Method for measuring stable isotope abundance based on tandem mass spectrometry
Technical Field
The invention relates to the technical field of stable isotope analysis, in particular to a method for measuring stable isotope abundance based on tandem mass spectrometry.
Background
The stable isotope labeling reagent is a very widely applied basic reagent in scientific research, and plays an irreplaceable role in the fields of food safety, medicine analysis, metabonomics, metabolic flow and the like no matter being used as an internal standard or a tracer. The isotopic abundance of a stable isotopically-labeled compound refers to the percentage of labeled atoms in a compound that are found to be the total number of labeled site atoms. The isotope abundance is an important quality control index for stabilizing the isotope labeling reagent, and is also an important research object in tracer applications such as metabolic flow.
Currently the main means of determining stable isotope abundance are nuclear magnetic resonance spectroscopy and mass spectrometry. The nuclear magnetic resonance spectroscopy is a well-known and accurate method, has application in metering traceability and standard substance definite value, but is limited by lower detection sensitivity of the nuclear magnetic resonance spectrometer and insufficient separation capability of a mixed sample, and the method is not suitable for measuring the abundance of the isotope-labeled compound with lower concentration in a complex sample matrix, and has higher consumption of the sample and higher detection cost in the application of pure quality control. The mass spectrometry and the nuclear magnetic resonance method also do not need to depend on standard substances in magnitude tracing, have absolute advantages in sensitivity, and can be used in combination with chromatography, so that the method has wider and flexible application in the determination of the abundance of the isotope-labeled components in complex matrix samples.
Mass spectrometry can be roughly classified into high-resolution mass spectrometry and low-resolution mass spectrometry according to the kind of mass spectrometer. The low-resolution mass spectrum mainly refers to quadrupole mass spectrum, is limited by instrument resolution, ions with similar mass-to-charge ratios (ions to be detected and impurity ions, ions to be detected and ions to be detected) cannot be effectively separated, and are counted into mass spectrum data in a convolution form, and complex deconvolution calculation is needed in the process of calculating isotope abundance results; meanwhile, the "impurity" ions that are not completely separated may also introduce errors in the detection results. The high-resolution mass spectrum mainly comprises a Fourier transform mass spectrometer, a time-of-flight mass spectrum, an orbit ion trap mass spectrum and the like, and the higher instrument resolution ensures the separation of mass spectrum peaks with similar mass-to-charge ratios, so that on one hand, the difficulty of result calculation is reduced, on the other hand, the selectivity is improved, and the interference of the determination of the peaks to be detected by the matrix background and the impurity peaks with similar mass-to-charge ratios in the components to be detected is reduced, thereby improving the accuracy. However, the high price of the high-resolution mass spectrometer greatly increases the detection threshold and the cost, and limits the popularization and the use of the method.
Disclosure of Invention
The invention aims to provide a method for measuring stable isotope abundance based on tandem mass spectrometry, which has high accuracy and high sensitivity.
The aim of the invention can be achieved by the following technical scheme: the method for determining the stable isotope abundance based on the tandem mass spectrum utilizes the tandem mass spectrum to quantitatively analyze the ion pair abundance of a stable isotope labeled compound MX n, so as to obtain the relative content of various isotope isomers of the compound, further obtain the isotope isomer distribution x 0、x1、x2、……、xn, and calculate the isotope abundance E of the compound according to the following formula;
Wherein X is a labeled isotope, n is the number of labeled atoms of the labeling element, and M is the residual molecular formula after removal of the labeled atoms.
Preferably, the X is a combination of one or more of 2H、13C、15N、18 O.
Preferably, the tandem mass spectrum comprises more than two mass spectrum mass analyzers.
Further preferably, the tandem mass spectrum comprises a triple quadrupole mass spectrum, a quadrupole-time of flight mass spectrum, a quadrupole-ion trap mass spectrum, a quadrupole-orbitrap mass spectrum.
Preferably, the ion pair abundance of stable isotope labeled compound MX n is quantitatively analyzed using tandem mass spectrometry using neutral loss scanning and/or parent (precursor) ion scanning.
Further preferably, the neutral loss scanning method comprises fixing the difference value (neutral loss) between the mass and charge ratios of the sub-ions monitored in the second-stage mass spectrum or the parent ions monitored in the first-stage mass spectrum and the second-stage mass spectrum, and scanning or detecting the parent ions in the corresponding mass and charge ratio range in the first-stage mass spectrum to obtain the relative abundance of the ions with the corresponding mass and charge ratios of the isotope heterosomes to be measured.
Further preferably, the parent ion scanning method comprises fixing the mass-to-charge ratio of the parent ions monitored in the second-stage mass spectrum, and scanning or detecting parent ions in the corresponding mass-to-charge ratio range in the first-stage mass spectrum to obtain the relative abundance of the ions of the corresponding mass-to-charge ratio of the isotope heteromer to be measured.
Preferably, when the abundance of the ion pair of the stable isotope-labeled compound MX n is quantitatively analyzed, the relative contents of the various isotopic isomers of the compound can be obtained based on the ionic strength data or the peak area.
Preferably, after obtaining the relative content of each isotope isomer of the compound, the data deconvolution treatment is performed to obtain the isotope isomer distribution x 0、x1、x2、……、xn.
Further preferably, the deconvolution processing method includes a mass clustering method.
Still further preferably, the deconvolution processing method includes: based on the following simultaneous solving equation set, the isotope heterodigital distribution x 0、x1、x2、……、x i is obtained:
Wherein, the single molecular mass of the non-labeling site part of the isotope labeling compound is M, alpha 0、α1、……、αi is the distribution coefficient of the part of natural isotope allotrope in the molecular mass M, M +1, … … and M+i, and I i is the mass spectrum peak intensity corresponding to the molecular mass M, M +1, … … and M+i.
Preferably, the mass spectrum peak intensity is relative ion intensity.
Preferably, the α i is obtained according to the natural isotope distribution law of the unlabeled fraction.
Further preferably, the α i is derived from theoretical calculations, simulator calculations (e.g., chemcalc website simulator, isotope abundance distribution calculator), or natural abundance mass spectrometry experiments.
Preferably, when calculating the isotopic heterodigital distribution x 0、x1、x2、……、x5, the deconvolution processing method includes simultaneous solving of the following system of equations:
I0=α0x0
I1=α1x0+α0x1
I2=α2x0+α1x1+α0x2
I3=α3x0+α2x1+α1x2+α0x3
I4=α3x1+α2x2+α1x3+α0x4
I5=α3x2+α2x3+α1x4+α0x5。
wherein, the single molecular mass of the non-labeling site part of the isotope labeling compound is M, alpha 0、α1、α2、α3 is the distribution coefficient of the part of natural isotope allotrope in the molecular mass M, M +1, … … and M+3, and I i is the mass spectrum peak intensity corresponding to the molecular mass M, M +1, … … and M+i.
Preferably, the total isotopic abundance E of the stable isotopically-labeled compound MX n when fragmented into AX x and BX n-x in the collision cell of the tandem mass spectrum is calculated by weighted average:
Preferably, the sample is introduced into the tandem mass spectrum using liquid chromatography or peristaltic pumps.
The component to be tested is MX n, wherein X is marked isotope, such as one or a combination of 2 H (D), 13C、15N、18 O and the like, n is marked atom number of the marked element, and M is residual molecular formula after marked atoms are removed.
The tandem mass spectrometry method of the invention adopts a parent ion scanning mode and a neutral loss scanning mode in triple quadrupole mass spectrometry, and adopts a sub-ion scanning mode and other types of tandem mass spectrometry to obtain the intensity of a parent ion (parent ion or precursor ion) and a sub-ion (product ion) ion pair with a specific mass-to-charge ratio (m/z), thereby obtaining the intensity data of specific ions to be detected with higher selectivity.
Specifically, it is assumed that the analyte component can be fragmented into AX x and BX n-x in the collision cell of tandem mass spectrometry, that its relative molecular (ion) masses are M A and M B when all sites are in an unlabeled state, and that AX x inherits the charge of parent ion MX n. Clearly, according to the above assumption, the relative molecular (ionic) mass M Z=MA+MB of the test molecule MX n in the unlabeled state at all sites.
The isotopic abundance of X in AX x part can be obtained by a scan mode of neutral loss or the same principle, a constant M/z difference is M B +n-X (for a marker element with a relative mass difference of 1 to H, 12C、14 N, such as D, 13C、15 N) or M B +2 (N-X) (for a marker element with a relative mass difference of 2 to 16 O, such as 18 O), obtaining the peak area (ionic strength information) where the M/z of the parent ion is equal to M Z+n-x,MZ+n-x+1,……,MZ +n (the M/z of the child ion is equal to M A,MA+1,……,MA +x), obtaining the isotopic heterodigital distribution X 0、x1、……、xx by performing necessary data deconvolution (such as "mass cluster") method, and calculating the isotopic abundance E A of AX x part by a defined expression:
The isotopic abundance of X in the BX n-x part can be obtained by scanning the parent ion or the scanning mode of the same principle, wherein the M/z of the constant daughter ion is M A + X (for the marker element with the relative mass difference of 13C、15 N and 12C、14 N being 1) or M B +2X (for the marker element with the relative mass difference of 18 O and 16 O being 2), the peak area (ionic strength information) of the parent ion M/z being equal to M Z+x,MZ+x+1,……,MZ + N is obtained, and the isotopic abundance E B of the BX n-x part is obtained by carrying out necessary data deconvolution treatment (such as a "mass cluster" method) and the like, and the isotopic heterodigital distribution X 0、x1、……、xn-x is obtained by calculating by a definition formula:
In most cases, the fragmentation sites of the parent ions can be controlled by adjusting the collision cell parameters so that the labeled isotopes are all present on fragments AX x or BX n-x, thereby simplifying the above steps. If the labeled isotopes are all present at AX x, i.e. x=n, only a neutral loss scan is required and the isotopic abundance e=e A of the component MX n to be measured; similarly, when the labeled isotopes are all present in BX n-x, i.e., x=0, only a parent ion scan is required and the isotopic abundance e=e B of the test component MX n.
When the labeled isotopes are inevitably present on both fragments simultaneously, the total isotopic abundance E of the component to be measured can be calculated by weighted averaging:
it should be noted that the above-mentioned selection of the parent ion/child ion m/z is suitable for the case that the labeling rate of the component to be detected is high and the isotopic abundance is high, in this case, the monitoring ion intensity obtained by such selection is the highest, which is beneficial to the accuracy of monitoring. If the labeling rate and the isotope abundance of the component to be detected are not high or even low (in the application of metabolic tracing and the like, the isotope abundance of the component to be detected is often obviously reduced compared with that of the tracer), the ion with the highest intensity can be selected on the basis of the guiding thought, so that the detection sensitivity and accuracy are ensured.
Compared with the prior art, the invention has the following beneficial effects:
1. The invention provides a stable isotope abundance determination method with high accuracy and high sensitivity based on tandem mass spectrometry;
2. The invention can more accurately and precisely measure the isotope abundance of stable isotope products;
3. the invention utilizes the tandem mass spectrum to quantitatively analyze the ion pair abundance of the stable isotope labeled compound to obtain isotope heterodigital distribution with higher signal-to-noise ratio, thereby obtaining more accurate stable isotope abundance through calculation;
4. The invention creatively utilizes the effect of tandem mass spectrometry on screening out 'impurity' ions with similar mass-to-charge ratios by utilizing the son/mother ions, improves the selectivity of the object to be detected from another way, and ensures that the detection precision can reach or even exceed the level of high-resolution mass spectrometry;
5. the invention exerts the advantage of the detection sensitivity of tandem mass spectrometry, so that the method has more application value in the application fields of extremely complex matrixes such as metabonomics and the like and extremely low concentration of the to-be-detected substance;
6. in the invention, the results measured by the triple quadrupole mass spectrometry and the high-resolution mass spectrometry have no obvious difference, the detection threshold and the cost can be reduced, and the popularization and the use of the mass spectrometry for measuring the stable isotope abundance are facilitated.
Detailed Description
The following examples of the present invention are described in detail, and are given by way of illustration of the present invention, but the scope of the present invention is not limited to the following examples.
Unless specifically indicated otherwise, the reagents, methods, apparatus and devices employed in the present invention are those conventional in the art. Reagents and materials used in the following examples are commercially available unless otherwise specified.
Example 1
Determining isotope abundance of enrofloxacin-D 5 (molecular formula C 19H17D5FN3O3) by triple quadrupole mass spectrometry, introducing a sample solution by a peristaltic pump, and controlling the flow rate to be 10 mu L/min; the mass spectrum scan polarity was positive ion mode, spray voltage was set at 3500V, sheath gas flow was set at 12Arb, and ion transport tube temperature was set at 275 ℃. It can be presumed by preliminary experiments that the following reactions of the analyte can occur in the collision cell:
Then M is C 19H18FN3O3, X is D, n=5, ax x is C 18H18FN3OD5,BXn-x is CO 2, where x=5, and M A=316,MB =44, mz=360. Since the marked atoms D are all present in the AX x part inheriting the charge of the parent ion, only neutral loss scanning is needed, the constant M/z difference is M B +n-x, namely 44, and the ion intensity data of the parent ion M/z equal to M Z+n-x,MZ+n-x+1,……,MZ +n (namely 360-365) is obtained. Preparing a sample solution with the concentration of 1mg/L by adopting a standard product with the deuterium isotope abundance of 99.25atom D (1 HNMR constant value), carrying out sample injection analysis under optimized mass spectrum ion source parameters and the scanning parameters to obtain m/z=360-365 ion intensity data of 2177, 339, 48, 24, 3044 and 354148 in sequence, and deconvoluting the data by adopting a 'mass cluster method' to obtain the distribution (after normalization) of the isotope isomer of MD0H5、MD1H4、MD2H3、MD3H2、MD4H1、MD5H0 of 0.0076(x0)、-0.0004(x1)、0.0001(x2)、0.0001(x3)、0.0106(x4)、1.2308(x5), and calculating according to the following formula:
E=((1×x1+2×x2+3×x3+4×x4+5×x5)/(5×(x0+x1+x2+x3+x4+x5)))×100%
=(1×-0.0004+2×0.0001+3×0.0001+4×0.0106+5×1.2308)/(5×
(0.0076-0.0004+0.0001+0.0001+0.0106+1.2308)))×100%=99.24%。
that is, the isotope abundance e=e A =99.24 atom D of enrofloxacin-D 5 was calculated, and the average value of the results of six replicates was 99.22atom D, relative standard deviation rsd=0.16%. In comparison, the same sample was subjected to the same equipment and conventional full scan method, and the average value of the results of six replicates was 96.53atom D, rsd=0.45%. Compared with the traditional method, the method has the advantages that the precision is slightly improved, and the accuracy is greatly improved.
In this example, the relative ionic strength I 0~I5 (corresponding ionic strength data/maximum ionic strength data) was obtained based on the ionic strength data of m/z=360 to 365, and the isotope distribution coefficients α 0、α1、α2、α3 of the natural abundance enrofloxacin were 0.811, 0.169, 0.018, 0.001, respectively, based on the isotope abundance distribution calculator.
The following system of equations is combined and calculated to give x 0~x5.
I0=α0x0
I1=α1x0+α0x1
I2=α2x0+α1x1+α0x2
I3=α3x0+α2x1+α1x2+α0x3
I4=α3x1+α2x2+α1x3+α0x4
I5=α3x2+α2x3+α1x4+α0x5。
Example 2
The isotopic abundance of glucose-6-phosphate- 13C6 (molecular formula 13C6H13O9 P) was determined by liquid chromatography-triple quadrupole mass spectrometry, a sample was introduced by liquid chromatography, a Waters BEH Amide (100 mm. Times.2.1 mm,1.7 μm) was used as column, mobile phase A was acetonitrile, mobile phase B was an aqueous solution containing 20mmol/L ammonium acetate, VA: vb=90: 10, isocratic elution at a flow rate of 200. Mu.L/min; the sample injection amount is 10 mu L; the mass spectrum scan polarity was negative ion mode, spray voltage was set at 3500V, sheath gas flow was set at 25Arb, auxiliary gas flow was set at 15Arb, and ion transport tube temperature was set at 300 ℃. It can be presumed by preliminary experiments that the following reactions of the analyte can occur in the collision cell:
Then M is H 12O9 P, X is 13C,n=6,AXx is H 2PO4,BXn-x is 13C6H10O5, where x=0, and M A=97,MB =162, Mz=259. Since the labeled atom 13 C is all present in the neutral lost BX n-x part which does not inherit the charge of the parent ion, only the parent ion scanning is needed, the constant child ion M/z is M A +x, namely 97, and the ion intensity data of the parent ion M/z which is equal to M Z+x,MZ+x+1,……,MZ +n (namely 259-265) is obtained. Analyzing a metabolic mixture obtained by metabolizing bacteria fed with glucose- 13C6 tracer for a certain time under optimized chromatographic separation conditions, mass spectrum ion source parameters and scanning parameters (a sample is subjected to proper pretreatment), obtaining m/z=259-265 ionic strength data of 5044, 788, 152, 305, 128, 1870 and 197049, deconvoluting the data by adopting a mass clustering method to obtain M13C0 12C6、M13C1 12C5、M13C2 12C4、M13C3 12C3、M13C4 12C2、M13C5 12C1、M13C6 12C0 isotope isomer distribution (after normalization) of 0.026, 0.004, 0.000, 0.001, 0.009, 1.000, and further calculated to obtain the isotopic abundance e=e B=96.97atom 13 c% of glucose-6-phosphate- 13C6. Meanwhile, the unlabeled glucose-6-phosphate standard solution with the concentration of 5mg/L is adopted, and the concentration of the detected glucose-6-phosphate in the sample can be obtained by detecting under the same conditions, wherein the ionic strength data of m/z=259-265 are 357275, 24996, 7177, 501, 108, 0 and 0 in sequence. The method of the invention is shown to possess potential for simultaneous determination of the isotopic abundance and content of metabolites.
Example 3
Determining isotope abundance of lysine- 13C6 15N2 (molecular formula 13C6H14 15N2O2) by triple quadrupole mass spectrometry, introducing a sample solution by a peristaltic pump, and flowing at 10 mu L/min; the mass spectrum scan polarity was positive ion mode, spray voltage was set at 3500V, sheath gas flow was set at 12Arb, and ion transport tube temperature was set at 275 ℃. It can be presumed by preliminary experiments that the following reactions of the analyte can occur in the collision cell:
Then M is H 15O2, X is 13C/15N,n=8,AXx is 13C5H10 15N,BXn-x is 133CH5 15NO2, where x=6, and M A=84,MB =63, Mz=147. Since the labeling atom 13 C and 15 N are present in both the sub-ion AX x and neutral missing BX n-x portions, the neutral missing scan and parent ion scan modes are required to be used simultaneously. in neutral loss scan mode, the constant M/z difference is M B +n-x, i.e., 65, and the ion intensity data for parent ions M/z equal to M Z+n-x,MZ+n-x+1,……,MZ +n (i.e., 149-155) are obtained. Sample injection analysis is carried out on self-made lysine- 13C6 15N2 sample solution with the concentration of 0.5mg/L under the optimized mass spectrum ion source parameters and the scanning parameters to obtain the ionic strength data of m/z=149-155, which are 27, 97, 237, 1678, 9012, 95275 and 827632 in sequence, deconvolution treatment is carried out on the data by adopting a 'mass cluster method', so as to obtain the distribution (after normalization) of the isotope heteronumber of AX 0、AX1、AX2、AX3、AX4、AX5、AX6, which is 0.000, 0.000, 0.002, 0.0011, 0.115, 1.000, and further calculating the isotopic abundance E A=97.86atom 13C(15 N)% of the daughter ion portion; In the parent ion scanning mode, the constant child ion M/z is M A +x, namely 90, and the ion intensity data of the parent ion M/z equal to M Z+x,MZ+x+1,……,MZ +n (namely 153-155) are obtained. The same sample was analyzed under the same mass spectrometry ion source parameters and the scanning parameters to obtain ionic strength data with m/z=153 to 155 of 438, 65309 and 3607273 in sequence, and deconvolution was performed on the data by a "mass clustering method" to obtain distribution (after normalization) of isotope heteromers of BX 0、BX1、BX2 of 0.000, 0.019 and 1.000, and further to calculate the isotope abundance E B=99.08atom13C(15 N)% of the neutral missing portion. The isotopic abundance fraction of the sub-ions and neutral missing fraction was weighted and averaged to give a sample of lysine- 13C6 15N2 having two isotopic abundances (mix) of 98.16%, e= (6 x 97.86% + (8-6) ×99.08%)/8=98.17%. The average abundance obtained for 8 replicates was 98.17%, rsd=0.01%. The sample was measured for its isotopic abundance using high resolution mass spectrometry (quadrupole-orbitrap mass spectrometry), with an average result of 98.25%, rsd=0.12 (n=8). it is shown that the method of the present invention does not have a significant difference from the results measured by high resolution mass spectrometry, and in contrast, the method of the present invention has higher precision, but cannot measure the abundance of each isotope as in high resolution mass spectrometry.
Example 4
The isotopic abundance of glucose- 13C6 (molecular formula 13C6H12O6) was determined by liquid chromatography-triple quadrupole mass spectrometry, a sample was introduced by liquid chromatography, a chromatographic column was a Waters BEH Amide (100 mm x 2.1mm,1.7 μm), mobile phase a was acetonitrile, mobile phase B was an aqueous solution containing 20mmol/L ammonium acetate, VA: vb=90: 10, isocratic elution at a flow rate of 200. Mu.L/min; the sample injection amount is 10 mu L; the mass spectrum scan polarity was negative ion mode, spray voltage was set at 3500V, sheath gas flow was set at 25Arb, auxiliary gas flow was set at 15Arb, and ion transport tube temperature was set at 300 ℃. It can be presumed by preliminary experiments that the following reactions of the analyte can occur in the collision cell:
then M is H 12O6, X is 13C,n=6,AXx is 13C3H5O3,BXn-x is 13C3H6O3, where x=3, and M A=89,MB =90, Mz=179. Because the labeled atom 13 C is simultaneously present in the part of the sub-ion AX x and the neutral loss BX n-x, the neutral loss scan and the parent ion scan are required to be simultaneously adopted, and in this example, the data acquisition function of the neutral loss scan and the parent ion scan is realized by using a selective response monitoring (SRM, or called multiple response monitoring, MRM) mode. In a neutral loss scanning mode, the constant M/z difference is M B +n-x, namely 93, and the ion intensity data of the parent ion M/z equal to M Z+n-x,MZ+n-x+1,……,MZ +n (namely 182-185) is obtained; in a parent ion scanning mode, the M/z of the constant child ion is M A +x, namely 92, and the ion intensity data of the parent ion with the M/z equal to M Z+x,MZ+x+1,……,MZ +n (namely 182-185) is obtained; When the SRM mode is used for replacement, only ion pair peak areas with the ion/parent ion m/z of 89/182, 90/183, 91/184, 92/185, 92/182, 92/183 and 92/184 need to be collected. Glucose- 13C6(E=98.5atom 13 C%) with known isotope abundance is prepared into 1mg/L sample solution, sample injection analysis is carried out under optimized mass spectrum ion source parameters and the scanning parameters to obtain peak areas corresponding to the m/z ion pairs of 0, 20, 801, 24279, 38, 63 and 1391, deconvolution treatment is carried out on the data by adopting a 'mass cluster method' respectively to obtain the distribution (after normalization) of the isotope heteronumber of AX 0、AX1、AX2、AX3 of 0.000, 0.001, 0.033, 1.000, and calculated to give a distribution (normalized) of the isotopic isomer of E A=98.9atom 13C%;BX0、BX1、BX2、BX3 of 0.000, 0.001, 0.033, 1.000, and calculated to give E B=97.9atom 13 C%. The isotope abundance of the glucose- 13C6 sample can be obtained by weighted average treatment of the isotope abundance of the sub-ion and the neutral missing part, and the isotope abundance is 98.4%. The average abundance obtained for 6 replicates was 98.3%, rsd=0.2%. It is shown that a relatively more common SRM or MRM mode can be used to perform data acquisition instead of neutral missing scan and parent ion scan, achieving a similar detection effect.
The invention utilizes the tandem mass spectrum to quantitatively analyze the ion pair abundance of the stable isotope labeled compound to obtain isotope heterodigital distribution with higher signal-to-noise ratio, thereby obtaining more accurate stable isotope abundance through calculation. Compared with the prior art, the method can more accurately and precisely measure the isotope abundance of the stable isotope product; on the other hand, the method has higher sensitivity and lower detection concentration limit, and can detect low-concentration samples.
The previous description of the embodiments is provided to facilitate a person of ordinary skill in the art in order to make and use the present invention. It will be apparent to those skilled in the art that various modifications can be readily made to these embodiments and the generic principles described herein may be applied to other embodiments without the use of the inventive faculty. Therefore, the present invention is not limited to the above-described embodiments, and those skilled in the art, based on the present disclosure, should make improvements and modifications without departing from the scope of the present invention.