Sodium-salt adduct fullerenes prevent self-association and amyloid β fibril formation: molecular dynamics approach

ABSTRACT Aggregation of amyloid β peptides (AβP) forming fibrils and senile plaques is associated with numerous neurodegenerative disorders such as Alzheimer’s disease (AD). While there is no cure for AD, there is a possibility to retard and prevent the impairment. Inhibiting or interfering the aggregation of Aβ using fullerenes has shown to be a promising strategy to treat AD. The hydrophobic nature of fullerenes compromises its interaction with living cells inducing toxicity; thus, it is necessary to functionalize the molecule promoting its water solubility. In this study, we evaluate the structural and dynamical properties of six diethyl malonate C60 fullerene adducts and its corresponding sodium salts in aqueous solution by molecular dynamics simulations. By means of radial distribution functions, hydrogen bond counting, density profiles, and solvent-accessible surface area, we demonstrate that the sodium malonate fullerene adducts have higher hydration ability while the corresponding diethyl malonate adducts show a hydrophobic tendency, forming self-aggregates. Additionally, we calculate the density profiles of ternary systems including amyloid β peptide 1–42 (AβP42) monomers and found that bis-, tris-, tetra-, and pentaadducts of C60 with disodium malonate addends interact with amyloid molecules, blocking partially their self-aggregation. These data support the understanding of previous reports that indicated the efficiency of sodium malonate fullerene as inhibitors of AβP aggregation. Additionally, we performe measurements in vitro by dynamic light scattering and found that fullerene aggregation is independent of incubation time.


Introduction
Accumulation of amyloid β peptide (AβP) forming fibrils and plaques in the brain leads to the onset of Alzheimer's disease (AD).The peptide, a product of the enzymatic cleavage by βand γ-secretase of amyloid precursor protein, a neuronal transmembrane protein, releases two species AβP 40 and AβP 42 (peptide isoforms truncated in the amino acid number 40 or in the 42), the last one being the more hydrophobic and amyloidogenic. [1]AβP aggregation results in several neuronal damages; different reports indicate membrane disruption, [2,3] the influence of signal pathways by aberrant binding receptors, [4] membrane fragmentation, and pore formation. [3]] Different strategies for effective inhibitors of AβP aggregation in AD brains have been developed, either by blocking the fibril formation or decreasing the load.[12] Fullerene C 60 , a molecular allotrope of carbon, is a promising therapeutic molecule in AD.Different studies have demonstrated its capacity to interfere in AβP fibril formation [13][14][15] and to permeate the blood-brain barrier. [16]Nevertheless, fullerene toxicity remains unclear, [17,18] but molecular design leads to the synthetization of more biocompatible molecules.The low hydration of fullerenes and self-aggregation preclude their use in most biological systems, thus constituting important obstacles to biomedical applications.Fullerene toxicity has also been related to the use of organic solvents that are necessary to dissolve them. [19,20]23] Experimental studies have demonstrated that fullerene carboxylic acids and their sodium salts in aqueous solution self-assemble and aggregate producing solid particles. [24]Nevertheless, other reports indicate that C 60 hydrates in the presence of AβP peptide block the fibril formation. [25]Different research groups have functionalized the molecule for biological applications.Both hydroxylated fullerenes synthesized by the addition of hydroxyl groups and the addition of phenyl butyric acid residues to C 60 carbon cage highly increase its mixing ability and reduce the formation of AβP aggregates. [26,27]Previous reports have demonstrated that the surface area and volume of C 60 regulate its binding activity to the target molecules. [28]In this work, we hypothesize that the high hydration ability of C 60 adducts under study leads to a decrease in the aggregate size.Decreasing the size of the nanoaggregates, in turn, causes an increase of the surface area per monomer and leads to an increase in the surface area relative to volume, thereby making the nanomaterial more reactive to its contiguous milieu for efficient fullerene-protein interaction (high-charge density and hydrophobic groups that are necessary to stabilize the α-helix structure of the AβP monomeric stage).
The Bingel-Hirsch reaction [29,30] is the most versatile, efficient, and widely used way to functionalize the surface of C 60 .This reaction is not restricted to C-H acidic carbonyl compound (reactive methylene functions) such as malonates, and various other groups with C-H acidic have been successfully obtained. [31]ith a variety of addition reaction base on the addition-elimination mechanism, almost any functional group or molecule can be attached to C 60 .Our research group has previously synthesized fullerenmalonates (adducts of C 60 ) and the corresponding sodium salts by Bingel-Hirsch reaction.The adducts have shown both inhibitory effect on Aβ fibril formation and low toxicity in neuroblastoma cells; variations in the activity were found according to fullerene functionalization. [32]hus, it is important to study particle size, surface area, and hydration ability of these compounds to understand their behavior during the inhibition of AβP aggregation.
35] Different atomistic MD studies in water employed few C 60 molecules in the simulation box; this is the appropriate strategy due to their low dispersity in water. [35]omistic studies using several C 60 molecules are computationally expensive when compared with a coarsegrained (CG) approach, which works properly only if the CG model contains the essential features of fullerene-water interactions.Choudhury has analyzed and compared simulations using atomistic and CG models; in both cases, he has demonstrated that solvent mobility (translational and rotational) is obstructed in the solute vicinity and has shown that pristine fullerene cannot form hydrogen bonds with water. [35]][40] The role of C 60 substituents to increase their hydration and capacity to inhibit AβP aggregates remains unclear.Bednarikova et al. reported that fullerenol (C 60 (OH) 16 ) tightly binds to AβP, thus reducing the formation of aggregates. [41]However, a recent study demonstrated that increasing the number of hydroxyl groups in C 60 (C 60 , C 60 (OH) 6 , C 60 (OH) 12 ) promotes slower binding dynamics and weaker binding strength to AβP. [38] The fullerene capacity to inhibit AβP fibrils depends on its hydrophobicity also, which is related to the number of polar substituents on the C 60 surface.In this research work, we have studied the hydrophobic/hydrophilic nature of fullerenemalonates and their corresponding sodium salts, related to their capacity to inhibit the AβP aggregation in water.These adducts are studied for the first time by MD, with the aim to understand the interactions of these compounds with the surrounding water molecules using several analysis tools: density profiles, hydrogen bond counting, solvent available surface area, and radial distribution functions.Additionally, we have performed dynamic light scattering (DLS) measurements to investigate the size and nature of the fullerene-adduct aggregates.This article is organized as follows.Section 2 describes the methodology employed for both calculations and experiments.In Section 3, we present the results and their discussion, and finally, conclusions are listed in Section 4.

Simulation Details
In this work, we investigate the hydration behavior of 12 fullerene derivatives; six adducts of C 60 bearing one to six diethyl malonate substituents and their corresponding sodium salts [C 60+n (COOR) 2n ] with n = 1-6 and R = -Et, -Na (see Table 1) by means of MD simulations using the GROMACS 2018.2 software package. [42]The molecular structures of the specific diethyl malonate fullerene and sodium malonate fullerene isomers are shown in Table 1.The coordinates of these molecules were obtained by means of Avogadro package, [43] and the topology files were constructed using automated topology builder (ATB), Repository Version 3.0. [44]The 54A7 all-atom GROMOS force field [45] together with the simple point charge (SPC) water model [46] was employed.Twelve fullerene systems were prepared introducing 10 molecules of each fullerene derivative and 12,000 water molecules in a box of 6.0 nm × 6.0 nm × 18.0 nm.We equilibrate the simulation systems by means of a standard procedure, using the steepest descendant minimization method first, followed by 5.0 ns of equilibration to constant density-isothermal (NVT) ensemble.The v-rescale thermostat [47] was used keeping the temperature constant at 310.0 K, using a temperature-coupling time constant of 1.0 ps.Next, the simulations were run during 25.0 ns in an isothermal-isobaric (NPT) ensemble (1.0 ns at 100.0 bars plus 24.0 ns at 1.0 bar).We use the Parrinello-Rahman pressure coupling algorithm [48,49] ; this is done by means of a time constant for pressure coupling of 1 ps and a compressibility factor of 4.5 Â 10 −5 bar −1 .All the simulations were run using a time step of 0.002 ps.
Simulation boxes of systems including AβP 42 were of the same size and features.We use the pdb file 1IYT AβP 42 monomer downloaded from Protein Data Bank [50] to obtain the topology and the coordinate files.To prepare these simulation boxes, four AβP 42 molecules are introduced, plus 20 fullerene derivative molecules, and 12,000 waters.To mimic the experimental conditions, [51] 29 molecules of dimethyl sulfoxide were also included (giving 0.15 M concentration).Dimethyl sulfoxide promotes AβP self-aggregation, and for this reason, it is employed in the experimental protocol.29 Na + ions and 29 Cl − ions were also included to reproduce the experimental conditions, keeping an isotonic solution.After thermalization, we perform the formal runs during 30 ns in the NVT to sample.We use the last configuration from the previous NPT simulation as the initial configuration and volume value to start this sampling.From the trajectories obtained, we calculate several averages such as radial distribution function.Sampling in the simulations including AβP is of only 10 ns of trajectory NVT.
Independent simulations of systems using only one molecule of solute were also investigated to calculate hydration shells at 298 K.This temperature was chosen in these simulations to compare with the results by Keshri and Tembe. [34]These authors investigated the thermodynamic properties of hydration of fullerols.All other properties presented in this article were calculated at 310 K because this is the temperature of the human body, and our final goal is the use of fullerene adducts to treat AD.
We find it difficult to obtain very low concentrations of AβP and fullerenes in water, to mimic the conditions of in vitro experiments. [32]To simulate these conditions, we would require a massive amount of water molecules, thus making the simulations almost impossible to perform.Due to this reason, we decided to construct our simulation boxes using the number of molecules to have enough particles to make a good statistical analysis and to get wellhydrated systems.The amount of water molecules also is chosen to reproduce the experimental density of water (0.99338 g ml −1 ).Additionally, we set a ratio of 5:1 fullerene to AβP to maximize the interactions.A representation of one of the systems can be seen in the snapshot shown in Figure 1.Verlet list algorithm is performed for neighbor searching, [52] updating the list every 10 steps.Periodic boundary conditions are applied in three directions, and for nonbonded interactions, a cutoff radius of 2.8 nm is employed for both Lennard-Jones and Coulombic potentials.The particle mesh technique is used to correct the long-range potential. [53]To constraint all bonds, a linear constraint solver [54] is employed.In supplementary figure S1, evidence can be found of a proper equilibration on simulation runs; total energy is plotted along time evolution of the 12 fullerene adducts in water during the last 10 ns of NPT runs.Standard GROMACS tools are used to calculate the radial distribution function, the number of hydrogen bonds, density profiles, and solventaccessible surface area (SASA).

GROMACS Analysis Tools
gmx rdf is a GROMACS tool to calculate radial distribution functions from one reference set of coordinates to one or more sets of coordinates.These coordinates can be of atoms, residues, and molecules, using the center of mass or geometrical center as the reference point.Rdf or pair correlation function gives the probability of finding a pair of atoms a distance r apart, relative to the probability for a completely random distribution at the same density. [52]x hbond is a GROMACS subroutine that computes and analyzes hydrogen bonds.The program gmx hbond analyzes the hydrogen bonds between all possible donors D and acceptors A. Hydrogen bonds are determined based on cutoffs for the angle Hydrogen -Donor -Acceptor and the distance Donor -Acceptor.A detailed explanation can be found elsewhere. [55]mx density computes partial densities across the box.A local density profile ρ z ð Þ is defined as the average number of atoms in a slice of width Δz, in this case, along the z-coordinate of the box.
gmx sasa is a GROMACS tool to compute the SASA.The used algorithm is based on the work by Eisenhaber et al. [56] The SASA is defined as the surface area of a solvate molecule which interacts with its solvent molecules; it can be an atom, a residue, or a whole molecule.SASA was first described by Lee & Richards in 1971 and is also called the Lee-Richards molecular surface. [57]namic Light Scattering DLS measurements are performed using a Zetasizer Nano-ZS DLS system (Malvern Instruments Ltd., Malvern, England), equipped with a red (633 nm) laser and an Avalanche photodiode detector (quantum efficiency >50% at 633 nm).
C 60 bisadduct with two addends of diethyl malonate (C 62 (COOEt) 4 ) is synthesized by cyclopropanation of C 60 (1 eq) with different equivalents of diethyl malonate (1.5 eq), CBr 4 (1.5 eq), and 1,8-diazabicyclo- [4,5,0] undec-7-ene (DBU, 3 eq) as auxiliary base, according to the reported procedures. [29,32]A sample of C 60 bisadduct as isomeric mixture is isolated and purified by chromatography column on silica gel with n-hexane/toluene (65:35) and characterized by electrospray ionization time-of-flight mass spectrometry (ESI-TOF-MS), ultraviolet-visible (UV-vis) and infrared (IR) spectroscopies.The sample of C 60 bisadduct shows identical spectroscopic data with those already reported. [29,32]The corresponding sodium salt (C 62 (COONa) 4 ) is synthesized by hydrolysis of the respective diethyl fullerenmalonato (C 62 (COOEt) 4 ), with a 1.5-fold (relative to ester groups) molar amount of NaOH (1 M) in tetrahydrofuran:methanol:water, according to a method described already. [32,58]The sample is purified by washing with methanol and centrifugation and characterized by UV-vis and IR spectroscopies. [32,58]olutions are prepared at three different concentrations, 5, 15, and 30 µM using Milli-Q water.Before the DLS analysis, each sample is dispersed by sonication for 5 min in a glass vial.The DNaMF adduct samples show good dispersity in water; however, the DEMF adduct samples exhibit a very poor dispersity as is expected.The measurements are conducted each minute, and 29 measurements are acquired for each sample.One month later, the experiments are repeated to check the stability of the formed aggregates.

Hydration of Adducts of C 60
To analyze the MD trajectories in heterogeneous systems, we have calculated several structural properties, such as density profiles (histograms of the number of particles calculated along the z-axis simulation box and normalized using the volume, local density is reported on the y-axis).The left side of Figure 2 shows fullerene adduct density profile for the DEMF series, from (a) to (g): pristine fullerene, mono-, bis-, tris-, tetra-, penta-, and hexaadducts.Systems of mono-and bisadducts showed density peaks around 250 kg m −3 , and penta-and hexaadducts around 750 kg m −3 , indicating agglomeration of fullerene derivative molecules.The systems of tri-and tetraadducts do not show locate peaks.For comparison purposes, we plot the density profile of pristine fullerene; as expected, the hydrophobic nature of fullerene induces the clustering of all molecules.Accompanying snapshots showing these situations can be found in the supplementary information in Figure S2.In contrast, the density profiles of the DNaMF series shown on the right side of Figure 2 do not present pronounced peaks, except for monoadduct, with the highest peak around 200 kg m −3 .The dispersed density profiles of bis-, tris-, tetra-, penta-, and hexaadduct indicate that functionalization with disodium malonate addends promote a homogeneous distribution of the fullerene along the whole simulation box.
Attachment of diethyl and disodium malonate substituents to the core of C 60 increases the polarity of both DEMF and DNaMF to n = 3; in consequence, its hydration increases and the aggregation decreases.For adducts with n = 4 to n = 6, the symmetry of the molecule plays a major role.In the case of both tetraadducts, three of four addends are in orthogonal position (equatorial position), which causes the dipole moment of two of them to be canceled (equal magnitude and oriented at 180°to each other).As a consequence, the polarity and the hydrophilic nature decrease, and the aggregation increases with respect to that of trisadducts.In the case of pentaadducts, four of five substituents are oriented at 180º to each other (trans-position to each other), while in the hexaadducts all addends are in trans position to each other.Adducts of C 60 with four to six substituents diethyl or disodium malonates have lower polarity and hydration ability in water owing to higher symmetry, which leads to the formation of larger aggregates in water compared to that of mono-, bis-and trisadducts.
To investigate the molecular mechanism of fullerene aggregation, we calculate the number of hydrogen bonds formed between fullerene adducts and water molecules.
This number per fullerene adduct of DEMF series and of DNaMF series is shown in Figure S3 in the supporting information section, and the average calculated from these plots can be found in Table 2. Figure 3a,b shows the number of hydrogen bonds per oxygen atom, for monoadduct of both cases: (a) DEMF and (b) DNaMF.The behavior of the other five adducts is similar (data not shown); carbonyl oxygen atoms of the substituents form more hydrogen bonds than the carboxyl oxygen atoms.The number of hydrogen bonds does not increase uniformly, in contrast with the almost linear relationship reported by Keshri and Tembe, [34] for the series of fullerols [C 60 (OH) n ] with n = 2-30, shown also in Table 2.In our calculations, we find one hydrogen bond in average per monoadduct molecule; this means that among the four oxygen atoms in this molecule, just one hydrogen bond (0.25 each one in average) can be formed.The  details of the two different types of oxygen atoms (oxygen atom double-bonded to carbon atom and oxygen atom bonded to carbon atom and diethyl group, see Figure 3c) suggest that the two carbonyl oxygen atoms are more susceptible to establish hydrogen bonds than the R-O-R oxygens.The low number of hydrogen bonds, probably, is related to the steric impediment in oxygen atoms bonded to the diethyl group due to the presence of this bulky group (see Figure 3c).Likewise, in Table 2, we present the calculations of hydrogen bonds corresponding to the DNaMF series.The presence of hydrogen bonds is higher compared to that for the DEMF series.An average of 2.5 hydrogen bonds per each oxygen atom in the monoadduct molecule was found, evaluated for the same four oxygen atoms in the malonate group.Values from Table 2 show that hydrogen bonds of DNaMF are around 10 times bigger than the numbers of DEMF.Carboxyl oxygen atoms on the malonate group have net charges and two lone-pair electrons of each atom plus the two lone-pair electrons of each of the carbonyl oxygens (see Figure 3d), now without the presence of the bulky ethyl group (see Figure 3c).This situation makes the four oxygen atoms more accessible to bond to hydrogen atoms from water molecules.We conclude that the availability of both two carbonyl oxygens and two terminal oxygens plus their net charges is responsible for the higher water hydration ability.
To define the surface area where the solvent molecules can approach the solute, the SASA was calculated using the GROMACS tool gmx sasa.Figure 4a shows that in the case of DEMF series, the correlation between SASA and the number of substituents is not clear; the pristine fullerene has a SASA equal to 2.6 nm 2 , while the monoadduct 3.6 nm 2 , following by the bisadduct with a SASA of 5.4 nm 2 , and then, the higher substituted adducts do not present the same tendency.The trisadduct has an SASA value similar to that the pentaadduct, while the tetraadduct has a slightly lower value, and finally, the hexaadduct with the higher SASA values.Nevertheless, SASA calculations of the DNaMF series show (Fig. 4b) that the surface area increases with the number of substituents, supporting the previous hydrogen bond study.
Radial distribution function reports the number of nearby water molecules to fullerenes, calculated between the center of mass from each fullerene derivative and that from water molecules.These calculations are obtained from simulations of only one solute molecule, surrounded by water, as already mentioned in the Simulation Details section.Figure 5 shows the rdf of DEMF series (a and b) and DNaMF series (c and d); split each series into two groups for clarity purposes.We see that water molecule structure close to the solute molecule depends on the number of fullerene substituents; for pristine fullerene, a compact shell of water encloses the symmetrical fullerene sphere.The exclusion volume is clearly delimited with no water penetration at distance r lower than 0.6 nm.Nevertheless, the r value where rdf increases corresponds to the increase of both the exclusion volume and the number of fullerene substituents, due to the bulky diethyl malonate groups.The first peak corresponds to the first hydration shell, for pristine fullerene, due to its hydrophobicity, sphere shape, and lack of atoms to establish hydrogen bonds; this shell is produced by very symmetric Van der Waals interactions.The substituents of the adducts break the symmetry of the sphere-shaped molecule, and the oxygens bond to water hydrogens, giving a nonrandom structure, more organized but with less water molecules.This first shell has less water molecules, and then, the height of the first peak decreases, but it SOFT MATERIALS produces a shielding effect, giving a hydrophilic environment improving the overall dispersity.In contrast, the DNaMF series demonstrated more defined hydration shells with a higher density of water molecules compared to the DEMF series.Figure 5c,d shows that pristine fullerene and DNaMF bear the same starting point for the first rdf peak.The excluded volume of pristine fullerene is almost the same as that of the excluded volume of all adducts of the DNaMF series, compared with the irregular starting point (see insets of Fig. 5, region close to r = 0.6 nm) of molecules of DEMF series.Disodium malonate group is much smaller than the diethyl malonate group, and then, closer to sphere shape of pristine fullerene.The exposure of four oxygen atoms without ethyl groups from the DNaMF series leads to a stronger bond with water molecules compared to that of the DEMF series, which produces a second peak almost as height and well-defined as the first one, corresponding to the second solvation shell.The sequential increase in the peaks of the DNaMF series follows different behaviors than that of the DEMF series, where the second peaks are less pronounced.
In Table 3, the number of water molecules of first and second hydration shells is reported.These values were calculated from the rdf (Fig. 5) and compared with the values obtained by Keshri and Tembe [34] in their investigations of the hydration shells of fullerols with an increasing number of substituents.Our results agree with their findings, and the general tendency is that the number of water molecules of the first hydration shell decreases with the number of substituents, whereas that for the second shell is not being so clear.
From the DLS experiments, we have obtained the following results.A reduced fraction of DEMF bisadduct (C 62 (COOEt) 4 ) is dispersed, while the rest of the sample remains on the surface due to low hydration and lower density than water; the DLS analysis is performed in the homogenous part of the solutions.As expected, the adduct-hydrophobic region tries to minimize their exposition to water, reducing their displayed area when aggregation occurs, as previously reported by Zhou et al. [24] , while in the case of DNaMF bisadduct (C 62 (COONa) 4 ) samples present higher hydration.Figure 6 shows the behavior of the mean hydrodynamic diameter of each sample (only shown the bisadducts) as a function of time; each point represents the corresponding value of the maximum intensity of the most intense peak of the size distributions obtained by the DLS measurements.On the left side of Figure 6, the graphs of bisadduct C 62 (COOEt) 4 are represented and, on the right, the corresponding plots of bisadduct C 62 (COONa) 4 for the three considered concentrations.The star symbols shown in the right plots correspond to some measurements made one month later.From these last results, we can conclude that the aggregation remains unchanged.
The kinetic behavior of the size distributions does not show a tendency in the size growth as a function of time, at least during the period we made the evaluation.Figure 6 shows just variations of the size of the aggregates; in fact, the mean size observed for C 62 (COOEt) 4 samples is 179 ± 27, 168 ± 20, and 196 ± 35 nm, while for C 62 (COONa) 4 the mean size is 224 ± 75, 178 ± 47, and 176 ± 142 nm, respectively for 5, 15, and 30 µM concentrations.The same behavior of aggregation was previously described by Zhou et al., [24] suggesting that the size and shape of C 62 (COONa) 4 may be a consequence of a variety of isomers.The MD simulation with a single isomer indicated higher solubility without aggregates.A mixture of isomers must be considered in the simulations to compare this behavior.

Fullerene Adducts and Amyloid β Peptide 42 Aggregation
In vitro experiments have demonstrated the different capacities of DEMF and DNaMF for blocking AβP fibril formation [32] .The molecular mechanism associated with the antiaggregatory effect of each molecule remains unclear.We performed simulations of each fullerene derivative in water, adding monomers of AβP, dimethyl  sulfoxide, and NaCl (to mimic the experimental protocol [32] ), in the conditions mentioned in the methodology section.In Figure 7 (left side), density profiles for the DEMF series indicate that for all the seven systems, including pristine fullerene, AβP monomers are aggregated, as it can be inferred from the big density peaks and snapshots of all the systems, found in Figure S4 of supplementary information.Fullerene adducts are all selfaggregated in the case of pristine fullerene, mono-, penta-, and hexaadduct, while in the case of bis-, trisand tetraadduct they are slightly dispersed along the z-coordinate in the simulation box.Density profiles show that a possible interaction exist between fullerene derivatives and AβP monomers, in the case of bis-, tris-, tetra-, and pentaadducts of DEMF. Figure 7 (right side) shows the density profile for adducts with disodium malonate addends.The pristine fullerene and monoadduct are both self-aggregated, but the other five compounds remain dispersed in the simulation box.In contrast, the four AβP monomers are selfassociated in all cases, except in penta-and hexaadducts and a possible interaction exists between DNaMF molecules and amyloid monomers when n = 2, 3, and 5 (number of disodium malonate addends on the C 60 ).

Conclusions
We have analyzed the solubility behavior of two series of fullerene adducts bearing one to six diethyl and disodium malonate substituents using MD simulations.From the density profile results, it is found that diethyl malonate fullerenes show the formation of agglomerates regardless of the number of addends attached to C 60 , while for disodium malonate fullerenes, only the monoadduct aggregates.The calculations of the hydrogen bond number, the solvent-available surface area, the number of water molecules in the first hydration shell, and the radial distribution functions correspond with the tendency of increasing the number of substituents.The higher number of oxygen atoms with lone electron pairs in the DNaMF series increases the hydration, forming hydrogen bonds with the surrounding water.This availability is not possible in diethyl malonate fullerenes; thus, their biomedical applications are restricted.The ionic adducts of C 60 forming sodium salts or other salts seem to be a promising approach for further investigation as a potential treatment of AD.
From the results of interactions between AβP fullerene, we found that the molecules with higher potential to be used in the AD treatment are the bis-, tris-, tetra-, and pentaadduct with disodium malonate addend, due to higher solubility and interactions between amyloid monomers and fullerene derivatives.It is plausible to think that there is an equilibrium between the hydrophobic fullerene cage and hydrophilic nature of disodium malonate substituents interacting with the different amino acid building blocks of AβP.To deeply understand these interactions, further investigation is required.

Figure 1 .
Figure 1.Snapshot of bisadduct of diethyl malonate fullerene in the simulation box surrounded by water.

Figure 3 .
Figure 3. Number of hydrogen bonds per oxygen atom calculated along the simulation time.(a) DEMF monoadduct showing the detail of each of the four oxygen atoms of malonate group; carbonyl oxygen, oxygen atom double-bonded to the carbon atom, and carboxyl oxygen, oxygen atom bonded to carbon atom and diethyl group.(b) DNaMF monoadduct with the same oxygen notation.Chemical structures of (c) diethyl malonate and (d) disodium malonate, showing lone-pair electrons of oxygen atoms.

Figure 6 .
Figure 6.Mean hydrodynamic diameter obtained by means of DLS measurements for samples of (ac) bisadduct DEMF, and (df) bisadduct DNaMF as a function of time for the three considered concentrations: 5, 15, and 30 μM.Stars are experiments performed after 1 month.

Table 1 .
Molecules studied in this work.

Table 2 .
Number of hydrogen bonds obtained from the analysis of the molecular dynamics results.

Table 3 .
Data obtained from the analysis of the molecular dynamics results, calculated from one-solute molecule system.