NMR and ESR study of the conformations and dynamical properties of poly(L-lysine) in aqueous solutions

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NMR and ESR study of the conformations and

dynamical properties of poly(L-lysine) in aqueous

solutions

B. Perly, Yves Chevalier, C. Chachaty

To cite this version:

B. Perly, Yves Chevalier, C. Chachaty. NMR and ESR study of the conformations and dynamical

properties of poly(L-lysine) in aqueous solutions. Macromolecules, American Chemical Society, 1981,

14 (4), pp.969-975. �10.1021/ma50005a015�. �hal-02846226�

valuesofu¡i+l andZy+1were keptat3.8Á, and thoseforcZy+2,

dy+3,and ay+4were _{adjustedbythe triangle inequality.} In

general, the valuesofuyandZyforsmall|Z

-j|havelittleeffect

in constrainingtheconformationof thewhole_protein.

(40) A cutoff distance of 10 A for both the “contact” and

“noncontact”distancesmeans that_u¡¡= _10AandL = _5Aif

d*¡j< 10A, and uy= _40Aand

Zy= 10Aif d*y> 10A. The

triangle inequalities(6)are then applied_{to every set}ofthree

pointstomodify all ofthe u¡¡s andl¡¡s,exceptuy+1andZy+1,

whichare thenused to calculate H.

(41) Sternberg, M.J._E.;Thornton,J.M. J.Mol.Biol. 1976,105, 367. Ibid.1977,110, 269, 285.

(42) Richardson, J.S.Nature(London) 1977,268, 495.

(43) Chothia,C.;Levitt,M.;Richardson, D. Proc.Natl.Acad. Sci. U.S.A. 1977, 74, 4130.

(44) Richmond, T.J.;Richards,F.M. J.Mol.Biol. 1978,119,537. (45) Cohen,F._{E.; Sternberg, M.}J.E.;Taylor,W. R.Nature

(Lon-don.) 1980,285, 378.

(46) Shannon,C.E.BellSyst. Tech.J. 1948,27, 379, 623.

NMR

and

ESR

Study of the Conformations

and

_Dynamical

Properties of Poly(L-lysine) in

Aqueous

Solutions

B.

Perly,*

Y.

Chevalier, and

C.

_Chachaty

Départementde_{Physico-Chimie,} Centred’Etudes Nucléaires deSaclay,

91191 _{Gif-sur-YvetteCedex,} France. ReceivedAugust13, 1980

ABSTRACT: The conformations and dynamical behaviorofpoly(L-lysine) (PLL)inaqueoussolutionshave been_{investigated by} andl8CNMRaswellasby ESRon the end-chain spin-labeled polymer. The ESR allowedthemotionofthe macromolecular chain tobestudied up topH 13,showingthatthe random coil

-* -helix transition_{at pH 11}

gives rise toatwofold increaseinthecorrelationtime,with evidenceofan anisotropic reorientation. Inthe random coil state at_pH7,where the segmentalmotion ofthe backbone

isquasi-isotropic, thecorrelation timegiven by ESRis_{compared to} thatobtained by therelaxationofthe methylprotonsofthe reduced Tempo radical residue and of thea carbons. Thedifferentmethodsyieldan activationenergyof6.5 kcalmol"1forthis motionwhereas_{the frequency dependence}oftheCarelaxation

maybe _{interpretedby}a Cole-Coledistribution of correlationtimes witha width_parameter = _{0.7. The}

rotationalisomerism and temperaturedependencesofinterconversion ratesofthe aminobutylsidechains

have beenanalyzed from theproton vicinalcouplings and the13Cand relaxation atdifferentfrequencies, assumingthatthe methylene groups undergo120°jumpsamongthreesites,twoofthem being equiprobable. Thesetwokindsof informationconcur toshowthatthePLLsidechainsare lessflexible thanahydrocarbon chainofsame _{length, possibly}becauseofthe_{hydration of}the NH3+terminalgroup.

Introduction

Among homopolypeptides, whichmaybeconsideredas

the simplestmodels

for natural

proteins, poly(L-lysine)

(PLL)

hasbeen _subjectedto a _{great deal}

of

_studyon its

conformational_propertiesas wellasits_{biological activity.1}

In

aqueoussolution, poly(L-lysine) isknown to exist in

several forms, namely,random coil,a _{helix, andßsheets,}

depending upon

pH

and_{temperature. The random coil}

—*·

-helix

transition which_occurs around

pH 11hasbeen investigatedby several

NMR

techniques,2in particularby

chemicalshifts3and 13C

_longitudinal

_relaxation,4the

latter

_{method giving semiquantitative information}on the segmental

mobility of

thepolymer. More recently, poly-(L-lysine) in the

-helix

formwas taken as a model in a

theoretical study ofthemotion

of

an _alkylchainattached

toa

_rigid

_{rod undergoing}an _{anisotropic overall}motion.5

The presentworkdeals_mainly

with

_{the dynamical}

be-haviorandtheconformational_propertiesofpoly(L-lysine)

in

therandomcoilstate by and13C

NMR

and

relaxa-tion,i.e.,below

pH

(orpD) 10,wherewell-resolved spectra

maybe obtained. Special

attention

hasbeen_paidto the

relationship between the nuclear relaxation data, the

proton vicinal

coupling constants, and the

rotational

isomerismabouteach

of

theC-Cbondsofthe_aminobutyl side chains.

Asa_{complement to the}

NMR

studies,ESRexperiments

on the spin-labeled polymer provide a _{straightforward}

determination

of

_{the segmental}motion

of

themain chain in both random coil and

-helix

structures. A

direct

comparison

with

proton relaxationdatahasbeen_provided

0024-9297/81/2214-0969$01.25/0

bya _{diamagnetic analogue}

of

the spin label.

Experimental

Section

Materials. Poly(L-lysine)has_{been preparedbypolymerization}

of L-lysine, the e-amino group being protected by

trifluoro-acetylation. Thisprocedurewas preferred to theoriginalone of Fasmanetal.6becausethe group mustberemovableundermild conditions, particularly in the case ofa spin-labeled polymer. N‘-(Trifluoroacetyl)-L-lysine was _prepared from _{L-lysine and} S-ethyltrifluorothioacetateaccording to theprocedureofCalvin et al.7 Conversion to N‘-(trifluoroacetyl)-L-lysine N-carboxy-anhydride(N'-TFA-L-Lys-NCA)was _{performedby treatment}with

4Mphosgenesolutionintetrahydrofuran.8 Priorto use NCA was _{recrystallized} from ethyl acetate/petroleum ether. N'-TFA-L-Lys-NCA [2.68g (10"2mol)] was dissolved in25 mL of anhydrousdimethylformamide. Afteradditionof10_mg(10"4mol) of n-hexylamine(monomer/initiator ratio=

100),polymerization was _{allowed to proceed at}room _temperatureundercontinuous stirring for2days. Precipitationin100mL ofwater yielded2.0

g(89%) of poly[N'-(trifluoroacetyl)-L-lysine]. Thetrifluoroacetyl group was _{removed by dissolving}0.34 gof

poly[N'-(trifluoro-acetyl)-L-lysine] into 7.5 mL of a 1 M piperidine solution in

methanol. After2_h,5mL of1M_{aqueouspiperidine}was added dropwise understirringtothelattersolution. After2_{days, the} resultingclearsolutionwas _{dialyzed for}5_{daysagainstcirculating} distilledwater at 5 °C andthen againsta 10"3M _{HC1 aqueous} solutionfor2_{days. Finally}thesolutionwas _{freeze-dried, yielding}

205 mg(80%)ofpoly(L-lysine)hydrochlorideas awhite fibrous material.

The spin-labeled poly(L-lysine) (Tempo-PLL)was synthesized following thesame _procedure as _reported above, replacing

n-hexylamine by 17 _mg (10"4 mol) of 4-amino-2,2,6,6-tetra-methylpiperidinyl-N-oxy(Tempo)asinitiator. _{The diamagnetic}

970 _{Perly, Chevalier,} andChachaty Macromolecules H(NH-CH-CO)„-NH (ch2)4 NH3CI" CH3 --S^-CH; Tempo-PLL

analogue of Tempo-PLL was obtained by adding to a 0.1 M solution of PLL 2 _equivoffreshly prepared sodiumascorbate

solution. Thereductionofthe Tempo group to

ch3/CH3

N—OH

ch3 ch3

occurredalmost immediately,as checkedby ESR. Theexcess reagentwas _{removed by dialysis for}5_daysagainstdistilled water at 5 °C.

The molecular weightsofthe polymerswere _{determined by} measurementoftheintrinsicviscosity of1MNaCl solutionsof

PLLatpH3,6yielding125<DP<145,accordingtothe samples.

The ESR measurementsofradicalconcentration in the

spin-la-beledpoly[TVf-(trifluoroacetyl)-L-lysine] yieldedaDP of146. After removaloftheTFAgroupsweobtainedaDP of138,showingthat

thereis_virtuallyneither chain degradationnor deletionof radical end groupsinthecourse of piperidine treatments. Likewise, the integratedintensity ofthemethylprotons in the diamagnetic reducedformsof Tempo-PLLgivesaDPof140. Sinceallthese

polymers were _{prepared under} identical conditions

([mono-mer]/[initiator] =

100),we _mayassume thatthe_{average degree} of polymerizationof the PLLunder studyis 140,witha com-parativelylow polydispersity.9

NMRand ESRExperiments. ForNMRexperiments,astock

solutionofPLLwas _{prepared in D20 after}treatmentat pD7.5

withChelex 100_{chelating resin to}remove _{metallic impurities.} The solutionwas then twice freeze-dried from99.8% D20 at pD

7(pHmeter reading). Beforeuse,PLL hydrochloridewas dis-solved in99.95% or 99.8% D D20for and13C_experiments,

respectively. AfterpDadjustment the solutionwas flushedwith drynitrogengasintheNMRtube toremove dissolvedoxygen.

AllNMRmeasurementshave been_{performed in the Fourier}

transformmode_bymeans of Bruker WH90[H13C) = _22.6MHz],

Varían XL-100

_M'H)

= _{100 MHz], and} CAMECATSN-250

[y(13C) = _{62.86 MHz,i/(*H)} = _{250MHz] spectrometers.}

Thelongitudinalrelaxation times, Tx,were obtained by the inversion-recovery method(180°-t-90°sequences),theinterval

between_{each sequence}being atleastequal to5TX. The nuclear

Overhauser enhancements (NOE)were _{obtained by the inverse} gated decoupling method,with long-durationaccumulations to ensure a _{signal-to-noise} rationot less than50 for the spectra

recordedwithoutenhancement. The actualaccuracyoftheNOE

measurementsis±5%. Inallexperiments,theprobetemperature was _regulatedwithin ±1 °C.

The ESR experimentson _Tempo-PLLwere performedwith aVarían E-109X-band_{spectrometer, the magnetic}fieldbeing calibrated bymeans ofa _{Varían F-8 magnetometer.}

Results

and

Discussion

Motion of the Macromolecular Backbone

and

the

Random Coil

->·

«-Helix

Transition.

The

conforma-tional

changes

of

poly(amino acids) in solution, in

par-ticular

PLL

andPLGA,have beeninvestigatedbya

va-riety

oftechniques,1including NMR.2 The random coil —*· «-helix

transition

_isclearlyevidenced by_asharp

var-iation

of chemical shifts.3 Similar measurements

performedon the polymer understudy (DP = _{140) gave}

us a

transition midpoint

_{at pD} 10.8. This

transition

has been alsostudied by 13C _Tx andchemical

shift

determi-nationsasfunctionsof_pH,4butthe broadeningofthelines

Figure1. pHdependenceofthereorientation correlation time of thenitroxideterminal_{group in}0.1_{M Tempo-PLL}measured

by ESR at5°C.

precluded experimentson the

-helix

formabove_pD11.

For the measurement of the changein thesegmental

mobility of

themain chain

of

PLL

atthe random coil-*

-helix

transition,

it

seemedto us

that

it

was preferable

to performESR experimentson _Tempo-PLLupto pD13

on

dilute

(<0.1

M)

H20 solutions. Above

pH

11, the

precipitation of PLL

inthe /3-sheetform was avoidedby

cooling at 5 °C.10 Undermost

of

our _experimental

con-ditions, the

nitroxide

radical at the chain end gives rise to _{three equally} spaced ESR lines (absorption

first

de-rivative),the _peak-to-peak

width

of whichdepends upon therelevant nitrogen quantum numbermN= _0,±1.

FromAvma, thereorientation correlationtime rcmaybe

obtained bythe relation11

= _T2~l(mN)

_{[3 2/20}

+

_{%5( 0)2}

+ (b2/8)mN2 -yi5bAyB0mN]Tc +

X

(1)

with

b = _(4tt/3)[A2Zn -y2(AZIN + AyyN)] =

2 (

-Aj4)

(2)

7

=

_-{e/h)[gzz

-y2(gxx + _gyv)] = _{(3/3/2ft)(szz}

-g¡J

(3)

In

_eq 1, B0,the static magnetic field,is 3250 G,and b

and

_{represent theanisotropy of the}

A

and g tensors, respectively. AieoN = _{47 MHz,}

AZZN = _{99.9 MHz,}

giao =

2.0055, andgzz = _{2.0022 were readily obtained from the}

ESR spectrumof Tempo-PLL inaqueoussolutionatroom

temperatureor frozenat100K.

X

isthecontribution to theelectron transverserelaxationrate

_Tf1,

independent of _tc.

70,7+,and

L

being the amplitudes of themN = _{0, +1,}

-1 ESRlines (absorption first derivatives),

it

is shown12

that

two correlation times may be obtained from the coefficients of_{m^ and} mN2 in eq 1: 15T2 8b AyB0 AT.

sier-te)·]

rifé)"*®"'-]

(4) (5)

The differencebetweenrcand rc* isacriterion for the

anisotropy ofthe motion

of

the

nitroxide

group.13

Figure 1 gives the

pH

dependence of the rc and t*

correlation times, which show a _{steep increase at} the

Figure2. (I)13CNOEat22.63MHz

_{( )}

and_7\relaxation times at 62.86

_(·)

and 22.63 MHz (O). The solid lines have been

calculatedforthe Cole-Coledistribution ofcorrelation timestr

(7= _0.7),taking

TR= 7.57X10"16exp(6500 calmol^/RTls. (II) Temperaturedependencesofcorrelation timesfR(dottedline) andtc,thelatterbeing obtainedfromESR linewidths (O)and methyl proton relaxation ofthereducedTempo group

(·).

These

diagrams are _givenfor PLL in the random coil state atpH 7.

H20, instead

of

pD10.8inD20 (meter reading;see_above), so

that

we assume as_previously14

that

_pD a¡ _pH.

At

room

temperature below

_pH

11,in the random coil form,

iso-tropic

motion is observed,

with

tc = _tc* =* 5 X 10"11 s,

whereasa marked anisotropy effectappearsabove_pH11,

with

tc 1.5 X 10'9_{and tc*} =* 2 X 10"9s. The

reorien-tationcorrelation timesinthe

-helix

formare _{significantly}

shorterthan_expectedfora

_rigid-rod

_{form, the diffusion}

coefficients

of

which are15

n 3kTM03

\

i(2V/2Md\

ZflX

D±

~

2 3 *[2

lis)

MqR /

!J

(6) D„ =

kTMoJ

6M02R2 ,

Z/2V/2Md\l

_

4 2

_[

Md2

_nV3Z

_MoR/

_\

1

M0and

M

are the_{molecular weights}

of

the monomer

residue and

of

the polymer,respectively;

M/M0

= _140,

d,

the increment

of

the _{helix lengthper} monomer residue, is 1.5_Á,R,thehelix radius, is 7.5_{Á, and , the viscosity}

of

waterat278_K,is 1.512cP. From _eq6and7,D± = _6.8

X 10sand _D\\ = _{1.7 X 107 rad s™1. Although and}

D±

cannotbe _{obtained by ESR}

in

the_presentcase sincethe

orientation

of

the

N-0

group

with

respecttothe

macro-molecule backboneisnotknown,

it

isseen

that

_tcandt*

are much smaller indeedthan2.7X _{10"8 s,}the value_{of (tc)}

=

y2(z)|| +

2D±yl.

The ESR measurements on

PLL in

the random coil stateindicatea_{quasi-isotropic motion}

of

the chain_end,

with

tc = t* (Figure _1).

This

correlation

time

_mayalso

becalculatedfrom the

longitudinal

relaxation

of

methyl protons in

Tempo-PLL

after reduction byascorbic acid. Sincethecorrelationtime fortheaxialreorientation ofCH3 is most

likely of

the order of 10™11 s or _less,

it

_may be

shown16,17

that

the relaxationrate

of

a_{proton pair}

of

this

group is 1

*7 4^

80r6 (3 cos2 -l)2

[

2tl 1 +

2 2

8rR

I

1 + _{4o>h2tr2 J} (8) where tr isthe correlation time forthe segmentalmotion atthe chain endsand

_,

the angle betweena

H-H

vector

andpH7,

and therotationaxisof_{CH3, is90°. Figure}2-IIshows

that

thereisan excellentagreement betweenrcandrRwhich

are closetothemean correlation time _{fRdetermined by}

13C relaxation

for

the _segmental motions

of

the whole chains. The

longitudinal

relaxationofa carbonsisgiven

by18

l/

—

% 7 27 2 2 ~6[1( (

_

)

+ 3Ji(cvc) +

6«/2( +

_)]

(9)

The nuclear Overhauser enhancement ofcarbons ob-served _{under proton}noise_decoupling is18

NOE = ^ + 6»72(^ + wc) ~ Jo(fa>H ~ wc) 7c

=^ (

~

)

3e/i(tóc) "b _{6«^2( +}

_^c)

In

eq9and10the J(w)are _{the spectral densitiesexpressed}

as a

function

of

_proton andcarbon

Larmor

angular

fre-quencies. The13Calongitudinal relaxationandNOEhave

beenmeasured at

different

temperatures at

pH

7,where

PLL

is_{entirely in}therandom coilstate.19 The_comparison of the data obtained at 22.6and 62.86

MHz

_(Figure 2-1)

suggeststhe existenceofadistribution ofcorrelation times represented by a

function

_G(tr),

the spectral densities

being expressed as

J(*>)

TrG(tr)

Jo

1 +

_{2 2}

E

01)

We assume, as in previous works14,20,21 a Cole-Cole

distribution.22 Therefore, the spectral densityis_givenby23

_1__cos

[(1

-7)(tt/2)]_

2a> cosh ₍₇ In

)

sin [(1

-7)( /2)]

^

where 7 is a _{parameter characterizing the}

distribution

width

and tr is the central value

of this

distribution.

The NOEand relaxation time as a

function of

_1/T

at _{the two spectrometer frequencies} are consistent

with

7 = _{0.7 and tr} = _{7.56 X 10™15}

exp(6500/RT). Thesame

activationenergyof6.5kcalmol-1isfoundin_ESR,

_,

and 13Crelaxation_{experiments (Figure2),}thecorrelation time

at the chain_{end given by the}two _{former methods being}

shorter by only

~12%

thanfR. The motional freedomat

chainends is therefore

slightly

higher than the average segmental

mobility

ofthe macromolecular backbone. Here again,therelevant correlationtimefRismuch smallerthan

972 _{Perly, Chevalier,} and Chachaty Macromolecules

Figure4. Proton NMRspectrum at250_{MHz, pH}= _7,and T = ₃₅₀K. The lower_{tracehasbeensimulated}withthe_parameters

ofTable I.

Figure5. Classicalrotamersabout theC-C bondsoftheside

chains.

where is the HCCH dihedralangle.

The populations

of

the classical

T

(trans), G, and G' (gauche)rotamersabout theC-Cbonds

of

thesidechains (Figure 5) are related by

PT+ PG + PG'

= _{1 G5)}

TableI

ProtonChemicalShiftsand _CouplingConstantsofPLLat 350KandpD 7 Usedin the Simulation of the NMR

Spectrum of PLL (Figure 4) ChemicalShifts”

Hq _{Hgi Hg, Hy, Hl2 H6||,}

HCi~

4.30 1.756 1.827 1.420 1.394 1.673 2.989 CouplingConstants6 Jaa =6.06 JaR = 7.76

Ja"

= 6.50

Jal

= 7.70

4‘

= 7.07

4e

= 7.56 =Z#3,|32 = ‘/7172= ‘/5152 = ^1e2= -14 “ _In

ppm from sodium 3-(trimethylsilyl )propionate-2,2,3,3-dt. 6InHz.

expectedfromthe overalldimensions

of

the macromole-cule, the gyration radius

of

whichis

(Rg2) =

)

₍₁₃₎

For DP = _140, l= _3.77Á (length of_{themonomer unit),}

and

K

= _{1.324 one finds}

(fiG2)1/2 = _{50.8 Á. For a}

rigid

spherical structureat20°Cin_aqueoussolution,one should haveindeed_rR= _{1.3X 10"7sinstead}of_{theobservedvalue}

of

5 X 10"10 s.

Conformations and Segmental Motions of

Side Chainsat

pD

7. Therotamersofthesidechain andtheir

interconversion rateshave beendetermined by and13C

NMR

relaxation. The 250-MHz

NMR

spectrum

of

PLL

at350

K

andpD7isshownin_Figure4. Underour

experimental conditions, the Hs and

resonances are

partially

superimposed,givinga_{complexpattern,}thetwo

componentsof whichhave been separatedby

inversion-recovery (Figure3). Fortime intervals of0.145and0.27

sbetween the180° and_{90° pulses,}theßand resonances are _{successively canceled,} allowing the other one to be selectively observed. The

NMR

spectrumof

PLL

has been simulated bymeans

of

theSIMEQprogram from

Va-rían, using the parameters given in Table

I

(Figure 4).

The proton vicinal couplingconstants have been inter-preted in terms

of

rotamer _{populations about the C-C} bonds,takingsJt= _12.4Hz_and

3=/g= 3.25Hzasgivenby

Kopple’s modification

of

the Karplusrelation25

Vhh

= 1L0_cos2 - 1.4

cos + 1.6 sin2 (14)

Thecouplings betweenthe a and_{ß protonsyield}

PT J«Ai ~ Jg

«W,

(16a) andtherefore Pg =

Jt

+

J.

-(Jalj ß1+ JaB)

Jt-J«

For theß and y protons, we have likewise

Pt

= 'Am 'Am

JfJg

ß

JfJ,

Pa' = Jt.

-J.

Pr

= ;A2T1 ~ _°

Jt

-J,

(16b) (17a) (17b) (17c) These_{populations may}bealsoexpressedasfunctions

ofthemean _{coupling constantsJBiy}=

VzCJflm+ and

ß

=

VziJ^n

+ J&tr) obtainedfromthesimulationofthe

NMR

spectrum

of

PLL

(Table I) Pg 2(Jait “ Jg)

Jt'Jg

(18a) P<y = 1 -2(Jfl87 ~ Jg)

Jt-Jg

(18b) PT = 2(Jai7 + Ja27 -2Jg)

4(J8y-Jt)

-7-7.--=

TV

" where_JBy = l/2(Jfsiy +

_J^)·

The Jgm andJs^2,whichare not directlyavailablefrom

the _analysis

of

the

NMR

spectrum of

PLL,

may be

ob-tained by combining eq 17 and 18

^ß ~ — 2^27 (19a) ^0272 ” ~ 2«/^i7 (19b) ^172— ^271 " ~

^av

(19c) where Jav = _(Jt+ 2Jg)/3.

Table II

Rotamer Populations of PLL Side ChainsObtained from Vicinal CouplingConstants

population Ca-C(3

Pt°

= 0.32 _Pc'a= 0.49 PG= 0.19 PT = 0.68 PG' = 0.03 _Pq= 0.29 C7-Cs Cs-Ce PT = PT = 0.67 0.88 PG + _pG'= 0.33 PG + _Pg' = 0.12 ° _Tentative assignment.

Figure6. (I)/3-carbon27\relaxation timesat22.63 (O)and62.86

MHz

(·).

(II) /3-proton T\ relaxationtimes at250 MHz. The solid lineshave beencomputedwith_{parameters of Table}III. In this figureandthe_followingones the13Crelaxation timesare _given astwicethe actual valuesincethe methylenecarbonsare relaxed by the two adjacent protons.

For the_{(CH2)7(CH2)j(CH2)t residue, where}onlyJySand

Jjeare _{available, the population of the trans rotamer} is given byan _expression similarto (18c).

It

isseen from_eq15-19

that

sincethe measuredvicinal couplingconstantscannotbegenerallyassigned togiven

proton pairs,thedetermination of the population

of

the three rotamers is achieved _{only for the (CH2)s(CH2)r} fragment. Inthecase ofthe

_(CH^CH^

residue,however, the G' rotameris_likelythemostpopulated,26asconfirmed

by experimentsinprogresson _{the paramagnetic relaxation}

induced by Gd3+ in

-amino

acids and _{oligopeptides.}

Among the rotamers about the

Cr-C{

and Cj-C,bonds,

only the population

of

thetrans ones can bedetermined

unambiguously. The populations

of

differentrotamersof the

PLL

side chains are _given in Table

II.

The protonand13Crelaxationtimesinsidechainshave been_interpretedby assuming

that

rotationaljumps about

C-Cbondsoccur between threesites,twoofthem, denoted

as 2 and 3, being equiprobable. The motion about the

thesebondsis _specifiedby the

_jump

rates (site 1 -*

site 2 or 3), W2 (site 2 or 3 -* _site

1), W3 (site 2 ^ site 3)5,20,27

jn

these calculations,

it

is assumed

that

site 1

corresponds to the trans conformer

of

the

C-C-C-C

fragments.

The populations

of

the sites are _{given by}

Pi

=

_V(2u

+ ₁₎

P2 =

P3 =

/(2

+

1) (20)

with

=

W1/W2; W3hasonlyan influenceon the effective

correlation times governing the relaxation of side-chain nuclei. The expressions

of

the spectraldensities

inter-vening in eq 9 and 10, whichdepend also on the

distri-bution of

correlation times _rR, maybe found in

ref

20. As _{pointed out} previously,21 the determination

of

Wh

W2,and W3 hasto bedone by relaxationmeasurements

at

different

spectrometer frequencies and preferablyon

different

nuclei. We havethereforedeterminedforeach

of

the methylene groups the 13C relaxation at 22.6 and

Figure7. (I)

2 ,

of_13Crat22.63 (O) and62.86MHz

_(·).

_(II) ProtonTx relaxation times at100 (O) and250MHz

(·).

The solidlinesare _computedwiththeparametersofTable . Inpanel

Ithedottedline corresponds to WJW2= _{0.232(parameter}

ob-tainedfrom_Vhh).Vf0 = 7 X 1011 s ,andAH= 3.7kcal/mol for

a _{spectrometer frequency}of62.86 MHz.

Figure8. _(I)

₂

of13C{at22.63 (O)and62.86MHz

(·).

The solid linesare _computedwith_{the parameters corresponding to} modelsIandII ofTableIII. (II) -proton 7\relaxationtimes at 250MHz

(·).

Solid line, modelI; dottedline, modelII.

Figure 9. (I)

2

relaxationtime ofC,at 22.63 (O)and62.86

MHz

(·).

(II)

ofH, at100 (O)and250MHz

(·).

Thesolid linesare calculatedwiththe parametersofTableIII formodels IandII.

62.86

MHz

as wellas the relaxation at250

MHz

and insome cases at100

MHz

also_{(Figure 6-9). The} meth-ylene protonsbeing separated by only 1.78

Á

(for

C-H:

C-H

= _{1.09 Á,}

H-C-H

= _109.5°),

their mutual dipolar

interactionisthe mainrelaxationmechanism. The

long-itudinal

relaxation

of

these_protonsis_{nearly exponential;} i.e.,thereisno _{significant deviation of}the_{semilogarithmic}

plot of

(M0

-MZ)/2M0 from the tangent at t = _0. The

contribution of

_{vicinal protons to the relaxation}

of

meth-ylene protons, whichisappreciably reducedby therotation

01I_i_i___i_i-1_i_i_i—

28 30 32 3i. 36

974 _{Perly, Chevalier,}and_Chachaty Macromolecules TableIII

Rotamer PopulationsandKinetic ParametersofPLL Side Chainsfrom ‘H and 13CRelaxationMeasurements P,= _P, Ca-Cff Cfl-C-y Cy-Cfi c5-ce f0.67 <0.88 0.2 0.5 II (0.2 10.2 (0.165 <0.06 0.40 0.25 =1;o.4010.40 (W,)o,·-1 W,(300 K),

s"1 _WJW, kcal mol"1

# , 2,

_(W,)o. s'1

W3(300 K), s"1

*

3, kcal mol"1 _r*HH, A Ca-Cp 2.5 X 1015 4.4X 107 2 10.6 5 X 10“ 6 X 10’ 4.0 1.738 C0-Cy 5.0 X 10“ 1.4X 109 0.5 3.5 a a a 1.730 Cy-C’S(I) 4.0 X 10“ 2.9X 109 0.25 4.3 a a a 1.710 Cy-CS

(II)

1.2 X 10M 1.3 X 10* 2 10.9 2.5X 10'4 1.4X 10“ 5.8 1.725 C8-Ce(I) 1.0 X 10M 3.8X 109 0.07 6.05 a a a 1.730 C8-Ce(II) 1.2 X 10“ 1.3 X 10s 2 10.9 7.0X 10“ 7.1X 109 8.2 1.740

The2 3transition rate is_probably too slowcompared with _Wli2 to _{influence appreciably} thenuclearrelaxations.

aboutC-Cbonds,was taken

into

accountbyintroducing inour calculationsan effectiveinterprotondistance_slightly

smallerthan 1.78Á. This correctionhasbeendiscussed elsewhere.21

The temperature dependences of the 13C and _Tx

relaxation timeshave been_{simulated byassuming}

_jump

rates

of

the form

W; =

(W,)0

exp(AHi/RT)

(21)

with

i = _1-3,

_{being thepotential barriersbetween}the

sites (Figures6-10). Agood agreement betweenthe

ex-perimentalandcomputed relaxationratesisachievedby

taking

WJ

W2constant inthe investigated temperature

range,285 <

T

< 360K. This approximation implies

that

the differencebetweenthe potential barriersAHX (1-* _2,

3) and AH2 (2, 3 — _{1) is}

comparatively small.

In

a

hy-drocarbon chainAHx

-AH2isindeedoftheorderof0.5-0.6

kcal/mol.24

The populations

Pw

oftherotamersaboutC-Cbonds

of

thesidechainas wellas thekinetic_parametersfor the

rotational

_jumps,deducedfrom the relaxation data,are

given in Table

III.

Thecalculationshave been

first

carried

out by introducing thevaluesof

_WJ

W2derivedfromthe

rotamerpopulations givenby the Kopple’srelationship(eq

14)andadjustingthejumprates _{W1; W2,}and W3

until

the

measured relaxation rates are

fitted with

an _accuracy

better than±5% atdifferent temperatures (Figures6-9).

This

process yields a _{satisfactory agreement} for the

re-laxationsofC9and HdlH6 (Figure6). Onthe otherhand,

the value

of

0.232 givenby

vicinal

couplings for Wx/W2 isnot convenient for the

rotation

about_C^-C7. A better

agreement between the observed and computedrelaxation rates

of

_Cy,

_Hw

₂

isachievedbytaking Wx/W2 = _0.5.

Thisdiscrepancy resultspossiblyfromthe large difference between thepopulations oftheGandG'rotamers(Table

II),

whichcannotbetakenintoaccountinthecalculations

of

relaxationrates. Ontheotherhand, therotamer pop-ulations about C7-CjandCs-C< derivedfrom the

vicinal

couplingconstantsseem

_fairly

consistent

with

the

relax-ationsoftheprotons andcarbonsofthe5-_{and e-methylene}

groups.

It

may be _{pointed out in}

particular that

the conformation

of

the

_C7-C6-C-N

residue is _{nearly trans} and

that

the effective

_H{-H,

distance, whichaccountsfor the proton relaxation, is _actually

that

of the trans

con-former

of

an

_alkyl

chain.

Several attempts have been made to check whether significantly

different

setsofparameterscan _give

reason-ablefits

of

the_temperaturedependenceofrelaxationrates. These attempts have not been successful for ß- and

-methylene

groups.

It

appears, however,

that

two sets

of parameters are convenient

for

(CH2)j and (CH2)e.

Figure10. 2TXrelaxationtimeofC<calculatedforaspectrometer

frequencyof125MHz(H0=11.75T) withthedataof TableIII.

The solid anddottedlines correspond to models I andII,

re-spectively.

One set, designated as

I

in Table

_III,

derived

_{in part}

from proton vicinalcouplingsas shownabove,corresponds

toan _{increasingpopulation}

of

the localtrans conformer from the macromolecular backbone _{through the amino} group

of

sidechains. The otherset

(II)

correspondstoa

segmentalmotion occurring by fastexchangeamongthe

two _equallypopulatedconformers

with

_PT< PG. TheW3

jumpratebecomestheneffectiveintherelaxationprocess. Figures8and9showthatthe agreementofmodels

I

and

II

with_experimentis_{equivalent, the}curves _computed

with

the correspondingsetsofparametersbeing superimposable except

for

Hs, where a small deviationbetween the ob-served and computed relaxation times is observed

for

model

I

as _{the temperature} increases.

It

shouldbe_expected

that

thediscriminationbetween these two modelscan be_{performed by}means

of

a

spec-trometer operating ata_magnetic

field of

the order

of

10

T, which isnow available. _Figure10shows

that

the

dif-ferencebetweentherelaxation times computedforC{

with

Wx/W2 =* 0.250and2isnot sufficient tomakean

unam-biguous choice between thetwomodels. Model

II

maybe

ruled out as _incompatible

with

the3JHh couplings given in Table I, even

if

_eq 14 is not

strictly valid for

the

(CH2)7(CH2)6(CH2)efragment.

This

exampleshows

that

the analysisofvicinalprotoncouplingsintermsofrotamer

populationsis sometimes essentialin the

interpretation

of

relaxation data.

Conclusions

The magnetic resonance _{study of}

PLL

in

_aqueous

segmental

mobility

inthe random coilstate and remains

flexibleeven inthe

-helix

form,up to pD 13. The

acti-vationenergyforthe segmentalmotion ofthemain chain isoftheorder

of

6

_kcal/mol

at pD7,like poly(L-glutamic

acid)14andpoly[N5- (3-hydroxypropyl)-L-glutamine]21

un-dersimilar conditions, confirming

that

in therandomcoil statethe

_flexibility

of polypeptidesisnearly independent

of

the nature ofside chains.28

The

rotational

isomerism andthe

_jump

rates of

side-chain methylene groupare _quite

different

fromthoseof a _{hydrocarbon chain attached} to a macromolecule,29,30 showing, in

particular, for

model

I

of_segmentalmotion, which seems the most likely, a _gradual decrease

of

the reorientationalfreedomfromthemainchain_throughthe

terminalgroup.

In

the presentcase_{the comparatively slow}

rotation

of

(CH2)fmaybeexplainedbythe highhydration

degree

of

the adjacent ND3+group, whichhas been evi-dencedby NMR.31,32

Acknowledgment.

Weare _{greatly indebted to Dr. H.}

R. Wyssbrod for his

helpful

comments and suggestions concerning theinterpretation of vicinalcoupling constants

in terms

of

rotamer populations. References

and

Notes

(1) Fasman, G. D. “Poly-Amino Acids”; MarcelDekker: New

York,1967, and referencestherein. (2) Bovey,F.A.Macromol.Rev. 1974,9, 1.

(3Í Bradbury,E. M.; Crime-Robinson,C.;Goldman,H.;Rattle,H. W. E.Biopolymers 1968,6,851.

(4) Saito,H.;Smith,I. C.P.Arch.Biochem.Biophys.1973,158,

154.

(5) Wittebort, R. J.; Szabo, A. J. Chem. Phys. 1978, 69, 1722. (6) Fasman,G.D.; Idelson,M.;Blout,E.R.J.Am. Chem. Soc.

1961,83, 709.

(7) Schallenberg, E.M.; Calvin, M. J. Am. Chem.Soc. 1955, 77, 2779.

(8) Fuller,W. D.; Verlander,M. S.; Goodman, M.Biopolymers

1976, 15, 1869.

(9) Lundberg,R.D.;Doty,P.J.Am. Chem.Soc. 1957, 79,3961. (10) Peggion, E.;Cosani, A.;Terbojevich, M.; Romanin-Jacur,L. J.

Chem. Soc.,Chem. Commun. 1974, 314. (11) Kivelson,D.J.Chem. Phys. 1960, 33, 1094.

(12) Stone,T.J.;Buckman,T.; Nordio,P.L.; McConnell, . M.

Proc.Natl.Acad. Sci. U.S.A.1965,54, 1010.

(13) Goldman,S.A.;Bruno,G.V.;Polnaszek,C.F.;Freed, J. H.J.

Chem. Phys.1972,56, 716.

(14) Tsutsumi, A.;Perly, B.;Forchioni,A.; Chachaty,C.

Macro-molecules1978, 11, 977.

(15) Price,C.;Heatley, F.;Holton,T.J.;Harris,P.A. Chem. Phys.

Lett. 1977, 49, 504.

(16) Navon, G.;Lanir,A. J.Magn.Reson. 1972, 8, 144.

(17) Marshall,A. G.; Schmidt,P. G.;Sykes, B. D.Biochemistry

1972, 11, 3875.

(18) Doddrell,D.;Glushko, V.;Allerhand,A.J._{Chem. Phys.}1972, 56, 3683.

(19) Myer,Y. P. Macromolecules 1969, 2, 624.

(20) Tsutsumi,A.; Chachaty,C.Macromolecules 1979, 12, 429. (21) Perly, B.; Chachaty,C.;Tsutsumi,A.J.Am. Chem.Soc. 1980,

102, 1521.

(22) Cole,K.S.;Cole, R. H.J.Chem. Phys. 1941,9, 329.

(23) Connor,T.M. Trans.FaradaySoc. 1964, 60, 1574. (24) Flory,P. J.“StatisticalMechanicsofChain Molecules”;

In-terscience: NewYork,1969.

(25) Kopple,K.D.;Wiley,G. R.;Tauke,P.Biopolymers 1973,12,

627.

(26) Fischman, A.J.;Wyssbrod, H.R.;Agosta, W.C.;Cowburn, D. J. Am. Chem.Soc. 1978, 100, 54.

(27) London, R.E.;Avitabile,J.J.Am. Chem.Soc. 1977, 99, 7765. (28) Tonelli,A. E.; Bovey,F.A.Macromolecules 1970, 3, 410. (29) Levy,G.C.;Axelson,D.E.; Schwarz,R.;Hochmann,J.J.Am.

Chem.Soc. 1978, 100, 410.

(30) Ghesquiere, D.;Tsutsumi,A.;Chachaty,C.Macromolecules

1979 12 775

(31) Woodhouse, D.R.;Derbyshire, W.;Lillford,P.J. Magn.Reson. 1975 19 267

(32) Darke, A.;Finer,E. G._{Biopolymers 1975, 14, 441.}

Conformation of cycle(L-Alanylglycyl-e-aminocaproyl),

a

_Cyclized

Dipeptide Model for

a _ß

Bend.

1.

Conformational

_Energy

Calculations1®

G.

_Némethy,

J. R.

_{McQuie, M.}

S.

Pottle,

and

.

A.

Scheraga*lb

Baker Laboratory of Chemistry, Cornell University, Ithaca,New York 14853.

Received August 7,1980

ABSTRACT: The cyclized peptide derivative cyclo(L-alanylglycyl-e-aminocaproyl) contains three peptide groups. Theseare constrained toformaßbendbecausethe distance between the C“ andC‘atomsof the e-aminocaproyl residue cannotexceed 5.04Á,even whenthealkylchainisfullystretched. Therefore,this moleculeserves as a_{model compound for}bends. Its experimentallyobserved_{physicalproperties}can beused

asstandardsfor the detectionofthe presenceofbendsinpeptides. Ananalysisofthe completeconformational

spaceofthis moleculehasbeencarried out, using energycomputation. The conformationalspaceoftheL-Ala-Gly dipeptidewas _mappedinasearchforlow-energy conformationswhich permit ringclosurewiththe e-aminocaproyl

residue. Anumericalsearchmethodwas usedto achieveringclosure. Locallystableconformations were found by energyminimization. _{Low-energy conformations}occur _{only when all three peptide groups}are in the trans conformationbecausethepresenceofeven one cispeptide groupraises_{the energy by at least}9.7

kcal/mol. Tenlow-energyconformationsof minimumenergywere found. Twoare _typeIIbends,withrelative

energies 0.00and0.93_kcal/mol. Fiveare _typeIandIII bends,withrelativeenergiesrangingfrom0.74to

1.59_kcal/mol. Threeare _type and bends,withrelativeenergiesrangingfrom2.80to 3.08_kcal/mol.

These results_suggestthatthe moleculeexistspredominantlyas a_typeII _bend,withsmall amounts of_type IandIII bendconformationspresent. This predictionwas borne_{out by experimental}measurements in solution and _{in the solid state (reported}in _{two accompanying papers).}

I. Introduction

Bendsconstituteone

of

the

_important

local

conforma-tional

features

of

proteins, along

with

a helices and

ex-tendedchains.2

About

17%

of

_{all dipeptidesequences}in

many proteins ofknown structure occur as bendsor

com-binationsofbends.2,3 _{The geometrical}features

of

bends have been _{characterized by Venkatachalam,4 who} de-scribed andclassified bendconformationsintotypesI,

II,

and

III.

Amore _{general classification}ofbendsintoseveral

additional _types was introduced _byLewis et al.5 _They 0024-9297/81/2214-0975$01.25/0 &copy;1981American Chemical Society