Mass Exchange and Equilibration Processes in AOT Reverse Micelles

Article Cite This: Langmuir 2018, 34, 2522−2530

pubs.acs.org/Langmuir

Mass Exchange and Equilibration Processes in AOT Reverse Micelles Gozde Eskici† and Paul H. Axelsen*,‡ †

Department of Biochemistry & Biophysics, University of Pennsylvania Perelman School of Medicine, Philadelphia 19104, United States ‡ Departments of Pharmacology, Biochemistry and Biophysics, and Medicine, University of Pennsylvania, 1009C Stellar Chance Laboratories, 422 Curie Blvd, Philadelphia, Pennsylvania 19104-6059, United States ABSTRACT: Reverse micelles (RMs) made with sodium bis(2ethylhexyl)sulfosuccinate suspended in isooctane are commonly used experimental models of aqueous microenvironments. However, there are important unanswered questions about the very characteristic that makes them of interest, namely their size. To explore the factors that determine the size of RMs, all-atom molecular dynamics simulations of RMs with different sizes but the same water-loading ratio were performed. An Anton 2 machine was used so that systems of the necessary size could be extended into the microsecond timescale, and mass exchange processes could be observed. Contrary to hypothesis, there were no net gains or losses of water by diffusion between RMs of different size. However, gains and losses did occur following fusion events. RM fusion followed RM contact only when waters were present among the hydrophobic surfactant chains at the point of contact. The presence of an encapsulated 40-residue amyloid beta peptide did not directly promote RM fusion, but it quickly and efficiently terminated each fusion event. Before fusion terminated, however, the size of the peptide-containing RM increased without a corresponding change in its waterloading ratio. We conclude that the mass transfer between RMs is most likely accomplished through transient fusion events, rather than through the diffusion of component molecules through the organic phase. The behavior of the amyloid beta peptide in this system underscores its propensity to embed in, and fold in response to, multiple interactions with the surfactant layer.

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function.13−15 Despite their popularity for this purpose, some basic questions persist without a definitive answer. For example, do RMs increase in size when they encapsulate a protein or does the protein merely displace water and lower the W0? Does an increased RM size imply an increased amount of surfactant or can an amphipathic peptide substitute for surfactant on an RM surface? Simulation systems large enough to address these questions require enormous computational resources to extend over meaningful time intervals. Recently, a next-generation Anton machine (Anton 2) has become available, which is capable of simulating multi-RM systems on a multi-microsecond timescale. The present study used such a machine to examine mass exchange behavior in nonequivalent RM pairs: a smaller, a larger, a same-size, and a peptide-containing RM were paired with an RM presumed to represent the equilibrium size for an RM with W0 = 11.4. The peptide was the 40-residue amyloid beta (Aβ40) peptide that aggregates in Alzheimer’s disease and which exhibits intriguing folding behaviors in RMs.16 Results show that RM pairs do exchange abundant material on the microsecond time scale by diffusion through the organic phase, but this process does not result in any net gains or losses.

INTRODUCTION Reverse micelles (RMs) made with sodium bis(2-ethylhexyl)sulfosuccinate (AOT), suspended in isooctane (isoO), are characterized by a water-loading ratio (W0) that determines their size. The distribution of RM sizes for any given W0 is narrow,1−8 but the precise value of their mean size, and the forces determining that size, remains unclear. Recent molecular dynamics simulation studies aimed at reaching an atomic-level understanding of these forces have yielded a relationship between equilibrium RM size and W0 that helps reconcile a large body of otherwise inconsistent experimental data.9 A logical next step in these investigations is to test whether this relationship predicts the net movement of exchangeable components between RMs in a nonequilibrium system and to examine the mechanism by which exchange is accomplished. It has been proposed that RMs exchange material through repeated cycles of fusion and fission.10 Alternatively, the formation of transient “channels” between RMs has been proposed.11,12 Prior simulation studies in this lab have suggested that RM components may escape into the organic phase and diffuse back into an RM.9 The effect of encapsulated peptides and proteins on RM size is also of interest because RMs are frequently used as experimental models of crowded biological microenvironments such as membranous organelles, intercellular spaces, and the interior of macromolecular chaperones in which proteins © 2018 American Chemical Society

Received: December 11, 2017 Revised: January 19, 2018 Published: January 24, 2018 2522

DOI: 10.1021/acs.langmuir.7b04192 Langmuir 2018, 34, 2522−2530

Article

Langmuir Table 1. Compositions of Simulated Systemsa system NS NN NL NNp a

RM type

nwater

nAOT

nISO

natoms

f iso (%)

cell dimensions (Å)

S N1 N2 N3 N4 L Np N5

724 1448 1448 1448 1448 2166 1448 1448

63 127 127 127 127 190 127 127

10 070

280 876

90

130 × 165 × 130

10 070

287 272

87

130 × 165 × 130

7500

226 764

81

130 × 150 × 130

7000

208 053

83

130 × 145 × 130

f iso is the mass fraction of isoO as a percentage of mass of all components in the system.

Figure 1. Stages in the simulation protocols for the four RM systems. Equilibration and conditioning was carried out on the Bridges system. Production simulation was carried out on Anton 2. The four RM types described above (N, L, S, and Np) were then placed as pairs, in a 130 Å × 165 Å × 130 Å unit cell, as far apart as possible. One system (designated “NS”) contained one type N and one type S RM. A second system (designated “NN”) contained two type N RMs. A third RM system (designated “NL”) contained one type L and one type N RM. A fourth system (designated as “NNp”) contained one type N and one type Np RM. Isooctane molecules (nISO) were added to each system such that the isoO mass was 84% of the total system. This percentage corresponds to an RM-forming portion of the AOT/water/isoO phase diagram.24 The compositions of the four systems are summarized in Table 1. All four systems were equilibrated in four stages, each stage consisting of 0.01 ns of minimization and 1 ns of NPT simulation. In stage 1, all atoms except those in the isoO solvent were fixed in position. In stage 2, the hydrocarbon chains of the AOT anions were released. In stage 3, the remaining portions of the AOT anions were released. In stage 4, water and sodium cations were released. The NNp system was subjected to two additional stages of minimization: stage 5, in which side chains of protein were released, and stage 6, in which all molecules in the system were released. After energy minimization, all four systems were conditioned by simulation as NPT ensembles for 30 ns using NAMD 2.9 to eliminate instabilities that cause them to crash with “momentum exceeded” errors on Anton 2. Simulation durations are summarized in Figure 1, and a 14.1 μs trajectory was generated with a 330 000 service unit allocation award from the Pittsburgh Supercomputer Center. Analysis. Interaction energies for each saved coordinate set were calculated using the VMD plugin NAMD ENERGY, and the same parameters used to create the trajectory. Accordingly, VMD and NAMD yield the same energies for any given structure. The VMD plugin SASA with a 1.4 Å solvent probe was used to calculate solventaccessible surface areas (SASAs). The extent of water exchange between the RMs in each system was calculated for each RM as a fractional approach to complete mixing, fcm(t), using eq 1

Instead, multiple fusion/fission events were observed, and the encapsulated peptide was consistently involved in terminating fusion and/or promoting fission.

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METHODS

Software, Hardware, and Parameters. Minimizations and preliminary equilibrations were performed with NAMD 2.917 and the CHARMM27 all-atom force field for proteins and lipids18 on a 16node Linux cluster. Secondary 30 ns equilibrations were performed with NAMD 2.9 on the Bridges system provided by the Extreme Science and Engineering Discovery Environment (XSEDE) as described previously.9,16 Production simulations were performed at 293 K using the Nosé−Hoover thermostat and the MTK barostat on an Anton 2 supercomputer19 (also on the Bridges system). The cutoff for van der Waals (vdW) and short-range electrostatic interactions was 9.79 Å. Long-range electrostatic interactions were computed using the Gaussian split Ewald method.20 Coordinates were saved every 0.24 ps. System Design, Equilibration, and Simulation. RMs were constructed with W0 = 11.4, the same ratio used in earlier experimental studies.21 Equation 7e in an earlier theoretical study9 indicates that the number of AOT molecules per RM (nAOT) should be 127. The number of water molecules (nwater) is therefore given by W0 × nAOT = 1448. This RM was designated type “N”. A smaller RM with nAOT = 63 and nwater = 724 was designated type “S”, and a larger RM with nAOT = 190 and nwater = 2166 was designated type “L”. To construct each RM, a spherical cluster of nwater + nAOT water molecules was created with the visual molecular dynamics (VMD) SOLVATE plugin.22 AOT molecules were added by replacing nAOT randomly selected water molecules with sodium cations and distributing the anionic portions randomly on the surface of the cluster with SO3 headgroups oriented inward. To construct an RM of type N with an Aβ40 peptide (designated type “Np”), the peptide was created as an extended linear chain with Pymol 1.8,23 energy minimized in vacuo with nanoscale molecular dynamics (NAMD) and solvated in a spherical cluster of 1578 water molecules. AOT molecules were added by replacing 127 randomly selected water molecules with sodium cations and distributing the anionic portions randomly on the surface of the cluster with SO3 groups oriented inward. Three randomly selected water molecules were replaced with sodium cations to neutralize the −3 charge of the peptides. Therefore, nwater = 1448 in this system.

fcm (t ) = 1 −

nout(t ) n water − ncm

(1)

where nout(t) is the number of water molecules originally in the RM that had left at time t and ncm is the number of waters originally in an RM that are expected to be in that RM after complete mixing has 2523


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Langmuir occurred. The value of ncm is 241, 965, and 1330 for S, N, and L systems, respectively. The mixing rate, (k), is the negative slope of ln|fcm(t)| versus t. To represent the sequence of events during RM fusion quantitatively, portions of the NN and NNp trajectories were analyzed at 4.8 ps intervals. The extent of mixing was quantified by considering each molecule in four component groups (water, sodium ion, AOT headgroup, and AOT hydrocarbon chains) of each RM and counting the number of molecules from the same component group within 5 Å that originated in the other RM. Thus, these counts are zero before contact, and they reach a maximum upon thorough random mixing. Results for each component group were summed and then normalized by their maximum values. To represent the events during RM fission after fusion, the same counts were made except that the number of molecules from the same component group that ended up in the other RM were counted.

between RMs without contact between the surfactant layers, that is, noncontact water exchange. To characterize the rate of noncontact water exchange, the fractional approach to complete mixing (eq 1) was plotted over time for each RM (Figure 3) and fitted to an exponential to

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RESULTS Conditioning. The total energies and volumes of each simulation system reached plateau values early in the 30 ns conditioning periods. Simulations on Anton 2 are susceptible to “overflow errors” if not suitably conditioned, however, and extending the conditioning periods to 30 ns eliminated such errors. Therefore, each system was well-conditioned with respect to total energy and volume when the Anton 2 simulations began. There was no water exchange between RMs during the conditioning period, although a few water molecules from each system had diffused out of the RM and into the isoO phase. Noncontact Water Exchange. As the simulations progressed, each RM deviated markedly from its original spherical shape, which increased its surface-area-to-volume ratio. As a consequence, gaps large enough to pass a water molecule were frequently observed between surfactant molecules, enabling direct contact between isoO molecules and components of the RM core. The surface area of water and sodium ions accessible to a 1.4 Å probe (i.e., the area of gaps in the surfactant layer) as a percentage of total RM surface area is shown in Figure 2. The gap area percentage for the type L RM is significantly larger than that for other types, most likely because it tended to deviate from a spherical shape to a greater extent. Water molecules periodically entered and exited through these gaps, facilitating the exchange of water molecules

Figure 3. −ln(fcm) for the four RM systems (see eq 1). The slopes of each graph are approximately equal, and there was no significant difference between the two slopes in the N2/N3 systems. The dramatic increase observed in the NN and NNP systems is because of contents mixing.

obtain a mixing rate, k. The mixing rates for all eight RM types in all four systems were indistinguishable, ∼9 × 104 s−1 (Table 2). This rate suggests that 7700 ns would elapse before mixing was half-way complete. Contact-Mediated Exchange. “Contact” between RMs is defined as a repulsive vdW interaction between any two AOT atoms from different RMs. By this definition, contact between RMs was observed frequently in all four simulation systems (Figure 4). Most instances of contact did not result in disruption of the RM surface or in the exchange of surfactant molecules or RM contents. However, one contact event in the NN system after 2800 ns did result in RM fusion and extensive mixing of RM contents. This event began with AOT “chain mixing”, defined as occurring when the distance between AOT headgroups in two different RMs is less than twice the average thickness of the AOT hydrocarbon chains (Figure 5a). Chain mixing was followed almost immediately by “water bridge formation”, defined as a continuous single-file line of water molecules extending between the two RM cores (Figure 5b).

Figure 2. SASAs of gaps in the surfactant layer as a percentage of total RM SASA. Error bars represent standard deviations for the distribution of each results. The asterisk indicates that the result for the RM of type L was significantly different from each of the other results with P < 0.05 by T-test. 2524


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Langmuir Table 2. Intermicellar Water Exchange Rates (k)a system NS NN NL NNp

RM

k (×10−5 ns−1)

fraction of leaving water per gap area (×10−5 Å2)

S N1 N2 N3 N4 L Np N5

9 9 9 9 9 9 9 9

11 3 9 5 5 1 3 3

following each fusion event was 1.0. The termination of fusion was characterized similarly, except that time = 0 (when counts were set to zero) was defined as the end of chain mixing and only simple contact was occurring. The results for the seven fusion events were averaged and plotted in Figure 6. For each fusion event, the intervals between contact, chain mixing, and water bridge formation were negligible (Figure 6a,c). AOT reorientation occurred 7−8 ns after contact (Figure 6b). The water molecules that exchanged in each of these events tended to exchange within another 2−3 ns (Figure 6d). Sodium-ion exchange lagged well-behind water exchange and was not complete until 25 ns after contact (Figure 6c). The AOT molecules that exchanged lagged even further, requiring ∼50 ns after the contact completed (Figure 6a,b). The sequence of events that terminated fusion (i.e., fission) did not correspond to the reverse of events that started fusion. The exchange of AOT headgroups and chains did slow as a constriction developed around the aqueous pore (Figure 6e,f). However, water exchange declined well before sodium ion exchange (Figure 6g,h). The late decline of sodium ion mixing appears due to the association of sodium ions with the negatively charged AOT headgroups along the water bridge. Termination of the water bridge occurred well before AOT reorientation (Figure 6f−h). Although each instance of fission proceeded through AOT reorientation (Figure 5g) to a point where the two RMs were merely in contact, the AOT chains from each RM remained in contact with a small amount of chain mixing (Figure 6e) until the next contents-mixing event started. As indicated in Figure 4, there were many instances of contact without contents mixing. Two factors were investigated to identify the conditions that caused RM contact to advance to contents mixing. One factor was the number of AOT molecules involved in the contact interface, that is, the size of the contacting surface. However, the number of AOT involved in any given contact event did not correlate with contents mixing (Figure 7). A second factor was the amount of water present among the AOT molecules making contact. As shown in Figure 8, the number of water molecules within 5 Å of an AOT molecule involved in the contact interface was consistently greater (>10) when contact was followed by contents mixing. These results are consistent with the aforementioned observation that hydration of the surfactant layer in the vicinity of contact appears to determine whether the contact led to contents mixing. Contents-mixing events in the NNp system resulted in the formation of two RMs with significantly different sizes (Figure 9). The nAOT and W0 of the peptide-containing RM increased with the first contents-mixing event, although the W0 trended lower with subsequent contents-mixing events. The two RMs in this system exhibited transient electrostatic imbalances, but no distinct trend.

a

Values of k in the NN and NNp systems pertain to contactindependent water exchange before contents mixing.

After water bridge formation, “AOT reorientation” occurred, in which some of the AOT molecules in each RM rotated so that their headgroups were oriented toward waters in the bridge (i.e., Figure 5c). Additional AOT molecules were recruited and reoriented as the water bridge expanded into an open pore (Figure 5d). A noteworthy feature of contact-mediated exchange was that the first waters to exchange, and the waters comprising the water bridge, were waters that had been situated in the surfactant layer at the point and time of contact, that is, these waters were adjacent to hydrophobic AOT chains rather than in the RM core. This observation suggests that the extent of surfactant layer hydration may determine whether RM contact leads to contents mixing. In the NNp system, there were seven distinct fusion and fission events, enabling an analysis of the mechanisms that were common to all seven events (Figure 4). Each fusion event was only “partial” in the sense that it did not involve a complete loss of distinction between the original RMs. Accordingly, one may view “fission” as the premature termination of fusion. Each fusion event followed the stereotypical sequence described for the NN system: contact, chain mixing, water bridge formation, and AOT reorientation (Figure 5a−d). As noted in the NN system, fusion events tended to follow contact when the surfactant chains at the point of contact were hydrated. Consequently, the intervals between contact, chain mixing, and water bridge formation were negligible. To quantify the extent of contents mixing over time, a counting algorithm was applied. Waters, for example, were designated either red or blue prior to each mixing event (as in Figure 5). The number of red waters within 5 Å of each blue water and the number of blue waters within 5 Å of each red water were counted at each time point. These counts were zero at time = 0, which is defined as the end of simple contact and the beginning of chain mixing. Analogous counts were made for AOT headgroups, AOT chains, and sodium cations. The counts for each event were normalized so that the maximum count

Figure 4. Collisions and contents-mixing events in the four RM systems. Collisions (black circles) and contents-mixing events (red circles) indicate when there is nonzero vdW interaction energy between surfactants of two RMs in the system. 2525


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Figure 5. Stages of RM fusion and fission. Red/blue-filled circleswater. Red/blue “+” symbolssodium ions. Red/blue squares with two chains AOT headgroups and chains. (a) Chain mixing is defined as occurring when the distance between the inner cores of two RMs is less than the length of two AOT molecules such that the chains of two AOT molecules overlap. Note that some waters are among the AOT chains and not in the RM core. (b) Water molecules in the surfactant layer organize to form a water bridge between the two RM cores. (c) AOT molecules rotate so that their headgroups are oriented toward waters in the bridge. (d) The water bridge expands into a pore allowing free mixing of RM contents. Stages (a−d) were observed in both NN and NNp simulations. (e) In the NNp simulation, the Aβ40 peptide (not shown) diffuses into the water pore and it constricts. (f) Water bridge termination occurs before rotation of AOT headgroups toward one or the other RM core. (g) AOT rotation follows water bridge termination. (h) In the NNp simulation, the RMs separate to the point where chain mixing no longer occurs, but contact between the AOT chains in two different RMs persists.

Figure 6. Time course of fusion and fission events in the NNp system. The components of each RM (water, AOT headgroup, AOT chain, and sodium ions) were designated either red or blue prior to each mixing event. The number of red components within 5 Å of each blue component and the number of blue components within 5 Å of each red component were counted for each component, at each time point. Time = 0 is defined as the end of simple contact and the beginning of chain mixing. The counts for each fusion event were normalized to a maximum of 1.0 and averaged over the seven fusion events. In (a−d), time = 0 is defined as the time when simple contact ended and chain mixing began. In (e−h), time = 0 is defined as the time when chain mixing ended and only simple contact occurred. Solid lines indicate results for the empty RM (type N), and dotted lines indicate results for the peptide-containing RM (type Np).

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Figure 7. The number of contacting AOT in each contact incidence in the four RM systems (i.e., the total number of AOTs having nonzero vdW interaction energy with AOT molecules of the other RM). The number of AOT molecules is represented with black circles, and contents-mixing events were represented with red circles.

Figure 8. The average number of water in the immediate vicinity of contacting AOT molecules (i.e., the total number of water within 5 Å of contacting AOTs divided by the number of contacting AOTs).

α-helix at 2.1 μs. By 3.4 μs, this loop had extended to residues 21−31 and three loops of α-helix, which persisted throughout the remainder of the simulation. Second, neither the helix nor any other portion of the Aβ40 peptide was directly involved in any of the seven fusion events. However, each fusion event was terminated by movement of the α-helix into the fusion pore. Indeed, diffusion of the entire C-terminal portion of Aβ40 appeared to be the trigger for pore constriction in each of the seven observed instances (Figure 5e). As previously reported,16 the side chains of residues Phe19 and Phe20 were anchored into the surfactant layer and formed a β turn, whereas those of

Polypeptide Effects and Behavior. In the NNp system, the peptide-containing RM was initialized by simply adding the peptide to the core; there were no waters deleted or AOT molecules added. The peptide-containing RM responded initially by recruiting both water and AOT from the other RM during the first fusion event. However, it subsequently lost water to restore its original W0 value (Figure 9). The behavior of the Aβ40 peptide in the first 2.3 μs of this 5.1 μs simulation was similar in most respects to its behavior in the 3.0 μs simulation previously described.16 However, two additional and remarkable behaviors were noted after 2.3 μs in the current simulation. First, residues 21−24 formed a loop of 2527


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pore. In each case, the large hydrophobic side chains of Aβ40 were oriented away from the aqueous core and embedded among the AOT chains. This behavior is significant because it highlights the potential for interactions between Aβ40 and lipid membranes that mediate its transport, folding, or toxicity. All but one of the observed fusion events in these simulations occurred in the peptide-containing system, which may have had more fusion events merely because the simulation was longer. The results appear to disprove hypotheses that RMs of different sizes (NS and NL systems) are more likely to undergo fusion, but this hypothesis may have been best addressed in an “SL” system, had resources been available to create one. The Aβ40 peptide appeared to have no direct involvement in initiating any of the RM fusion events, although indirect effects mediated through the water or surfactant cannot be ruled out. A stereotypical series of steps at the initiation of RM fusion was briefly described for a series of self-assembling W0 = 5 systems.25 One of these steps involved a sodium ion interacting simultaneously with the water of two different RMs before water bridge formation. In contrast, sodium ions lagged considerably behind water bridge formation in the current simulations. Because the previously reported simulations were of similar overall sizes, 0.9−1.0 μs in duration, and they used the same AOT and isoO parameters as the current simulations, it is possible that the difference was due to the use of an SPC/E water model or the different computational platform used for the earlier simulations. However, it seems most likely that relatively little water in the W0 = 5 systems led to an earlier participation of components other than water in fusion events. As outlined by Luisi and Magid,26 three distinct schemes for accommodating proteins into RMs have been considered: (a) displacement of water in the RM core, resulting in a decrease in W0 but no change in RM dimensions; (b) addition of peptide volume to the RM core volume, with the recruitment of AOT from other RMs, a decrease in W0, and an increase in RM dimensions, and (c) recruitment of both water and AOT from other RMs, resulting in an increase in RM dimensions but no change in W0. Experimental evidence for scheme (a) has been provided by Levashov et al.27 and Zampieri et al.,28 who found that RMs containing α-chymotrypsin did not change in size or nAOT, but exhibited lower W0 values. If protein encapsulation leads to a lower W0, however, it raises questions about whether sufficient water remains in the RM to solubilize both the polypeptide and the sodium ions that are required for electrostatic balance of the AOT anions. Prior simulation studies have shown that the shielding of charges within an RM by water is one of the largest energetic considerations in the thermodynamics of RM formation.9 Therefore, the need for hydration water and its dielectric effects may be an important thermodynamic driving force opposing the reduction of W0 in both a protein-containing RM and an empty RM. One may also expect that the encapsulated protein has its own requirements for hydration water, which would increase both W0 and RM size. Secondary structure formation by a polypeptide chain is an efficient means to eliminate unmatched hydrogen bond donor/acceptor pairs, and the formation of α-helical structure in the NNp system may reflect the need to eliminate such unmatched pairs when hydration water is severely limited. Alternatively, excluded volume effects may be particularly effective at inducing secondary structure formation within the confines of an RM or the various side chain and surfactant interactions described above may contribute. The relative contributions of such factors cannot

Figure 9. Changes in the number of AOT molecules, W0 values, and net charge of RM complexes after seven contents-mixing events in the NNp system (the protein-containing RM is represented with a dashed line, and the other RM is represented with a solid line).

Phe4, Leu17, Ile31, Ile32, and Leu34 anchored into the surfactant individually (Figure 10).

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DISCUSSION These studies reveal a remarkable and unexpected involvement of the Aβ40 peptide in the termination of RM fusion events. All seven instances of RM fusion were terminated by diffusion of the C-terminal 20 residues of Aβ40 into the fusion pore, which then sterically prevented the diffusion of water through the

Figure 10. The onset of fission in a fused pair of RMs. This configuration is representative of the relationship between the Aβ40 peptide shortly after it enters and blocks the water bridge between the type N (right half of image) and type Np (left half of image) RMs in the NNp system. Pinkthe surface of AOT molecules, with molecules in the foreground deleted. Bluethe surface of water and sodium ions. Yellowthe Aβ40 peptide. Note that residues 21−31 of the peptide have formed a helix, and the water bridge adjacent to the rightmost portion of the peptide is tightly constricted. The labeled residue side chains are clearly visible, implying that they are oriented away from the core and embedded in an AOT layer that is not shown. 2528


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Insight into the microsecond time scale events comprising these processes was made possible by access to an Anton 2 machine which, compared to a first-generation Anton machine, was able to accommodate the larger systems involved, for meaningful lengths of time. Nevertheless, still longer simulations will be required to reach equilibrium conditions and clarify the relationship between RM size and W0.

be distinguished in simulations such as these, which were not designed for this type of analysis. It is clear that the net transfer of components between RMs has not reached an equilibrium condition by the end of the 5.1 μs NNp simulation, but trends suggest that the peptidecontaining RM will have a significantly larger nAOT than the empty RM and that W0 will remain unchanged. These observations support scheme (c) of Luisi and Magid and are consistent with an experimental study of myoglobin by Murakami et al.29 Differences among the various published experimental results may be due to the differences in the size and other physicochemical properties of the proteins being encapsulated. Differences between experimental results and these simulation results may arise because there was only one empty RM with which the peptide-containing RM may equilibrate in these simulations, rather than the semi-infinite ensemble available in an experimental system. Another unexpected finding in these simulations was that no net water exchange occurred between RMs of different sizes. It was hypothesized that the net transfer of water between RMs would occur via noncontact exchange, such that RMs that were too large or small for the W0 of the system would compensate with a net loss or gain of water. This hypothesis was disproved by finding that mixing rates were identical for all RM sizes. Identical mixing rates, despite marked differences in size, also suggest that the larger gap percentage for the RM of type L (Figure 2) did not lead to faster losses than the RM of type N, with which it was paired. Experimentally determined exchange rates have been reported from several labs, but comparisons to the simulation-derived mixing rate in this work are tenuous because of differences in the nature of the experimental data, the choice of mathematical model employed, and the system composition. In addition, rates of this nature are sensitive to experimental conditions such as solvent, temperature, and W0.30 For example, Johannsson et al. determined an exchange rate of 3 × 106 s−1 from phosphorescence decay curves in RM suspensions with and without quencher.31 However, experimentally determined exchange rates must necessarily reflect all exchange mechanisms, not merely the noncontact diffusive mechanism, so it is not surprising that this experimental measurement is ∼30-fold larger than the simulation result. It should be noted that the rate of noncontact exchange suggested by the simulations is not negligible, as commonly assumed when interpreting the data from some experimental studies.10

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 215-898-9238. ORCID

Paul H. Axelsen: 0000-0002-7118-1641 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by grants from the NIH (GM76201) and the Alzheimer’s Association (to P.H.A.). It made use of the Extreme Science and Engineering Discovery Environment (XSEDE), supported by the National Science Foundation grant number OCI-1053575 and the Bridges system at the Pittsburgh Supercomputing Center (PSC) supported by NSF award number ACI-1445606. Access to the Anton machine was made possible by the National Center for Multiscale Modeling of Biological Systems through grant number MCB150023P from the Pittsburgh Supercomputing Center.

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REFERENCES

(1) Ric̆ka, J.; Borkovec, M.; Hofmeier, U. Coated Droplet Model of Microemulsions: Optical Matching and Polydispersity. J. Chem. Phys. 1991, 94, 8503−8509. (2) Amararene, A.; Gindre, M.; Le Huérou, J.-Y.; Urbach, W.; Valdez, D.; Waks, M. Adiabatic compressibility of AOT [sodium bis(2ethylhexyl)sulfosuccinate] reverse micelles: Analysis of a simple model based an micellar size and volumetric measurements. Phys. Rev. E 2000, 61, 682−689. (3) Kotlarchyk, M.; Chen, S. H.; Huang, J. S. TemperatureDependence of Size and Polydispersity in A three-Component Micro-Emulsion by Small-Angle Neutron-Scattering. J. Phys. Chem. 1982, 86, 3273−3276. (4) Kotlarchyk, M.; Chen, S.-H.; Huang, J. S.; Kim, M. W. Structure of three-Component Microemulsions in the Critical Region Determined by Small-Angle Neutron-Scattering. Phys. Rev. A: At., Mol., Opt. Phys. 1984, 29, 2054−2069. (5) Robertus, C.; Philipse, W. H.; Joosten, J. G. H.; Levine, Y. K. Solution of the Percus-Yevick Approximation of the Multicomponent Adhesive Spheres System Applied to the Small-Angle X-Ray-Scattering from Microemulsions. J. Chem. Phys. 1989, 90, 4482−4490. (6) Farago, B.; Richter, D.; Huang, J. S.; Safran, S. A.; Milner, S. T. Shape and Size Fluctuations of Microemulsion Droplets: the Role of Cosurfactant. Phys. Rev. Lett. 1990, 65, 3348−3351. (7) Robinson, B. H.; Toprakcioglu, C.; Dore, J. C.; Chieux, P. SmallAngle Neutron-Scattering Study of Microemulsions Stabilized by Aerosol-Ot. Part 1. Solvent and Concentration Variation. J. Chem. Soc., Faraday Trans. 1 1984, 80, 13−27. (8) Yan, Y. D.; Clarke, J. H. R. Dynamic Light-Scattering from Concentrated Water-In-Oil Microemulsions the Coupling of Optical and Size Polydispersity. J. Chem. Phys. 1990, 93, 4501−4509. (9) Eskici, G.; Axelsen, P. H. The Size of AOT Reverse Micelles. J. Phys. Chem. B 2016, 120, 11337−11347. (10) Fletcher, P. D. I.; Howe, A. M.; Robinson, B. H. The Kinetics of Solubilisate Exchange between Water Droplets of a Water-In-Oil Microemulsion. J. Chem. Soc., Faraday Trans. 1 1987, 83, 985−1006.

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CONCLUSIONS Mass exchange and equilibration processes in RMs proceeded more efficiently via transient fusion/fission events than via diffusion through the organic phase, which is consistent with early inferences from experimental studies.10 The factor that appears to determine whether RM−RM contact evolves into fusion with mixing of contents is the degree to which water molecules are present in the surfactant layer at the point of contact. Contrary to expectation, net mass exchange via diffusion could not be demonstrated between RMs of different size in these systems. Peptide encapsulation caused RM size to increase, without a change in W0. At least seven large hydrophobic side chains of encapsulated Aβ40 were persistently embedded in the surfactant, attesting to the affinity of this peptide for membranes. Aβ40 had no apparent role in initiating RM fusion, but it efficiently terminated fusion events soon after they began by diffusing into the fusion pore. 2529


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Langmuir (11) Jada, A.; Lang, J.; Zana, R. Relation between Electrical Percolation and Rate-Constant for Exchange of Material between Droplets in Water in Oil Microemulsions. J. Phys. Chem. 1989, 93, 10− 12. (12) Howe, A. M.; Mcdonald, J. A.; Robinson, B. H. Fluorescence Quenching As A Probe of Size Domains and Critical Fluctuations in Water-In-Oil Microemulsions. J. Chem. Soc., Faraday Trans. 1 1987, 83, 1007−1027. (13) Walde, P.; Giuliani, A. M.; Boicelli, C. A.; Luisi, P. L. Phospholipid-Based Reverse Micelles. Chem. Phys. Lipids 1990, 53, 265−288. (14) Zhou, H.-X. Protein folding in confined and crowded environments. Arch. Biochem. Biophys. 2008, 469, 76−82. (15) Yeung, P. S.-W.; Eskici, G.; Axelsen, P. H. Infrared spectroscopy of proteins in reverse micelles. Biochim. Biophys. Acta, Biomembr. 2013, 1828, 2314−2318. (16) Eskici, G.; Axelsen, P. H. Amyloid Beta Peptide Folding in Reverse Micelles. J. Am. Chem. Soc. 2017, 139, 9566−9575. (17) Phillips, J. C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kalé, L.; Schulten, K. Scalable molecular dynamics with NAMD. J. Comput. Chem. 2005, 26, 1781− 1802. (18) Foloppe, N.; MacKerell, A. D., Jr. All-atom empirical force field for nucleic acids: I. Parameter optimization based on small molecule and condensed phase macromolecular target data. J. Comput. Chem. 2000, 21, 86−104. (19) Shaw, D. E.; Grossman, J. P.; Bank, J. A.; Batson, B.; Butts, J. A.; Chao, J. C.; Deneroff, M. M.; Dror, R. O.; Even, A.; Fenton, C. H. Anton 2: raising the bar for performance and programmability in a special-purpose molecular dynamics supercomputer. International Conference for High Performance Computing, Networking, Storage and Analysis; IEEE, 2014; pp 41−53. (20) Shan, Y.; Klepeis, J. L.; Eastwood, M. P.; Dror, R. O.; Shaw, D. E. Gaussian split Ewald: A fast Ewald mesh method for molecular simulation. J. Chem. Phys. 2005, 122, 054101. (21) Yeung, P. S.-W.; Axelsen, P. H. The Crowded Environment of a Reverse Micelle Induces the Formation of beta-Strand Seed Structures for Nucleating Amyloid Fibril Formation. J. Am. Chem. Soc. 2012, 134, 6061−6063. (22) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual molecular dynamics. J. Mol. Graphics 1996, 14, 33−38. (23) The PyMOL Molecular Graphics System, version 1.8; Schrödinger, LLC, 2016. (24) Abel, S.; Waks, M.; Marchi, M. Molecular dynamics simulations of cytochrome c unfolding in AOT reverse micelles: The first steps. Eur. Phys. J. E 2010, 32, 399−409. (25) Marchi, M.; Abel, S. Modeling the Self-Aggregation of Small AOT Reverse Micelles from First-Principles. J. Phys. Chem. Lett. 2015, 6, 170−174. (26) Luisi, P. L.; Magid, L. J. Solubilization of Enzymes and NucleicAcids in Hydrocarbon Micellar Solutions. Crit. Rev. Biochem. 1986, 20, 409−474. (27) Levashov, A. V.; Khmelnitsky, Y. L.; Klyachko, N. L.; Chernyak, V. Y.; Martinek, K. Enzymes Entrapped Into Reversed Micelles in Organic-SolventsSedimentation Analysis of the Protein-Aerosol OtH2O-Octane System. J. Colloid Interface Sci. 1982, 88, 444−457. (28) Zampieri, G. G.; Jaeckle, H.; Luisi, P. L. Determination of the Structural Parameters of Reverse Micelles After Uptake of Proteins. J. Phys. Chem. 1986, 90, 1849−1853. (29) Murakami, H.; Nishi, T.; Toyota, Y. Determination of Structural Parameters of Protein-Containing Reverse Micellar Solution by NearInfrared Absorption Spectroscopy. J. Phys. Chem. B 2011, 115, 5877− 5885. (30) Kitchens, C. L.; Bossev, D. P.; Roberts, C. B. Solvent effects on AOT reverse micelles in liquid and compressed alkanes investigated by Neutron Spin−Echo spectroscopy. J. Phys. Chem. B 2006, 110, 20392−20400.

(31) Johannsson, R.; Almgren, M.; Alsins, J. Fluorescence and Phosphorescence Study of AOT/Water/Alkane Systems in the L2 Reversed Micellar Phase. J. Phys. Chem. 1991, 95, 3819−3823.

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Mass Exchange and Equilibration Processes in AOT Reverse Micelles

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