Use of Electronic Computers in Searching Out Nutritio nuI Interrelatio nships SIR: I n the course of a long metabolic investigation which is still in progress a need arose for identifying and cataloging a variety of relationships which were changing while the experiments were in progress. These studies, the specific details and findings of which will be reported elsewhere, deal primarily with the dietary needs of human beings. Although the present paper describes the use of electronic computers in searching out nutritional interrelationships, the technique is not limited to nutritional work. I t should be applicable wherever there is a need for identifying and cataloging interrelated behaviors among large numbers of variables. particularly where the great speed of electronic computers makes possible the performing of calculations so numerous that other equipment would not be fast enough. I n those fields of analysis where vast multitudes of complex calculations are desirable, the use of electronic computers not only saves time and makes feasible the undertaking of otherwise impractical operations, but also undoubtedly. contributes to the accuracy of the calculations. I n the example outlined below, several thousand items of raw data distributed among 184 variables were processed. The printed results, although filling 674 pages, were obtained precisely arranged in a form convenient to manage and easy to use for further reference. Under controlled dietary regimes and standardized procedures of collecting bioloqical materials, analytical data and laboratory measurements were obtained for more than 50 con\tituents which included vitamin?, minerals, other nutrients, selected blood components, and certain personal characteristics of the experimental subjects. For some elements such as nitrogen, data were obtained for as many as 6 within-nutrient Table I. Categories of Change Correlation coefficients Column 1 Column 2 Category (Early) (Late) number
XS
NS * * * at
** **
1848
* **
1 2
3-S
3 4
* ** 1-S * **
ANALYTICAL CHEMISTRY
5 6
7 8
variables, namely, pre-experimental and experimental intakes, amounts excreted in urine and feces, and the computed amounts absorbed and retained. Data for a total of 184 variables were available for interrelational examination. The expression, [ ( T L ) ~ - n],;2, where n = 184, signifies a total of 16,836 different pairs of variables for which correlation coefficients may be computed. Throughout a 7-week experiment 12 human subjects received a t each meal appropriate amounts of commonly served foods which provided dietary intakes of all nutrients a t levels meeting the recommended allowances of the Xational Research Council with the sole exception of protein,/the intake of which was below the NRC recommended level, yet was sufficient to maintain positive nitrogen balance in each subject. Laboratory measurements and analyses of biological materials obtained during 12 consecutive days (days 7 through 18) early in the experiment provided data for a correlational matrix of 184 variables. Replicate measurements and analyses during a similar period (days 37 through 48) near the end of the experiment provided data for a second matrix. By means of an electronic computer 16,836 correlation coefficients representing all possible pairs of variables in each matrix were obtained. Differences between corresponding correlation coefficients in the two matrices were also computed. The results were listed sequentially in a table which when printed required 674 continuous IRlI tabulator leaves and contained a total of 33,672 horizontal lines of computed data. In this table these data were also aligned in three vertical columns: column 1, correlation coefficients from the first matrix: column 2, those from the second matrix: and column 3, the difference between corresponding correlation coefficients in columns 1 and 2 . I n this complete tabulation, the format of which was especially designed for convenience in use as a reference source, all the correlation coefficients with their differences were each listed twice-once under each of the two members of the 16,836 pairs of variables-and arranged in sequence variable by variable starting with variable 1 us. variable 2, and continuing on through variable 184 2's. 183. A computer ( I n 1 1 40K 1620) was programmed to inspect all the values in
columns 1 and 2, select and identify those which were significant, marking with one star for 5% level, and with two stars for 1% level of significance. Significant values for a given pair of variables sometimes occurred only in column 1, sometimes only in column 2, and sometimes in both columns. The changes in magnitude and direction of the interrelationships while the experiment was in progress were classified under 8 major categories arbitrarily numbered as shown in Table I. The machine was programmed to classify the starred correlation coefficients according to this scheme in which the abbreviation, SS, stands for nonsignificant values The correlation coefficients in category 1 were not significant during the early part of the experiment but they were significant at the 57, level at the end of the experiment. I n category 2 they were not significant at the start but they climbed to the 1% level before the experiment ended. In categories 3, 4, and 5 the correlation coefficients were significant at the 5 7 , level at the outset. 1 s the experiment progressed, those in category 3 fell below the 5% level; those in category 4 continued at the same level: and those in category 5 increased to the 1% level. In categories 6, 7, and 8 the correlation coefficients were significant at the lY0 level at the beginning. ?;ear the end, those in category 6 dropped belox the 5% level: in category 7 they decreased to the 5% level; and in category 8 they remained a t the 1% level. These eight, categories of change were subjected to frequency counts as an initial step in probing the hypothesis that numerous and extensive interrelationships exist among a great variety of physiological responses, metabolic processes, and biochemical reactions occurring in the human body. The frequency counts totalled 3580 distributed as follows among the eight categories: 1. 666; 2, 873: 3. 416; 4. 211: 5 , 182: 6, 305: 7, 85; a n d & 842. Categories 2, 5 , and 8 were all significant at the 17, level at the end of the csperiment. and these threp together account for 1897 double-starred ralues. This number, by comparison. is more than 11 times greater than 168, the approximate number of double-starred values (0.01 X 16,836 = 168) nhich woiild have hem expected to appear. by chance had no
intcrrelationships existed among the variables. I3esides the two arrangements, sequential and categorical described above, a third provocative tabulation was obtained by listing for each variable its correlation coefficients with each of the other 183 variables in descending order of rank by difference between values for days 7-18 and those for days 37-48 without regard to sign. This gave clusters of variables having similar magnitudes of change. For example, the correlation coefficients which changed the most during the experiment (and presumably representing the most labile interrelationships) c,lustered a t the beginning of the tabulaation for each variable, while those which changed least (prcsiimably representing the most stable interrelationships,) were found a t the end of the list. Our studies of these
clusters and the changes which they undergo with respect to their labile and stable components are in progress. These three complementary tabulations, each obtained by means of electronic computers, together constitute a heuristic device for systematically searching out evidence for the existence of hitherto unrecognized nutritional interrelationships. Very recently, in the realm of taxonomy, a similar technique of using computers in claqsifying bacteria was described by Sneath ( I ) . ACKNOWLEDGMENT
The author thanks the Human Sutrition Research Division of the Agricultural Research Service of the U. S. Department of Agriculture for its recognition of the importance of searching out nutritional interrelationships. He is
indebted to Elliot J. Bueche, ,Jr., Carole Rose Anderson, and Maureen Mitchell for their technical assistance in processing the multitudes of data, and to Director B. 13. Townsend and his colleagues a t the LSC' Computer Research Center for their help and advice in programming the computers and operating the machines. LITERATURE CITED (1)
Sneath, P. H. A., Advan. Sci. 2 0 , N o .
88, 572 (1964).
WILLIAM H. JAMES Department of Food Science and Technology Louisiana Agricultural Experiment Station Louisiana State Cniversity and Agricultural and Mechanical College Baton Rouge 3, La. 70803 RECEIVED for review March 9, 1964 cepted June 4, 1964.
Ac-
Bracket Method for Molecular Weight Determination of Pyrolysis Products Using Gas Chromatography with a Gas Density Detector SIR: The Martin gas density balance was first proposed by Liberti, Conti, and Crescenzi (3) for molecular weight determination of components by chromatographing aliquots of the sample with two carrier gases. Accurate area measurements of unknown and standard were required because calculation was such that small ,mea errors were magnified in the molecular weight value. Phillips and T'imms ( 5 ) obtained greater accuracy (19;) by trapping out an individual chromatographic component and introducing the component gas into a calibrated gas density balance by careful pressure volume measurements. We have investigated the Gow-Mac gas density detector '(1,4 ) for molecular weight determination of certain volatile pyrolysis products from polymers as an aid in identification cl-f these substances. By using several carrier gases and in particular a carrier gas of higher molecular weight than the unknown substance and one of lowei- molecular weight, the molecular weight of the unknown may be bracketed with good accuracy. The positive and n1:gative peaks obtained (depending on whether the unknown substance has a higher or lower molecular weight tha,n the carrier gas) often serve to classify several components of a complies mixture in a molecular weight range. This qualitative information is an. advantage when using a selective column where retention
times of polar substances are not related to order of molecular weight or boiling point. Molecular weight determinations on two differentiating peaks present in the pyrolysis products of polyethylene glycol adipate and polypropylene glycol adipate (Figures 3 and 4) illustrate an application of the technique. By obtaining chromatograms in carrier gases with molecular weights greater and less than that of the unknown, the calculation of results is an interpolation and gives greater accuracy of molecular weights than the extrapolation method used by Liberti, where the molecular weights of the two carrier gases were more than 100 units less than the unknown. EXPERIMENTAL
Instrumentation.
T h e Gow-Mac gas density detector (hot wire Model 091) was installed in the Podbielniak 9580 chromatograph in place of t h e T / C cell. Operation details are similar to conventional gas chromatographs with one exception: flow rate of the reference gas should always be greater than column flow rate. The instrument has a polarity reversing switch for conveniently obtaining negative peaks. The column was 10 feet long, 1/4-inch diameter stainless steel and packing was 25Tc Paraplex U-148 polyester and 270 phosphoric acid on 60- to 80-mesh Chromosorb P diatomaceous silica. Column temperature was 96" C. and
flow rate was approximately 40 ml. per minute; reference flow rate was 75 ml. per minute and detector current was 140 ma. Pyrolysis was carried out in an evacuated quartz tube, Q, a t approximately 450" C., as shown schematically in Figure 1. The tube (25 cm. x 1-cm. diameter) had ball joints, B, on both ends. One end was attached to a stainless steel socket joint', B , with a syringe needle, N , attached so that the needle could be inserted into a collector syringe, S Y . The other half of the quartz tube remained outside the oven (furnace, F , hinged; inside length, 4 inches; catalog KO. F-9285, Scientific Glass Apparatus Company, Inc., Bloomfield, N. J.) and had a socket joint attached with a suitable cutoff valve, V , to the vacuum pump. The sample, S, contained in a small porcelain boat or wrapped in aluminum foil, was inserted in the cold part, of the tube and pushed near the furnace entrance with a quartz poker, P . An iron ball, d d , placed after the poker was used to move the sample into the hot furnace with an external magnet,, AfG, after the system was evacuated. The collector syringe (50-ml. hypodermic, B-D, glass tip) had a septum attached to the end with a polytctrafluoroethylene sleeve, T, and a small serum stopper, SP. 'The syringe was wrapped with a heating t'ape, H , a n d kept a t about 85' C. for the present work. X porcelain perforated disk was 111 aced in the syringe to aid in mixing the gasps. A small amount of Xliiezon grease was used on the upper portion of the syringe VOL. 36, NO. 9, AUGUST 1964
1849
