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A simple and fast method of integrating amino acid analyzer data
ANALYTICAL
49,
BIOCHEMISTRY
A Simple
589-591
(1972)
and Fast Method of Integrating Acid Analyzer Data
Amino
The commonly used method for integrating amino acid analyzer data is made very tedious by the use of nonlinear (absorbance) scales to make measurements on the pen recorder chart. Different regions of these scales are subdivided in different ways, and this means that care is needed both in reading the principal value and in interpolations. Absorbance scales are used because the succeeding calculations then require only simple arithmetic, whereas the corresponding calculations on corresponding transmission values are more complex. However, the availability of electronic desk calculators has made these calculations as easy as simple arithmetic, and analysis using the transmission values has now become faster and easier than the traditional method. The principle of the method can be explained by reference to Fig. 1. The transmittance at a point i is represented by a length xi from the line corresponding to 0% T. x0 is the distance between the lines representing 0% T and 100% T. The scale on which the values of x: are measured is arbitrary. -
O%T
K)O%T F’IG. 1. Schematic Copyright All rights
drawing
of peak
@ 1972 by Academic Press, of reproduction in any form
in an amino 589 Inc. reserved.
acid
analyzer
output
trace,
590
SHORT
By definition,
COMMUNICATIONS
the absorbance at a point i
If xb and x,, represent the transmittances at the baseline and at the maximum of a peak, the net height in absorbance units is =
lo&&&,>
=
log&
-
lo&O(~O/~b)
b/xp)
Hence, the absorbance half-height =
3 log,&b/~,)
=
of the peak lo!$(zb/x,)1’2
and the gross absorbance value corresponding =
lo&&O/~,)
-
=
loglO[(~O/x,)
(xp”‘/x
to this net half-height
lo&O(~b/~,)1’2 b1’2)
1
= log10bh/(x~g)1’21 The corresponding transmittance is xh = (Xb~~)1’2. In other words, the transmittance value at which the peak width is to be measured (by the usual “dot-counting” procedure) is just the geometric mean of the values corresponding to the peak maximum and baseline. As in the common method, three calculations are required for each peak. First the net height of the peak in absorbance units is found. Then the half-height is determined, and the width measured by “dot-counting.” Finally the width and the net height are multiplied to give a number which represents, for Gaussian peaks, 0.84 of the area under the absorbance peak. The third of these calculations is the same in both techniques. For the simpler mental arithmetic of the normal method of calculation we have substituted calculations which involve finding the square root, the log to base 10, and so on, and this is the price that is paid for the simplicity of measuring the peaks with a linear scale. Since the charts used in amino acid analyzer pen recorders are nominally 10 in. wide, the calculations of net height A ( = log,, (%/xp) ) , half-height xh( = (x~x~)~/~) and the area (=A X (width at half-height)) could be carried out without loss of accuracy on a standard lo-in. slide rule. However, it would be necessary to enter the values of xb and X~ twice, unless a special-purpose slide rule were constructed, and even then there would be no saving of time. The situation has been transformed by the availability of cheap calculators, such as the Hewlett-Packard model 35, with built-in square root and log functions. This allows all calculations to be made with only one entiy of the data. The procedure for the Hewlett-Packard machine is straightforward and is listed in Scheme 1. The peak area of a peak can
SHORT
591
COMMUNICATIONS
Key the value of q 1 press “enter” twice 1 Key the value of q, 1 press “store,” “multiply,” “42’ 1 Read value of XI, and transfer to chart 1 press “clear 2,” “recall,” “divide,” ‘Llog,O,” “enter” 1 Key peak width in dots 1 press “multiply” and read value of peak area SCHEME
1
be found in about half the time required by the usual method, and the use of linear scales means that less attention is necessary. Since the measurements are made on the same chart as in the conventional technique, there is no change in the accuracy of the calculation. A further small increase in convenience can be obtained by the use of a programmable calculator (such as the Wang 500) which will itself print the peak areas and intermediate results. A program has been written for the Wang 500 which operates in the same manner as Scheme 1, and which prints out the peak number and all intermediate results as well as the final peak area. If the pen-recorder chart has a scale which is linear in transmittance, the values of xb and xP can be read off directly ; otherwise+since the scale is arbitrary-they can be measured with a millimeter ruler. For measuring peaks on expanded scales-X3 or X 10-a constant has to be added to each measured value of zi. If the chart scale is linear or the chart width is an exact number of centimeters, this presents no problem. Otherwise, offset scales can be made by renumbering the scales of millimeter rulers, or a measuring frame can be improvised from a drawing board with a parallel ruler. Millimeter scales offset by suitable lengths are fixed to the base of the drawing board, and the amino acid analyzer output chart taped to the board for measurement. A. F. W. Johnson
University Philadelphia, Received Accepted
Research
Foundation
of Pennsylvania Pennsylvania April May
19, WY.% 82, 1971
19104
COULSON
49,
BIOCHEMISTRY
A Simple
589-591
(1972)
and Fast Method of Integrating Acid Analyzer Data
Amino
The commonly used method for integrating amino acid analyzer data is made very tedious by the use of nonlinear (absorbance) scales to make measurements on the pen recorder chart. Different regions of these scales are subdivided in different ways, and this means that care is needed both in reading the principal value and in interpolations. Absorbance scales are used because the succeeding calculations then require only simple arithmetic, whereas the corresponding calculations on corresponding transmission values are more complex. However, the availability of electronic desk calculators has made these calculations as easy as simple arithmetic, and analysis using the transmission values has now become faster and easier than the traditional method. The principle of the method can be explained by reference to Fig. 1. The transmittance at a point i is represented by a length xi from the line corresponding to 0% T. x0 is the distance between the lines representing 0% T and 100% T. The scale on which the values of x: are measured is arbitrary. -
O%T
K)O%T F’IG. 1. Schematic Copyright All rights
drawing
of peak
@ 1972 by Academic Press, of reproduction in any form
in an amino 589 Inc. reserved.
acid
analyzer
output
trace,
590
SHORT
By definition,
COMMUNICATIONS
the absorbance at a point i
If xb and x,, represent the transmittances at the baseline and at the maximum of a peak, the net height in absorbance units is =
lo&&&,>
=
log&
-
lo&O(~O/~b)
b/xp)
Hence, the absorbance half-height =
3 log,&b/~,)
=
of the peak lo!$(zb/x,)1’2
and the gross absorbance value corresponding =
lo&&O/~,)
-
=
loglO[(~O/x,)
(xp”‘/x
to this net half-height
lo&O(~b/~,)1’2 b1’2)
1
= log10bh/(x~g)1’21 The corresponding transmittance is xh = (Xb~~)1’2. In other words, the transmittance value at which the peak width is to be measured (by the usual “dot-counting” procedure) is just the geometric mean of the values corresponding to the peak maximum and baseline. As in the common method, three calculations are required for each peak. First the net height of the peak in absorbance units is found. Then the half-height is determined, and the width measured by “dot-counting.” Finally the width and the net height are multiplied to give a number which represents, for Gaussian peaks, 0.84 of the area under the absorbance peak. The third of these calculations is the same in both techniques. For the simpler mental arithmetic of the normal method of calculation we have substituted calculations which involve finding the square root, the log to base 10, and so on, and this is the price that is paid for the simplicity of measuring the peaks with a linear scale. Since the charts used in amino acid analyzer pen recorders are nominally 10 in. wide, the calculations of net height A ( = log,, (%/xp) ) , half-height xh( = (x~x~)~/~) and the area (=A X (width at half-height)) could be carried out without loss of accuracy on a standard lo-in. slide rule. However, it would be necessary to enter the values of xb and X~ twice, unless a special-purpose slide rule were constructed, and even then there would be no saving of time. The situation has been transformed by the availability of cheap calculators, such as the Hewlett-Packard model 35, with built-in square root and log functions. This allows all calculations to be made with only one entiy of the data. The procedure for the Hewlett-Packard machine is straightforward and is listed in Scheme 1. The peak area of a peak can
SHORT
591
COMMUNICATIONS
Key the value of q 1 press “enter” twice 1 Key the value of q, 1 press “store,” “multiply,” “42’ 1 Read value of XI, and transfer to chart 1 press “clear 2,” “recall,” “divide,” ‘Llog,O,” “enter” 1 Key peak width in dots 1 press “multiply” and read value of peak area SCHEME
1
be found in about half the time required by the usual method, and the use of linear scales means that less attention is necessary. Since the measurements are made on the same chart as in the conventional technique, there is no change in the accuracy of the calculation. A further small increase in convenience can be obtained by the use of a programmable calculator (such as the Wang 500) which will itself print the peak areas and intermediate results. A program has been written for the Wang 500 which operates in the same manner as Scheme 1, and which prints out the peak number and all intermediate results as well as the final peak area. If the pen-recorder chart has a scale which is linear in transmittance, the values of xb and xP can be read off directly ; otherwise+since the scale is arbitrary-they can be measured with a millimeter ruler. For measuring peaks on expanded scales-X3 or X 10-a constant has to be added to each measured value of zi. If the chart scale is linear or the chart width is an exact number of centimeters, this presents no problem. Otherwise, offset scales can be made by renumbering the scales of millimeter rulers, or a measuring frame can be improvised from a drawing board with a parallel ruler. Millimeter scales offset by suitable lengths are fixed to the base of the drawing board, and the amino acid analyzer output chart taped to the board for measurement. A. F. W. Johnson
University Philadelphia, Received Accepted
Research
Foundation
of Pennsylvania Pennsylvania April May
19, WY.% 82, 1971
19104
COULSON