Patent Application: US-201414278003-A

Abstract:
this disclosure provides for new methods for quantification of metabolite concentrations in metabolomics studies , which addresses the difficulties in quantification through 1d peak integrals due to significant peak overlaps in metabolomics samples . for samples from uniformly 13 c - labeled organisms the 2d nmr 13 c - 13 c constant - time tocsy experiment provides high - resolution information about individual metabolites that allows their identification via database searching or , in the case of novel compounds , through the reconstruction of their backbone - carbon topology . this disclosure further demonstrates using ct - tocsy spectra for quantification purposes .

Description:
computational approaches for quantification of 2d 13 c - 13 c ct - tocsy the nmr pulse sequence of the 2d 13 c - 13 c ct - tocsy experiment 18 is shown in fig5 . constant - time evolution during t 1 removes the dominant homonuclear 1 j ( 13 c , 13 c ) couplings along the indirect dimension ω 1 . the 2d time - domain signal is given by where a is a spectrometer - dependent prefactor , c i is the concentration of the metabolite that contains 13 c spin s i , t is the duration of the constant - time interval , 1 j ik denotes the 1 j ( 13 c , 13 c ) coupling of spin s i to its directly bonded neighbor 13 c spin s k , t 2i is the t 2 relaxation time of spin s i and ω i is its larmor frequency . n denotes the number of spins s i and 2 2 - n is a normalization factor . s iz denotes the spin angular momentum product operator along z of spin i , “ tr ” denotes the matrix trace and h iso the isotropic mixing hamiltonian during tocsy mixing : 19 2d fourier transformation of s ( t 1 , t 2 ) of eq . ( 1 ) leads to the 2d nmr spectrum s ( ω 1 , ω 2 ). because of the linearity of the fourier transform , the integral ( volume ) of the cross - peak between spins s i and s j corresponds to it follows that the concentration c i of the metabolite that contains the two spins can be estimated according to c i = v ij / af ij where the transfer function and the universal prefactor a can be empirically determined as described below . the transfer function of eq . ( 4 ) can be computed because all parameters are either known or can be estimated with good accuracy . specifically , because in 13 c spin systems the 1 j ( 13 c , 13 c ) couplings , which range between 30 - 55 hz , dominate the geminal 2 j ( 13 c , 13 c ) and vicinal 3 j ( 13 c , 13 c ) couplings , knowledge of the backbone topology of a metabolite permits the straightforward determination of h iso ( eq . ( 2 )). furthermore , since for metabolites the transverse relaxation times t 2 by far exceed the constant - time period t , e − t / t 2i is close to 1 for all metabolites so that it can be incorporated in prefactor a . t 1 and t 2 relaxation effects during the tocsy mixing time τ m can be treated in the same way . the constant - time period t is chosen so that t = 1 / 1 j cc ≈ 1 / 37 . 6 hz = 26 . 6 ms . therefore , the product in eq . ( 4 ) is where m is the number of directly bonded 13 c to spin s i , which explains the modulation of the absolute sign of diagonal and cross - peaks along ω 1 in 13 c - 13 c ct - tocsy experiments as a function of carbon branching , i . e . primary vs . secondary vs . tertiary vs . quarternary carbon . strategies for the determination of metabolite concentrations from 2d 13 c - 13 c ct - tocsy . eqs . ( 1 )-( 4 ) can be directly used for the quantitative prediction of cross - peak and diagonal - peak volumes . the tocsy transfers , which are dominated by the 1 j ( 13 c , 13 c ) couplings , are relatively insensitive to their precise values . by comparing the computed ct - tocsy peak volumes with the corresponding experimental volumes the relative concentrations of the different compounds can be determined . this approach is demonstrated in 3 different variants , which in the following will be referred to as methods a , b , c ( see also results and discussion ): method a uses a ct - tocsy spectrum with a relatively long mixing time , e . g . τ m = 47 ms , which ensures magnetization transfer across the whole 13 c spin system . this spectrum displays a maximum number of cross - peaks . those peaks that are not affected by overlap can be used for quantification by comparing the experimental peak volumes with the ones computed based on eq . ( 1 ). method b uses a ct - tocsy spectrum with a relatively short - mixing time , e . g . τ m = 4 . 7 ms , where cross - peaks appear only between directly connected carbons . therefore , this spectrum has fewer cross - peaks than the one of method a . they can be used for quantification by comparing the experimental peak volumes with the ones computed based on eq . ( 1 ). method c uses , like method b , a ct - tocsy spectrum with a relatively short - mixing time , e . g . τ m = 4 . 7 ms . however , the compound quantification is not based on the full quantum - mechanical expression of magnetization transfer . instead it uses empirically derived approximations given below . for all three approaches , the topology of each compound of interest is required . this can be achieved by direct compound identification by querying a 13 c tocsy trace , such as a 13 c consensus tocsy trace , 20 of the compound of interest taken from a long - mixing ct - tocsy spectrum against the toccata database . 21 alternatively , the carbon topology can be reconstructed ab initio based on the analysis of ct - tocsy spectra measured at long and short tocsy mixing times . 14 once the carbon topology is known , the scalar 1 j ( 13 c , 13 c ) network ( j ij of eq . ( 2 )) is established by setting 1 j ( 13 c , 13 c )≈ 35 - 40 hz , except for 1 j ( 13 c , 13 c ) that involve carbonyl or carboxyl carbons , which are set to ˜ 55 hz . these couplings can also be double - checked from cross - sections of the ct - tocsy along ω 2 . since all multiple - bond j - couplings are much smaller , they can be safely ignored ( i . e . set to zero ) for the tocsy mixing times considered here . for methods a and b , j - coupling constants j ij are inserted in eq . ( 2 ) to define the isotropic tocsy hamiltonian h iso to compute the transfer amplitudes f ij of eq . ( 4 ) at the same mixing time τ m used in the experiment . this is accomplished by numerical evaluation of eq . ( 4 ). it is noted that the transfer function ƒ ij of eq . ( 4 ) is normalized , i . e . ƒ ij ( τ m = 0 )= δ ij (− 1 ) m ( where δ ij is the kronecker symbol ). the average ratio of the experimentally determined peak integrals by the simulated transfers yields the quantity a c i . in addition , the measurement of the peak volume of a component with a known concentration allows the determination of the prefactor a . this can be achieved , for example , by calibration of the spectrum by the addition of a pure compound with known concentration , e . g . 4 , 4 - dimethyl - 4 - silapentane - 1 - sulfonic acid ( dss ). at short mixing times τ m the full numerical integration of eqs . ( 1 )-( 4 ) can be avoided by using approximate analytical solutions . the following expressions give the tocsy transfer amplitudes where s = sin ( π 1 j cc τ m ) and c = cos ( π 1 j cc τ m ): s 1z → c 2 s 1z + s 2 cs 2z s 2z → s 2 cs 1z + c 4 s 2z + s 2 cs 3z s 3z is analogousto s 1z ( d ) linear five - spin system : s 1 - s 2 - s 3 - s 4 - s 5 analogous expressions hold for longer linear carbon chains by simply taking into account the number of next and second - next neighbors on each side of the donor spin . for example , for a linear chain s 1 - s 2 - s 3 - s 4 - s 5 - s 6 the transfers starting from s 1 and s 2 are the same as for the linear 5 - spin system . for symmetry reasons , they also represent the transfers starting from s 6 and s 5 , respectively . the transfers starting from s 3 and s 4 are identical and they correspond to the one starting from s 3 in the linear five - spin system . ( e1 ) branched chain ( valine - like without — cooh ): s 1 - s 2 - s 3α (- s 3β ) ( s 2 is a tertiary carbon ) ( e2 ) branched chain ( leucine - like without — cooh ): s 1 - s 2 - s 3 - s 4α (- s 4β ) ( s 3 is a tertiary carbon ) ( e3 ) branched chain ( isoleucine - like without — cooh ): s 1 - s 2 -( s 3β )- s 3α - s 4 ( s 2 is a tertiary carbon ) ( f ) star - like topology : s 1 - s 2α - s 2β - s 2γ - s 2δ ( s 1 is the quarternary carbon ) to convert the tocsy transfer amplitudes given by the above expressions into ct - tocsy peak volumes , they can be multiplied with cos ( π 1 j cc t ) m where m is the multiplicity of the donor carbon ( which is the carbon whose diagonal peak has the same ω 1 frequency as the cross - peak of interest ). this is accomplished by numerical implementation of eq . ( 1 ) using carbon chemical shifts , the carbon - backbone topology , and one - bond 1 j ( 13 c , 13 c ) coupling constants of each molecule as input followed by 2d fourier transformation . for amino acids all 1 j ( 13 c , 13 c ) coupling constants were set to 35 hz , except for coupling to the carboxyl carbons , which are set to 55 hz . for the carbohydrates 1 j ( 13 c , 13 c ) couplings constants are generally larger than 35 hz 22 and they were set to 40 hz in the simulations . 2d 13 c - 13 c ct - tocsy 18 data sets of the carbohydrate and amino acid mixtures were collected at 800 mhz proton frequency with 110 ppm 13 c spectral width at 25 ° c . with n 1 = 576 and n 2 = 2048 complex data points with 16 scans per increment and a relaxation delay of 4 seconds . tocsy mixing by flopsy - 16 of 4 . 7 ms for short mixing and 47 ms for long mixing were used . 23 2 d 13 c - 13 c ct - tocsy data set of galactose was collected at 700 mhz proton frequency with 82 ppm 13 c spectral width at 25 ° c . with 4 . 7 ms for short mixing and 37 . 6 ms for long mixing times using flopsy - 16 . 23 quantitative 1d 13 c nmr reference spectra were recorded for all samples with a long relaxation delay of 60 seconds . all experimental nmr data sets were zero - filled , fourier transformed , phase and baseline corrected using nmrpipe 24 and converted to a matlab - compatible format for subsequent processing and analysis . a uniformly 13 c labeled amino acid mixture consisting of isoleucine , lysine , alanine and valine with concentrations of 5 , 10 , 15 and 20 mm , respectively , was prepared in d 2 o . all amino acids were purchased from cambridge isotope laboratories , inc . the carbohydrate mixture was prepared from uniformly 13 c - labeled glucose ( purchased from sigma - aldrich ) and fructose , galactose , and ribose ( purchased from cambridge isotope laboratories , inc .). a nmr sample was prepared by dissolving these carbohydrates in d 2 o each with a 10 mm final concentration . individual carbohydrate samples were prepared by dissolving each carbohydrate in d 2 o with a 10 mm final concentration . the quantification method of 13 c - 13 c ct - tocsy spectra is based on the promise that tocsy transfers can be quantitatively predicted by numerical integration of the liouville - von neumann equation that describes the underlying many - spin physics . this is illustrated in fig1 showing a region of the experimental 13 c - 13 c ct - tocsy spectrum of uniformly 13 c - labeled galactose at a long mixing time ( fig1 a ) in comparison with the computed spectrum ( fig1 b ). in aqueous solution , galactose consists of 2 slowly interconverting isomers , each of which with its distinct resonances . the simulated ct - spectrum of fig1 b was computed according to eq . ( 1 ) by the co - addition of the spectra simulated for each of the 2 isomeric states . the high degree of similarity between the simulated and experimental spectra of fig1 exemplifies the potential of ct - tocsy spectra for quantification of metabolite concentrations . our compound quantification method using a long mixing time tocsy spectrum ( method a ) was first tested for a carbohydrate mixture consisting of uniformly 13 c - labeled ribose , glucose , fructose and galactose . in aqueous solution , each of these carbohydrates is present in multiple isomeric forms , which are in slow exchange : 2 isomers in the case of galactose and glucose and three isomers in the case of fructose and ribose . long mixing time ct - tocsy simulations were performed for each sugar isomer . in the simulated spectra , the peak integrals of each sugar isomer were measured and plotted against the peak integrals of the experimental mixture spectrum . the results for 4 of the sugar isomers are plotted in fig2 ( first row panels a , b , c , d ) and the spectra of all sugar isomers are given in fig6 . as can be seen from the figure , the experimental and computed peak integrals align well along the diagonal with a correlation coefficient r between 0 . 92 and 0 . 98 . for the plots , the experimental peak amplitudes were normalized such that the points lie along the main diagonal . the relative concentrations of the various isomers are indicated by the constant α given in each panel , which correspond to the actual slopes . consistently good results are obtained for all peaks with the exception of peaks whose donor carbon frequency exceeds 100 ppm . this behavior is presumably caused by the larger radio - frequency offset effects and they were excluded from analysis ( and are not shown in the figures ). overlapping diagonal peaks were also excluded . a distinctive feature of long - mixing ct - tocsy is the large number of cross - peaks as the number of peaks grows with the square of the chain length . for example , for a linear 6 - carbon chain , such as α - glucose , the total number of cross - peaks and diagonal peaks is 36 . even in the case of some overlaps , the number of peaks available for quantification of the compound is therefore large . it not only helps reduce the statistical uncertainty , but it also allows identification of ‘ outliers ’, which includes peaks whose volumes are affected by spectral artifacts , and thereby increases the confidence and precision of the concentration estimates . the same procedure used for the analysis of the long - mixing ct - tocsy spectra was applied to short mixing time ct - tocsy ( method b ). the results for 4 of the carbohydrate isomers are plotted in fig2 e , f , g , h and the results for all sugar isomers are shown in fig7 . the correlation coefficients between computed and experimental peak volumes vary between 0 . 88 and 0 . 98 . the short - mixing ct - tocsy has significantly fewer cross - peaks than the long - mixing tocsy as the number of peaks grows linearly with the chain length . for example , for a linear 6 - carbon chain , such as α - glucose , the total number of peaks is 16 . at long mixing times , analytical solutions do not exist for all but the simplest spin systems . on the other hand , for sufficiently short mixing time , the exact transfer amplitudes can be empirically approximated as shown in the methods section ( method c ). the accuracy of these approximations can be assessed in fig2 i , j , k , l and 8 where the approximate peak volumes at 4 . 7 ms mixing time are compared with the experimentally extracted volumes at the same mixing time . the correlation coefficients vary between 0 . 86 and 0 . 95 , which is very similar to the performance of the exact treatment at short mixing times ( method b ). the ability to accurately determine the populations of each isomer of a given carbohydrate is a useful indicator for the accuracy of the different methods . for this purpose , the relative isomer populations determined by 5 different methods are compared in table 1 . two of these methods are based on a 1d 13 c nmr spectrum of either a sample of a pure compound or the 1d 13 c nmr spectra of the mixture . the other 3 approaches use 2d ct - tocsy information according to methods a , b , c . in the case of galactose , method a yields populations of its two isomers α - pyranose and β - pyranose of 35 . 3 % and 64 . 7 %, respectively . these percentages are close to the ones observed in 1d 13 c nmr spectra of individual galactose ( 33 . 3 % vs . 66 . 7 %) as well as galactose peaks in 1d 13 c nmr spectra of the carbohydrate mixture ( 33 . 2 % vs . 66 . 8 %). methods b and c , which rely on short - mixing ct - tocsy , yield results with larger deviations ( method b : 36 . 2 % vs . 63 . 8 % and method c : 28 . 1 % vs . 71 . 9 %). this is primarily due to the smaller number of peaks leading to larger statistical errors and distorted peak shapes caused by the presence of zero - quantum effects . overall , the 5 methods produce consistent results for both galactose and glucose . for the other 2 carbohydrates , which both have at least one isomer with notably low concentration (& lt ; 20 %), fructose isomer concentrations were determined quite accurately by method a . ribose isomer concentrations could be determined less accurately by all three methods , since peaks of the high - population isomer β - pyranose and the low - population isomer α - pyranose overlap throughout the spectrum . taken together , the long - mixing tocsy ( method a ) produces somewhat more robust population estimates as judged by their better agreement with the 1d methods than the short - mixing tocsy . this sample consists of an aqueous mixture of isoleucine , lysine , alanine and valine with concentrations of 5 , 10 , 15 and 20 mm , respectively . long - mixing ct - tocsy simulations were performed for each amino acid ( method a ). from the simulated spectra , peak integrals were extracted and plotted against the corresponding peak integrals of the experimental mixture spectrum ( fig3 a , b , c , d ). peaks whose donor carbon is a cα gave relatively large errors and they were excluded from analysis . the correlation coefficients lie between 0 . 83 ( valine ) and 0 . 98 ( isoleucine ). the results for the short - mixing tocsy ( method b ) is shown in fig3 e , f , g , h with correlation coefficients between 0 . 99 and 1 . 00 . the relative concentration of isoleucine , lysine and valine can be obtained with reasonably high accuracy . only for alanine , for which only 2 peaks were used , severe peak distortions leads to a worse performance than for long - mixing ct - tocsy . the same conclusions hold for the approximate treatment of the short - mixing tocsy ( method c ) with the results shown in fig3 i , j , k , l . the concentration ratios of the amino acids were extracted from fig3 and with the results listed in table 2 . they show that the relative concentrations of isoleucine , lysine and valine can be obtained with high accuracy by all 3 methods . for alanine with only 2 cross - peaks , and hence poorer statistics , the accuracy is clearly lower . identification and quantification of metabolites in complex mixtures is a key challenge of metabolomics . quantification of components by nmr spectroscopy is traditionally based on peak integrals of 1d nmr spectra . this method can provide very accurate concentration estimates , but it is limited to spectra with relatively little peak overlap . for complex metabolite mixtures , such as the ones encountered in metabolomics , peak overlaps in the 1d spectrum are typically prevalent to the extent that they significantly hamper or prevent the use of 1d spectra for quantification . although the overlap issue can be addressed by taking advantage of the substantial resolution enhancement offered by 2d nmr spectra , magnetization transfers during 2d experiments lead to non - uniform scaling across the spectrum , which impairs the direct proportionality relationship between peak volumes and compound concentration . the course of magnetization transfer in 2d 13 c - 13 c ct - tocsy experiment is however complex especially at longer mixing times . this experiment is ideally suited for the study of uniformly 13 c - labeled organisms , such as bacteria , yeast , and plants , permitting the ab initio determination of the carbon - backbone topologies of sizeable numbers of known and unknown metabolites . 14 we demonstrate here that this experiment cannot only be used for metabolite identification , but also for quantification purposes provided that the dependence of the cross - peak amplitudes on the mixing time is explicitly taken into account . this can be achieved either through the explicit quantum - mechanical treatment of the underlying spin physics at arbitrary tocsy mixing times or , in case of short mixing times , by the use of the analytical expressions presented here . our results for carbohydrates and amino acids show that at long mixing times , the fully quantum - mechanics based calculation of magnetization transfer during tocsy well reproduces the experimental observations . at shorter mixing times , the accuracy is slightly reduced because of the smaller number of amenable cross - peaks and potentially distorted peak shapes . the achievable accuracy by the 2d ct - tocsy - based approach is not as high as for the traditional 1d 1 h nmr approach . however , the use of ct - tocsy for compound quantification overcomes the need of well - resolved resonances in the 1d nmr spectrum . application of this quantification method to 1 h - 1 h tocsy spectra is possible , but it requires accurate knowledge of all geminal and vicinal j ( 1 h , 1 h ) couplings , which can strongly depend on the metabolite conformation ( s ). on the other hand , since 13 c ct - tocsy approach is 13 c - based during both evolution and detection , it does neither require any 1 h resonance assignments nor knowledge of j ( 1 h , 1 h )- couplings . it can be applied to the very same 13 c - 13 c tocsy spectra used for compound identification and backbone - carbon topology reconstruction . moreover , the protocol should be applicable to fractionally 13 c - labeled metabolites , such as ones encountered in flux analysis , provided that cross - peaks of differentially labeled variants of the same molecule do not overlap to an extent that might hinder the accurate measurement of individual cross - peak volumes . these properties make ct - tocsy spectra a powerful tool for metabolomics studies of 13 c - labeled organisms that aim at compound identification and quantification . while the methods disclosed herein are demonstrated for carbohydrate and amino - acid mixtures , but are applicable across a wide range of systems . for example , the methods and techniques disclosed here can be applied to biological mixtures generally including metabolic mixtures that include carbohydrates , amino acids , peptides , polypeptides , nucleobases , nucleosides , nucleotides , or any mixtures or combinations thereof . 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( 24 ) delaglio , f . ; grzesiek , s . ; vuister , g . w . ; zhu , g . ; pfeifer , j . ; bax , a . j . biomol . nmr 1995 , 6 , 277 - 293 . each of the references or citations provided in this disclosure is incorporated herein by reference in pertinent part . to the extent that any definition or usage provided by any document incorporated by reference conflicts with the definition or usage provided herein , the definition or usage provided herein controls . in any application before the united states patent and trademark office , the abstract of this application is provided for the purpose of satisfying the requirements of 37 c . f . r . § 1 . 72 and the purpose stated in 37 c . f . r . § 1 . 72 ( b ) “ to enable the united states patent and trademark office and the public generally to determine quickly from a cursory inspection the nature and gist of the technical disclosure .” therefore , the abstract of this application is not intended to be used to construe the scope of the claims or to limit the scope of the subject matter that is disclosed herein . moreover , any headings that are employed herein are also not intended to be used to construe the scope of the claims or to limit the scope of the subject matter that is disclosed herein . any use of the past tense to describe an example otherwise indicated as constructive or prophetic is not intended to reflect that the constructive or prophetic example has actually been carried out .