ANALYTICAL BIOCHEMISTRY 69, 474-484 (1975)

A Computer Program for Processing Data from

Amino Acid Analysis and for the Calculation of

Molecular Weights from Those Data’

KEITH SCOTT,~ GRAEME R. CANNELL,~ AND BURT ZERNER~

Department of Biochemistry, University of Queensland, St. Lucia, Queensland, Australia 4067

Received February 3, 1975; accepted June 5, 1975

A computer program is described for the calculation of the complete amino acid composition of a protein from the analytical data. The program also derives a molecular weight on the basis of the amino acid composition. The use of the pro- gram for the determination of the molecular weights of the liver carboxylesterases of chicken, horse, ox, and sheep is described.

Several computer programs have been reported for processing data from amino acid analysis. Most are concerned with facilitating integra- tion (e.g., by transferring the digitized photocell signal to punched paper tape), and the calculation of the amino acid content of the solution analyzed (l-7). Whereas the various techniques for the accurate deter- mination of the amino acid composition of proteins are well established, there are no reports in the literature of a computer program designed to carry out all the necessary calculations. In this respect, the programs reported by Starbuck et al. (8) and Gerding (9) come nearest to per- forming this task.

Ozawa and Tanaka ( 10) have reported a program for the calculation of molecular weights from amino acid compositions, but its usefulness would appear to be limited to relatively small proteins. There are several mathematical procedures reported for the calculation of molecular weights from amino acid composition which are based on finding a minimum in the function

y(w) = 2 Wi [x&w) - nearest integer (w)]*, i=l

(1)

where i is the amino acid being considered, x is the analytical value, W is

1 This work was supported in part by the A.R.G.C. (Australia) and by Grant GM 13759 from the Institute of General Medical Sciences of the U.S. National Institutes of Health.

2 Commonwealth Postgraduate Student. 3 To whom correspondence should be addressed.

474 Copyright Q 1975 by Academic Press, Inc. All rights of reproduction in any form reserved.

PROGRAM FOR AMINO ACID ANALYSIS 475

some weighting factor, and w is the trial molecular weight (11-14). In these procedures the weighting depends on the accuracy of the analysis (12), the relative abundance of the amino acid (12,13), or the variance in the analyses (14). In only one of these reports is a computer program available (13).

In this paper we report a computer program for the calculation of the complete amino acid composition of a protein from the analytical data, and of a molecular weight from this composition. The results of the application of the program to the amino acid analyses of liver car- boxylesterases are also reported.

METHODS

Amino acid analysis. Amino acid analyses were carried out on a modified Technicon AutoAnalyzer or a Technicon TSM Amino Acid Analyzer. Half-cystine + cysteine was measured as cysteic acid after oxidation of the protein with performic acid (15). Tryptophan was deter- mined spectrophotometrically (16). The preparation and hydrolysis of the samples, oxidation of the protein, amino acid analysis, and tryp- tophan determination have been described by Scott and Zerner (17).

The precision of the results from a series of calibrating analyses was examined, and the maximum average deviation from the mean was found to be r+ 1.2% ( 17). The equivalent figure for a series of analyses of a protein hydrolysate was -+ 1.3%.

The computer program. The program was prepared in Fortran IV for use with a Digital Equipment Corp. computer, model PDPlO. It has been designed for our particular analytical procedure but is sufficiently flexible for general use. It is written in three parts.

The program, part 1. The input data for this part of the program are given in Table 1, in the form in which they are printed out with the output.

The standard values for each amino acid are averaged, and this average is used in the following calculations. The input analytical values for each amino acid, a, are taken separately and treated as follows:

F . (area for (Y in sample) * (nmoles of (Y in standard) (area for a in standard) 3

where

F = (area for nleu in standard) * (nmoles nleu in sample) (area for nleu in sample) * (nmoles nleu in standard)

sample refers to the actual sample analyzed, and nleu is the internal standard, norleucine. This process converts the values to nanomoles and adjusts all analyses to bring the norleucine values equal to the theoreti-

476 SCOTT, CANNELL, AND ZERNER

TABLE 1

INPUT DATA FOR PART 1 OF COMPUTER PROGRAM; ANALYSIS OF CHICKEN CARBOXYLESTERASE, JUNE 16, 1973

Integration data”

Column 1 Residue weights0 Columns 2 and 3 20-hr hydrolysate (in duplicate) Columns 4 and 5 40-hr hydrolysate (in duplicate) Columns 6 and 7 70-hr hydrolysate (in duplicate) Columns 8 and 9 20-hr hydrolysate of oxidized protein (in duplicate) Columns IO-16 Standard analyses for native protein Columns 17-23 Standard analyses for oxidized proteinC

Other input data

1. 25.0 nmoles of each amino acid was used for each standard analysis 2. 25.0 nmoles norleucine was present in each sample analyzed 3. 2500 nmoles norleucine was present in each sample hydrolyzed 4. Separate standards were used for oxidized protein 5. Hydrolysis times were 20.00, 40.00, and 72.00 hr 6. Azso is 0.791 and AZ,,* is 0.535 for trp calculation 7. Enzyme concentration in spectrophotometer cell is 0.704 (53) g/liter

a Areas under peaks, in integrator counts or other arbitrary units. b Residue weights are stored in the computer, and not included in each input. ’ When the same standards are used for both native and oxidized proteins, these columns

are omitted and the appropriate statement included in other input data No. 4. Values for cysteic acid are then included in columns 10-16.

cal amount present in each analysis. Thus, the six analyses become directly comparable, as do the duplicate analyses of the oxidized protein. These data are then printed out, as well as being stored in the computer. At this stage, the operator can examine the data to detect any clearly erroneous results, which can then be deleted in Part 2 of the program.

The program, part 2. This part of the program makes any necessary deletions and extrapolations, and then calculates the amount of each amino acid (nanomoles), including (l/2 cystine + cysteine) and tryp- tophan, in the sample analyzed.

Where a value is to be deleted, the input includes a card punched with the row and column numbers for that value, and the computer will sub- stitute a zero.

The release of valine, isoleucine, and leucine from peptides may be in- complete in 20 and even 40 hr. Therefore, any low 20- and 40-hr values can be deleted as described above. Duplicate values from each hydrol- ysis time are averaged.

The amounts of serine, threonine, and possibly tyrosine present in the sample at zero hydrolysis time are calculated by plotting versus time, the

PROGRAM FOR AMINO ACID ANALYSIS 477

logarithms of the values found for the three hydrolysis times. The inter- cept is found by the method of least squares. The input data include the row numbers of those amino acids to be extrapolated by this method.

For all other amino acids, the values from the three hydrolysis times are averaged.

The cysteic acid value is corrected for an amount of destruction as defined in the input data. In this work, a value of 6% was used (15). The molar ratios of cysteic acid to glutamic acid, glycine, alanine, and phenyl- alanine are then calculated. These ratios are applied to the values (nanomoles) for the respective amino acids calculated from the analysis of the native protein to give four values for the (l/2 cystine + cysteine) content of the sample analyzed. The four values are averaged, and this figure is incorporated into the amino acid composition.

The tryptophan content of the sample of protein analyzed is calculated from the measurements taken from the ultraviolet spectrum of the pro- tein in 6 M guanidine hydrochloride, after allowing for the contribution of cystine. The percentage of cysteine residues which exist as disulfides is used to derive a correction factor which is included in the input data. In the present work, this percentage was assumed to be 100. The com- puter calculates the contribution of the derived cystine content to the A,,, and AZS8 values and subtracts accordingly. This subtraction is incor- porated into Eq. (2), which is used to calculate the number of tryptophan residues corresponding to the weight of protein analyzed.

Trp= (106’W.b)- 0.01173 c-cys

c- 186.22b ’

where Trp is the number of nanomoles of tryptophan in the sample analyzed, W is the weight (milligrams) of the sample analyzed (excluding tryptophan) found from X [(number of residues) x (residue weight)], c is the concentration (grams per liter) of protein in the spectrophotometer cell, cys = (l/2 cystine + cysteine, in the sample analyzed) x (a correc- tion factor), and b = (3.223 X 1O-4 Azss) - (9.692 x 1O-5 A,,,).

Equation (2) is derived from Eq. (3), which is taken from Edelhoch (16).

N,,, = (e2J3 103) - (~&10,3 18); (3)

where N,, is the number of moles of tryptophan per mole of protein. The tryptophan value obtained from Eq. (2) is incorporated into the

amino acid composition of the sample analyzed, which is then complete. The weight of protein analyzed (as its hydrolysate) is found from

Z [(number of residues) X (residue weight)], and this is multiplied by the ratio of norleucine in the sample hydrolyzed to that in the sample analyzed to give the weight of protein hydrolyzed (theoretical).

478 SCOTT, CANNELL, AND ZERNER

TABLE 2 OUTPUT FROM PART 2 OF COMPUTER PROGRAM; CHICKEN

CARBOXYLESTERASE, JUNE 16, 1973

Nanomoles in Amino acid sample analyzed Residuesi68,OOO

Ala 26.87 53.39 GUY 22.02 45.40 Phe 15.69 32.34 ASP 23.99 49.46 Glu 37.87 78.08 ‘4% 12.65 26.07 Leu 23.55 48.56 Ile 14.02 28.90 His 5.37 11.07 LYS 19.03 39.24 Met 7.34 15.14 pro 14.12 29.12 ‘br 10.37 21.39 Val 24.52 50.54 CYS 3.52 7.26 Ser 18.23 37.59 Thr 11.89 24.52 Trp 4.46 9.20

(4 cystine + cysteine) from each molar ratio Ala 0.00 GUY 3.57 Phe 3.47 Glu 0.00

Other data

1. Weight of protein analyzed was 0.033 mg 2. Weight of protein hydrolyzed was 3.30 mg 3. Partial specific volume is 0.738 cm3g-i 4. Amino acids extrapolated were ser and thr 5. Percentage cysteic acid destroyed was 6.0 6. Cystine content is 50% of (1 cystine + cysteine).

The final output gives the amino acid composition in nanomoles of each amino acid in the sample analyzed and the number of residues of each amino acid for any given molecular weight.

The partial specific volume is calculated from the residue numbers (nonintegral) using the method of Cohn and Edsall (18).

The data previously stored in the computer from Part 1 of the pro- gram are printed out with the output, the requested deletions being shown. The remainder of the output is given in Table 2.

The program, part 3. This part of the program aims to find from the

PROGRAM FOR AMINO ACID ANALYSIS 479

data produced by Part 2, the most likely set of integral residue numbers, and from this, the most likely molecular weight.

A “key” amino acid is chosen and a range of integral values selected for it such that the required molecular weight range is covered. For each value the amino acid composition is calculated from the analytical data. The deviation of the number of residues of each amino acid from the nearest integer is found and expressed as a percentage of that integer. This value is referred to as D (Table 3). An expected analytical error is deduced by inspection of the experimental results (e.g., + 1.5%). Where D is less than this expected error, its value is set equal to that of this error, the assumption being that the analysis does not distinguish between different values of D when they are less than the analytical error. The D values are averaged for each set of residue numbers corre- sponding to each integral value of the “key” amino acid. This average value, E, is a measure of the nearness of the set of nonintegral residue numbers to the corresponding set of integers.

If any residue number is so large that the D value cannot exceed the

TABLE 3 OUTPUT FROM PART 3 OF COMPUTER PROGRAM"; CHICKEN

CARBOXYLESTERASE, JUNE 20, 1973O

Amino acid Residues Residues D

Ala 54.19 54 GlY 44.41 44 Phe 31.64 32 Asp 48.38 48 Glu 76.38 76 Au 25.50 26 Leu 47.50 48 Ile 28.27 28 His 10.83 11 LYS 38.39 38 Met 14.81 15 pro 28.49 28 Tyr 20.93 21 Val 49.44 49 CYS 7.10 7 Ser 36.77 37 Thr 23.99 24 Trp 9.00 9

Mol Wt 66,524 66,480

0.34 0.94 1.13 0.80 0.50 1.91 1.03 0.97 1.55 1.02 1.26 1.74 0.36 0.90 1.46 0.61 0.05 0.00

n This output was produced for the calculations based on Trp = 9.00. A similar output is produced for each such calculation.

* Residue numbers over 33 excluded from calculation of E. Percentage analytical error = 1.50. E = 1.57; 3 = 0.738 cm3g-I.

480 SCOTT, CANNELL, AND ZERNER

analytical error, the value of E for the set including that residue number will be biased toward a low result. Such numbers are therefore excluded from the calculation of E.

The whole process is repeated for a number of “key” amino acids (generally three or four in this work) thus giving a set of E values each corresponding to a particular molecular weight in the range selected. The most likely solution is taken to be that which gives the lowest value of E.

This part of the program also provides for the calculation of the partial specific volume of the protein by the method of Cohn and Edsall (18). The calculation is carried out for each set of integral residue numbers.

An example of the output from this part of the program is shown in Table 3.

RESULTS

The computer program described herein has been applied to the amino acid analysis of five liver carboxylesterases. The amino acid composi- tions of these enzymes calculated using Parts 1 and 2 of the program are reported elsewhere (17).

Part 3 of the program was applied to analytical data obtained with bovine ribonuclease and produced a minimum value of E for which the corresponding set of integral residue numbers exactly agrees with the known amino acid composition of this protein. The results are shown in Fig. 1. The application of the program to an amino acid analysis of beef spleen acid phosphatase produced a molecular weight value of 22,500 which is in good agreement with the value of - 23,000 measured for the same enzyme by Glomset and Porath (19) using equilibrium sedimenta- tion. The outputs from the application of Part 3 of the program to the analytical data from one of the liver carboxylesterases are summarized in Table 4. The molecular weights derived from each set of integral resi-

FIG. 1. Determination of the molecular weight of bovine ribonuclease using Part 3 of the computer program described. The minimum value of E corresponds to the most probable set of integral residue numbers within this molecular weight range.

PROGRAM FOR AMINO ACID ANALYSIS 481

TABLE 4

EVALUATION OF MOLECULAR WEIGHTS OF CHICKEN LIVER CARBOXYLESTERASE DERIVED FROM AMINO ACID COMPOSITION”

Molecular weight Eb

44,512 1.87 49,088 2.17 49,508 2.21 51.877 2.61 53,920 2.10 54,918 2.17 58,367 2.10 59,117 2.10 61,480 2.36 63,088 2.24 66,480 1.57 67,290 1.63 67,419 1.67 73,864 1.65 76,287 2.00 79,969 2.08 80,866 1.90 81,290 1.86 88,633 2.39

a Calculated using Part 3 of the computer program as described in text. * E is a measure of the nearness of the set of nonintegral residue numbers calculated

from the analytical data to the corresponding set of integral residue numbers. For this calculation, residue numbers greater than 33.0 were excluded, the analytical error being taken as ? 1.5%.

TABLE 5 MOLECULAR WEIGHTS OF LIVER CARBOXYLESTERASES DERIVED FROM

AMINO ACID COMPOSITIONS

Esterase MW (I)* MW (2)

Chicken 66.480 67.290 Horse 67.081 78,798 ox 67,766 79,033 Sheep 65,956 78,085 m 79,582 67,181d

u Calculated using Part 3 of the computer program described in the text. b Molecular weight corresponding to the minimum value of E. c Molecular weight corresponding to the value of E nearest to the minimum. d Taken from the set of E values calculated excluding (4 cystine + cysteine).

482 SCOTT, CANNELL, AND ZERNER

due numbers (i) are shown together with the corresponding values of E. The molecular weights corresponding to the minimum values of E ob- tained for each of the five esterases are shown in Table 5. The nearest alternatives are also given in this Table.

DISCUSSION

Parts 1 and 2 of the computer program described herein have pro- vided a convenient and time-saving means of calculating the amino acid composition of a protein from the raw analytical data. The program has been written so that a number of factors involved in the calculations have to be included in the input data thereby making it more readily adaptable to different proteins and different procedures. Although it is designed to carry out all the necessary calculations involved in the con- ventional determination of the complete amino acid composition of a protein, it could as easily be used to compute the amino acid composi- tion of a single sample, e.g., when only one hydrolysis time has been used.

We have used the program for analyses in which the peak areas were integrated on a manually operated integrator. It could be readily modi- fied to accept data on a punched paper tape produced by a teletype con- nected to an automatic integrator.

The application of Part 3 of the program to analytical data from ribonuclease and beef spleen acid phosphatase indicates its validity for proteins of this size.

For each of the five liver esterases, this part of the program has selected the same two values for the molecular weight derived from the amino acid composition, namely, - 67,000 and - 80,000. In four of the five cases, the value of - 67,000 is favored, although possibly not signifi- cantly. In the case of the pig esterase, the value of - 80,000 is favored, but that of - 67,000 is a near alternative when (l/z cystine + cysteine) is excluded from the calculations. A comparison of our analysis of the pig esterase with those from other laboratories suggests that our value for (l/2 cystine + cysteine) may be low (17).

The results produced by this part of the computer program will be valid when the molecular weight of the protein is appropriately low in relation to the analytical accuracy. That the application of this program to the analyses of four esterases has derived molecular weights which are in agreement with those obtained in this and other laboratories by other physicochemical methods (20-22) is further evidence for the valid- ity of the procedure. However, as it has barely distinguished between two possible molecular weights, we are probably near the limiting condi- tions of the technique in these cases.

The program reported by Ozawa and Tanaka (10) would appear to be difficult to apply to proteins with molecular weights greater than

PROGRAM FOR AMINO ACID ANALYSIS 483

- 20,000. In the case of larger proteins the program would produce up to several integers for many residues, in which case it is not clear how one would select probable combinations.

The work described herein is essentially a process of finding a min- imum in the function

2 (I (xi - nearest integer) 1 X 1 OO/nearest integer)

Y=i=’ n . (4)

Weighting is’ therefore inversely proportional to the abundance of the amino acid.4 Katz (12) investigated different weighting procedures and found that, in general, all procedures gave a minimum at the same molecular weight. A similar investigation by Rickert and Elliott (14) produced the same general result, except that when a wide molecular weight range was studied, the correct value was obtained only when weighting was inversely proportional to the variance. However, such a procedure is not very practical, as the latter authors calculated that more than 20 analyses could be necessary to find the variance.

Our procedure differs from that of Gibbs and McIntyre (13) in that certain values are excluded from the calculation when they are so large that their percentage deviation from the nearest integer cannot exceed the percentage analytical error, and, when the percentage deviation is less than the analytical error it is made equal to that error before averaging is carried out. In the case of the program of Gibbs and McIn- tyre, the largest protein for which a definite minimum was given con- tained - 350 residues and in this instance the agreement was +25 resi- dues, i.e., an agreement of -&2500 for a molecular weight of - 35,000. In comparison, the program reported here has been significantly more successful in that it has given agreement of within 22000 for proteins with molecular weights of - 65,000.

It may be concluded that the procedure reported here can give a reli- able estimation of the molecular weight of a protein, given analytical accuracy of the order available in current techniques of amino acid anal- ysis and a molecular weight as high as 50,000, or even higher.

Copies of the computer program are available on request.

ACKNOWLEDGMENTS

We are pleased to acknowledge the assistance of the Computer Centre, University of Queensland. We are also grateful to Miss A. I. Keto and Mr. H. D. Campbell for the use of analytical data on ribonuclease and acid phosphatase, respectively.

4 This function will decrease with increasing molecular weight, as seen in Fig. 1. A number of procedures reported prevent this decrease by a different weighting term (1 I-13, 23, 24) and we are currently investigating the relative values of these modifications.

484 SCOTT, CANNELL, AND ZERNER

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