Patent Application: US-43525303-A

Abstract:
a pulsed field gradient nmr method using stimulated echoes for determining the translational isotropic or anisotropic diffusion coefficient of a molecule or supra - molecular assembly or the flow rate and direction of fluids containing such molecules is characterized in that the molecule or supra - molecular assembly contains one or several isotopes of non - zero nuclear spin other than protons having longitudinal relaxation times t1 that are longer than the longitudinal relaxation times t1 of the protons , and that the information about the localization of the molecule or supra - molecular assembly during the diffusion or flow interval is temporarily stored in the form of longitudinal magnetization of said isotope or isotopes . thus , the determination of translational diffusion coefficients or flow rates of supra - molecular assemblies or molecules with short t1 values , in particular of supra - molecular assemblies or molecules with m ≧ 50 kda is accomplished .

Description:
to estimate the radius and hence the mass of macromolecular assemblies comprised of amphiphilic membrane proteins solubilized by detergents , translational diffusion coefficients d have been measured with a novel pulsed - field gradient nmr method . in this new approach , the information about the localization of the molecules is temporarily stored in the form of longitudinal magnetization of isotopes such as nitrogen - 15 , thus allowing one to increase the duration of the diffusion interval by up to two orders of magnitude because of long spin - lattice relaxation times . unlike standard nmr methods using pulsed - field gradients and stimulated echoes , which are not suitable to measure the diffusion of biological macromolecules or supra - molecular assemblies , the new method can be extended to determine diffusion coefficients well below d = 10 − 10 m 2 s − 1 corresponding to molecular masses larger than 100 kda . the method is illustrated by applications to an aqueous solution of the hydrophobic transmembrane part of the bacterial outer membrane protein ompa solubilized in octyl - polyoxyethylene micelles . the diffusion coefficient is found to be close to d = 10 − 10 m 2 s − 1 which corresponds to an effective mass of about 50 kda , i . e . 19 kda for the protein itself and about 30 kda for the bound detergent . in accordance with the invention , the useful duration of the diffusion interval can be considerably increased by storing the information in the form of longitudinal magnetization of less abundant isotopes such as nitrogen - 15 , which usually have much longer spin - lattice relaxation times than protons . this allows one to gain more than one order of magnitude in the measurement of d , so that diffusion coefficients of molecules with molecular mass higher than 100 kda should be amenable to study . the method is illustrated by applications to an aqueous solution of the transmembrane part of the bacterial outer membrane protein ompa solubilized in octyl - polyoxyethylene micelles . the diffusion coefficient is found to be close to d = 10 − 10 m 2 s − 1 which corresponds to an effective mass of about 50 kda , i . e . 19 kda for the protein itself and about 30 kda for the bound detergent . since nitrogen - 15 enrichment is a prerequisite for most modern bio - molecular nmr methods , we assume that solubilization studies can be carried out with isotopically enriched proteins or nucleic acids . it is therefore possible to transfer magnetization between amide protons 1 h n and 15 n nuclei through the scalar couplings 1 j ( 1 h n , 15 n )≈− 95 hz . most hetero - nuclear correlation methods exploit the advantages of the favorable dispersion of the 15 n chemical shifts in so - called hsqc representations . in the present paper however , we do not use the 15 n chemical shifts , but we exploit another favorable feature of 15 n spins in bio - molecules : the fact that their longitudinal relaxation times t 1 ( 15 n ) are usually much longer than the t 1 ( 1 h ) of the protons . typically , in the solutions of ompa protein with detergent discussed below , t 1 ( 15 n )≈ 1 s whereas t 1 ( 1 h )≈ 30 ms . this makes it attractive to store the information in the form of longitudinal nitrogen magnetization n z . we shall refer to the new method as “ x - ste ” for “ longitudinal homonuclear magnetization stimulated echoes ”. [ 0064 ] fig1 shows a pulse sequence designed for the measurement of diffusion coefficients using storage of longitudinal nitrogen - 15 magnetization with stimulated echoes ( n z - ste ). narrow and wide pulses represent 90 ° and 180 ° pulses respectively . unless otherwise stated , all pulses are applied along the x - axes of the doubly rotating frame . the sine - shaped gray pulses are water flip - back pulses ( 8 ), typically gaussian 90 ° pulses of 1 . 2 ms duration . such pulses are also used between points e and f to suppress the solvent signal with the ‘ watergate ’ method ( 9 ). the perpendicular gradients g x or g y are used to purge unwanted magnetization components . these gradients can also be applied along the z - axis provided suitable precautions are taken to avoid accidental refocusing . the initial 90 ° nitrogen - 15 pulse at point a and the subsequent gradient g 1 serve to saturate the equilibrium nitrogen magnetization . the gradients g z of duration δ = 1 . 3 ms and variable amplitude g encode and g decode are used for ‘ bipolar encoding ’ in the first two τ delays and for ‘ bipolar decoding ’ in the last two τ delays . their effect can be summed up by the factor κ = γ 1 sg max δwhere γ 1 is the ( proton ) gyromagnetic ratio , s the surface of the ( usually not rectangular ) shape of the gradient pulses g encode and g decode , g max their peak gradient amplitude , and δ their duration . the phase accumulated by the magnetization during each gradient pair is proportional to the spatial position of the molecule along the vertical z - axis of the sample , φ = 2κz . the peak amplitudes g max were incremented from 5 . 6 to 52 . 9 g . cm − 1 to dephase ( and later re - phase ) the transverse proton magnetization during the τ intervals . at point b , after an inept - type sequence with τ =( 4j hn ) − 1 = 2 . 72 ms ( j hn =− 92 hz ), the longitudinal two - spin order 2 h z n z cos ( 2κz ) is spatially modulated along the z axis of the sample tube because of the two bipolar gradient pulses , slightly attenuated by the factor exp {− dκ 2τ ′} because of the onset of diffusion between encoding and point b ( for simplicity , we shall assume that the two encoding gradients are close to each other , and that they are both separated by an interval τ from point b .) the sequence between points b and c with τ =( 4j hn ) − 1 converts longitudinal two - spin order 2h z n z cos ( 2κz ) into nitrogen - 15 zeeman order n z cos ( 2κz ), now attenuated by a diffusion factor exp {− dκ 2 ( τ ′+ 2τ )} at point c . the re - conversion of n z into observable proton magnetization h y at point f follows a roughly symmetrical path . assuming again that the two decoding gradients are close to each other and separated by an interval τ from point e , the resultant signal is attenuated by translational diffusion during 6 short τ intervals and during the much longer a interval ( in our case , the total duration was 200 ms ). a four - step phase cycle ( φ 1 = y , − y , y , − y , φ 2 = y , y , − y , − y , receiver phase φ rec = x , − x , − x , x ) is used to eliminate signals of protons that are not coupled to 15 n ( isotope filtration ) and to ensure that longitudinal relaxation causes the signals to converge asymptotically to zero rather than towards their equilibrium value . the ratio of the signal s attenuated by diffusion ( recorded with g encode = g decode ≠ 0 ) and the reference signal s 0 ( recorded with very weak gradient amplitudes ) obeys the following equation both the reference signal s 0 and the attenuated signal s are damped by transverse proton and nitrogen relaxation and by longitudinal nitrogen - 15 relaxation , which may be expressed by a common factor f = exp {− 4 τ / t 2 ( 1 h )} exp {− 4 τ / t 2 ( 15 n )} exp {− δ / t 1 ( 15 n )} ( 2 ) this may be compared to a similar attenuation factor in the widely used homonuclear stimulated spin - echo ( ste ) method ( byrd and co - workers ( 6 )): f ′= exp {− 4 δ / t 2 ( 1 h )} exp {− δ / t 1 ( 1 h )} ( 3 ) it should be emphasized however that in equation ( 2 ) the delay is constrained to τ =( 4j hn ) − 1 , ( say , 2 . 7 ms ) while in equation ( 3 ) δ is equal to the duration of the bipolar gradients ( say , 1 to 10 ms ). in equations ( 2 ) and ( 3 ), the effective transverse relaxation rates are averages of the relaxation rates of in - phase and anti - phase coherences : 1 / t 2 ( 1 h )={ 1 / t 2 ( i x )+ 1 / t 2 ( 2 i x s x )}/ 2 ( 4 ) 1 / t 2 ( 15 n )={ 1 / t 2 ( s x )+ 1 / t 2 ( 2 i z s x )}/ 2 ( 5 ) if we neglect for simplicity the effects of transverse relaxation in the τ intervals , the main difference between equations ( 2 ) and ( 3 ) lies in the factors exp {− δ / t 1 ( 15 n )} and exp {− δ / t 1 ( 1 h )}. if we assume that we can accept a loss in signal intensity exp {− i }= 0 . 35 in both experiments , the delay δ can be extended from ca 30 ms in the ste method to about 1 s in the new n z - ste method , which opens the way to studying much slower diffusion constants . the n z - ste method was applied to a solution of a transmembrane segment of outer membrane protein a ( ompa ) solubilized with the detergent octyl - polyoxyethylene . the protein was cloned in a strain of e . coli using a plasmid . the bacterial culture was grown in a minimum m9 medium enriched in nitrogen - 15 , purified and re - natured . the nmr sample was a solution of 1 mm protein in a buffer of tris with h 2 o : d 2 0 = 9 : 1 at ph = 8 . 0 with 80 mg / ml of octyl - polyoxyethylene ( c 8 - poe ). the ch 3 ( ch2 ) 7 octyl chain had a well - defined length , but the ( ch 2 o ) n polyoxyethylene chain had a variable length with & lt ; n & gt ;= 5 . the detergent has an average molecular mass of 360 da . the molar concentration of the free detergent was 240 mm . it was estimated from neutron diffraction evidence that the aggregates comprise 30 kda detergent for each protein of 19 kda . not surprisingly , the proton spectra of this solution of ompa with detergent are rather poorly resolved . the dispersion of both 1 h and 15 n spectra ( hsqc not shown ) indicate that the protein is largely folded , but the resonances are broad and poorly resolved , probably because of some form of heterogeneity of the sample . nevertheless , the experiment of fig1 can be applied successfully , as shown in fig2 . this figure shows a one - dimensional nitrogen - 15 - filtered proton spectra , obtained with the n z - ste sequence of fig1 with a sample of the transmembrane segment of outer membrane protein a ( ompa ) enriched in nitrogen - 15 and solubilized in octyl - polyoxyethylene micelles in h 2 o : d 2 o = 9 : 1 at ph = 8 . 0 and t = 30 ° c . the total diffusion interval was δ + 6τ = 300 ms . the amplitudes of the gradients g encode = g decode were incremented from 5 . 6 to 52 . 9 g . cm − 1 . each experiment was acquired with 512 transients , while the recovery delay between subsequent experiments was 1 s . arrows indicate the limits of the region between 7 . 55 and 9 . 45 ppm over which the signal was integrated . note that the signals stem from proton magnetization that has been transferred back and forth to nitrogen - 15 nuclei , and that the overall pulse sequence lasted about 300 ms . fig3 shows the gaussian decay of the signal intensity of the ompa - detergent complex of fig2 at 30 ° c . as a function of the amplitudes of the encoding and decoding gradients g encode = g decode which were incremented in 16 steps from 5 . 6 to 52 . 9 g . cm − 1 . the proton signals where integrated over the amide region ( see fig2 ). the diffusion coefficient determined by fitting this decay to equation ( 1 ) is d =( 9 . 84 ± 0 . 12 ). 10 − 11 m 2 . s − 1 . for the sake of comparison , tanford reports a diffusion coefficient d = 10 . 10 − 11 m 2 . s − 1 for ovalbumin ( 45 kda ). both are about a factor 20 slower that the diffusion coefficient of water , since d ( h 2 o )= 2 . 3 . 10 − 9 m 2 . s − 1 at 30 ° c . the diffusion of the ompa - detergent complex is a factor 2 . 4 slower than that of the protein ubiquitin ( m = 8 kda ) in aqueous buffer at ph = 5 . 5 , for which we measured d = 2 . 4 . 10 − 10 m 2 s − 1 at 30 ° c . if we assume that diffusion of the ompa - detergent complex is not impeded by the presence of micelles formed by excess detergent ( the critical micellar concentration of the detergent is 8 . 4 mm at ph 6 . 5 and t = 30 ° c . ), this diffusion coefficient corresponds to a mass of about 50 kda per complex , which must result from the association of 19 kda for each protein and about 30 kda of detergent , corresponding to about 80 detergent molecules for each protein . like in the study of sanders and co - workers ( 7 ), the sequence proposed by byrd and co - workers ( 6 ) allowed us to observe the polyhistidine tag of ompa . however , the intense signals of the detergent led to dramatic variations of the baseline , which made the processing of the data difficult . moreover , this experiment only enables the observation of the polyhistidine tag , which is exposed to the solvent . exchange or cross - relaxation with water protons can thus lead to an overestimate of the diffusion constant of the protein - detergent complex . this effect can be partly avoided by pre - saturation of the water resonance , but this leads to a loss of signal ( 8 ). finally , cross - relaxation between the proton and nitrogen magnetization may occur for long diffusion intervals δ . this can be largely suppressed by applying ( composite ) π pulses to the nitrogen magnetization at δ / 4 and 3δ / 4 in the diffusion intervals . in the case of the ompa - detergent complex illustrated here , which is believed to have an overall mass of about 50 kda and a rotational diffusion characterized by a correlation time τ c of about 20 ns , the theoretical advantage is approximately n & gt ; 30 since t 1 ( 15 n )≈ 1 s and t l ( 1 h )≈ 30 ms . the larger the complex , the slower the diffusion constant , and the more favorable the factor n as long as nitrogen - 15 nuclei relaxation is dominated by csa and the dipolar interaction with its bound proton . one should also take into consideration losses due to transverse proton and nitrogen relaxation during the fixed τ intervals in the sequence of fig1 . it has been shown that slow translational diffusion constants can be determined accurately for nitrogen - 15 enriched bio - molecules or aggregates by using a variant of stimulated echo pulsed field gradient nmr where the information is stored in the form of longitudinal zeeman magnetization of the nitrogen - 15 nuclei . this method should considerably simplify the optimization of detergents and amphiphilic agents for the solubilization of membrane proteins . measurement of the spatial anisotropy of translational diffusion or the direction of flow by using encoding and decoding gradients in three orthogonal directions ; measurement of isotropic or anisotropic translational diffusion of molecules in viscous fluids , electrolyte solutions , and liquid crystalline phases , including micellar and bicellar phases ; measurement of isotropic or anisotropic diffusion or flow of molecules through porous solids such as zeolites , oil - containing rocks , aerogels , and other porous materials ; measurement of isotropic or anisotropic diffusion or flow of molecules in fluids through devices containing macroscopic or microscopic channels and / or reactors ; measurement of isotropic or anisotropic diffusion or flow of molecules contained in fluids , in particular blood , through vessels such as arteries and veins in living organisms ; and measurement of isotropic or anisotropic diffusion of molecules contained in fluids , in particular in blood , through organs , such as muscle , brain , liver , etc ., both in - vivo and in - vitro . 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