In other experiments we have determined the reproducibility of sedimentation distance in separate runs. When the utmost care is exercised to control temperature and speed, the reproducibility is on the order of *0.06 cm., which corresponds to a *2.5% variation in absolute sedimentation coefficient. Since the machine was built, 5 or 6 workers have been using it routinely and over 1000 gradients have been satisfactorily generated. We have found it a rapid, convenient, flexible, and accurate method. ACKNOWLEDGMENT
Figure 4.
Test sedimentation of T 7 DNA in gradients
in measuring the refractive index of the solutions. We have tested the gradients produced by the machine in centrifugation experiments using T7 bacteriophage deoxyribonucleic acid as a standard. Figure 4 shows the profiles obtained in two runs of different durations in which identical samples were sediniented in the three buckets of the Spinco SW39
rotor. Samples of P3*-labcled DNA were spun for 3 hours (peak 1) and 6 hours (peak 2) at 35,000 r.p.m. The positions of the centers of gravity of the three peaks varied by no more than 10.01 cm. in both experiments. This reproducibility makes it possible to determine the relative sedimentation coefficients of samples run in different buckets.
The authors thank C. A. Thomas, who gave this project impetus through his realization of the need for a precision gradient maker. We also thank T. C. Pinkerton and T. J. Kelly for help in performing some of the experiments reported, and W. E. Love for the use of his Ro17al McBee LGP-30 computer. This work was done while both of us were pre-doctoral fellows of the Public Health Service. LITERATURE CITED
(1) Britten, R. .J., Roberts, R. B., Science 131, 32-3 (1960). (2)(de Duve, C., Berthet, J., Beaufay, H., Progress in Bio hysics and Biophysical Chemistry,” Vof: 9, 326-69, Pergamon Press, New York, 1959. WORKsupported by Atomic Energy Commission Grant AT(30-1)-2119.
A Nomogram for Calculating the Results of an Automatic Amino Acid Analysis W. A. Schroeder, W. R. Holmquist, and J. Roger Shelton, Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, Calif. 91 109
the description by Spackman, S Stein, and Moore (6) of an automatic amino acid analyzer, continued INCE
improvement has increased the number of analysis from one to several per day. On the other hand, because the time required to calculate the results of the analysis by hand from the automatic record can not be appreciably shortened per analysis, commercial integrators have become available and computer systems have been devised to do all or part of the calculation (7). Manual calculation is normally done by the formula H x TV/C = pmoles, where H is the net absorbance of the peak, W the width a t half net absorbance (in terms of the number of dots) , and C a constant from the standardization (6). For convenience, calculation done in this way will be referred to as “the usual method.” This formula is valid for Gaussian shaped curves, and, in practice, is sufficiently accurate even for curves which deviate slightly from
a true Gaussian form. However, experimentally W is constant to within a few per cent over a wide range of H ; theoretically, also W is independent of H for Gaussian-shaped curves if the concentration of solute is not so high as to alter the number of theoretical plates and the distribution coefficient of the system (6) Consequently, the quantity of an amino acid is directly proportional to H itself to the same degree that W remains constant. Because of this relationship all calculations may be made readily with a nomogram. We shall describe the construction and use of a nomogram which permits the calculation of the results of an amino acid analysis in 5 minutes. It should be emphasized that this nomogram is a graphical representation of the relationship between four variables that is expressed by I
p=-
(P - B) K
where p is an amount of material whose dimensions depend on the constant K , P is the peak height, and B is the base line. It should be useful wherever such a relationship exists as it does, for example, in gas chromatograms. USE OF THE NOMOGRAM
The five scales of this nomogram are designed to subtract the base line absorbance B from the maximum absorbance P of the peak and to convert this difference H , by appropriate intersection of a straight line with other scales, to read directly the pmoles of each amino acid. The manner in which this is accomplished is shown in Figure 1. On the left-hand scale P , the maximum absorbance of the peak is found (for example, at R ) whereas, on the righthand scale B , the absorbance of the base line is located (say a t S ) . The net absorbance is at T where the line from R to S intersects scale H . Scale A A , which is on the left-hand side of scale VOL. 38, NO. 9, AUGUST 1966
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fiducial line is adjusted to the proper absorbances on scales P and B. The pin is depressed to the bottom of the slot to form an axle about which the indicator is rotated so that the fiducial line may be moved to the appropriate mark on scale A A . The quantity of the amino acid is read a t the point where the fiducial line crosses the pmoles scale.
1.0-
-
Figure 1. An illustration of the use of the nomogram for calculating the quantity of an amino acid
0.oL B , has two marks which are designated as ‘(ala” and “lys” in Figure 1. If the quantity of lysine is to be calculated, a line is drawn between T and “lys” as shown. At the intersection of this line with the diagonal pmoles scale, the quantity of lysine in pmoles is read off. I n practice, intermediate lines need not actually be drawn, because the various intersections prior to the final result can be found with a specially designed straight edge to be described later. Furthermore, the complete nomogram will have a mark on scale A A for each amino acid because scales P , B , H , and Hmoles are equally applicable to all the amino acids. Thus, if a peak of alanine had the indicated absorbance and base line, its quantity would be given by the intersection of the line T to “ala” with the pmoles scale as also shown. Figure 2 is a full-scale nomogram that is designed for use with data from the accelerated analytical system of Benson and Patterson (2) with highsensitivity cuvettes (3). All scales have been calibrated except scale A A for which variations will occur among analyzers. The size of Figure 2 is such that it may be duplicated directly from the page and calibrated for use. B e cause some duplicating processes may introduce distortion, the original and the duplicates should be carefully compared. If the difference is no more than inch in length or width of the nomogram, the error introduced will be inconsequential. Calibration of scale A A may be made as follows. Suppose the standardization of the analyzer had been made with 0.2 pmole of each amino acid. For each amino acid, the value of H is found and a line is drawn from the equivalent of T (Figure 1) through 0.2 pmole on the Hmoles scale and extended to scale A A where a mark is 1282
0
ANALYTICAL CHEMISTRY
made and designated with the name of the amino acid. Although unnecessary, complete linear calibration of scale A A can be made, if desired, by using the two numerical points that are given. For other analytical systems, the nomogram may need to be modified as described in the following section. The facility with which the nomogram can be used is hampered by the fact that the point of intersection at T must be remembered or marked so that the line from T to scale A A may be determined. The device that is shown in Figure 3 greatly speeds the use of the nomogram. For a nomogram of the size in Figure 2, a slot is milled in a plastic sheet (Figure 3a). After the nomogram has been taped to this sheet so the scale H is over the center of the slot, the paper over the slot is cut away. The indicator with a fiducial line has the dimensions in Figure 3b. The fiducial line on the under side of the indicator is made by scoring the plastic with a sharp point and filling with India ink or a graduation marker for thermometers. At a point 3 inches from the end of the indicator, a short length of Lucite rod is cemented and drilled as shown in Figure 3c. A spring supports a pin of drill rod to which a head has been soldered, but the pin is allowed to extend about inch below the lower surface of the indicator. In use, the indicator is placed over the nomogram, and the pin is allowed to fall into the slot. Regardless of how the fiducial line is moved along scales P or B, the pin always follows along scale H . (A l/le-inch drill and a l/le-inch mill head will cut the plastic sufficiently oversize so that a l/ls-inch pin will move readily in the hole and in the slot but will not fit so loosely that positioning is inaccurate.) To make the calculation, the
CONSTRUCTION OF THE NOMOGRAM
Theory and methods for the construction of nomograms have been d e scribed by Allcock and Jones (1). The information to be given will allow the construction of a nomogram to fit the requirements of various analyzer systems now in use. Let h and w be the height and width of the nomogram, P M and BM the maximum absorbance values of scales P and B , and k and K the minimum and maximum values of scale A A . I n practice, the nomogram can be conveniently designed on a 7- X 10-inch grid of graph paper where the larger dimension is h. P M and BM use the entire height h, and scales P and B are separated by the width w . Scale P of length h is drawn at the left of the grid with zero absorbance a t the bottom and maximum absorbance P Mat the top and is graduated linearly. At distance w from scale P , scale B of length h is drawn. Scales P and B form two sides of a rectangle. Scale B is also graduated linearly with zero absorbance a t the top and BM a t the bottom. The scale H is drawn a t a distance
(A). to the right of and parallel BM+ PM to scale P. It starts at
~
(B,B+MpM>h above the zero value of scale P and extends to P M . This scale need not be graduated but, if desired, can be graduated linearly between 0 (bottom) and PM. Scale A A represents the net absorbance per pmole of amino acid. T h e r e fore k and K should be chosen as somewhat less and more, respectively, than the minimum and maximum values of C/W for all amino acids. I n Figure 2, the values 1.5 and 6.5 were selected for k and K , respectively. Scale A A is calibrated for each amino acid as already described but it need not be graduated numerically. If it is desired to do so, the graduation is linear with k opposite the zero value of B and K a t (B,B,”pM)h above BM. A mark is now made a t a distance ~
[1 - (k) (e
M ) ] w to the right
PM. A line .. (the pmoles scale) is then drawn between this mark and the lower end of scale H .
of scale P at the level of
H
Figure 2. Full-scale nomogram without calibration of scale AA
VOL. 38, NO. 9, AUGUST 1966
b
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The pmoles scale is graduated by the formula d =
r - P"'1
,-soldered
3/8" dio. L u c i t e w ,
where d is the distance along the pmoles scale from the point of intersection with scale H and p is the number of pmoles. This line then reads directly in pmoles of amino acid. This formula re-
AA.
The nomogram is now ready for use. Recalibration will be necessary if the response of the analyzer should be altered by some factor such as repouring of columns, different photometer dimensions, variation in response of the ninhydrin reagent, change in flow rate, pH and salt concentration of the developer, and temperature. DISCUSSION
Accuracy and Precision. The nomogram is, of course, inapplicable where the analytical procedure or the degree of control by the operator does not meet the requirement that the peak width a t half net absorbance be independent of net peak height. The precision and accuracy of any calculation that is made with the nomogram will be lessened to the degree that this ideal is not met. Regardless of what method of calculation is used, frequent standardization of the analyzer is necessary if meaningful analyses are to be obtained. These standardizations, therefore, should be used to determine whether recalibration of the nomogram is required just as they determine whether different constants should be used in the usual method of calculation. For example, a new preparation of developer may alter chromatographic conditions slightly so that the peaks may be somewhat broadened or narrowed with resultant lowering or raising of the height. The standardization should be used to determine whether this has occurred; if it has, the ANALYTICAL CHEMISTRY
1111e-
on this
SUI*face
i 3 / 1611 Lucite
7-
i
ap -
p+b when the constants have been entered. For making the graduation, useful values of p such as 0.01, 0.02, . . ., 0.1, , , ,, 0.2 etc. should be chosen. Also, between relatively close points such as 0.01 and 0.02, for example, linear graduation does not introduce significant error. Graduation need not be extended beyond pmax6 P M / ~ . Scale A A is now calibrated for each amino acid as already described: the maximum absorbance and base-line values from a known number of pmoles are located on scales P and B , the pin of the indicator is depressed, the fiducial line is passed through the pmoles scale at the appropriate number, and a mark for the given amino acid is made on scale
1284
to drill rod
-spring
x
duces to the simple form d =
"!
1/16" drill rod-
See ( c )
Fiducial line
1/16" Lucite
(b)
1
Figure 3.
Indicator with fiducial line for use with the nomogram
values of the constants as calculated by the usual method will probably be little affected because the area will not be significantly altered but the calculation by nomogram will be affected more because the height has changed. The use of an internal amino acid standard can be helpful in maintaining proper accuracy of the nomogram. In the accelerated procedure of Benson and Patterson (29,the peaks from the short column have a pronounced tendency to broaden as the column is repeatedly used. If this occurs, the nomogram must be recalibrated with a standard run or the column must be returned to its original state by regeneration and reequilibration. In assessing the applicability of the nomogram, more than 50 analyses have been calculated both by the usual method and by the nomogram. The results from the two methods have not differed from eqch other by more than 150/, in the range zero to 0.3 pmole, and, actually, in about four out of five instances, the two results have agreed within *2%. This variation is of the same order as that between two independent calculations by the usual method. This accuracy of the nomogram is all that is required for calculating the results of the analyses of peptides or of biological fluids, but the nomogram should be applied with caution for calculating the analytical data for a protein where the maximum accuracy is desired.
The necessary proportionality between net peak height and quantity t h t is required for accurate calculation with the nomogram appears to be met over the range of 0 to 1.0 absorbance unit for most amino acids; aspartic acid has shown the greatest variation. The particular amino acid analyzer for which this nomogram was devised produces amino acid peaks that visibly depart from Gaussian shape. I t may be that the proportionality would be more strictly maintained and the accuracy of the nomogram thereby improved with an analyzer that produced peaks essentially Gaussian in form. Proline. The amount of proline can be calculated in the following way without resort to a special nomogram. After the values of peak absorbance a t 440 mp and base-line absorbance of a standard have been doubled mentally, the doubled values are found on scales P and B after which the mark for proline is located in the usual way on scale A A . When calculating an unknown amount, the peak and base-line absorbances must, of course, also be doubled. Application to the Shorter Photometer Cuvette. As indicated above, the necessary proportionality for SUCcessful use of the monogram extends, in general, over the range from 0 t o 1.0 absorbance unit. In most instances, the width of a peak increases a t a higher absorbance than that and
the height is proportionally less. However, if the peak is very sharp as in the case of valine, isoleucine, and leucine, the proportionality is maintained up to 2.0 absorbance units. The datz, from the shorter photometer cuvette can then be used with the nomogram in the following way to make the calculation. Peak absorbance and base line from the shorter cuvette are located on the nomogram, and the result in pmoles is multiplied by the appropriate factor that relates the response of the two cuvettes. Modification of the Nomogram. Certain properties of the nomogram in Figure 2 should be pointed out. If scales P , B , and H are left unchanged, then the pmoles and AA scales may be altered in inverse relation to each other. Suppose the 20-mm. cuvettes of Jones (4) were substituted for the 6-mm. cuvettes on which Figure 2 is based : the maximum absorbance for a given amount of amino acid would be about 3.33 times greater. The present pmoles scale can be used to graduate a scale for the longer cuvette on the opposite side. Thus, the response from the longer cuvette will be such that any quantity in micromoles p will lie op-
posite 3.33 p on the present scale. For example, 0.1 pmole will be opposite 0.333 pmole, 0.05 pmole opposite 0.167, etc. After this modification, the marks 1.5 and 6.5 on scale AA of Figure 2 would have the values of 5.0 and 21.6, respectively. Similar modification will make the nomogram applicable to the 15-and 150-cm. columns and the shorter cuvettes of the original automatic procedure (6). Such modifications as these, which permit the calculation of proline and regraduation for different dimensions of cuvettes, follow from the formulas that were used to construct the nomogram initially. In addition, it should be pointed out that all scales may be extended. For example, if the nomogram in Figure 2 were calibrated on scale AA with the data from another analyzer, the geometry of this analyzer might be such that some calibration marks would be above or below the margins of the nomogram: this will not nullify the results. Practical Considerations. Once a nomogram for specific analytical conditions has been devised, it has proved practical to duplicate some tens of copies of the nomogram without
any calibration of scale A A . After attachment to the plastic sheet for use with the indicator of Figure 3, scale AA can be calibrated. If some change in analyzer constants makes it necessary to recalibrate the nomogram or if usage mars it, a new copy can be mounted on the plastic sheet and calibrated. LITERATURE CITED
(1) Allcock, H. J., Jones, J. R., “The Nomogram,” 4th Ed., Sir Isaac Pitman and Sons, Ltd., London, 1952. (2) Benson, J. V., Jr., Patterson, J. A., ANAL.CHEM.37, 1108 (1965). (3) Hubbard, R. W., Kremen, D. M., Anal. Biochem. 12,593 (1965). (4) Jones, R. T., Weiss, G., Ibid., 9, 377 (1964). (5) Morris, C. J., Morris, P., “Separation Methods in Biochemistry,” Equation 4.48 on p. 62, Interscience, New York, 1964. (6) Spackman, D. H., Stein, W. H., Moore, S., ANAL. CHEM. 30, 1190 (1958). (7) Yonda, A,, Filmer, D. L., Pate, H., Alonzo, N., Hirs, C. H. W., Anal. Biochem. 10, 53 (1965). Investigation supported in part by the U. S. Public Health Service, National Institutes of Health, Grant HE-02558.
Cryoscopic Molecular Weight Determinations Using Dimethyl Sulfoxide as the Solvent R. S. George and R. K. Rohwer, University of California, Los Alamos Scientific Laboratory, P. 0. Box 1663, Los Alamos, N. M.
nitro comM pounds encountered in explosives research are so insoluble in the common ANY OF THE ORGANIC
cryoscopic solvents that their molecular weights cannot be determined with acceptable accuracy by the freezing point method. Since dimethylsulfoxide (DhfSO) appeared to be a reasonably good solvent for most organic explosives, we decided to determine whether it was otherwise suitable for cryoscopic work. DMSO has not commonly been used for this purpose in the past, although its convenient melting point (18.5’ C.) and its solvent properties (2) would appear to make it an obvious choice. While there are disadvantages also in its use, our conclusion from the work reported below is that DMSO is a useful and exceptionally versatile cryoscopic solvent. EXPERIMENTAL
Chemicals. Baker Analyzed Reagent DMSO and National Bureau of Standards naphthalene were used as received. Eastman Kodak phenanthrene and xanthone were recrystallized to a constant melting point. The nitro compounds were obtained from military sources. Octahydro1,3,5,7 - tetranitro - 1,3,5,7- tetrazocine (HMX) and hexahydro-l,3,5-trinitro-
s-triazine (RDX) were obtained in a purified form and have a minimum purity of 99.9%. The purity of the other nitro compounds was checked by thin layer chromatography. In several cases where further purification was indicated, the compounds were recrystallized until the desired purity was obtained. Apparatus. Measurements were made with a modified Aminco-Bowman Freezing Point Depression instrument (Xo. 5-2050). Although the mechanical features were retained, the electrical circuit was considerably modified to permit recording of the thermistor bridge output rather than visual observation of an electric eye deflection. The new circuit consists of an unbalanced Wheatstone bridge whose output is fed to a 0-100 millivolt recording potentiometer. Provision has been made for coarse adjustments of one arm of the bridge so that the pen of the recorder may be kept on scale as the thermistor cools. il line operated, Zener diode regulated power supply was used to operate the bridge. With this arrangement, the thermistor provided a readability of 0.004 degrees centigrade. The modified circuit diagram is shown in Figure l. Procedure. The freezing point depression measurements could not be made reproducibly if the solutions
were in contact with the atmosphere because of the highly hygroscopic nature of DMSO. Therefore, the molecular weight apparatus was enclosed in a dry box that was constantly purged with helium. The helium was monitored with a Consolidated Electrodynamics Corp. moisture monitor, and only helium tanks containing less than 10 p.p.m, water were used. It was not possible to monitor the dry box because the moisture monitor will also detect DMSO. All samples were placed in an entry port and purged overnight with helium before bringing them into the dry box. DMSO solutions should be handled cautiously as on contact DMSO is absorbed rapidly through the skin and can carry toxic materials with it. No attempt was made to measure the freezing point temperature directly with this apparatus. Instead, the recorded thermistor bridge output in millivolts corresponding to the freezing point of the solution was used. The values obtained for standard solutions of known concentrations were used to construct a calibration curve from which concentrations of unknown solutions could be interpolated. The thermistor bridge values were obtained by slightly supercooling the solution and then initiating freezing by scratching the side of the test tube with the VOL 38, NO. 9, AUGUST 1966
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