral angle remain in a trans state, in agreement with previous simulations of octyl-β-glucoside micelles.44 Nevertheless, we found that CHARMM-Opt has a pg+- 25 % smaller than that of CHARMM-K, closer to GLYCAM06 and in agreement with QM/MM calculations carried for the α- and β-anomers of maltose.67 For the O10C1′O7C7 (Φ) dihedral angle we observed that for all the simulations, this angle is in gauche+ (> ∼ 90 %) for the α- and β-anomers. Also, our results show that for all the micelles the Ψ dihedral angle, C1′O7C7C8, is always found in a trans state. Compared to CHARMM-K, in CHARMM-Opt the pt of this angle decreases by ∼13 units to 18 % depending on the anomer, and is closer to the values obtained for the GLYCAM force field.

In the last two rows of Table 6, we have listed for all the simulations, the average relative population of the two ω dihedral angle in the reducing (GlcA) (ω1 = O6C6C5O5) and non-reducing (GlcB) (ω2 = O11C6′C5′O10) glucose units of the maltose head. In glucopyranose, due to rotational freedom of the ω dihedral angle, three stable conformers exist, defined by the position of the OH oxygen relative to oxygen ring atoms (here, O5 and O10), termed gauche-gauche (gg), gauche-trans (gt), and trans-gauche (tg) which correspond to ω= -60°, -60° and 180°.102, 103,104 Computational results on maltose have shown that ω has a strong preference for gauche values.58,105 This is due to steric repulsions between the hydroxyl groups in position 4 and 6, described as the “gauche effect”.106

In contrast to maltose in vacuum, where the ω angle adopts preferentially a gt conformation, for maltose in solution, MD simulations performed in condensed phase28,37 and experimental studies107 have shown that the gg conformation is favored, Our results for CHARMM-K and CHARMM-Opt show a different behavior for ω, for which the conformation gt is favored with respect to gg (gt/gg ≈60:40). For GlcB, we find that these angles are mainly in its gg conformation except for the β- anomer where ω2 highly similar gg and gt populations. These results, can be explained by the incomplete hydration of the maltose headgroup in the detergent and the existence of inter maltose HB.

Turning our attention to the maltose head linkage conformation, the P(r) functions (not shown here) present peaks at dG2 ≈ 8.8 Å (α-anomer) and dG2≈ 9.8 Å (β-anomer). These values change slightly (0.2 Å) with the potential employed and are smaller than the length for a maltose molecule in an elongated conformation (10.3 Å, with ΦH = ΨH = 0.0°). On Figure 6, we have plotted the distribution maps of the P(ΦH,ΨH) glycosidic dihedral angles pair in population percentage for all simulations. We find that, except for the α-C12G2 micelle simulated with the new CHARMM potential, all of the P(ΦH,ΨH) present a compact elliptic shape with a maximum point near (-40°, -25°) ± 10°. In the former system, instead, two areas are sampled, around (-25°; -20°) and (-65°; -50°), for 70 % and 30 % of the total simulation time, respectively. It is difficult to validate these results, as no experimental data exist in the literature for P(ΦH,ΨH) of C12G2 micelles and these results differ for a maltose molecule in water where experimental (such as NMR32,38,108,109 or optical rotation 110) and theoretical studies (such as QM38,111,112 and MD 28,32,37,69,113) predicted two peaks for P(ΦH,ΨH) around (-50°; -30°) ± 20° and (-40°; -30°) ± 20°.

Figure 6.

Figure 6

Distribution map of the ΦH/ΨH glycosidic dihedral angles pairs in population percentage for α- (a) and β-anomers (b) of C12G2 micelles for the CHARMM-K ((a) and (d)), CHARMM-Opt ((b) and (e)) and GLYCAM06 ((c) and (f)) force fields, respectively. The grid interval is 5.0° and contour lines are spaced every 0.2 %.

F. Water Dynamics at the Micelle Surface

To examine the dynamic behavior of water molecules around the micelles, we have computed the mean square displacement (MSD) of the translational diffusion 〈|r(t) − r(0)|2〉 for water molecules at the micelle surface. Water molecules included in this calculation were at a distance of less than 4.0 Å from any detergent molecule at a given time of the trajectory (details about the calculation are available in ref.47). For the different micelles studied in this work, the MSD functions are shown in Figure 6 and the translational diffusion parameters are reported in Table 7. MSD functions are compared with the results obtained from a NPT simulation (T = 297 K and P = 0.1 MPa) for 1000 TIP3 water molecules simulated in a cubic box for 1 ns. As shown previously for water molecules near protein surfaces 114,115, direct micelles116,117 or reverse micelles79,118 the water MSD presents a sub-diffusive regime and can be fitted with a power law (i.e. 〈|r(t) − r(0)|2〉 ∝ tθ) rather than a linear dependence in time as observed in bulk water. This behavior is assumed to be the consequence of the geometric/energetic disorder found at the micelle and protein surfaces.114 For all micelles, the fit to a power law leads to similar values for θ, around 0.34 and 0.40. These values are comparable to the θ values found previously by one of us (MM) for water around the C12E6 micelle surface (0.3 and 0.4 at T = 283 K and 318 K, respectively).117 In this micellar system, it has been shown that the water interact with the long hydrophilic ethylene oxide (EO)6 chain through a large hydrogen bonds network.119 For a subdiffusive regime, it is useful to define a rough estimate of the water residence time, τw, as the time needed by a water molecule to cover a distance of 9 Å2, i.e. corresponding to a path spanning a water molecular diameter.120 The ratio, between τw and the residence time of the bulk water values (τwb = 2.7 ps) are reported in the 4th and 5th rows in Table 7. We find that the τw values change significantly with the force field employed, but not with the surfactant headgroup conformation. τw values are calculated for all the simulations between 18.9 and 30.5 ps. In the GLYCAM06 simulations, water dynamic retardation, or τwbw, are ∼ 11.3 for the α- and 11.7 for the β-anomers. The differences obtained for water diffusion is probably the results of the headgroup conformation variations and the number of trapped water at the micelle interface for the six micelles.

Table 7. Translational diffusion of the hydration waters.

θ is the dispersion regime parameter obtained by fitting the 〈|r(t) − r(0)|2〉 function to tθ. τw is the water residence time, defined as the time (in ps) for a water to cover a distance equal to its own diameter (i.e. 3 Å) and τwwb is the retardation or the ratio between the water residence time in the micelle and the bulk.

Force field CHARMM-K CHARMM-Opt GLYCAM06
System α-C12G2 β-C12G2 α-C12G2 β-C12G2 α-C12G2 β-C12G2
θ 0.39 0.40 0.34 0.36 0.38 0.35
τw (ps) 18.9 18.3 24.8 24.8 27.2 30.5
τwwb 6.7 6.5 8.5 8.5 11.7 11.3

To the best of knowledge, no experimental data on water dynamics are available for C12G2 micelles. Notwithstanding, Chong et al.47 have computed the residence time of water near each headgroup oxygen atoms for micelles of octyl-glucose (C8G1) and galactose (C8Gal). The authors found that τw maximum values are between 41.0 - 164.0 ps (C8G1) and 28.4 ps - 88.0 ps (C8Gal) depending the localization of the hydroxyl group in the headgroup and the cutoff employed. The largest τw values are found for water molecules trapped within the crevices and clefts at the micelle surface. Finally, the τw values obtained here largely exceed the average residence time found by MD for water in the first shell of maltose (∼11.6 ps) in water 31 or in QENS experiments at 320 K (∼3.4 ps).121

IV. Conclusion

In this paper, we have presented the development of two new potential models, based on the CHARMM36 and GLYCAM06 force fields, to be used in the molecular modeling of the α- and β-anomers of C12G2 GL. These surfactants are widely employed to extract and solubilize membrane proteins. To validate these potentials, we have investigated the structure of significant C12G2 micelles by MD simulations. In particular, we have studied the structural properties of the micelles with the two anomeric forms, and described the dynamical properties of water molecules at the micelle/water interface. The results obtained for the new potentials were also compared with those obtained with older parameters developed for carbohydrate for CHARMM22.

We found that the three force fields studied here lead to different results particularly for the properties related to the headgroup conformation and micelle hydration. In particular, our calculations show that the α- and β-C12G2 micelles have a 〈Rg〉 close to 20.2 Å and 25.4 Å, respectively. The computed 〈Rg〉's agree reasonably well with SAXS and SANS experiments13 when the micelles are simulated with the new parameters developed for CHARMM36 CHARMM and GLYCAM06.

Concerning the global shape of the micelles, we observed no significant differences between the three force fields and the different micelles studied. The α-C12G2 micelles have an average major-to minor semi-axis ratio 〈aM/cM〉 close to 1.20 whereas the β-C12G2 micelle has a more pronounced oblate shape with 〈aM/cM〉 values around 1.38 - 1.43, in qualitative agreement with published experimental observations.13,26,75 The computed radial density profiles indicate that water penetrates deeply at the micelle headgroup and hydrates preferentially the outermost glucose ring (GlcA). Due to the difference in the surfactant headgroup conformations, we also observed slight differences in the headgroup hydration. Consistently with previous simulations carried out with others glycolipid systems,44,46,47 we found that the micelle/water interfaces are highly corrugated with a rugosity factor values around 1.6 - 2.0. The average solvent surface area for the α- and β-C12G2 anomers simulated with CHARMM-Opt and GLYCAM06 are found to be around 60.6 Å2 and 55.5 Å2 per molecule, respectively, which is close to experimental values.13

Concerning micelle hydration, we found that the alkyl chains of C12G2 are in all the cases sturdily protected from the solvent, as less than ∼10% of the water penetrate the micelle core. Due to the strong entanglement of the maltose head at the micelle surface, within each micelle we observed a large hydrogen bond network consisting in a complex combination of inter- and intra-HB between adjacent headgroups. HB between water and headgroups do not depend on the headgroup conformation, as we found a highly similar patterns for headgroup/water HB's for both α- and β-anomers (with only on average ~0.6 units of difference).

Finally, investigations of the dynamic behavior of the hydrating water for all the micelles show that the water translational diffusion is strongly retarded with respect to the bulk by a factor of 7.0 to 11.7, depending on the potential. Interestingly, the headgroup conformation does not affect the water diffusion for the three force fields examined here. In particular, water diffusion results near the micelle interface are similar for CHARMM-Opt and GLYCAM06 (∼ 8.5 and ∼ 11.7 smaller than for the bulk, respectively) and are ∼1.5 time larger than the diffusion values obtained in CHARMM-K based simulations

In conclusion, the molecular modeling and simulation results reported in this paper are a first and necessary step to improve our atomic level knowledge of the C12G2 micelles. In addition, because our potential parameters are consistent with two major protein force fields (CHARMM and AMBER) they offer a solid starting point for further studies on the interaction and aggregation of membrane proteins with C12G2 detergents.

Supplementary Material

1_si_001

Figure 7.

Figure 7

Interfacial water mean square displacement (MSD) as function of time for α- (continuous line) and β-anomers (dotted line). The black dashed line gives the distance for computing the residence time τw (see the main text).

Acknowledgments

This work was, in part, granted access to the HPC resources of CCRT/CINES under the allocation 2009-t2009076076 made by GENCI (Grand Equipement National de Calcul Intensif) and financial support from the NIH (GM070855) to ADM.

Footnotes

Supporting information. Force field parameters, dihedral parameters for α- and β-anomer molecules and additional figures and tables. This information is available free of charge via the Internet at http://pubs.acs.org.

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