studying a membrane protein inside or 
 on the surface of a lipid membrane is a challenging task .
the complexity of the protein  lipid system , its dynamics and 
 in most cases experiment has to be performed under physiological conditions , 
 limit the use of conventional biophysical methods such as x - ray crystallography . 

a great number of topologies that a protein can adopt in a lipid environment 
 are known already ; e.g. , membrane embedded helices can span through 
 the bilayer or form various loops , they can enter at different angles 
 into the membrane , they can be short or kinked or interrupted , etc . exact protein location and topology within the 
 membrane , its orientation , and solvent exposure of its residues are 
 crucial pieces of information for both membrane embedded and membrane 
 anchored proteins . in the case of antimicrobial peptides ,
whose activity 
 can result in the rupture of lipid membranes , it is important to characterize 
 how exactly and at which concentrations the peptides proceed from 
 a surface bound to a channel forming state . for membrane proteins , in order to understand their functionality , 
 it is also important to follow their dynamic properties , as they may 
 change both their orientation and position in the membrane .
such detailed information , however , is 
 challenging to access with conventional methods like fluorescence , ftir , epr , or scanning cysteine accessibility 
 mutagenesis techniques . in the case of fluorescence and 
 epr ,
the precision is limited to 1.53.0  due to the 
 size of the fluorescent probe or spin - label , respectively . in the 
 case of epr distance measurement experiments like eseem or deer
, a sample 
 has to be cooled down to liquid nitrogen temperature or lower , which 
 brings it far away from physiological conditions ( some recent findings 
 show that it is possible in some cases to collect deer measurements 
 at room temperature ) . in the case of 
 scanning cysteine accessibility mutagenesis
, the technique provides 
 qualitative results on a protein embedding by discrimination between 
 the intra- and extracellular location of a certain domain of the protein . with p nmr data of phospholipids , however , it is possible 
 to conduct relaxation experiments at any temperature .
in addition , p nuclei are 100% naturally abundant and have a relatively 
 high gyromagnetic ratio .
thus , p nmr spectra can be acquired 
 relatively fast with an outstanding signal - to - noise ratio , making 
 it an excellent target isotope .
introducing strong paramagnetic species 
 into a sample helps to overcome the problem of short distance interactions . 
 a paramagnetic label will interact with surrounding atoms via a dipole
dipole 
 coupling mechanism , which can be probed by a number of well - established 
 nmr techniques like pre , pcs , etc .
distance information can be determined 
 from such coupling measurements with potential limits up to 20  . over the past decade ,
inclusion of paramagnetic 
 species in biological systems gained increasing popularity in biochemical 
 nmr research in three directions : site - directed spin - labeling ( sdsl ) , 
 where in most cases a nitroxide spin - label is attached to a molecule 
 of interest ( applications include but are not limited to protein assignments 
 and fold determination ) , dissolution of paramagnetic species 
 in order to study the surface properties of molecular assemblies , and high - pressure o dissolution which is known to enter 
 and concentrate inside a lipid bilayer in a gradient manner .
previous nmr studies showed a possibility of protein depth estimation 
 based on lipid c pre from dissolved mn , but the dephasing curves were nonlinear and 
 challenging to analyze .
thus , new experimental biophysical methods 
 are needed that will greatly facilitate the process of obtaining residue - specific 
 information on protein  membrane complexes .
most nmr interactions 
 are rather short ranged , and epr spectroscopy does not provide enough 
 specificity .
the right combination of them , however , combines their 
 strengths and can be utilized to develop a technique that will successfully 
 address both the topology and immersion depth questions . here 

we present an extension of our previously published work on phospholipids to a membrane peptide in a phospholipid bilayer . 

we show that the lipid headgroup p pre induced by nitroxide 
 spin - labels at different amino acid positions of a protein can serve 
 as a molecular ruler inside the lipid bilayer for protein immersion 
 depth calculations .
for our purposes , we have chosen the -subunit 
 of the transmembrane segment m2 of nicotinic acetylcholine receptor 
 ( m2 nachr ) , as it is well studied and is often used as a model membrane protein system ( figure 1 ) .
report a 12 tilt of the protein 
 inside dmpc bilayers that has been measured with pisema nmr and oriented 
 bilayers deposited on the glass slides which was in agreement with 
 the structure from the electron diffraction map . no other published result on the tilt angle in different 
 lipid environments is available at the moment .
however , the depth 
 of insertion has not been directly tested . in order to measure it , 

we have synthesized a wild - type sample as well as a set of mutants 
 with cys - substituted amino acids at positions 3 , 5 , 6 , 9 , 11 , 12 , 
 16 , 18 , 20 , 21 , and 22 .
the cys mutants were spin - labeled with mtsl 
 and reconstituted into popc multilamellar vesicles ( mlvs ) .
measured p pre nmr rates showed a smooth and predictable behavior 
 over the whole range of immersion depths , making it easy to map the 
 relaxation enhancements to immersion depths .
another set of samples 
 was prepared to verify how sensitive the relaxation data are to exact 
 the sample preparation conditions .
nachr m2 peptide samples were 
 synthesized with a cem liberty microwave - enhanced peptide synthesizer 
 using fmoc - protection chemistry .
each sample , except for the wild type , had one of 
 its amino acids replaced with a cysteine .
nine different positions 
 along the amino acid sequence were selected for cys mutations : 3 , 
 6 , 9 , 11 , 14 , 16 , 18 , 20 , and 22 . the peptides were cleaved from the 
 resin by a 20 ml cleavage solution containing 85% tfa ( trifluoroacetic 
 acid ) , 5% water , 5% anisole , and 5% triisopropylensilane . a cem discovery 
 microwave unit and cem accent accelerated the cleavage process by 
 running for 30 min at 38 c with a stir bar at high speeds . the peptide 
excess tfa was gently 
 evaporated off by passing pure n2 gas over it for 23 
 h. to remove the rest of the solvents , ice - cold methyl tert - butyl ether was added , ice bathed for 30 min , centrifuged for 10 
 min , and the supernatant poured off .
the ether wash was repeated three 
 times in total , and then , the resulting precipitate was lyophilized 
 overnight .
the crude protein was purified with a ge akta hplc 
 system using a reverse - phase preparation size c4 column ( vydac cat . 

the solvent system consisted of h2o with 
 0.1% tfa ( solvent a ) and a mixture of 90% acetonitrile and 10% water 
 with 0.1% tfa ( solvent b ) .
maldi - tof data 
 were collected to confirm that the sample had the correct molecular 
 weight . in order to label with mtsl ,
mtsl ( s-(2,2,5,5-tetramethyl-2,5-dihydro-1h - pyrrol-3-yl)methylmethanesulfonothioate spin - label ) purchased 
 from toronto research chemicals was added with 10 molar excess to 
 the peptide solution .
the sample was sonicated , then stirred for 24 
 h at room temperature , and lyophilized until full removal of dmso . 

hplc was run to purify the labeled protein , and maldi - tof data was 
 used to confirm the resultant molecular weight of the peptide .
each multilamellar vesicle sample was prepared with 5 wt % protein / lipids 
 and vacuum - dried overnight .
a buffer solution 
 was prepared with 1.17 mg of nacl , 7.15 mg of hepes , and 1 ml of deuterium 
 depleted h2o , resulting in a 20 mm solution of salt and 
 a 30 mm buffer .
the buffer 
 was added to the sample in a ratio of 20 l for each 1 mg of 
 protein .
five freeze / thaw cycles were performed consisting of 1 min 
 of freezing in liquid nitrogen , 3 min of thawing at 50 c , and 
 2 min of vortexing .
the quality of mlvs was assessed by dynamic 
 light scattering ( dls ) and static p direct acquisition 
 single pulse experiments , producing the well - known powder pattern 
 without any sign of isotropic component .
four reference samples with wild - type protein and doxyl - labeled 
 lipids were made with 5 mol % protein / lipid and 5 mol % spin - labeled 
 lipid / lipid .
the lipids in these samples were avanti doxyl pc lipids , 
 each labeled at a different carbon number : 5 , 7 , 10 , or 12 .
the same 
 sample protocol was used as described for the mtsl labeled protein 
 samples .
two wild - type samples and three unlabeled cysteine - mutated 
 samples at position 18 were made to demonstrate the reproducibility 
 of relaxation results .
all nmr data were collected on a bruker avance 
 500 mhz wide - bore nmr spectrometer equipped with a bruker triple cp - mas 
 probe .
p longitudinal relaxation times ( t1 ) were measured at 5 khz mas speed using a standard quasi-2d 
 direct p saturation recovery pulse sequence with 64 saturation 
 loops , 10 ms saturation delay , and 7 s 90 pulses .
32 t1 points in indirect dimension were collected 
 for each sample with variable delay ranging from 1 ms to 5 s. the 
 data were fitted with one exponent model in standard bruker topspin 
 software .
several samples were made in duplicate , while a total of 
 six samples were prepared and measured for the wild - type case to establish 
 the uncertainty in the relaxation measurements .
pre relaxation curves 
 were measured with saturation recovery pulse sequence , and the resulting 
 curves were fitted in igor pro with a single exponential model .
a very good description of the relaxation processes 
 occurring within the lipid membranes is given in the literature .
have shown that for strong magnetic 
 fields ( > 2 t ) longitudinal relaxation rates for p 
 of lipids are dominated by csa relaxation , rather than by dipolar 
 coupling with the proton bath .
however , the situation changes when 
 we incorporate a large magnetic dipole such as a spin - label .
the strong 
 dipolar coupling ( 657 times stronger than protons ) in this case adds 
 another relaxation mechanism to the system that depends on the distance 
 between phosphorus atoms and the spin - label .
most applications , however , are more qualitative rather than quantitative , 
 e.g. , obtaining structural constraints and topology information from h or c pre in nmr of proteins , resonance assignments , protein  protein 
 and protein  ligand interactions , conformational heterogeneity 
 and exchange , etc .
other paramagnetically 
 induced phenomena like pseudocontact shifts ( pcs ) and residual dipolar 
 couplings ( rdc ) work better in the liquid state nmr than in the solid 
 state due to moderate line broadening and restricted mobility in the 
 latter case .
lattice relaxation enhancement , however , 
 does not depend on the spectral line width or mobility of the system , 
 making it an excellent candidate for quantitative studies .
the 
 general theory of paramagnetic relaxation enhancement in materials 
 with paramagnetic impurities was founded by blumberg and goldman in 19591965 
 following works of bloembergen and van 
 vleck .
they calculated the transition 
 probability of a nucleus at a certain distance from the paramagnetic 
 center ( averaged over the angular dependence):1where p and n are gyromagnetic ratios of the paramagnetic 
 center and the corresponding nucleus , r is the distance 
 between the two , s is the spin of the paramagnetic 
 center ,  is the electron correlation time of the paramagnetic 
 center , and  is the nuclear larmor frequency .
the total 
 relaxation rate of the nuclei can be defined as2where rref is the relaxation rate of 
 a diamagnetic ( no spin - label ) 
 control sample and rpre is the actual 
 paramagnetically induced relaxation enhancement .
rpre can be separated into two components : the actual pre 
 of an atom at a certain distance from the paramagnetic center ( rpre ) and the relaxation enhancement 
 rate due to spin duffusion ( rsd ) .
rpre can be described in terms of 
 the transition probability of a nucleus at a certain distance from 
 the paramagnetic center given in eq 1 and will 
 be used for calculations of the spin - label depths inside the membrane , 
 while rsd can be calculated for a set 
 of samples prepared in the same way and measured under the same conditions 
 so their spin - label concentration , lipid vesicle architecture , and 
 mobility are the same .
blumberg in his works has distinguished 
 three modes of impurity controlled relaxations based on spin - diffusion 
 speed : ( i ) no spin diffusion , ( ii ) limited spin diffusion , and ( iii ) 
 rapid spin diffusion .
this theory was developed for rigid crystalline 
 samples , and in the case of phospholipid vesicles was found to be 
 quite rapid ( compared to typical p spin 
lattice 
 relaxation time ) , where lipid lateral diffusion up to 8.6  10 cm / s occurs . without any kind of diffusion , the p nmr spin 
lattice 
 relaxation of a lipid sample ( independently of protein presence ) should 
 yield a curve representing several components , resulting from lipid 
 head groups placed at different distances from the paramagnetic center 
 governed by eq 1 .
such curves would be very 
 hard to analyze due to a complex multiexponent behavior .
mlvs at room 
 temperature , however , do show very nice single - exponential behavior 
 ( figure 2 ) that clearly shows the effect of 
 the diffusion processes .
such an averaging can also be exploited in 
 order to estimate the strength of lipid  protein interactions ; 
 e.g. , in the case of strong interactions when nearby lipids can not 
 diffuse at the common rate , a second , fast - relaxing component can 
 appear in the t1 graph . in our case ,
the 
 nmr experiments indicate that the lipid lateral diffusion speed is 
 enough to produce just one relaxation component .
the fit for the m211 sample is shown 
 with  = 0.603  0.006 s as squares and the m222 
 sample with  = 0.384  0.008 s as triangles with corresponding 
 single - exponential fits .
when no spin - label is present in the sample , the p spin diffusion also helps to average the relaxation rate .
however , 
 in spin - labeled samples , it also helps to increase the overall relaxation 
 rate by  draining  the polarization toward the p atom that is closest to the paramagnetic center .
the value 
 of the nuclear spin diffusivity was estimated by bloembergen:3where a is the typical p 
p internuclear distance , which is estimated to be ( 67 )  for popc lipids at room temperature , and t2 is the transverse 
 relaxation time of the nuclei .
the t2 value 
 can be measured with hahn echo or cpmg experiments . in order to calculate 
 the corresponding relaxation rate correction factor ,
first we have 
 to calculate the  exclusion radius  defined by khutsishvili as4where c is the constant in eq 1 and d is the nuclear spin diffusivity from eq 3 .
thus , the relaxation rate correction is5where n is the spin - label 
 concentration . for a typical value of t2 = 200 s and 5 mol % spin - label concentration in popc lipids ,
rsd is 0.2 hz . the equation for the nuclear 
 spin magnetization density is given by6where rn is the location of the nth phosphorus atom around the paramagnetic center positioned 
 at r and 0 is the equilibrium value 
 of . in general , the total nuclear magnetization after time t is obtained by integration of the solution of eq 6 by sample volume . on short intermolecular distances , 

however , we have to take into account real p spin - label 
 distance distributions , rather than averaged by the sample volume 
 phosphorus atom density which will give a singularity at the spin - label 
 position . from geometric considerations based on lipid headgroup size 
 and spin - label depth
, it can be estimated how much the pre effect 
 will be for the nearest , second nearest , and other phosphorus atoms . 

such calculations for the cases of the protein labeled at positions 
 3 and 11 are presented in figure 3 .
it is clearly 
 seen that the error of the pre calculation drops fast as more atoms 
 are included in the calculation and it is generally safe to consider 
 the first five nearest atoms even for the case of a spin - label very 
 close to the surface for the theoretical calculation of the pre curve 
 with 2% accuracy . in the case of experimentally measured values
, the 
 result indicates that rpre contains mostly information about only several closest phosphorus 
 atoms and can be utilized to study protein 
, it is easy to deduce the immersion depth of the spin - label 
 inside the lipid bilayer:7to 
 calculate the corresponding backbone position 
 from the pre data , it is also necessary to know the size of the spin - label 
 and the protein tilt angle .
protein tilt , however , as well as protein 
 shift inside the bilayer can be calculated from a set of pre measurements 
 with different spin - labeled positions .
theoretical pre effect 
 calculated for different numbers of lipid molecules closest to the 
 spin - labeled protein molecule .
100% is calculated for the case when 
 all lipid molecules are considered for pre calculation . when the spin - label 
 is located close to the bilayer surface ( m2-3 case ) ,
the same 
 number of neighboring lipids produces a bigger error than for the 
 case of a centrally located spin - label ( m2-11 ) . on the basis 
 of reproducibility of experimental results ,
23% error in pre 
 calculation in general can be achieved with less than five lipid molecules 
 taken for the calculation . in order to get relaxation rates from molecular dynamics 
 simulations ,
a pre effect was calculated for every p 
 atom of every simulation frame and then averaged for the number of 
 frames . due to the rapid lateral diffusion of the lipid molecules 
 when compared to the nmr experimental time , a simplifying assumption 
 was made that during the course of the experiment every lipid molecule 
 can be found at any other lipid molecule s position in the 
 simulation .
first , such a simplification allows the simulation time 
 to be significantly decreased , and second , it is reasonable because 
 at diffusion rates of around 10 m / s the simulation time of 10 ns is enough to sample 
 the local movements of most lipid molecules .
it has to be taken into 
 account , however , that 10 ns is not enough to sample all of the molecular 
 motions and motional states , and therefore simulation results have 
 to be considered with care .
the total relaxation rate following 
 eq 1 can be calculated as8where 
 conc is the spin - label concentration relative to the amount of lipid 
 molecules , nframes is the number of frames 
 in the simulation , np is the number of 
 all p atoms present in the simulation , and rn is the distance between the nth phosphorus atom and the spin - label .
p is an excellent nmr probe of biomolecules due to 
 its relatively high gyromagnetic ratio , 100% natural abundance , location 
 in the lipid headgroup region , and relatively fast t1 relaxation in lipids , usually on the order of seconds .
p pre nmr membrane depth measurements were conducted on 24 
 m2 protein samples incorporated into popc mlvs .
samples were 
 spin - labeled at the following positions : 3 , 5 , 6 , 9 , 11 , 12 , 16 , 18 , 
 20 , 21 , and 22 .
the m2 sample spin - labeled 
 at position 22 has a shorter t1 value 
 ( 384 ms , see table 1 ) when compared to position 
 11 ( 603 ms ) , because it is located closer to the membrane surface . 

the m2 sample spin - labeled at position 11 is buried near the 
 center of the membrane and still has a t1 value smaller than the wt control sample ( 694 ms ) .
the p 
 nmr relaxation data collected in this study were well fit with a single 
 exponential to glean out the corresponding t1 values .
this is surprising given the number of p nuclei in a phospholipid bilayer poised at different positions 
 and distances relative to the spin - labeled protein .
the overall position 
 of a spin - label relative to the p atoms and overall dynamics 
 of the system need to be considered .
figure 3 shows the theoretical / computational p pre effect calculated 
 as a function of the number of p lipid molecules with 
 spin - labeled m2 at positions 3 and 11 .
a total of 32 data points 
 per relaxation curve were calculated in order to eliminate possible 
 issues with the number of relaxation components .
taking lipid lateral 
 diffusion into account , which is on the order of 1010 cm / s , it becomes clear that , unless a lipid molecule is strongly attached 
 to a protein so it does not diffuse , their natural diffusion within 
 the bilayer will effectively average out all the relaxation differences 
 during the course of the nmr measurement , which takes on the order 
 of a fraction of a second to several seconds .
resulting p nmr pre values for several mutated positions of the m2 
 protein are presented in figure 4a in a bar 
 graph format .
the green bars show the p t1 pre % when compared to a control sample , while the blue 
 bars represent the best structural modeling results with a 12 
 helical tilt of m2 with respect to the membrane . for comparison , 

figure 4b shows the same modeling procedure 
 used for the m2 protein with a 0 helical tilt with respect 
 to the lipid bilayer ( perpendicular to the bilayer surface ) .
figure 4b is a good example of what relaxation behavior 
 can be expected at different immersion depths .
it is clearly seen 
 in this case that the relaxation enhancement is a smooth function 
 of the spin - label depth inside the bilayer and has enough sensitivity 
 to pinpoint spin - label positions clearly discriminating different 
 labeling sites or residues . due to the natural nonlinearity of the 
 pre effect
, the most sensitivity is achieved for the labeled positions 
 close to the membrane surface , whereas the difference between most 
 immersed spin - labels is somewhat diminished .
experimental results ( green ) 
 and model fitting ( blue ) : ( a ) case of 12 protein tilt inside 
 the bilayer ; ( b ) modeled 0 protein tilt ( experimental green 
 bars are the same as in part a ) . in order to probe the structural properties of the protein 
 within the lipid bilayer and their effect on pre , we developed a straightforward 
 model that describes the whole complex .
an -helix of the protein 
 was taken as a rigid cylinder of corresponding size ( the cc 
 diameter was set at 5.4 and 34  length ) , and all mtsl labels 
 were placed perpendicular to the cylinder axis with 8  length 
 ( equal to the distance between c and n of mtsl ) ( figure 5 ) .
a pentamer of protein models was placed in a lipid bilayer , and 
 the pre effect was calculated for all labeled positions .
parameters 
 to fit were the tilt angle  , roll angle  , vertical shift s inside the membrane , and electron correlation time c .
the phospolipids were modeled as a sparse network of 15 p atoms around the protein on both sides of the bilayer . 

the number 15 was chosen on the basis of the error estimation coming 
 from the fact that at the same time several p atoms will 
 be affected by the spin - label and therefore will have different momentary 
 relaxation rates .
figure 3 shows how the error 
 in pre calculations depends on the number of lipid molecules considered 
 and the spin - label position . in order to account for the diffusion 
 processes
, a simple assumption was made that all lipids are equally 
 mobile during the course of the nmr experiment ( i.e. , have the same 
 lateral diffusion speed and the incorporation of the peptide does 
 not affect it ) .
this assumption basically means that all lipid molecules 
 will find themselves in all of the accounted 15 lipid positions equally , 
 which allows us to easily calculate a single relaxation rate .
such 
 an assumption should be valid for the majority of the protein / lipid 
 systems .
all 
 experimentally available spin - labels were put on the model protein 
 to be fitted simultaneously . for details , see the text .
experimental results from all spin - labeled positions 
 to the p atoms were fit globally .
as seen 
 from the graph , this simple model fits very well with the experimental 
 results and agrees well with the results from the literature : a tilt 
 angle of 12 is known for nachr m2 , and the n - terminus side of the peptide is shifted closer 
 to the membrane headgroup ( 1.5  shift estimated ) due to a higher 
 concentration of polar amino acids at that end and was theoretically 
 predicted by amit kessel et al .
no deviation from the straight helix was observed on the basis of 
 fitting results , which corresponds to the majority of the results 
 for nachr m2 in popc vesicles from the literature .
the m2 helix is known to rotate rapidly along its helical 
 axis when in monomeric form .
it is known 
 that under physiological peptide concentrations it tends to form pentamers 
 and this type of rotation is hindered due to the interaction of neighboring 
 helices which results in  kinky  rather than smooth 
 behavior of the relaxation curve in figure 4a , when compared to figure 4b .
this can be 
 seen as indirect evidence for pentamerization of the peptide at higher 
 concentrations .
an area of uncertainty in these membrane depth 
 measurements lies in an estimation of the electron correlation time 
 c .
first , it is temperature dependent and can be 
 obtained from several t1 measurements 
 at different temperatures . in this case
, however , it is also necessary 
 to consider the temperature dependence of rref and rsd as well as lipid mobility changes 
 and phase transitions .
also , it can be obtained with a combination 
 of both t1 and t2 measurements , but lipid samples 
 usually have very short t2 values that 
 are not easy to measure precisely and in the static case it tends 
 to be anisotropic consisting of several different components .
mas 
 measurements of t2 are also not a good 
 option because short t2 values have to 
 be measured at very high spinning speeds to get reasonable resolution 
 and several points on the corresponding relaxation curve .
third , ccan be deduced from measurements 
 of the same sample at different magnetic fields .
all of these methods , 
 however , can be used to give approximate values of the correlation 
 time for our model fitting .
our method proposes another way to calculate 
 c based on fitting rsd and rpre simultaneously . 

indeed , both of them depend on c , but while rsd governs the size of the gap , rpre governs the incline of the  wings  . 

the calculated value for c of 12 ns was found to 
 be well in the range for nitroxide spin - labels .
it is , however , for the first time that c was calculated for a real biologically relevant sample using this 
 technique .
we have presented a novel method for membrane 
 protein topology and immersion depth based on site - directed spin - labeling 
 and paramagnetic relaxation enhancement p nmr .
the method 
 can be utilized as a molecular ruler to measure positions 
 of labeled amino acids within the lipid membrane .
it allows precise 
 determination of the spin - label immersion depth , and hence , membrane 
 protein structural and topological properties can be measured under 
 physiological conditions .
the method shows predictable behavior of 
 the relaxation rate enhancements depending on the paramagnetic center 
 immersion depth , making it easy to interpret the data .
it also allows 
 for an easy and precise calculation of the electronic correlation 
 time , which is otherwise an elusive quantity that can be useful in 
 other experiments : some pre based spectroscopic distance measurement 
 methods rely on precise knowledge of the electronic correlation time . 

the nmr data are presented for a set of samples with nachr m2 
 protein mutated at different positions , showing the applicability 
 of the method to complex biological systems .
particularly , it was 
 shown that the peptide tends to take a shifted position within the 
 bilayer with the n - terminus shifted 1.5  closer to the lipid 
 surface than the other c - terminus .
a theoretical background is given 
 describing the phenomena and their relevance behind the pre in lipid 
 vesicles as well as error estimation from different sources for calculation . 

the stronger 
 lateral interaction between the pes may reflect how the interfacial 
 process is involved .
another possibility is to test lipid in the gel phase in which the 
 water amount and lateral interactions of the head groups are considerably 
 altered with respect to the liquid crystal .
 paramagnetic 
 relaxation enhancement ( pre ) is a widely used approach for measuring 
 long - range distance constraints in biomolecular solution nmr spectroscopy . 
 in this paper , we show that 31p pre solid - state nmr spectroscopy 
 can be utilized to determine the immersion depth of spin - labeled membrane 
 peptides and proteins . 
 changes in the 31p nmr pre times 
 coupled with modeling studies can be used to describe the spin - label 
 position / amino acid within the lipid bilayer and the corresponding 
 helical tilt . 
 this method provides valuable insight on protein  
 lipid 
 interactions and membrane protein structural topology . 
 solid - state 31p nmr data on the 23 amino acid -helical nicotinic 
 acetylcholine receptor nachr m2 transmembrane domain model 
 peptide followed predicted behavior of 31p pre rates of 
 the phospholipid headgroup as the spin - label moves from the membrane 
 surface toward the center of the membrane . 
 residue 11 showed the smallest 
 changes in 31p pre ( center of the membrane ) , while residue 
 22 shows the largest 31p pre change ( near the membrane 
 surface ) , when compared to the diamagnetic control m2 sample . 
 
 this pre ss - nmr technique can be used as a molecular ruler to measure 
 membrane immersion depth . 
Introduction
Materials and Methods
Results and Discussion
Conclusions