Amyloid- peptide structure in aqueous solution varies with fragmentsizeOlivia Wise-Scira, Liang Xu, Taizo Kitahara, George Perry, and Orkid Coskuner Citation: J. Chem. Phys. 135, 205101 (2011); doi: 10.1063/1.3662490 View online: http://dx.doi.org/10.1063/1.3662490 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v135/i20 Published by the American Institute of Physics. Related ArticlesPhase diagram of polypeptide chains J. Chem. Phys. 135, 175103 (2011) Phase diagram of polypeptide chains JCP: BioChem. Phys. 5, 11B602 (2011) Effects of surface interactions on peptide aggregate morphology JCP: BioChem. Phys. 5, 08B624 (2011) Effects of surface interactions on peptide aggregate morphology J. Chem. Phys. 135, 085102 (2011) Does amino acid sequence determine the properties of A dimer? J. Chem. Phys. 135, 035103 (2011) Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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THE JOURNAL OF CHEMICAL PHYSICS 135, 205101 (2011)

Amyloid-β peptide structure in aqueous solution varies with fragment sizeOlivia Wise-Scira,1 Liang Xu,1 Taizo Kitahara,1 George Perry,2 and Orkid Coskuner1,2,a)

1The University of Texas at San Antonio, Department of Chemistry, One UTSA Circle,San Antonio, Texas 78249, USA2The University of Texas at San Antonio, Neurosciences Institute, One UTSA Circle,San Antonio, Texas 78249, USA

(Received 11 July 2011; accepted 1 November 2011; published online 28 November 2011)

Various fragment sizes of the amyloid-β (Aβ) peptide have been utilized to mimic the propertiesof the full-length Aβ peptide in solution. Among these smaller fragments, Aβ16 and Aβ28 havebeen investigated extensively. In this work, we report the structural and thermodynamic propertiesof the Aβ16, Aβ28, and Aβ42 peptides in an aqueous solution environment. We performed replicaexchange molecular dynamics simulations along with thermodynamic calculations for investigatingthe conformational free energies, secondary and tertiary structures of the Aβ16, Aβ28, and Aβ42peptides. The results show that the thermodynamic properties vary from each other for these peptides.Furthermore, the secondary structures in the Asp1-Lys16 and Asp1-Lys28 regions of Aβ42 cannot becompletely captured by the Aβ16 and Aβ28 fragments. For example, the β-sheet structures in the N-terminal region of Aβ16 and Aβ28 are either not present or the abundance is significantly decreasedin Aβ42. The α-helix and β-sheet abundances in Aβ28 and Aβ42 show trends – to some extent –with the potential of mean forces but no such trend could be obtained for Aβ16. Interestingly, Arg5forms salt bridges with large abundances in all three peptides. The formation of a salt bridge betweenAsp23-Lys28 is more preferred over the Glu22-Lys28 salt bridge in Aβ28 but this trend is vice versafor Aβ42. This study shows that the Asp1-Lys16 and Asp1-Lys28 regions of the full length Aβ42peptide cannot be completely mimicked by studying the Aβ16 and Aβ28 peptides. © 2011 AmericanInstitute of Physics. [doi:10.1063/1.3662490]

I. INTRODUCTION

The amyloid-β (Aβ) peptide is at the center of cere-bral amyloid angiopathy and Alzheimer’s disease (AD).1–3

Aβ is formed naturally from the amyloid precursor protein(APP), usually as a 39–42 residue peptide, but the most fre-quently formed species are the Aβ40 and Aβ42 peptides.4

The Aβ peptide is shown to be the principal component in theparenchymal plaques that occur in AD patients. The extracel-lular amyloid plaque core mostly consists of the Aβ42 frag-ment; however, cerebrovascular amyloid contains the Aβ39and Aβ40 fragments.5, 6 The Aβ28 and Aβ(29–42) fragmentsthat are composed of residues Asp1-Lys28 and Gly29-Ala42,respectively, occupy the extracellular and transmembrane do-mains within APP.5–7 Aβ is a disordered peptide that is ableto adopt an ensemble of significantly different conformationsdue to the presence of polar and structure-breaking aminoacid residues in its sequence. The monomeric and oligomericforms of Aβ have recently been reported as being toxic toneuronal cells.8–10 The stabilization of specific conformations– to some extent – of disordered Aβ is proposed to be the ini-tial step in the fibrillogenesis process.11, 12 As a result, Aβ

monomers and oligomers have been the subject of variousstudies.

In general, the large size, fast conformational changes,solvent effects, and rapid aggregation provide challenges inthe studies of the full-length Aβ monomers and oligomers.

a)Electronic mail: orkid.coskuner@utsa.edu.

Therefore, experimental studies using various techniquessuch as circular dichroism (CD), NMR, and Raman spectro-scopies have often been performed utilizing smaller Aβ frag-ments rather than the full-length Aβ peptide.13–17 The smallerfragments have been assumed to mimic the physical andchemical characteristics related to the aggregation mechanismand interactions of Aβ. For instance, several spectroscopicstudies investigating the coordination chemistry mechanismbetween inorganic species, such as metal ions, and Aβ haveusually used the Aβ16 fragment.18–21 Another fragment thathas been utilized extensively is the Aβ28 fragment.14, 17, 22–24

We should note that stark and fast conformational changes ofthe full-length Aβ peptide could alter the chemical and phys-ical characteristics of a small region and its chemical reactionmechanisms with other compounds. The chemical and phys-ical properties of the Asp1-Lys16 and Asp1-Lys28 regionsutilizing the Aβ16 and Aβ28 fragments might differ fromthose in the corresponding regions of the full-length Aβ42peptide. Such differences may impact the reaction mecha-nisms of Aβ with organic and inorganic species. In addition toAβ16 and Aβ28, various other fragments including Aβ(10–35), Aβ(16–35), Aβ(16–22), Aβ(21–30), and the C-terminalregion have been studied using both experimental and theoret-ical tools.13, 25–30 Important information has been gained fromthese studies about various regions of the full-length Aβ40 orAβ42 peptides, which have been directly linked to AD.

Given the long standing importance of Aβ, it is inter-esting to note the lack of validation studies that comparethe physical and chemical properties of all these extensively

0021-9606/2011/135(20)/205101/13/$30.00 © 2011 American Institute of Physics135, 205101-1

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205101-2 Wise-Scira et al. J. Chem. Phys. 135, 205101 (2011)

investigated small Aβ fragments to those of the full-lengthAβ peptide. In fact, most recent computational studieshave even reported significant variations between the struc-tural properties of the two full-length Aβ40 and Aβ42peptides.31–33 To the best of our knowledge, the structuraland thermodynamic properties of the Aβ16, Aβ28, and Aβ42peptides have not been compared to each other before. Thisstudy presents the free energy landscapes and structural pa-rameters of the Aβ16, Aβ28, and Aβ42 peptides in aque-ous solution utilizing replica exchange molecular dynamics(REMD) simulations coupled with thermodynamic calcula-tions. The enthalpic and entropic contributions to the confor-mational Gibbs free energies of the Aβ16, Aβ28, and Aβ42peptides are presented and compared to each other. The sec-ondary and tertiary structures of the Aβ16, Aβ28, and Aβ42peptides are provided and compared to each other. Our re-sults clearly demonstrate that the structural and thermody-namic properties of the Aβ16, Aβ28, and Aβ42 peptidesdiffer from each other. In other words, the structural prop-erties of the Asp1-Lys16 and Asp1-Lys28 regions of the full-length Aβ42 peptide cannot be captured fully by studying thesmaller Aβ16 and Aβ28 fragments.

II. METHODS

All-atom REMD simulations using an implicit solventmodel were performed to increase the configurational sam-pling of the structures without facing limitations due to theconfined aqueous volume effect.34, 35 Usage of an implicit wa-ter model further avoids inaccuracies associated with constantvolume REMD simulations utilizing explicit water models.36

Most recent studies showed that the specific heat does not re-main constant in REMD simulations, which impacts the ac-curacy of calculated thermodynamic properties for pure wa-ter using an explicit water model at constant volume. TheNMR structure of the Aβ42 monomer (PDBID 1Z0Q) wasused as the initial geometry in our simulations.37 This struc-ture was measured in a solution with 2,2,2-trifluoroethanol(TFE), which is an α-helix stabilizer. This experimentally de-termined helical structure was chosen to aid in understand-ing the impact of the fragment size effect on the debatedsecondary structure transformations in the current literatureincluding the α-helix to β-sheet transition. Truncating theAβ peptide and converting the backbone carbonyl to a car-boxylate created the initial structures for the smaller peptides.The simulations were performed with the AMBER 10 softwarepackage38 utilizing the Amber ff99SB potential functions39

and the Onufriev-Bashford-Case generalized Born implicitsolvent model.40 The long-range interactions were treatedwith the particle mesh Ewald (PME) method using a cut-off value of 25 Å.41, 42 The temperature was controlled usingLangevin dynamics with a collision frequency of 2 ps−1.41

The initial conformations were first equilibrated for 200 ps foreach replica. The integration time step for each replica was 2fs and each trajectory was saved every 500 steps (1 ps). Thetime interval for exchange attempts between the replicas wasset to 5 ps. Different replicas for each system were utilizedwith temperatures exponentially distributed between 280 Kand 400 K with an exchange ratio of 0.83, 0.77, and 0.74 for

the Aβ16, Aβ28, and Aβ42 peptides, respectively.43 The pro-duction run in separate simulations for each replica (for eachpeptide) was 100 ns with a total simulation time of 2.4 μs.

In order to assess the physical relevance of our sim-ulations, the Cα and Hα chemical shift values were calcu-lated for the Aβ42 peptide from the 280 K replica, which isclosest to the experimental temperature of 278 K, using theSHIFTS program.44 The experimental values were providedby Dr. Michael Zagorski.45 The correlation between the ex-perimental values obtained via NMR measurements and thechemical shift values of the structures from our simulationswas determined using the Pearson correlation coefficient. Allother structural and thermodynamic calculations of the Aβ16,Aβ28, and Aβ42 peptides were performed on a total num-ber of 120 000 structures obtained after convergence fromthe ∼310 K replica (physiological temperature). To study theconformational preferences of the peptides, the Gibbs freeenergy (G) values were calculated using the molecular me-chanics/generalized Born surface area (MM/GBSA) methodto enable predictions of thermodynamic properties of largebiocomplexes in solution.46–48 For the Gsolvation-electrostatic cal-culations, the internal and external dielectric constant valueswere set to 1 and 80, respectively, and dipolar boundary con-ditions were applied. The nonpolar Gibbs free energy con-tribution was approximated employing the solvent accessiblesurface area (SASA) based on the following relationship inEq. (1):46, 49

Gnonpolar = 0.00542 × SASA + 0.92. (1)

The normal mode analysis (NMA) method50 was used to cal-culate the entropy values. We should mention here that thisharmonic method does not capture anharmonic effects. How-ever, various groups have reported successful studies of Aβ

using this harmonic approximation.51–53 Furthermore, we cal-culated the entropy using the Schlitter method, which hasbeen used in the theoretical studies of proteins:54–56

S < Sapprox = 1

2kB ln det

[1 + kbT

2e

¯2Mσ

], (2)

where kB is the Boltzmann constant, T is the temperature, eis Euler’s number, h is Planck’s constant, M is a diagonal ma-trix of masses associated with the atomic degree of freedom,σ is the covariance matrix of atom fluctuations defined as σ ij

= 〈(xi − 〈xi〉)(xj − 〈xj〉)〉, where xi are the coordinates withrespect to all peptide atoms. The secondary structure compo-nents of the peptides were analyzed using the DSSP program,which uses the hydrogen bond criteria.57 Intra-molecular pep-tide interactions were considered to exist when the center ofmass of the residues were within a distance of 9.0 Å. To thetest the impact of this criteria on the predicted intra-molecularinteractions, the same calculations were performed using adistance criteria of ≤4.5 Å between the heavy atoms (C,N, O, S) of different residues (Fig. S1 in the supplementarymaterial58). Obtained results with both criteria yield the sametrends. Following recent studies, a hydrogen bond exists if thedistance between donor hydrogen atom and the acceptor atomis ≤2.5 Å and the hydrogen bond angle is larger than 113◦.59

A salt bridge exists when hydrogen bonded atoms have oppo-site electrostatic charges.

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205101-3 Amyloid-β peptide fragment size J. Chem. Phys. 135, 205101 (2011)

FIG. 1. The calculated (a) potential energy values and (b) α-helix content for the Aβ16 (black), the Aβ28 (red), and the Aβ42 (blue) peptides. Correlationbetween the (c) Cα and (d) Hα chemical shift values for the Aβ42 peptide in aqueous solution at 280 K utilizing the structures after convergence from oursimulation (δcalc.) and experimental (δexp.) chemical shift values provided by Dr. Michael Zagorski. The calculated Pearson correlation coefficient value is0.980 for Cα and 0.930 for Hα .

III. RESULTS AND DISCUSSION

Before embarking on detailed analyses of the aqueouspeptides, the accuracy of the obtained results was confirmedby testing the convergence of the simulations. The potentialenergy and the α-helix content were calculated to test the con-vergence (Fig. 1). In addition, the physical relevance was as-sessed by calculating the Cα and Hα chemical shift values forAβ42 (from the 280 K replica) and comparing these valuesto experimental data.45 Figures 1(c) and 1(d) show that thecorrelation between the calculated (δsim.) and experimental(δexp.) values for the chemical shifts is large after the first60 ns of simulation time, with a Pearson correlation coef-ficient of 0.98 and 0.93 for the Cα and Hα chemical shifts,respectively. The simulated potential energy, α-helix content,Pearson correlation coefficients, and the small statistical devi-ation of the calculated chemical shift values from experimentsdemonstrate that the simulations reach a convergence and thatthe converged structures reproduce results in agreement withexperiments. These results support previous simulation stud-ies that presented 60 ns of simulation time are required toreach a convergence for Aβ42.32, 60

As illustrated in Fig. 2 and Table I, all three peptides areflexible and adopt conformations that override Gibbs free en-ergy (G) barriers based on enthalpic (H without Gsolvation) andentropic (TS) contributions. The most stable Aβ16 conforma-tions have H − Gsolvation values smaller than −500 kJ mol−1,indicating that the enthalpic effect (without the contributionof the solvation free energy term) plays a role in the stabi-lization of Aβ16 structures. A similar trend is also obtainedfor the Aβ28 structures, which adopt more stable conforma-tions at H − Gsolvation < −300 kJ mol−1. Despite, a cleartrend between the magnitudes of H − Gsolvation and G couldnot be obtained for the structures of Aβ42. The Aβ42 pep-tide conformations are more stable than those of Aβ28 andAβ16 by 1015.9 and 2723.9 kJ mol−1, respectively, and theAβ28 peptide conformations are more stable than those ofAβ16 by 1708 kJ mol−1 based on the calculated average Gvalues using the harmonic approximation (Table I and Fig. 2).Utilizing the quasi-harmonic Schlitter method, we find thatthe structures of Aβ42 are more stable than those of Aβ16and Aβ28 by about 3796 and 1415 kJ mol−1 (Table I). Thetopic of this study is the comparison of the structural and

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205101-4 Wise-Scira et al. J. Chem. Phys. 135, 205101 (2011)

FIG. 2. Calculated Gibbs free energy (G) surfaces according to their en-thalpic (H) and entropic (TS) contributions for the (a) Aβ16, (b) Aβ28, and(c) Aβ42 peptides in aqueous solution.

thermodynamic properties of Aβ16, Aβ28, and Aβ42, andboth harmonic and anharmonic methods yield the same trends(Table I) for these peptides. Therefore, we continue our fur-ther analyses using the results obtained from the harmonic

approximation calculations. Furthermore, we should empha-size that the thermodynamic properties of the Aβ peptide us-ing the harmonic approximation have been successfully deter-mined by various groups.51, 52 However, we should mentionhere that the applications of methods that treat the systemsvia both harmonic and anharmonic approximations, such asthe second generation data mining M2 method developed byGilson and co-workers, might yield different characteristicsfor these peptides.61–64 The M2 method has been success-fully applied to various systems. However, it has yet to beapplied to a large-size fully flexible disordered protein, suchas Aβ42 in solution, which possesses of structures that canoverride large free energy barriers. To the best of our knowl-edge, RMSD calculations and energy criteria are used to as-sign structures to local energy minima but we have found thatthe RMSD values are not directly related to the conforma-tional Gibbs free energy of the Aβ42 peptide. Thus, differentclustering methods, such as radius of gyration, spectral algo-rithms, or Laplacian score maps, that have been previouslyshown to yield useful insights into the structural propertiesof the disordered Aβ42 peptide may be useful in modify-ing the quasi-harmonic methods. Another recently developedmethod calculates the change in configurational entropy ofAβ42 structures between the organic and aqueous phase us-ing a combination of MD simulations and the integrated-equation theory of liquids.65 Although the Aβ42 structureswere clustered using the radius of gyration values,66 Chongand Ham stated that this method is only applicable to struc-tures simulated using an explicit solvent model. We shouldnote that the confined aqueous volume, i.e., the chosen solventvolume around the peptide, may impact the simulated struc-tures and that MD simulations without special sampling tech-niques cannot capture the many various structural changeswithout being trapped in one energy well. Therefore, fur-ther studies are still required to enhance the quasi-harmonicmethods for use in a wider variety of systems includingfully flexible large size disordered proteins and simulationconditions.

A. Secondary structure properties

The most prominently formed secondary structure com-ponents are the coil and turn conformations in all three pep-tides (Fig. 3 and Table S1 in the supplementary material58).The average abundance of β-sheet is 2.4%, 1.9%, and 0.4%for Aβ16 and for the Asp1-Lys16 region of Aβ28 and Aβ42,respectively, and presents more prominent β-sheet forma-tion for the structures of Aβ16 and Aβ28 rather than thoseof Aβ42. β-sheet formation occurs at residues Phe4, Arg5,Tyr10, and Glu11 (<10% per residue) of Aβ16. In Aβ28,the formation of β-sheet structure at Phe4, Tyr10, and Glu11almost disappears. Instead, residues Arg5, Val12, and His13adopt β-sheet structures with abundances smaller than 10%per residue. On the other hand, β-sheet formation is detectedat Arg5, Glu11, and Val12 in the Asp1-Lys16 region of Aβ42(Fig. 3). In the Asp1-Lys28 region, β-sheet formation also oc-curs at Phe19 (<10%) in Aβ28. However, the Phe19-Glu22and Gly25-Asn27 regions as well as residues Gly33, Met35,Val36, Val40, and Ile41 of Aβ42 adopt β-sheet with abun-

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205101-5 Amyloid-β peptide fragment size J. Chem. Phys. 135, 205101 (2011)

TABLE I. The calculated average enthalpy (H), H − Gsolvation, entropy (−TS) and Gibbs free energy (G) values for theAβ16, Aβ28, and Aβ42 peptides in aqueous solution using the normal mode analysis and the Schlitter method.

〈H − Gsolvation〉 〈H〉 −TS G −TSSchlitter GSchlitter

(kJ mol−1) (kJ mol−1) (kJ mol−1) (kJ mol−1) (kJ mol−1) (kJ mol−1)

Aβ16 −510.3 −2089.2 −1017.4 −3106.6 −2475.7 −4564.9(16.3) (9.0) (1.2) (9.1) (30.4) (31.7)

Aβ28 −330.8 −2740.1 −1620.7 −4360.8 −4206.2 −6946.2(32.6) (16.6) (6.9) (18.0) (59.1) (61.4)

Aβ42 −175.4 −2579.9 −2206.6 −4786.5 −5781.3 −8361.2(44.6) (24.3) (4.1) (24.6) (131.3) (133.5)

dances up to 23%, which is about three times more abundantthose residues of Aβ28. Residues located in the Arg5-Gln15region adopt α-helix in all three peptides; however, the prob-abilities are larger in both Aβ28 and Aβ42 than in Aβ16(Fig. 3). Furthermore, the Lys16-Asp23 region of Aβ28adopts α-helix (20%–43%), which is also detected withsmaller probabilities in Aβ42. Although CD measurementsof Aβ28 in pure water predict a mainly random coil struc-ture, previous theoretical studies reported α-helical regions inAβ28.17, 23, 67, 68 Despite these residual differences, the over-all average α-helix probability in the Asp1-Lys28 region ofAβ42 (16.7%) is similar to that of Aβ28 (16.9%). These re-sults show that the difference in α-helix probability is largerbetween the structures of Aβ16 and Aβ42 rather than Aβ28and Aβ42. In addition, the Gly29-Val36 region of Aβ42adopts α-helix (<10%). Turn structure formation occurs ad-jacent to the central hydrophobic core (CHC) region in Aβ28(<55%). For Aβ42, we detect turn conformation for residueslocated in the Arg5-Val12 and Glu22-Lys28 regions (20%–60%), with the largest probability occurring in the Ala21-Ala30 region. These results support the NMR measurementsthat reported turn and bend-like conformations for the Asp7-Glu11 and Phe20-Ser26 regions of Aβ42.45 Experimentalstudies also showed turn conformation for the Ala21-Ala30decapeptide in solution.15

FIG. 3. Calculated secondary structures for the residues of the Aβ16 (black),Aβ28 (red), and Aβ42 (blue) peptides. The values for the abundance of π -helix and coil for the residues are not depicted.

We should mention here that the literature includes alarge number of Aβ studies and all previous studies cannotbe described herein. Dong et al. performed ART-OPEP simu-lations of Aβ28 and reported β-sheet formation at residuesGlu3-Arg5, Ser8-Glu11, Lys16, Leu17, and Asp23-Ser26for the structures in lowest energy regions.22 Furthermore,Baumketner and Shea studied the Val12-Lys28 region viaREMD simulations using an explicit model for water and de-tected β-sheet formation at Phe19 among other residues butno β-sheet was reported for Val12 and His13 at a tempera-ture of 280 K.69 Our findings are quite different from thosereported in these studies (see above). These discrepancies canbe attributed to fragment size differences, different potentialfunctions, simulation techniques, and/or to convergence.

Our results for Aβ42 partially agree with the most re-cent studies of Velez-Vega and Escobedo using the OPLS-AA and TIP3P potential functions for the peptide andwater molecules in REM/APE simulations.70 They presentedα-helix formation only in a small region located in the mid-domain with propensities less than 10%. This study furthershowed β-strand formation with large propensities in the N-terminal region and between Tyr10 and Leu17 of Aβ42. Wefind α-helix and β-sheet formations at these residues as well(Fig. 3) but our simulations show that other residuesalso adopt α-helical and β-sheet structures. Furthermore,MD simulations without special sampling using the GRO-MOS9643A1 parameters and the SPC model for waterpresented helical structure at Glu3-Asp7, Ser8-Asp23, andLys28-Gly38 of Aβ42. This is in partial accord with our re-sults (Fig. 3).71 The same study also showed β-sheet forma-tion in the C-terminal region, which we detect as well (Fig. 3).Garcia et al. used various clustering algorithms including thespectral algorithm and detected β-sheet formation at Phe4-His6 and Gly38-Val40, and α-helix formation at Ser8-Val12in the Aβ42 structures located in a conformationally distinctcluster.60 Based on our results, Phe4-His6 and Gly38-Val40adopt β-sheet formation as well but with small probabilities.Our findings also agree with the recent studies of Côté et al.,who showed β-strand formation at Ala2-Arg5, Glu10-His13,Lys16, and Val17 with smaller abundances than at Ala30-Ile32, Val39-Ile41, and in the CHC region of Aβ42.72 Fur-thermore, they reported α-helix formation at Glu22-Asn27and Met35-Val40. Moreover, our findings are in good agree-ment with the studies of Yang and Teplow, who performedREMD simulations using an implicit model for water.31

They reported β-strand structure in the CHC region and at

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205101-6 Wise-Scira et al. J. Chem. Phys. 135, 205101 (2011)

adjacent residues as well as in the C-terminal region of Aβ42.The formation of α-helix was detected in the N-terminal,mid-domain, and C-terminal regions of Aβ42 whereby theresidues in the mid-domain adopt α-helix with larger abun-dances than those in the N- and C-terminals. Small differencesexist between our results and those of Yang and Teplow (prob-abilities of secondary structure components) and these canbe due to differences in convergence time (10 ns equilibriumtime was utilized in their simulations). The prominent β-sheetstructure in the C-terminal region of Aβ42 (Fig. 3), which hasbeen related to the structuring of this region, was also reportedby various groups via experimental and theoretical investiga-tions and shows an accord with our findings.30–32, 45, 60, 73, 74

A direct relationship between the probabilities of α-helical and β-sheet structures and the magnitude of G couldnot be detected without the characterization of the structuresbased on clustering methods (Fig. S4 in the supplementarymaterial58). Potential of mean force (PMF) calculations inthe coordinates of the end-to-end distance (RE-E; distance be-tween the N-terminus ammonium group N atom and the C-terminus carboxylate group C atom) and the radius of gyration(Rg) was shown to be useful in relating structural proper-ties of Aβ to PMF. For instance, trends were obtained be-tween the structural parameters and PMF for amyloidogenicpentapeptides.75 We find two distinct favorable PMF basinsfor Aβ28 and Aβ42, but only one such basin for Aβ16(Fig. 4). For Aβ16, the most preferred PMF basin (within 1kBT) consists of conformations that have small abundancesof α-helix (∼8%) and β-sheet (∼2%) (Table S1 in the sup-plementary material58). The calculated α-helix and β-sheetabundances of the Aβ16 structures do not show a clear trendwith increasing/decreasing PMF (Table S2 in the supplemen-tary material58). However, the turn structure abundance de-creases with increasing PMF of the Aβ16 structures (TableS2 in the supplementary material58).

For Aβ28, one favorable PMF basin (Fig. 4(b), basin IA)is located at Rg values varying between 9.2 Å and 10.8 Åand is composed of structures with 12% α-helix and 3% β-sheet (Table S2 in the supplementary material58). The sec-ond basin for Aβ28 with the same PMF values (Fig. 4(b),basin IB) is located at Rg values varying between 10.9 Åand 13.4 Å. In contrast to basin IA, basin IB is composedof Aβ28 structures with ∼23% α-helix and to some extentβ-sheet (∼1%). These results indicate that Aβ28 structureswith different α-helix and β-sheet abundances are capable ofpossessing similar PMF values. The small difference in thePMF values (<1 kBT) of the regions between basin IA andIB indicates that the interconversion of the Aβ28 structureslocated in these two basins is energetically not retarded. Theabundance of α-helix and β-sheet decreases with increasingPMF value of the Aβ28 structures (Table S2 in the supple-mentary material58). In addition, the turn structure probabil-ity in the Asp1-Lys16 region is larger in the Aβ28 and Aβ42structures located in basin IA and basin IB than in the Aβ16structures found in basin I. Furthermore, the α-helix probabil-ity in the Asp1-Lys16 region of Aβ42 structures in basins IAto IIIA and IB to IIIB is larger than those for Aβ16 locatedin basins I to III. Moreover, the Asp1-Lys28 region of Aβ42structures in basins IA to IIIA and IB to IIIB adopt 3%–12%

more abundant turn structures than those of basins I to III ofAβ28.

The Aβ42 structures with most favorable PMF values canbe categorized into two basins (Fig. 4(c), basin IA and basinIB). The IA and IB basins are located at Rg values varyingbetween 10.6 Å and 11.4 Å and 10.3 Å and 10.7 Å. Basin IAof Aβ42 is composed of structures that have 10% α-helix and6% β-sheet, respectively. Despite, the structures in basin IBwith the same PMF values as basin IA adopt α-helix and β-sheet structures with ∼22% and 1% abundances, respectively(Table S2 in the supplementary material58). This finding indi-cates that Aβ42 structures with varying α-helix and β-sheetabundances are capable of having the same or similar PMFvalues. For basins IA to IIIA of Aβ42, β-sheet abundance de-creases with increasing PMF while α-helix abundance showsthe opposite trend (Table S2 in the supplementary material58).This trend is vice versa for the Aβ42 structures located inbasins IB to IIIB. Unlike Aβ28, transitions of Aβ42 struc-tures from basin IA to IB or vice versa require overriding alarge energy barrier (>1 kBT).

B. Intra-molecular peptide interactions

The intra-molecular peptide interactions with corre-sponding probabilities are shown in Fig. 5. In the Aβ16peptide, the N-terminal residues (Glu3-Ser8) interact withthe mid-domain and C-terminal residues (Ser8-His14, 30%–90%) whereby Phe4, Arg5, Tyr10, and Glu11 adopt β-sheetstructure (Figs. 3 and 5(a)). The Aβ16 structures includingthese interactions possess a smaller average G value (−47kJ mol−1) than the average G value of all converged Aβ

structures without structural characterization (using the har-monic approximation). This free energy difference – eventhough other important factors can influence the free energiesas well – might indicate that these interactions play a rolein the stabilization of Aβ16 structures. Similar interactionsare detected in the Asp1-Lys16 region of Aβ28 and Aβ42(Fig. 5) whereby Arg5, Val12, His13 of Aβ28 and Arg5,Glu11, and Val12 of Aβ42 adopt β-sheet. However, the N-terminal and Ser8-His14 interactions are less abundant inAβ42 than in Aβ16.

Regarding Aβ28, we note that the CHC region inter-acts abundantly with itself, Tyr10-Gln15 and Glu22-Ser26whereby Val12, His13, Phe19 form β-sheet. Residues ad-jacent to the CHC region of Aβ28 interact with Glu3-Asp7, which correspond to a prevalent turn conformation(Figs. 3 and 5(b)). Structures including these interactions havean average G value that is 57 kJ mol−1 smaller than the av-erage G values of all converged Aβ28 structures utilizingthe harmonic approximation. Interactions between residuesSer8-Val12 with the region adjacent to the CHC and theCHC region are more prominent in Aβ42 in comparisonto Aβ28 (Fig. 5(c)) whereby Glu11, Val12, Phe19-Ala21,Gly25-Asn27 form β-sheet structure. Relative to Aβ28, in-teractions between the CHC region and residues of theprotease-resistant region that are not directly adjacent to theCHC (Gly25-Ala30) of Aβ42 are more abundant by 10%–40%. Additionally, the N- and C-terminal regions of Aβ42

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205101-7 Amyloid-β peptide fragment size J. Chem. Phys. 135, 205101 (2011)

FIG. 4. Potential of mean force (PMF) surfaces of the aqueous (a) Aβ16, (b) Aβ28, and (c) Aβ42 peptides along with the coordinates of the end-to-end distance(RE-E) and radius of gyration (Rg) in units of kBT. For these figures, PMF = − kBT log (P). Representative structures for basin I of Aβ16, basin IA of Aβ28,basin IB of Aβ28, basin IA of Aβ42, and basin IB of Aβ42 are depicted next to the PMF surfaces.

interact with the mid-domain, however, the latter is moreabundant (Fig. 5). Structures of Aβ42 that include N-terminaland mid-domain region interactions are 76 kJ mol−1 less sta-ble than those including interactions between the mid-domainand C-terminal regions. The larger number of residues form-ing prominent β-sheet structures within the C-terminal region

in comparison to those in the N-terminal region might be asso-ciated with these interactions. We note that Arg5 plays a cru-cial role in the formation of salt bridges in all three peptides(Schemes S1–S3). This finding was also recently reported forAβ42 by Ball et al. via REMD simulations using an explicitmodel for water.76

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205101-8 Wise-Scira et al. J. Chem. Phys. 135, 205101 (2011)

FIG. 5. Intra-molecular peptide interactions for the aqueous (a) Aβ16, (b)Aβ28, and (c) Aβ42 peptides. The color scale corresponds to the probabil-ity (P) of the distance between the centers of mass of two residues being≤9.0 Å from each other. Regions Asp1-Lys16 and Asp1-Lys28 in the Aβ28and Aβ42 peptides are highlighted with inscribed boxes.

Our tertiary structure map (see above) for Aβ28 is inpartial agreement with the one that was reported by Donget al. by ART-OPEP simulations.22 Specifically, they pre-sented interactions between Ala2-Phe4 and Tyr10-Val12 orAsp23-Ser26, which our studies capture as well. Furthermore,they showed interactions between the CHC and C-terminal

regions of Aβ28, which is in accord with our findings. Ourresults for the intra-molecular interactions of Aβ42 are inexcellent agreement with those reported by Yang and Teplowvia REMD simulations.31 Specifically, they also found abun-dant interactions between Glu3-Ser8 and Tyr10-His14, theCHC region and Ser8-Val12 or Gly25-Ala30, the N-terminaland mid-domain regions, and the C-terminal and mid-domainregions of Aβ42. Furthermore, they also found that the mid-domain and C-terminal interactions are more abundant thanthe mid-domain and N-terminal region interactions. Our re-sults also support the intra-molecular interactions presentedby Côté et al. that include interactions between Glu3-Ser8and Ser8-His14, the CHC region and Tyr10, the N-terminaland mid-domain regions, and abundant interactions betweenthe C-terminal and mid-domain regions of Aβ42.72 In ad-dition, abundant mid-domain and C-terminal region interac-tions were detected by Lee and Ham via MD simulations ofAβ42.77 Velez-Vega and Escobedo presented similar interac-tions via performing REM/APE simulations but the probabil-ities of these interactions were not shown.70 Moreover, us-age of a Laplacian score algorithm presented discriminativeinteractions between Ala2-Arg5 and Val24-Ser26 or Leu34-Val40, Gly25-Lys28, and Val36-Val40 of Aβ42 with smallprobabilities, which we detect with small abundances as well(see above and Fig. 5(c)).60 MD simulations of the Aβ42peptide using an explicit water model performed by Shenet al. presented that residues Leu34-Val36 interact with Ile31-Ile32 in the C-terminal region, which is in agreement with ourresults.78

The stabilities of the Lys28 and Glu22 or Asp23 saltbridges were determined by comparing the distributions ofthe distances between the carboxylate Cγ (Glu22, Asp23) andside-chain Nζ (Lys28) atoms (Fig. 7). The most stable saltbridges between Lys28 and Glu22 or Asp23 of Aβ28 occurat a distance of 4.0 Å between the Cγ and Nζ atoms, withthe latter being 61% more stable using all converged struc-tures for Aβ28. The Asp23-Lys28 salt bridge is 73% less sta-ble whereas the Glu22-Lys28 salt bridge is 37% more sta-ble for Aβ42. This results in the Glu22-Lys28 salt bridgebeing 54% more stable than the Asp23-Lys28 salt bridgeat the most probable distance of 4 Å for Aβ42 (Fig. 7(b)).This switch in preference may be associated with the switchin preference for the Arg5 and Asp23 or Glu22 interactionsfrom the Aβ28 to Aβ42 peptides (Schemes S2 and S3). Aprominent turn conformation and abundant interactions be-tween Val24 and Lys28 (36%) are also detected in the Ala21-Ala30 region of Aβ42 (Figs. 3 and 5(c)). Even though thepreference between the Lys28-Asp23 and Lys28-Glu22 saltbridges is inverted from the Aβ28 to Aβ42 peptides, theseresults still agree with previous studies that report a linkbetween the prominent turn conformation and salt bridgeformation in this region of Aβ42.8, 23, 29–31 Furthermore, theimportance of the Asp23-Lys28 salt bridge formation inthe stabilization of the Aβ42 structures was also shown byCôté et al.72

The intra-molecular interactions of each peptide werealso characterized using the calculated PMF surfaces ofeach peptide (Figs. 4 and 6, and S5–S7 in the supplemen-tary material58). For the Aβ16 structures, the probability

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205101-9 Amyloid-β peptide fragment size J. Chem. Phys. 135, 205101 (2011)

FIG. 6. Intra-molecular peptide interactions in (a) basin I of Aβ16, (b) basin IA of Aβ28, (c) basin IB of Aβ28, (d) basin IA of Aβ42, and (e) basin IB ofAβ42. The basins are shown in Fig. 4. The color scale corresponds to the probability (P) of the distance between the centers of mass of two residues being ≤9.0Å from each other. Regions Asp1-Lys16 and Asp1-Lys28 in the Aβ28 and Aβ42 peptides are highlighted with inscribed boxes.

of the interactions between Glu3-Asp7 and Glu11-His14 aswell as His6-Ser8 and Phe4-Arg5 decreases as the PMF in-creases (Figs. 6(a) and S5 in the supplementary material58).In the case of the Aβ28 structures, we note that theinteractions between Glu3-Asp7 (N-terminal) and Glu11-

His14 (mid-domain) become less prominent with increasingPMF in basins IA to IIIA (Figs. 6(b) and S6 in the supple-mentary material58). Furthermore, interactions between Val12and Phe19, which form β-structure, are more prominent withdecreasing PMF values of the Aβ28 structures in basin IA

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205101-10 Wise-Scira et al. J. Chem. Phys. 135, 205101 (2011)

FIG. 7. The calculated probability distribution of the distance between the Cγ atom of the Glu22 (solid) or Asp23 (dashed) residue and the Nζ atom of theLys28 residues for the (a) all converged Aβ28 structures, (b) basin IA of Aβ28, (c) basin IB of Aβ28, (d) all converged Aβ42 structures, (d) basin IA of ofAβ42, and (f) basin IB of Aβ42. The basins are shown in Fig. 4.

(Figs. 6(b) and S6 in the supplementary material58). Theprobability of interactions between the C-terminal and mid-domain or N-terminal regions are less prominent with in-creasing PMF of Aβ28 structures located in basins IA to IIIA

(Figs. 6(b) and S6 in the supplementary material58). In addi-tion, the interactions between Leu17-Ala21 and Gly9-His14are less probable with increasing PMF values of the Aβ28structures located in basins IB to IIIB (Figs. 6(c) and S6 in

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205101-11 Amyloid-β peptide fragment size J. Chem. Phys. 135, 205101 (2011)

the supplementary material58). The abundance of the interac-tions between Phe4-Arg5 and Asp7-Gly9 decreases with in-creasing PMF values of Aβ42 structures located in basins IAto IIIA (Figs. 6(d) and S7 in the supplementary material58).The structures of Aβ42 that have interactions within the N-terminal, within the C-terminal, between the N-terminal andCHC or C-terminal region and between the CHC region andAsp23-Gly29 become less abundant with increasing PMF val-ues (Fig. S7 in the supplementary material58). Further analy-sis using the basins IB to IIIB of Aβ42 (Figs. 6(e) and S7 inthe supplementary material58) not only shows similar trendsbut also that the interactions between the CHC region and C-terminal become less abundant with increasing PMF valuesand the CHC region and N-terminal interactions are almostlacking in the structures located in basin IB in comparison tothose in basin IA. For the Aβ28 structures located in basinsIA and IB, the Asp23-Lys28 salt bridge is more stable than theone between Glu22 and Lys28 at a distance of 4.0 Å; however,the difference in stability between these salt bridges is largefor the basin IA structures (Figs. 7(c) and 7(e)). In addition,the Aβ42 structures located in basins IA and IB (Fig. 4(c))present a more stable salt bridge between Glu22-Lys28 ratherthan Asp23-Lys28 (Figs. 7(d) and 7(f)).

We should note that an implicit model of water ignoresthe impact of inter-molecular hydrogen bonding interactionsbetween the solute and solvent on the simulated Aβ structure.Current literature includes simulations of Aβ42 with explicitwater models, however, these are limited in confined aqueousvolume. Generally, these simulations were performed via sol-vating the peptide in water utilizing hydration shells that varybetween 5Å and 20 Å around the solute. These might resultin not representing the bulk aqueous solution environment ac-curately in the small number of hydration shells around thepeptide. Second, the peptide might not be allowed to adoptconformations that would exceed the space available in suchsmall volumes. As described in detail above, our REMD sim-ulations using an implicit water model clearly show that theAsp1-Lys16 and Asp1-Lys28 regions of the full-length Aβ42cannot be completely mimicked by Aβ16 and Aβ28, respec-tively. This finding is not affected by the usage of a struc-tural analysis without the characterization based on the PMFsurface (clustering) or by characterizing the peptide struc-tures utilizing their PMF values along with their RE-E and Rg

values.

IV. CONCLUSION

The calculated thermodynamic properties using eitherharmonic or quasi-harmonic approximations show that theAβ42 peptide structures are more stable than those of Aβ28and Aβ16, and the Aβ28 conformations are more favorablethan those of Aβ16 in aqueous medium. Comparison of thesecondary structural properties of the Asp1-Lys16 and Asp1-Lys28 regions present that the β-sheet forming residues andtheir probabilities vary between the three peptides with a fewnotable exceptions. For example, Arg5 adopts a β-sheet struc-ture in all three peptides and Val12 and Phe19 form a β-sheetstructure in Aβ28 and Aβ42 with differing abundances. Fur-thermore, we observe similar regions of α-helix formation

between the three peptides (Arg5-Gln15) but the probabil-ity difference of α-helix formation is starker between Aβ16and Aβ42 than between the Aβ28 and Aβ42 peptides. In-vestigation of the secondary structure component abundancesof the peptides along their PMF surfaces indicate that the fa-vorability of the conformations of the Aβ28 and Aβ42 pep-tides but not the Aβ16 peptide are associated with the α-helixand β-sheet contents of the peptides. Interestingly, the Aβ28structures located in the two most favorable PMF basins withvarying α-helix and β-sheet abundances are capable of inter-changing their structural characteristics without being ener-getically retarded. Despite, the structures of Aβ42 located inthe two most favorable PMF basins with different α-helix andβ-sheet probabilities have to override large energy barriers tointerchange their secondary structure parameters.

Similar interactions between the residues in the Asp1-Lys16 region are obtained for all three peptides but the abun-dances differ from each other. The intra-molecular interac-tions between the N-terminal region and Glu11-His14 occurin all three peptides and show a decrease in abundance withincreasing PMF values. This might indicate that these interac-tions stabilize the structures of Aβ16, Aβ28, and Aβ42. Lessprominent interactions between the CHC and N-terminal re-gion or Gly25-Ala30 exist in Aβ28 in comparison to Aβ42.The N- and C-terminal regions of Aβ42 both interact with theCHC region but the latter is more abundant and energeticallymore preferred. Interestingly, Arg5 forms many various saltbridges in all three peptides with large abundances. We alsodetect the salt bridge formation between Lys28 and Glu22or Asp23 in the structures of the Aβ28 and Aβ42 peptides.However, their probability distribution shows different trendsfor Aβ28 and Aβ42. Namely, the probability of Asp23-Lys28salt bridge is larger than that of Glu22 and Lys28 in Aβ28but this trend is vice versa for Aβ42. This switch in tendencymight be associated with the switch in the tendencies for saltbridge formation of Arg5 with either Glu22 or Asp23.

Experimental and theoretical studies that use the Aβ16and Aβ28 fragments to mimic the chemical and physicalproperties of the Asp1-Lys16 and Asp1-Lys28 regions of thefull-length Aβ42 peptide in solution should take the variancesthat we report herein into account. The stark dynamic differ-ences that we present for the Aβ16, Aβ28, and Aβ42 peptidesin solution might impact the prediction of their reaction mech-anisms with different species in solution. For example, the co-ordination chemistry mechanism between metal ions and Aβ

might be affected by the varying dynamic structural proper-ties of different Aβ fragments. Currently, we are studying theimpact of the Aβ fragment size on the coordination chemistrywith transition metals and the associated chemical and physi-cal properties of the resulting metalloproteins in solution.

ACKNOWLEDGMENTS

This research was supported by an allocation andcomputing resources provided by the National ScienceFoundation (Grant No. TG-CHE110044) and the financialsupport provided by SALSI-UTSA. The calculations and sim-ulations were performed on Kraken at the National Insti-tute for Computational Sciences. The authors are thankful for

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205101-12 Wise-Scira et al. J. Chem. Phys. 135, 205101 (2011)

support from The University of Texas at San Antonio. Theauthors thank Michael G. Zagorski (CWRU) for the experi-mental data and helpful discussions and Dr. Michael Gilson(UCSD) for helpful discussions. The authors also acknowl-edge Carlos A. Gonzalez (NIST), Jeffrey Hudgens (NIST),and Hank Ashbaugh (Tulane University) for helpful discus-sions related to this project.

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