the aggregation and 
 fibrillation of some intrinsically disordered 
 proteins ( idps ) appear to be involved 
 in the development of neurodegenerative disorders such as parkinson s 
 disease , alzheimer s disease , and type ii diabetes . it has been proposed that -helix - like conformations are important 
 intermediates during amyloid fibril formation . some idps form 
 -helix - like conformations upon association with membranes through 
 a mechanism that involves further aggregation and fibrillation . for 
 example , -synuclein ( s , associated with parkinson s 
 disease ) upon binding to membranes or surfactant micelles forms -helices 
 that appears to mediate s aggregation and fibrillation . for amyloid -peptide ( a , associated with alzheimer s 
 disease ) , the monomer peptide binds to surfactant micelles and lipid membranes , forming -helix - like conformations 
 that facilitate aggregation and fibrillation . similar phenomena occur for other idps , such as medin and islet amyloid polypeptide ( iapp , associated 
 with type ii diabetes ) . idps protofibrils 
 or oligomeric aggregates are more toxic than 
 are the insoluble fibrils . recently , it was shown 
 that the toxic idps protofibrils or oligomeric aggregates form pores 
 in membranes , apparently sharing a common mechanism with antimicrobial 
 peptides ( amps ) . when amps are associated with anionic lipid membranes , 
 many of them also form -helix - like conformations that display antimicrobial activity.an understanding of the 
 -helix formation mechanism of these peptides would help understanding 
 the overall fibrillation mechanism of these idps , as well as help 
 in the design of amps . in this paper , we study the interactions 
 between an undecapeptide 
 xao ( ac  x2a7o2nh2 ; mw = 985 ; x : diaminobutyric acid ( dab ) side chain , ch2ch2nh3 ; o : ornithine ( orn ) 
 side chain , ch2ch2ch2nh3 ) with sodium dodecyl sulfate ( sds ) . the xao peptide 
 was chosen because ( 1 ) it has a large content of hydrophobic residues 
 ( seven ala ) and multiple cationic residues ( two dab and two orn ) , 
 similar to many of those idps and amps . uversky proposed a simple relationship between mean hydrophobicity and mean 
 net charge to predict whether a peptide sequence is intrinsically 
 disordered or natively folded . the xao has a mean hydrophobicity of 
 0.47 and a mean net charge of 0.36 , indicating that xao should be 
 intrinsically disordered . ( 2 ) in aqueous solution , monomeric xao predominantly 
 adopts a polyproline ii ( ppii ) conformation , similar to that of some idps and amps . xao does not exhibit any detectable -helical content , 
 presumably due to its short polyala repeat length and electrostatic 
 repulsion between its flanking cationic dab and orn side chains . the 
 structural similarities between xao and some idps / amps make xao a 
 relevant model to study mechanisms of interactions between these idps / amps 
 and lipid membranes . sds micelles have been widely used as a model membrane 
 to study interactions between idps / amps and lipid membranes . we showed here that xao adopts -helix - like conformations 
 upon aggregating with sds . we used ultraviolet resonance raman ( uvrr ) 
 spectroscopy to determine the structure of the aggregated xao . we measured the diffusion coefficients of xao and sds by employing 
 pulsed field gradient nuclear magnetic resonance ( pfg - nmr ) . based 
 on the stoichiometry and association constants extracted from the 
 diffusion coefficients , we propose a two - state model for the aggregation 
 between xao and sds . the 
 undecapeptide xao was prepared by the 
 pittsburgh peptide facility by using a solid - state peptide synthesis 
 method . sds ( 99% ) , dodecyltrimethylammonium chloride ( dtac , 99% ) and 
 sodium perchlorate ( naclo4 , 98% ) were purchased from sigma - aldrich 
 co. sodium decylsulfate ( sdes , 99% ) , sodium octylsulfate ( sos , 99% ) 
 and sodium pentylsulfate ( sps , 99% ) were purchased from alfa aesar . sodium ethylsulfate ( ses , 98% ) was purchased from tokyo chemical industry 
 co. , ltd . dodecylphosphosphocholine ( dpc , 99% ) and dodecyl--d - maltoside ( ddm , 99% ) were purchased from avanti polar lipids , 
 inc . water ( 18.2 mcm ) was purified by a nanopure infinity 
 ultrapure water purifier . we used a temperature - controlled 
 quartz cuvette with a 0.2 mm path length for 1.0 mg / ml ( 1.0 mm ) samples . the cd spectra were collected at 0.2 nm intervals and averaged 
 over 5 scans and smoothed by the second order savitzky - golay method 
 over 15 data points . briefly , 
 the third harmonic of a nd : yag laser ( coherent infinity ) was anti - stokes 
 raman shifted five harmonics in 40 psi hydrogen gas to 204 nm . the 
 204 nm light is in resonance with the peptide bond first allowed  * 
 electronic transition . the excitation beam was directed to a spinning 
 quartz nmr tube containing the room temperature ( 20 c ) 
 sample solutions . the backscattered raman light was collected and 
 dispersed by a partially subtractive double monochromator and detected 
 by a lumogen coated back - thinned ccd detector ( princeton instruments 
 spec-10:400b ) that is cooled by liquid nitrogen . the sample uvrr spectra 
 were obtained by subtracting appropriate amounts of water and the 
 empty quartz nmr tube uvrr from the raw spectra and normalized to 
 the intensity of the 0.1 m naclo4 internal standard . all diffusion coefficient 
 measurements were performed using a bruker avance iii 600 mhz spectrometer 
 with a bbfo plus probe . the temperatures were controlled to 1 
 c accuracy using a bruker bvt3000 temperature control system . the spectrometer was calibrated against the water self - diffusion coefficient 
 at 25 c . the samples were prepared in d2o and the 
 residual hod resonance at  = 4.70 was used as an internal chemical 
 shift standard . diffusion coefficients were determined using a stimulated 
 echo pulsed field gradient pulse sequence with bipolar gradients . to obtain the diffusion coefficient , the peak intensity versus gradient 
 strength data were fit to the stejskal tanner equation1where i and i0 are the intensities of a specific band ( or the intensity 
 at a specific chemical shift ) with and without the magnetic field 
 gradient ;  is the gyromagnetic ratio and equals 42.58 mhzt for h nuclei ;  and  are 
 the pulse width and pulse interval , ds is the diffusion coefficient of the species in d2o ; and g is the gradient strength applied to the sample . sixteen 
 spectra were taken with gradient strengths that varied between 0 and 
 50 g / cm , while the duration of the gradient  was held constant 
 throughout the experiment . to plot the results as two - dimensional 
 diffusion - ordered spectroscopy ( dosy ) contours with respect to the 
 chemical shift and diffusion coefficient , these 16 spectra were fitted 
 to eq 1 to obtain ds( ) and the intensity i0( ) at each chemical shift . a normal distribution 
 of intensities was generated along the diffusion coefficient axis 
 at each chemical shift . the peak height , center position , and standard 
 deviation of the normal distribution are labeled as i0( ) , ds( ) , and ds( ) ( standard error of ds( ) ) , respectively2 the integrated 
 intensities of resonances from the same species 
 were globally fit to obtain a single diffusion coefficient for qualitative 
 analysis by using eq 1 . figure 1a shows the cd spectra of xao as 
 a function of sds concentration in 0.1 m naclo4 aqueous 
 solutions at 20 c . in the absence of sds , the cd spectrum of 
 xao is similar to previously reported cd spectra of xao in pure water 
 or in low salt concentration solutions . the cd spectra show characteristic ppii features 
 such as the intense negative band at 197 nm . these features 
 indicate that xao adopts mainly a ppii - like conformation in 0.1 m 
 naclo4 aqueous solutions in the absence of sds . as the 
 sds concentration increases , the cd spectrum begins to show -helix 
 features , with two negative bands at 222 and 206 nm and a strong positive 
 band at 190 nm . a well - defined isodichroic point occurs at 
 202 nm , indicating that xao apparently undergoes a two - state transition 
 from a ppii - like conformation to an -helix - like conformation . ( a ) cd 
 spectra of 1.0 mm xao in 0.1 m aqueous naclo4 solution 
 at different sds concentrations . the inset shows the dependence 
 on the sds concentration of the cd spectra 222 nm ellipticity . ( b ) h nmr spectra of xao in 0.1 m naclo4 at different sds concentrations . ( c ) 204 nm excited uvrr 
 spectra of xao in 0.1 m naclo4 at different sds concentrations . the difference spectrum calculated emphasizes the ala methyl group 
 umbrella bending band at 1382 cm . ( d ) sds concentration 
 dependence of the -helical fraction of 1.0 mm xao in 0.1 m 
 naclo4 calculated from the cd , h nmr and uvrr spectra . the negative mean residue ellipticity at 222 nm is proportional 
 to the fraction of -helix - like conformations3to calculate the -helical fraction fh , the 222 nm mean residue ellipticities of 
 the -helical state [ ]h and the ppii state 
 [ ]p need to be determined . [ ]p is the mean residue ellipticity of the xao ppii - like conformation . this value can be obtained from the cd measurement of xao in the absence 
 of sds . the determination of [ ]h is challenging , 
 because 
 it is difficult to force xao to adopt a pure -helix state . the commonly used strong -helix promoting solvent trifluoroethanol 
 ( tfe ) does not induce substantial amounts of -helix . in a previous 
 study , the 222 nm mean residue ellipticity 
 of xao in tfe was measured to be 7000 degcmdmol , which is less negative than xao in 
 10 mm sds . the cd spectrum of xao in tfe does not resemble the pure 
 -helix cd spectra , indicating that xao does not exist in its 
 pure -helix conformation in tfe . another common approach to estimate [ ]h uses eq 4,4where , [ ] = 40000 
 degcmdmol is the mean 
 residue ellipticity at 222 nm of an infinitely long -helix 
 segment ; n is the number of residues ( n = 11 for xao ) ; k is a parameter that accounts for 
 the end effects , since the end residues can not effectively form -helix 
 conformations . k can varies from 4.6 to 6.3 . for the 21-residue polyala peptide ap , k was reported to be 7.6 . the 
 large variance of k results in a large uncertainty 
 of [ ]h estimated for short peptides . the inset 
 of figure 1a shows the dependence 
 of the xao 222 nm ellipticity on the sds concentration in 0.1 m naclo4 at 20 c . the sigmoid shaped titration curve clearly 
 indicates that sds concentrations < 1 mm have little impact on the 
 xao conformation . xao is dominated by ppii - like conformations and 
 shows a 222 nm mean residue ellipticity [ ]p = 850 
 degcmdmol . the ppii to 
 -helix transition midpoint occurs at 3 mm sds . above 
 10 mm sds , the -helix conformation we assign this value to a 
 helical fraction of 0.69 that we calculated from the uvrr spectra 
 ( see below ) , and calculate [ ]h = 18200 degcmdmol . this value is much more negative 
 than that found for xao in tfe , indicating 
 that , as expected , the maximum helical state is not achieved in tfe . figure 1b shows the one - dimensional h nmr spectra of xao at different sds concentrations 
 in 0.1 m naclo4 aqueous solutions . the h nmr 
 peaks of xao overlap . in the absence of sds , the h chemical shifts range from 4.184.42 . the addition 
 of 0.5 mm sds does not affect the resonances of xao ( the triplet at 
 4.0 ppm arises from sds ) . as the sds concentration increases , 
 the peaks shift further upfield with a significantly changed pattern . conformation , the reference chemical shift is 4.26 for the h of both ala and lys . presumably the chemical shifts are somewhat larger for dab and orn 
 than lys due to the fewer methylene groups between the amine group 
 and c in dab and orn . the h chemical shift for the ppii conformation differs little from  random 
 coil  . in -helices , the h chemical shifts of ala and lys decrease 
 to 4.03 and 3.99 , respectively . our observed 
 upfield shifts of xao h resonances upon 
 addition of sds indicate a transition of ppii to an -helix - like 
 conformation , supporting the conclusions obtained from the cd spectra . the 
 uvrr spectra of xao with and without 0.1 m naclo4 are 
 essentially identical ( figure s1 ) , indicating 
 that 0.1 m naclo4 has negligible impact on the xao conformation . we measured the 204 nm excited uvrr spectra of 1.0 mm xao at different 
 sds concentrations with 0.1 m naclo4 at room temperature . the xao uvrr spectrum shows an am i band at 
 1660 cm , an am ii band at 1550 
 cm , overlapped with an interfering molecular oxygen 
 band at 1556 cm , two ch 
 bending bands at 1392 cm and 1373 
 cm , and an am iii3 band at 1255 
 cm . as the sds concentration increases , the am 
 iii3 band frequency slightly upshifts , while the intensities 
 of the am iii3 band and the ch 
 bending bands significantly decrease , indicating that xao undergoes 
 a transition from a ppii - like conformation to -helix - like conformations 
 that show hypochromism . these xao spectra can be modeled as the sum 
 of xao spectra without sds and xao spectra with 100 mm sds , confirming 
 that this transition appears spectroscopically as a two - state system . the uvrr results are fully consistent with the cd and nmr results . the ch bending vibrations are resonance 
 enhanced due to their coupling with n in -helix - like conformations , 
 the ch bending decouples from the n  h 
 bending and disappears . therefore , the 
 ch bending band intensities are mainly contributed 
 by the ppii - like conformation . consequently , the ch bending bands can be used to calculate the ppii and -helical 
 fractions based on two - state modeling . the difference spectrum , 
 shown in figure 1c , between the uvrr spectra 
 of xao at 20 mm sds and 0 mm sds shows a band at 1382 cm , that can be assigned to the methyl group umbrella bending of the 
 ala side chains . we expect that the relative intensity of this methyl 
 group umbrella bending band at 1382 cm is independent 
 of the xao conformation . we fit the xao c-h 
 bending region ( from 1350 to 1420 cm ) of the uvrr 
 spectra at different sds concentrations with three lorentzians . two 
 lorentzian bands at 1371 and 1394 cm model the 
 ch bending band spectra of the 11 residues . 
 a lorentzian band at 1382 cm models the ala methyl 
 group umbrella bending . assuming there are only two states , the -helix - like 
 conformation and the ppii conformation , the ppii fraction can be calculated 
 from the 1371 and 1394 cm lorentzian band intensities 
 at different sds concentrations . the -helical fractions of 
 1.0 mm xao at different sds concentrations calculated from uvrr spectra 
 are shown in figure 1d . when the sds 
 concentration is above 10 mm , xao shows a  saturated  
 helical fraction of 0.69 calculated from the uvrr . -helical fraction of 0.69 indicates that , on average , 
 around 7.6 of the 11 residues in xao peptide are -helical . the 7.6 residue long helical segment most likely occurs as a single 
 segment in the middle of the peptide . helical fraction of 0.69 to estimate [ ]h via eq 3 . with this [ ]h value , 
 we can calculate the xao helical fraction at any sds concentration 
 from the cd spectra . the chemical shifts 
 of the xao h , 
 as discussed above , depend upon the xao conformation . we calculate 
 the first moment , which is the intensity weighed average chemical 
 shift of the xao h nmr bands at various 
 sds concentrations . the first moment decreases from 4.26 ppm in the 
 absence of sds to 4.12 ppm in 20 mm sds . as shown by the cd and uvrr 
 spectra , the xao -helix - ppii transition appears spectroscopically 
 to be two - state . if the first moment of the ppii conformation is at 
 4.26 ppm , and the first moment of the sds  saturated  
 xao conformation ( 69% -helix - like and 31% ppii ) is at 4.12 
 ppm , assuming these two conformations are in the fast exchange limit , 
 we can calculate the -helical fractions of xao in sds aqueous 
 solutions from the first moments of the xao h nmr bands using5where  is the first moment 
 of the xao h nmr band at a given sds 
 concentration . p = 4.26 ppm is the xao ppii conformation h nmr chemical shift and h = ( ( 4.124.26  0.31)/0.69 ) ppm = 4.06 ppm is the xao 
 -helix - like conformation h nmr 
 chemical shift . the calculated -helical fractions from 
 the first moments 
 of the xao h nmr spectra ( eq 5 ) are shown in figure 1d . these -helical fractions are similar to those calculated from 
 the cd and uvrr spectra . figure 2a shows the dependence 
 of the 222 nm mean residue ellipticities of xao on the concentrations 
 of surfactants that have the same anionic sulfate headgroup as sds 
 but different alkyl chain lengths . ses and sps that possess relatively 
 short alkyl chains have negligible impact on the xao conformation 
 even up to 0.71.0 m concentrations . figure 2a shows that the surfactant concentration required to induce 
 the xao ppii to -helix transition decreases as the surfactant 
 alkyl chain length increases . the critical micelle concentrations 
 ( cmc s ) of these surfactants are similarly dependent on chain 
 length . the ppii to -helix transition of xao induced by sos 
 occurs between 50 mm to 120 mm with a midpoint at 
 80 mm , while the transition induced by sdes occurs between 
 10 mm to 40 mm with a midpoint at 17 mm . the 
 transition induced by sds occurs between 1 mm to 10 
 mm with a midpoint at 3 mm . 222 nm ellipticities of 1.0 mm xao in 
 the presence of different 
 surfactants . sds : 
 sodium dodecyl sulfate ; sdes : sodium decylsulfate ; sos : sodium octylsulfate ; 
 sps : sodium pentylsulfate ; ses : sodium ethylsulfate . sds : sodium dodecyl sulfate ; dpc : dodecylphosphocholine ; 
 ddm : dodecyl--d - maltoside ; dtac : dodecyltrimethylammonium 
 chloride . figure 2b compares the dependence of the 
 xao 222 nm mean residue ellipticities on the concentrations of surfactants 
 with identical alkyl chain lengths but different head groups . these 
 surfactants include anionic sds , zwitterionic dpc , nonionic ddm and 
 cationic dtac ( scheme 1 ) . only sds induces 
 xao to form -helices , while the other three surfactants have 
 little impact on the xao conformation , even at concentrations much 
 higher than their cmc s . this suggests that the anionic sds 
 interacts with cationic xao to form -helix conformations through 
 electrostatic interactions with the four positively charged xao side 
 chains . sds 
 aggregates by measuring the dependencies of the xao and sds diffusion 
 coefficients on the sds concentration . the nmr dosy spectra of 1.0 mm xao at 0 , 0.5 mm , 4.0 mm and 10 mm 
 sds concentrations are shown in figure 3 . the 
 intensity of the resonance in the absence of a magnetic field gradient 
 ( i0 , that was calculated via eq 1 ) was plotted as a function of chemical shift at 
 the top of contour plots . along the right is a pseudo chromatograph , 
 indicating the calculated diffusion coefficient associated with each 
 chemical shift . the contour at  = 4.7 ppm with d =  2  10cms derives from hod in d2o . h nmr dosy spectra of xao in ( a ) 0 mm , ( b ) 1.0 mm , 
 ( c ) 4.0 mm and ( d ) 10 mm sds solutions . the calculated one - dimensional nmr spectrum without 
 a magnetic field gradient is shown at the top of each figure . along 
 the right are pseudo chromatographs indicating the concentration of 
 species as a function of diffusion coefficient . in the absence of sds , figure 3a shows 
 xao 
 proton resonances at d = 2.0  10 cms . upon addition of sds , 
 the nmr spectrum shows sds proton resonances . at 0.5 mm sds , monomer 
 sds peak appears in the diffusion chromatograph at d = 4.3  10 cms ( figure 3b ) . as the sds concentration increases 
 ( figure 3c , d ) , the diffusion coefficients of 
 both the sds and xao species decrease , the xao h resonances shift upfield , indicating -helix formation as 
 discussed above . figure 4a shows the 
 dependence of the diffusion 
 coefficients of 1.0 mm xao and sds in 0.1 m naclo4 on the 
 sds concentration . also shown are the sds diffusion coefficients in 
 0.1 m naclo4 ( without xao ) as a function of sds concentration . the sds diffusion coefficient in the absence of xao begins to decrease 
 at 1.8 mm , indicating formation of micelles at a value similar 
 to the cmc of sds in 0.1 m nacl ( 1.62 mm ) . the data were experimentally 
 measured by pfg - nmr ; the curves are calculated by using parameters 
 obtained from experimental data . solutions containing 0.1 m naclo4 , 1.0 mm xao 
 and < 0.5 
 mm sds , show constant xao and sds diffusion coefficients . the sds 
 diffusion coefficient is identical to that of 0.5 mm sds in 0.1 m 
 naclo4 . these results indicate that xao and sds remain 
 monomeric with dxao = ( 2.02  0.01 ) 
  10 cms and dsds = ( 4.30  0.03 )  
 10 cms , 
 respectively ( table 1 ) . measured at 25 
 c in d2o in the presence of 0.1 m naclo4 by pfg - nmr . einstein equation d = ( kbt/6r ) , where  = 1.098 mpas is the d2o viscosity at 25 c . obtained by extrapolating the sds 
 diffusion coefficient to infinite sds concentration in 0.1 m naclo4 without xao . above 
 0.5 mm sds , the xao and sds diffusion coefficients decrease , 
 indicating the formation of xao  sds aggregates . this 0.5 mm 
 sds concentration is significantly lower than the cmc of sds in 0.1 
 m naclo4 without xao , indicating that xao sds aggregates 
 are formed between xao monomers and sds monomers . to confirm that 
 the xao sds aggregate formation does not require sds micelles , 
 we measured the dependence of the xao cd spectra on sds concentration 
 in the absence of naclo4 . removal of naclo4 increases 
 the sds cmc to 8 mm . if the xao  sds 
 aggregation requires sds micelle , it should show a different xao conformational 
 dependence on sds concentration than in the presence of naclo4 . in contrast , we observed a very similar sds concentration 
 dependence ( figure s2 ) . sds aggregation occurs between xao monomers 
 and sds monomers . at sds concentration greater than 5 
 mm , the xao diffusion 
 coefficient remains constant at ( 6.9  0.2 )  10 cms . the sds diffusion coefficient decreases 
 above 10 mm sds due to the formation of sds micelles ( dmic = ( 6.0  0.3 )  10 cms ) . thus , aggregation 
 between xao and sds monomers occurs at sds concentrations 
 between 0.5 mm to 5 mm sds . above 10 mm sds , micelle 
 formation occurs among sds itself as evidenced by the decreased sds 
 diffusion coefficient . the diffusion coefficients of the xao monomer , 
 the sds monomer , the xao sds aggregate and the sds micelle 
 are listed in table 1 along with the hydrodynamic 
 radii estimated using the stokes einstein equation that assumes 
 spherical species . for 
 a system in fast exchange , the apparent diffusion coefficient is a 
 weighted average of the diffusion coefficients of all fast exchanging 
 species6where qi , ci , and di are the stoichiometry , the 
 concentration , and the diffusion coefficient of the ith species ; c = i=1nqici is the total concentration . 
 from the diffusion coefficients of the xao monomer , the sds monomer , 
 the xao sds aggregate , and the sds micelle listed in table 1 , we can use eq 6 to calculate 
 the concentrations of xao monomer ( cxao ) and sds monomer ( csds ) , xao sds 
 aggregates ( cagg ) , and sds micelles ( cmic ) at each sds concentration . the binding 
 equilibrium between xao and sds monomers , assuming only one aggregate 
 species , can be described aswhere kagg is 
 the equilibrium constant for the xao sds aggregate , and a and b are the numbers of xao and sds 
 molecules in the xao sds aggregate . fitting this model 
 with species concentrations calculated using 
 eq 6 at sds < 5 mm finds b / a = 3.9  0.3 , a = 4.3  
 0.1 , and kagg = ( 3.8  0.1 )  
 10 mm . the ratio b / a suggests that in the aggregate , each xao molecule 
 is bound to four sds monomers . each xao  sds aggregate 
 contains 4 xao molecules and 16 sds molecules . as the sds concentration increases , the xao monomer becomes depleted . in contrast , the sds monomer concentration increases until it reaches 
 the cmc and micelles form . if m sds monomers form 
 a micellewhere kmic is 
 the micelle formation constant . fitting this model with species concentrations 
 calculated using eq 6 for sds concentrations 
 from 6 mm to 50 mm finds an aggregation number , m = 38  8 and kmic = ( 1.1  
 5.5 )  10 mm . thus , we 
 estimate cmc = 1.8  0.1 mm , identical to the cmc of sds measured 
 in 0.1 m naclo4 solution ( figure 4a ) . this is close to the reported 1.62 mm cmc of sds in 0.1 m nacl . the presence of 1.0 mm xao does not appear to 
 affect the sds cmc equilibrium . however , xao binds to sds monomers 
 and lowers the effective sds monomer concentration , thus increasing 
 the apparent total sds concentration required to form sds micelles . the 
 diffusion coefficients ( figure 4a ) and 
 the solution species concentrations ( figure 4b ) as a function of total sds concentration were modeled using the 
 parameters obtained above . the sds concentration dependencies of solution 
 species shown in figure 4b can be divided into 
 three regions : no interactions ( < 0.5 mm total sds ) , xao  sds 
 binding ( 0.55 mm total sds ) , and sds micellation ( > 5 mm 
 total 
 sds ) . below 0.5 between 0.5 to 5 mm total sds concentrations , 
 sds binds to xao forming xao the concentrations of aggregated xao and aggregated sds increase at 
 the expense of xao monomer . the sds monomer concentration also increases . however , it remains below the cmc of sds until 5 mm total 
 sds concentration . above 5 mm total sds , the micellation is 
 triggered , and all species remain at constant concentrations , except 
 the sds micelle concentration increases . figure 5 compares the fraction of the aggregated 
 xao calculated from the diffusion coefficients , to the -helical 
 fractions calculated from the cd , h-nmr 
 and uvrr spectra . upon scaling by 0.69 , the fraction of the aggregated 
 xao exactly tracks the -helical fraction , indicating that the 
 xao -helix - like conformation correlates directly with xao  sds 
 aggregation . sds aggregates , some of the 
 xao residues , most likely the flanking orn and dab , remain in a ppii 
 conformation . comparison between fractions of aggregated xao and -helical 
 xao as determined by cd , nmr , and uvrr . figure 6 shows a schematic model for 
 the 
 interactions between xao and sds that lead to -helix formation . the negatively charged head groups of the sds monomers electrostatically 
 bind to the four xao positively charged side chains . this significantly 
 reduces electrostatic repulsion between dab and orn side chains and 
 allows xao to adopt the more compact -helix - like conformations 
 from the extended ppii conformation . this results in a hydrophobic 
 inner core comprised of the sds alkyl groups , while one face of the 
 -helix backbone is probably exposed to water medium . the other 
 face of the xao -helix backbone is buried within the hydrophobic 
 inner core . mechanism of the xao4sds16 aggregation 
 and the formation of xao -helix - like conformations . the four 
 sds alkyl chains bound to each xao partition into a hydrophobic core 
 that minimizes the hydrophobic area exposed to water . neutralization 
 of the flanking xao charges enables -helix formation such that 
 one -helix peptide face is buried within the hydrophobic core 
 while the other face is in contact with the water environment . our results expose some of the 
 fundamental interactions between 
 some idps / amps and lipid systems . our results show that charged side 
 chains of idps / amps electrostatically bind to oppositely charged lipids , 
 forming stable aggregates involving multiple peptides and lipids . this aggregation causes peptide partial dehydration , which increases 
 -helix stability as shown previously . the formation of peptide - lipid aggregates also increases the effective 
 local peptide concentration . indeed , we observed large xao aggregates in solutions containing 
 1 mm to 10 mm sds concentration ( 1 < [ sds]/[xao ] < 10 ) after 
 incubation at room temperature for 3 days . in contrast , aggregation 
 does not occur in pure xao solution during this period . the uvrr 
 spectra contain information on the aggregated xao conformations . 
 by subtracting appropriate amounts of the measured ppii - like conformation 
 uvrr spectrum , we can calculate the pure -helix - like spectrum 
 associated with the aggregated xao at each sds concentration . the 
 pure -helix - like spectra at different sds concentrations are 
 essentially identical ( figure s3 ) , although 
 there is somewhat less inhomogeneous broadening at higher sds concentrations . we thus averaged over these calculated pure -helix - like spectra 
 at different sds concentrations ( s(,csds ) ) weighted by their respective 
 -helical fractions ( f(csds)):7the averaged -helix - like 
 uvrr spectrum 
 ( s( ) ) of aggregated xao is 
 shown in figure 7 . the am iii3 band 
 of this pure -helix - like uvrr spectrum can be modeled by three 
 gaussian bands at 1210 cm , 1238 
 cm and 1270 cm . the 
 1210 and 1238 cm bands probably 
 resulted from turn structures , while the 1270 cm band likely originates from -helix - like conformations . bands resolved 
 am iii region of the room temperature pure -helix - like 
 uvrr spectrum of xao  sds aggregates . this pure -helix - like 
 xao  sds aggregate uvrr spectrum is calculated by averaging 
 the essentially identical pure -helix - like xao uvrr spectra 
 at different sds concentrations as weighted by their respective -helical 
 fractions . the -helix - like uvrr spectrum at each sds concentration 
 is calculated by subtracting the ppii spectrum contribution . the two presumed 
 identical 1270 cm am iii3 gaussian 
 bands derive from the c - terminal and n - terminal peptide bonds in the 
 -helix segment . at 20 c , the am iii3 band frequency depends 
 on 
 both the  ramachandran dihedral angle and peptide bond hydrogen 
 bonding.8where 
 0 depends on the peptide 
 bond hydrogen bonding . to calculate the  angle , table 2 lists the relevant peptide bond hydrogen 
 bonding states in an -helix segment and their respective 0 values . values are estimated from ref ( 77 ) for aggregated 
 xao , we calculated above from the cd and uvrr that 
 7.6 residues occur in -helix - like conformations . thus , there 
 are essentially no peptide bonds where both the carbonyl and amino 
 groups form intrapeptide hydrogen bonds . in the xao -helix - like 
 conformations , there are approximately 4 n - terminal and 4 c - terminal 
 peptide bonds . at room temperature ( 20 c ) , the 0 difference between n - terminal and c - terminal peptide bonds 
 is 5.4 cm ( table 2 ) due 
 to their different hydrogen bonding states . therefore , we fit the 1270 cm amiii3 band to two gaussian bands that are separated by 5.4 cm with identical band areas and identical widths . the 
 low frequency band ( 1267 cm ) simulates 
 the c - terminal peptide bonds , while the high frequency ( 1272 
 cm ) band simulates the n - terminal peptide bonds 
 ( figure 7 ) . we previously developed a 
 method to calculate the peptide 
  angle distribution from the measured am iii3 band . the am iii3 band of the uvrr spectra from single crystal 
 peptides show a homogeneous bandwidth of 15 cm . we deconvolute the am iii3 band into a set of lorentzian bands that have a fwhm of 15 cm . the corresponding  angle associated with 
 the center frequency ( l ) of each of these lorentzian 
 bands was calculated from eq 8 . the probability 
 of an xao peptide bond occurring at a particular 
  angle can be calculated from the intensity of the lorentzian 
 band at this  angle , i():9where  is the resolution 
 interval 
 between  angles that are determined from the spacing ( l ) between deconvoluted lorentzian frequencies l . rewriting eq 8:10 in the absence of sds , xao peptide 
 bonds exist in ppii - like conformations 
 that are fully hydrogen bonded to water . therefore , the deconvoluted 
 am iii3 band in this xao uvrr spectrum can be used to calculate 
 the  angle distributions of the ppii - like xao  sds aggregate 
 conformations by using eq 8 with 0 = 1253.8 cm at 20 c ( table 2 ) . the  angle distribution of the -helix - like 
 conformation 
 can be calculated from the am iii3 band of the xao pure 
 -helix - like uvrr spectrum . to reflect the different hydrogen 
 bonding states of peptide bonds , different 0 ( table 2 ) are used in eq 8 to calculate 
 the  angles from figure 7 deconvolved 
 different am iii3 bands . the aggregated xao  
 angle distributions shown in figure 8 contain 
 a ppii - like conformation centered at 153 
 and an -helix - like region centered at  43. 
 the -helix - like region  angle distributions deviate 
 from a single gaussian distribution , indicating multiple -helix - like 
 conformational states . the 
 black envelope curve derives from the -helix - like  angle 
 distribution , that was fit to four gaussians corresponding to - 
 ( filled with green ) , - ( filled with orange ) and 310- ( filled with cyan ) helices and turn structures ( filled with yellow ) . the blue curve indicates ppii - like  angle distribution in the 
 xao  sds aggregates . we thus 
 fit the -helix - like region  angle distributions of aggregated 
 xao to four normal distributions , modeling the  angle distributions 
 as - , - , and 310- helices and a turn structure , 
 respectively ( figure 8) . three conformational 
 distributions are found at  = 76 , 45 , 
 and 17 , in agreement with the expected -helix - like 
  angles . note torsional 
 force constant is 
 related to standard deviation of the distribution by f = ( rt/ ) . we 
 used cd , nmr , and uvrr spectroscopy to demonstrate that xao , 
 which is predominately ppii conformation in aqueous solution , forms 
 -helix - like conformations in xao sds aggregates . from 
 the uvrr spectra , we calculated the  angle distributions of 
 xao  sds aggregates . we resolved - , - , and 310- helix conformations , a turn structure and a ppii - like conformation . sds aggregation by measuring the diffusion 
 coefficients of the xao monomer , the sds monomer , and the xao the sds monomers bind to 
 the xao peptide , neutralizing the four positively charged side chains . sds4 further associate to from a stable 
 aggregate of stoichiometry xao4sds16 , where the xao adopts a predominantly -helix - like conformation , 
 which also contains turn and - and 310- helices , 
 rather than the predominant ppii conformation of the xao monomers 
 in aqueous solution . our work suggests that the xao  sds aggregates 
 form a hydrophobic core that minimizes the hydrophobic surface area 
 in contact with water . neutralization of the flanking charged side 
 chains decreases the electrostatic penalty for -helix formation . the exterior of the aggregate exposes the faces of the -helix - like 
 xao peptide to water . this self - assembly mechanism may be relevant 
 to the assembly of antimicrobial peptides and intrinsically disordered 
 peptides into membranes .
xao peptide ( ac  x2a7o2nh2 ; x : diaminobutyric 
 acid side chain , ch2ch2nh3 + ; o : ornithine side chain , 
 ch2ch2ch2nh3 + ) in aqueous solution shows a predominantly polyproline ii 
 ( ppii ) conformation without any detectable -helix - like conformations . 
 here we demonstrate by using circular dichroism ( cd ) , ultraviolet 
 resonance raman ( uvrr ) and nuclear magnetic resonance ( nmr ) spectroscopy 
 that sodium dodecyl sulfate ( sds ) monomers bind to xao and induce 
 formation of -helix - like conformations . 
 the stoichiometry and 
 the association constants of sds and xao were determined from the 
 xao  sds diffusion coefficients measured by pulsed field gradient 
 nmr . 
 we developed a model for the formation of xao  sds aggregate 
 -helix - like conformations . using uvrr spectroscopy , we calculated 
 the ramachandran  angle distributions of aggregated xao peptides . 
 we resolved - , - and 310- helical conformations 
 and a turn conformation . 
 xao nucleates sds aggregation at sds concentrations 
 below the sds critical micelle concentration . 
 the xao4sds16 aggregates have four sds molecules bound to each xao to 
 neutralize the four side chain cationic charges . 
 we propose that the 
 sds alkyl chains partition into a hydrophobic core to minimize the 
 hydrophobic area exposed to water . 
 neutralization of the flanking 
 xao charges enables -helix formation . 
 four xao 
 sds4 aggregates form a complex with an sds alkyl chain - dominated 
 hydrophobic core and a more hydrophilic shell where one face of the 
 -helix peptide contacts the water environment .