Digital computer method for quantitation of gas-liquid chromatography as applied to fatty acid esters

Chem. Phys. Lipids I (1967) 393-406 qb North-Holland Publ. Co., Amsterdam

DIGITAL

COMPUTER OF

METHOD

GAS-LIQUID

AS APPLIED

TO

FOR

QUANTITATION

CHROMATOGRAPHY FATTY

ACID

ESTERS*

W. O. CASTER,** PHILIP AHN + and R I C H A R D P O G U E t t School of Honw Economics and Institute of Comparative Medicine, University of Georgia, Athens, Georgia,** School ~f Home Economiest and Bio-Medical Data Processin,~, Unit of College o/ Medical Seiencestt, University of Minnesota, Minneapolis, Minnesota Received 5 March 1967 Peak measurements and area conlputations provide a substantial portion of the working man-hours required in gas-liquid chromatography, GLC, work. Modern electronic digital computers not only speed simple routine calculations but make it feasible to employ a series of systematic correction factors designed to increase the over-all accuracy of the analytical restllts in GLC work. Basic to most computation procedures is the assumption that there exists a simple relationship between peak area and sample component weight. For component i: Wti

k (peak area)~

(I)

Bartlet and Smith t) have indicated that GLC peaks closely approximate Gaussian probability curves whose areas can be computed from the equation: Area

x/ 2n Ha .2.507 H a

(2)

where H is the peak height and er is the standard deviation. Furthermore, they report that a is proportional to the retention time expressed either in time or chart distance units. Equation constants become more general when retention time is expressed as a retention ratio, RR, in which the retention time for each component is divided by the retention time for methyl stearate. A combination of these considerations leads to the relationship frequently used to compute routine GLC results: Wti : k H ( R R i )

(3)

where k is a proportionality constant. The utility of this equation is increased by the fact that in many cases retention ratios are more easily and more precisely measurable than are the standard deviations required by equation (2). The work reported here demonstrates that k ofeq. (3) is not a constant, but is a systematic function of retention time and injected sample size. The determination and use of this function in routine calculations can help to avoid analytical errors of 10-407/,, in the case of certain components.

Experimentnl The methyl esters of caprylic (8:0), capric (10:0), lauric (12:0), myristic ( 1 4 : 0 ) , p a l m i t i c ( 1 6 : 0 ) , s t e a r i c ( 1 8 : 0 ) , a r a c h i d i c ( 2 0 : 0 ) , a n d e r u c i c (22: 1) * Institute of Comparative Medicine Publication Number 666

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( ' A S F E R E1 AL.

acids used for standards in this work were obtained in chromatographic purities in excess of 99% from the Hormel Foundation, Austin, Minnesota. Mixture A contained 0.815, 1.381, 2.409, 4.297, 7.634, 13.74, 24.74, and 44.98 o,~ioct ' - -ne above esters. This standard mixture was prepared in two parts. Aliquots (0.8 to 4.6 g) of the low molecular weight esters, caprylate through myristate, were weighed to _+0.02 mg in amounts approximating the desired proportions, and thoroughly mixed. The higher molecular weight esters, palmitate through erucate, were similarly combined, heated to melting, mixed and cooled to room temperature. Methyl erucate was used rather than methyl behenate because erucate provided a chemically stable final mixture that readily liquified at temperatures below 3 5 ' C and showed little tendency for solid separation at temperatures above 20':C. An aliquot of 0.8626 g of the caprylate-to-myristate mixture was added to 8.8280 g of the palmitateto-erucate mixture in a vial, and sealed under nitrogen. The vial was warmed, thoroughly agitated, and cooled to room temperature. This final liquid mixture was subdivided and promptly sealed into a series of small vials and designated as mixture A. The sample preparation procedure was designed to minimize volatilization and weighing errors involved in the handling of small amounts of the liquid components. The composition of mixture A was designed to provide an amount (within 1 2'~;) of each component which was directly proportional to the retention time for that component as seen in table 2 (when values were extrapolated to zero sample size). The composition is thus related to the carbon numbers z) of the components. The G L C records were obtained by the use of a Beckman GC-2A o1" a Beckman GC-4 chromatography unit with thermal conductivity detector and a Honeywell variable speed, extended range recorder allowing peak heights up to 51 inches to be measured (0.1 mV per inch). The G L C unit contained a six foot column of 4~ inch aluminum tubing packed with 80 100 mesh, acid washed, Gaschrom P coated with 201"o by weight of butanediol-succinate polyester. This column was operated at 193~C. The helium gas flow rate was 50 cc/min. Samples were injected with a 1/~1 or 10 H1 Hamilton syringe. In order to check the injection precision for sample sizes less than 1 HI, an aliquot of standard was prepared as a 103o solution in redistilled petroleum ether (35-60"C boiling range), and tenfold higher amounts were injected in each case, and peak heights were compared. On G L C records, heights and widths of less than 5 cm were measured to ___0.02 mm with a cathetometer. Longer distances were generally measured to _+0.2 mm using a machine-divided steel rule and a pair of dividers. Each peak width was measured at various points but expressed as a standard deviation, or, by referring to table 1 which describes the relationship between

395

QUANT1TAT1ON OF GLC TABLE I

Width of a Gaussian curve at different heights above the base line. The width is expressed in relation to the standard deviation, o-, of the curve Height as % ofmaximun2 height

Width a

Height as % of maximum height

Width a

80 75 70 65 60 55

1.336 1.517 1.690 1.857 2.022 2.188

50 45 40 35 30 25

2.356 2.528 2.707 2.898 3.105 3.331

a and the width of the G L C peak as measured at any one of several different heights above the base line. To test the consistency of this method of determining standard deviation, 3 to 5 measurements were made in the region between 30 o/,oand 75 '!;;, of total peak height on each of 8 peaks in 25 consecutive records. The several estimates of standard deviation obtained for each peak agreed with each other within _+0.09 mm for peaks with retention times less than that of methyl stearate and within 2 "~, for the later peaks, when obtained under most operating conditions. Retention times were similarly measured with a steel rule using the initial rise of the solvent (or air) peak as a zero reference time. Estimates of R R were obtained by dividing the retention time of each peak in a given record by the retention time for methyl stearate. Computations were carried out on the Control Data 1604 digital computer at the University of M in nesota or the I B M 7094 at the U niversity of Georgia. C o m p u t e r programs were written in FORTRAN language.

Area-weight relationship If equation (2) is valid, it would follow that mixture A, in which the percentage contribution of each c o m p o n e n t is directly proportional to the retention time for that component, should provide a G L C record in which all peak heights are equal. They were not. Fig. 1 shows the results obtained on three occasions when measured samples of mixture A were injected into the G L C unit. There were systematic and substantial differences. Between each subsequent record, the weight of injected mixture A was increased ten-fold and the attenuation setting of the instrument was increased simultaneously by ten-fold. Had the G L C response been linear over this range, one would have expected all three records to be superimposable. They were not. In all three records the peak heights are lower than expected for samples with lowest and highest molecular weights. The extent of this peak depression

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CASTER

ET AL.

,i ,i i ~,

1

v_

C

iI

Fig. I.

G L C records for 0.3/tl (A), 3/~1 (B) and 30/d (C) aliquots of mixture A (see text) obtained from a Beckman GC-2A unit. Attenuation was changed 10-fold between each record.

was not constant or even proportional from record to record, particularly in the low molecular weight range. There were changes in the shape and position of the peaks. The RR for arachidate and erucate increased with increasing sample size. Very little change was found in the retention times of most earlier peaks. The shape of the peaks observed with a 301d sample was sufficiently bizarre that one might not consider this to be a reasonable operating condition. This is characteristic of a marked over-load in the system employed. These data are of interest, however, because they will serve to demonstrate that the proposed calculation procedures apply, with little loss of accuracya), to records such as this which are something less than ideal, In fig. 2, the peak height data for mixture A are plotted as deviations from the average peak height. They are represented as smooth curves, plotted against retention time. If eq. (3) provided a precise and adequate representation of G L C response, all of these curves should coincide with a single

397

QUANTITATION OF GLC

o

30

20

)

o

t

o

lc

o

g

-10

-20 Retention

time

Fig. 2. Systematic nonlinearities of GLC response. Circles represent relative errors reported on standard mixtures by 13 laboratories (table 2 4)). Curves are members of the family of 5-parameter exponential curves used by eq. (4) to correct for this effect.

horizontal straight line corresponding with zero error. They do not. The smallest errors were observed with the smallest sample. Systematic errors, both positive and negative, increased with increasing sample size. In terms of eq. (3), this means that k is not a constant but varies systematically with both sample size and retention time. One general equation that fits the family of curves shown in fig. 2 involves the sum of two exponential terms. A more precise form of eq. (3), therefore, would substitute this exponential function for k. Rearrangement of the terms yields the equation : Wti = RRi x

Hi

x W//[A + B e x p ( - F x RRi) - C e x p ( - G x RRi)]

(4) which can be used to compute the weight of any component, i, in a mixture. The first portion of this equation includes the variables of eq. (3). The exponential function in the denominator corrects for the nonlinearity G L C response. All five constants (A, B, C, F, G) in the denominator must be determined from G L C data obtained with standard mixtures with known composition. These constants were dependent upon the total injected sample weight. The term, IV,,.,that appears in the numerator was equal to 1.00 for saturated acids. This term was a correction for the broadening of the peaks routinely seen in G L C records involving polyenoic acid esters. The exact

398

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CASTER EI" AL.

values of W,. differ with conditions and must be determined empirically, but were typically around 1.10 for dienes and 1.15-1.20 for trienes and tetraenes. Equation (4) was used to evaluate the three G L C records shown in fig. 1. The average analytical errors observed using eq. (4) in the computation procedure were 0.54, 0.39, and 0.90,~i (absolute) or 2.60, 2.09, and 6.1571, (relative) error for the 0.3 l~l, 3.0 pl and 30 ~tl aliquots, respectively. Repeated determinations with a more limited range of sample sizes, with the use of an inlet heater, and allowing greater peak heights on the extended-range recorder, resulted in average relative analytical errors of 1-2 !!,i, routinely. Precision and accuracy

The computations described in the previous section were sufficiently complex that the aid of a digital computer was required for routine application. It is therefore logical to ask whether the magnitude of the analytical errors to be eliminated, and the improvement in results to be obtained are of sufficient importance to justify the use of such methods. Fig. 3 shows two sets of error data plotted together. The curved lines were derived from our data as described above. They can be interpreted directly in terms of relative analytical error. The points were derived from an interlaboratory survey 4) and represent the relative analytical errors observed on known mixtures of pure esters by 13 laboratories using 5 different types of commercially available G L C units incorporating 3 types of detectors. It is seen that over 80% of the survey data points fall within the range of error distribution predicted by the curves ill fig. 2. At R R = 0 to 0.1, most points fall in the range - 10 to + 38"//,, error; from 0.1 to 1.0 ill the range 0 to + 30'!,,, error; and beyond R R = I . 5 in the range of 0 to -301~;; error. Equation (4) uses a family of curves, members of which are shown in fig. 2, to eliminate these systematic errors. The application of eq. (4) to biological samples, or unknown mixtures, poses some problems unless the injected sample weight precisely coincides with that of one of the standards represented in fig. 2. In practice 6 to 12 different known samples of mixture A were run, and an exponential curve fitted to each set of G L C data. The denominator terms of eq. (4) could then be evaluated at any given RR for each of these sample weights. For intermediate sample weights the denominator was evaluated for any RR by interpolation methods. The ultimate precision of G L C measurements was estimated by ,lanak '~) to be of the order of 0.5 ~,~,relative error in all but the earliest (narrow) peaks. By application of analysis of variance techniques to data from repeated runs of like aliquots of mixture A we found that the internal consistency of results

QUANTITATION OF GLC

399

(estimated from the measurement-by-run interaction term) was in the range of 0.7 to 1.6 "J~ relative error for both height and ~ measurements. The relative analytical errors of 1-2 ~,, reported in the previous section suggest that eq. (4) eliminates systematic effects and reduces analytical error to levels very close to the repeatability of this method. Remaining problems handled by this computer procedure relate to component identification and peak resolution.

Peak width We have expressed the width of G L C peaks in terms of the standard deviation of the peak, as estimated with the aid of table I. Bartlet and Smith t) report a substantially linear relationship between RR and peak width. These considerations lead to the relationship: PW=a+bRR

(5)

in which peak width, PW, is expressed as a standard deviation, and terms a and b are the intercept and slope of the line. Hopefully, a is zero or small. To evaluate a, one must define a starting point on the time scale. When we used the time of the initial recorder response (initial rise in the solvent or air peak) as the zero for all time measurements in a given record, a approached zero. The least squares straight lines relating RR to standard deviation (expresssed in cm) for the curves in fig. 1 are, for 0.3 Ill: PW = 0.03176 + 1.024 RR for

(6)

318: PW = - 0.1347 + 1.569 RR

(7)

for 30 id: PW = - 0.6643 + 4.475 RR

(8)

In each case the correlation between cr and RR exceeded r=0.995. With increasing sample size, there was an increase in standard deviation reflecting the decrease in theoretical plate efficiency of the column under these conditions. With increasing sample size the value of a in eq. (5) decreased and became negative. This was true not only in the equations shown, but also For intermediate sample sizes, The effect was consistent and progressive. As seen in table 2, these negative values of a can lead to negative estimates of a whenever RR is small. This raises some question concerning the adequacy of the linear model, and produces very large errors whenever these estimates are

TABLE 2

8:0 10:0 12:0 14:0 16:0 18:0 20:0 22:1

Acid

0.060 0.100 0.173 0.310 0.556 1.000 1.804 3.570

RR

0.092 0.140 0.224 0.379 0.663 1.132 2.004 3.982

obs.

0.093 0.138 0.219 0.369 0.641 1.132 2.020 3.970

eq.(4)

Peak width (o-)

0.3 ,ul aliquot

0.092 0.140 0.225 0.380 0.654 1.142 2.020 3.949

eq.(8) 0.06l 0.101 0.172 0.306 0.551 1.000 1.841 3.728

RR 0.091 0.141 0.224 0.386 0.684 1.216 2.431 5.929

obs. -0.037 0.025 0.136 0.346 0.728 1.432 2.748 5.700

eq,(4)

Peak width (o-)

3 pl aliquot

0.091 0.141 0.231 0.406 0.735 1.376 2.688 6.032

eq.(8)

0.054 0.090 0.156 0.282 0.525 1.000 1.982 4.246

RR

0.120 0.186 0.336 0.651 1.377 3.122 7.212 19.005

obs.

0.427 -0.262 0.034 0.598 1.685 3.81 I 8.206 18.337

eq.(4)

Peak width (a)

30 ld aliquot

0.119 0.191 0.336 0.646 1.360 3.090 7.440 18.716

eq.(8)

Relationship between retention ratio (RR), peak width in centimeters, and injected sample volume in microliters for each component of standard mixture A. Observed peak widths are compared with peak widths estimated from equations of the types shown in eqs. (4) and (8) in the text

C,

QUANTITATION O F GLC

4"01

used as a basis for area calculation (as in eq. (2)). Further indications of nonlinearity can be seen in table 2 by comparing the slope (b in eq. (5)) of each line as estimated from the lower molecular weight components with that estimated from the higher molecular weight components. In the case of the data from the 0.3 Itl sample the two slope estimates are in agreement. In the 3/d case the lower molecular weight components provide a slope estimate 50 ":/olower. In the 30/xl case the slope from the lower components is only 20"/,o that estimated from the higher components. This suggests that the early portion of this line curves, and the curvature is dependent upon sample size. Empirically, we have used, to fit these data, least squares equations of the type: PW = a + b R R -

c e x p ( - d RR)

(9)

in which a and c are substantially equal. This type of equation fits the data better (see table 2) and avoids the possibility of negative values. The equations used for obtaining the estimates in table 2 are, for 0.3 I¢l: PW = 0.0489 + 1.0924 RR - 0.028 e x p ( - 4.0124 RR)

(10)

for 3 ILl: PW = - - 4.0199 + 2.2858 RR + 4.0342 e x p ( - 2.2600 RR)

(I 1)

for 30 IA: P W - - - 3.0634 + 5.1222 R R + 3.0836 e x p ( - 1.0955 RR)

(12)

The fitting of these curves was accomplished by means of the Gauss-Newton method. These functions converge smoothly to near zero values as RR approaches zero. As seen in table 2, the results fit the data much more satisfactorily. A reliable measure of peak width is useful in correcting peak heights in those cases in which there is incomplete resolution of peaks. Battler and Smith 1) have presented the appropriate correction equations and have described the conditions of changing peak shape which influence this correction. In our computer program, the equation: corrected height(,)= height(,,) - height(h) e x p ( -

$2/2)

(13)

was applied to correct the higher of two unresolved peaks, a and b, and then was applied to correct the smaller member of the pair. S is the distance, expressed in standard deviation units, between the two peaks. Where more than two peaks were involved, the same process was applied sequentially

402

w'. o . CASTER EF A [ ,

down the series. In practice it was applied to all peaks, even though the correction factor was frequently trivial.

Identification of components There is no substitute for positive chemical identification procedures. However, chemical and mass spectrographic procedures are too costly and time-consuming to be applied to each of the several dozen different components typically appearing in each analytical run for a biological sample. The carbon number~), CN, scale has been used in routine analytical work. It depends upon the fact that there is an approximately linear relationship between RR and the logarithm of the number of carbon atoms in the (saturated) acid portion of the ester which is observed in this homologous series. In fig. 1, retention times were not constant but were dependent upon the injected sample size. This was particularly evident in the case of components with high molecular weights. This general observation can be expressed in the form: R R i = T + antilog[(CN i - 18)/U] + V X i

(14)

for any component i, where T, U, and V are constants to be determined, and X~ is some function of sample size and molecular weight (or RR) of the components with carbon numbers equal to or less than that of i. The nature of this function is determined by the following observations. Corrections are additive. The presence of a large amount of any component delays the appearance of all later components in the record. The magnitude of the delay is not linearly related to component weight, but is more nearly proportional to the square root of the weight. The magnitude of the delay is also dependent upon, and is proportional to, the RR of the component. Even large amounts of solvents, or other components of low RR, have small effects in shifting the position of subsequent peaks. These considerations lead to the relationship: C N i = 18.0 + a I o g [ ( R R , - h Y , ) / ( 1 . 0 - bY18 : o)]

(I 5)

where a and b are constants (approximately 8.33 and 0.009, respectively) that must be determined for each new set of experimental conditions. Y~ is the summation of the products of the term (RR x/component weight) for each of the components appearing prior to i, and Yl~:o is Yi evaluated for methyl stearate. When equation (l 5)was applied to the data of table 2, the average errors of estimation were 0.11, 0.09 and 0.25 carbon number units for the 0.3, 3 and 30/H samples, respectively. This was approximately the error observed

QUANrITATION OF GLC

403

if a different straight line (with RR expressed on a logarithmic scale) was fitted to each case separately. The advantage to eq. 0 5 ) was that it was general and could be applied equally well to unknown samples.

Digital computer program A digital computer program 6) was developed that used the above principles in the computation of G L C results. It accepted G L C chart measurements as input and printed out information on sample composition and component identification. A FORTRAN version of the program that we have used routinely is available.* A substantial part of this program is concerned with the mechanical problems of data input and output. The computational section makes use of eqs. (4), (9), (13), and (15). Many of these equations are interrelated in that they require estimates of component weight, sample weight, peak width and peak height (corrected for errors due to incomplete resolution). The program, therefore, applies iterative procedures in which successive approximations of all of these quantities are obtained until a stable result is achieved. Each of the equations requires certain constants that must be obtained on the basis of G L C output from a series of standard mixtures of known composition. This involves nonlinear curve fitting by procedures which are generally available in computer centers, or by computer procedures that can be furnished.* It takes the Control Data 1604 computer approximately one minute to read in, translate, and assemble this FORTRAN program in machine language. The calculations on each G L C run (with 20-50 ester components) requires 5-10 sec to read in the data, carry out the above computations, and punch out the initial tabulation of results. The final tabulation, listing all identified components, for all G L C samples (up to 100) in a given series is printed out in another 5-10 sec. The primary considerations in designing the program were those of obtaining the maximum precision of output when the input was limited to those quantities which were easily and precisely measurable (height and retention time) plus a minimum of constants from standardization runs. Constants

Appended to the end of the program deck are a series of constants which are used in the computation results from each of a large series of G L C records. Each time the operating conditions on the G L C equipment are changed, a different set of these constants must be determined and substituted * Available from: Dr. Richard Poque, Bio-Medical Data Processing Unit, College of Medical Sciences, University of Minnesota, Minneapolis, Minnesota 55455.

404

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at this point. The first deck of constants includes estimates of W~(see eq. (4)) for each of the group of identified fatty acids. Next are a series of 6 to 12 cards carrying the other constants needed for eq. (4). Each card gives the value for constants A, B, C, F, and G and indicates the size aliquot of mixture A which corresponds to this particular 5-parameter exponential curve. The next constant deck includes the same number of cards, and each gives the 4 coefficients (see eqs. (10) (12)) needed to estimate the peak widths. Other constants (such as the initial estimates required for eq. (15)) are included within the program and can be changed if necessary by repunching one card in the program deck.

Data hTput The initial card in the input data deck contains the problem identification number and descriptive statements. Each subsequent card for that problem contains data relating to a single component in the G L C record, and gives its retention time and peak height. The card either identifies the peak by giving its carbon number (which will later set its position in an array of identified compounds) or else it must give an estimate of Wi to be used with respect to calculation of this component. We frequently assume that all unidentified early components are saturated or monounsaturated, whereas all late unidentified components are polyunsaturated. They are then given the values for Wi which are characteristic of these different types of compounds. It is obligatory that methyl stearate be identified (as 18:0). During the process of reading the data cards, the data for each identified component is placed in a specific position in an array of 24 common esters. Those which are marked as unidentified are placed in sequential positions following this array (up to a maximum of 60 components).

Sample weight estimation The initial step in the calculations is to convert retention time to retention ratio by dividing all retention times by that for methyl stearate. The sample weight (on a solvent-free basis) is estimated by application of eq. (4) to each component and then summing the weight of all components. However, in order to evaluate the 5-parameter exponential term in the denominator of eq. (4), it is necessary first to have an estimate of the sample weight. With the thermal conductivity detector, this weight is usually in the range of 0.1-10 rag. The program uses the 1.01d data to provide initial estimates of the numerical value of the denominator of eq. (4) evaluated for the RRi corresponding to any desired component, i. The sum of component weights calculated in this fashion provides a new and closer estimate of sample weight. This process is repeated (usually 3-5 times until a subsequent

QUANTITATION OF GLC

405

estimate agrees within 0.5% or until 20 iterations have been completed). When an estimated sample size is intermediate between two known standard sizes (for which 5-parameter exponential curves have been determined) the denominator values are calculated for each RRi by linear interpolation between the values estimated from each of the two known standards. This process requires that standards be available for extreme ranges of operation. For this reason our standards have covered the range of 0.01-301tl of mixture A (on a solvent-free basis) for work with thermal conductivity detector. Should the unknown sample fall outside of this range, a print out of this fact is made and the program proceeds to the next GLC problem.

Calculations Using this estimate of sample size, it is now possible to estimate peak width (see table 2). Sequential application of eq. (13) to all components corrects peak heights for incomplete resolution of peaks. Using these corrected peak heights, the weight of each component is recalculated using eq. (4). The sum of these new weights provides a new estimate of sample weight. This entire process is repeated 3 times to provide a constant result. The final total sample weight and individual component weights are used to estimate the percentage of each component in the mixture. Carbon numbers are now calculated with the aid of eq. (15).

Ou@ut The initial line of the output, which is printed at the completion of each problem, provides the problem number and other desired identification together with the final estimate of sample size. Subsequent lines provide, for each component (giving the identified components first), the input data followed by estimates of carbon number, percentage of this component in the total sample, standard deviation (as estimate of peak width), and the corrected peak height. When the results from the final problem have been printed out (a "stop code" is reached) the computer prints out a final tabulation giving the percent of each identified component for all samples.

Summary A digital computer program is described that accepts, as input, peak heights and retention time measurements, and provides, as output, tables of sample composition (both in weight and percentage terms) and information on component identification. Computations are based upon results from GLC records obtained with standard mixtures. A 5-parameter exponential function is used to correct for systematic nonlinearities of GLC. Corrections are introduced for incomplete resolution of peaks. A nonlinear function

406

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is used to correct c a r b o n n u m b e r (equivalent chain length) d a t a for the systematic errors related to fact that each c o m p o n e n t delays the a p p e a r a n c e of all later c o m p o n e n t s . The result o f these corrections is an increase in analytical accuracy by a factor o f up to 10-fold.

Acknowledgments The a u t h o r s wish to t h a n k the Minnesota, and the C o m p u t e r assistance with the c o m p u t a t i o n s by US Public Health G r a n t A M M e t a b o l i c Diseases.

Numerical Analysis Center, University of Center, University o f G e o r g i a for their involved. This work was s u p p o r t e d in part 08595 from the Institute o f Arthritis and

References I) 2) 3) 4)

.I.C. Bartlet and D. M. Smith, Can. J. Chem. 38 (1960) 2057 F. P. Woodford and C. M. van Gent, J. Lipid Res. 1 (1960) 188 B.C. Cox and B. Ellis, J. Chromatog. 20 (1965) 598 E. C. Homing, E. H. Ahrens, Jr., S. R. Lipsky, F. H. Mattson, J. F. Mead, D. A. Turner and W. H. Goldwater, J. Lipid Res. 5 (1964) 20 5) J. Janak, J. Chromatog. 3 (1960) 308 6) W. O. Caster, Federation Proc. 22 (1963) 235