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A general bioassay program for desktop computer: Application to somatomedin bioassay
COMPUTERS
AND
BIOMEDICAL
RESEARCH
A General Bioassay Application
8,362-369
(1975)
Program for Desktop Computer: to Somatomedin Bioassay*
L. S. PHILLIPS? AND A. C. HERINGTON: Metabolism Division, Department of Medicine, Washington University School of Medicine, St. Louis, Missouri 63110 Received May 14,1974 This program for desktop computer processes general bioassay data where responses are of the form: z = kl k2 [(x - k&l, Designed for the Hewlett-Packard 9800 computer system with specific application to somatomedin bioassays, the program contains options for manual or paper tape data entry, for variable or constant amount of substrate, for log-log or semi-log transformation, and for computer plotting of dose-response lines. Parallel-line analysis includes calculation of index of precision (A), F (linearity), t (slope), t (parallelity), potency and fiducial limits. This convenient system allows easy examination of the full dose-response lines and rapid selection of the portions appropriate for analysis, which can then proceed without tedious reentry of raw data. INTRODUCTION
Biological assays are frequently required during the isolation and characterization of natural products. These assay systems measure potency by comparing the responses generated by test samples to those generated by a given standard. Since biological systems may be affected by a variety of extraneous factors, the measured responses must be shown to be qualitatively similar for the standard and the unknowns. Dose-response lines are calculated for each substance tested, and assays are accepted as valid only if the lines satisfy predetermined criteria for linearity and parallelity (I, 2). If the paired standard and test substances do not have dose?e?ionse lines which are satisfactory over the full dose range, valid potency ratios * This study was supported in part by Research Grant 5 ROl AM01526 and Training Grant 2 TO1 AM05027 from the National Institute of Arthritis, Metabolism, and Digestive Diseases, Bethesda, Maryland. (William H. Daughaday, M.D., Principal Investigator). t Trainee in Metabolism, supported by Training Grant 2 TO1 AM05027 from the National Institute of Arthritis, Metabolism, and Digestive Diseases, Bethesda, Maryland. Current address: Northwestern University Medical School, Ward Memorial Building, 303 East Chicago Avenue, Chicago, Illinois 60611. Reprint requests to Dr. Phillips. 2 Senior Fulbright-Hays Scholar. Current address: Medical Research Centre, Prince Henry’s Hospital, St. Kilda Road, Melbourne, Australia. Copyright Q 1975 by Academic Press, Inc. 362 All rigbts of reproduction Printed in Great Britain
in any form reserved.
GENERALBIOASSAYPROGRAM
363
may be calculated only for the portions of the lines which meet the criteria for parallel-line assays. The appropriate portions of the lines are not known in advance, and a desirable analytic system must provide for selection of the proper portions of the lines after computation of the full dose-response lines. Manual statistical analysis is prohibitively laborious for assayswith a large number of samples, and existing computer programs often require elaborate hardware or expensive terminals which may not be easily adapted to laboratory needs (3). Desktop computers are readily available, relatively inexpensive, and may be programmed without special training. They are especially well-suited for analysis of biological assays, since they can allow the investigator to examine the full doseresponse lines and to choose those portions appropriate for quantitative comparison. Somatomedin, a polypeptide which is thought to mediate the action of growth hormone in promoting skeletal growth (4,5), is measured in bioassays by the stimulation of sulfate incorporation by cartilage in vitro (6). Tracer (35S)S0, is used to monitor incorporation of sulfate, and results are expressed as pg SO4 incorporated per 100 mg (dry weight of cartilage). In current somatomedin bioassays, pieces of cartilage may be of variable or constant weight, and dose-response lines are calculated after either log-log or semi-log transformation. We report here a general bioassay program for desktop computer, with specific application to somatomedin bioassays. Designed for the Hewlett-Packard 9800 computer system, the program contains options for manual or paper tape data entry, for variable or constant cartilage weight, for log-log or semi-log transformation, and for computer plotting of dose-response lines. Parallel-line analysis includes calculation of index of precision (A), F (linearity), t (slope, t (parallelity), potency and fiducial limits. This convenient system allows easy examination of the full dose-response lines and rapid selection of the portions appropriate for analysis, which can then proceed without reentry of raw data. SYSTEM
This program was originally written for a Hewlett-Packard 9800 desktop computer system, which consists of the 9810A calculator with option 001 (111 datastorage registers), option 003 (2036 program steps), and option 004 (printer). Plug-in instruction blocks ROM 11211A (printer) and 11214A (statistics) are also required. Programming requires direct instructions, without a special language such as FORTRAN; the computer may be programmed manually or by magnetic cards. The statistics block performs simple arithmetic operations and statistical analysis. The optional 9863A tape reader and 9862A calculator plotter (with ROM 11215A) allow data entry by paper tape (teletype) and automatic plot of doseresponse lines, respectively. Using this program, the 9800 computer system will accept dose-response lines composed of ~30 total points at ~5 concentrations; the number of points for each concentration must be constant.
364
PHILLIPS AND HERINGTON PROGRAM
A major feature of this program is the maintenance of accessto the complete dose-responsedata for both standard and test samplesuntil a satisfactory comparison has been made. To accomplish this, the standard dose-responseline is assigned a “line number” of 0 and test samplesare assignedline numbers with values >O. Standard or test dose-responsedata are given different storage locations depending on the assignedline number. Responsesand doses(concentrations) are stored in sequence, separately. Each concentration is designated by its “concentration
FIG. 1. Programflow-chart.A, B, C, D, andE denoteimportantlocationswithin the program.
GENERAL
BIOASSAY
PROGRAM
365
number” (1,2. . . 5 for the first, second. . . fifth concentration entered). The combination of line number and concentration number allows access to any selected concentration with its corresponding group of points. The dose-response data are not erased until new data are entered. A flow-chart is shown in Fig. 1. Data Entry and Line Plot. Unless the plotter option is omitted, graph axes are
RSSRY
ea
I.
IX-Its.-73.
? 1 .L-l
I .3
I .r
1.1
I .a
q .m
8.R
PI. I .
I.7
a.
E.5 1:::
J3.
1:::::::::::::::::::::::
FIG. 2. Computer plot of axes and of full dose-response lines from a representative bioassay. The ordinate (log pg SO,/100 mg dry weight) has been scaled according to the expected maximum and minimum responses. The abscissa has been incremented by one unit for each successiveconcentration (in this assay, 5,10,20, and 40% for each line). The “line number” is automatically printed below each dose-response line. 14
366
PHILLIPS AND HERINGTON
drawn and the ordinate scaled according to the highest and lowest expected responses. Data are then entered for background correction of raw CPM, and for calculation of specific activity. Options are selected for variable or constant weight, and for log-log or semi-log transformation. The standard potency, maximum t for fiducial limit calculations, and number of points for each concentration (all constant) are entered and stored. The line number and total number of points for that line are entered, followed by the uncorrected CPM in sequence. Optional data entry by paper tape is determined by a keyboard signal, “FLAG.” Variable weights are then entered manually unless a constant weight was previously entered, and the data arc stored as “tS0,” (pg SO, incorporated per 100 mg of cartilage). If the log-log option was previously selected, each value is restored as its logarithm. The concentrations are then entered and stored in sequence as their logarithms. The mean response (with SEM) is printed for each concentration. With the plotter option. the full dose-response line (Fig. 2) is plotted by incrementing the abscissa by one unit for each successive concentration and scaling the mean responses by their relation to the highest and lowest expected responses (stored earlier). If a standard line has been entered, a new (test) line is requested: if a test line has been entered, analysis follows. Analysis
From the full standard and test dose-response lines. portions of each line are selected for trial parallel-line analysis. The portion of the standard line is chosen first, by selection of the appropriate concentration numbers. After a set of concentra tions has been chosen, actual line analysis (regression analysis; 3.: test of slope, linearity, and parallelity; potency; and fiducial limits) is signaled from the keyboard by “FLAG.” (The standard is compared to itself for calculation of its fiducial limits). An option allows the use of the portion of the standard line selected previously, omitting the selection of a new line. The concentration numbers for a trial portion of the test line are chosen after the standard line has been selected; an option allows the omission of analysis of the test line (if obviously nonlinear and/or nonparallel) and leads to the request for a new line. After completion of the comparison of trial portions of the standard and test lines, the analysis may be repeated with selection ofdifferent concentrations, or a new sample (line number) is requested.
A partial printout tape from a sample assay is shown in Fig. 3. To minimize operator error, specific instructions appear prior to each separate entry of data. Assay number, date, estimated maximum and minimum responses, background CPM and standard CPM (a dilution of total CPM/tube), total /leg SO, per tube (a constant), dilution factor (to convert specific activity to chosen units), options for variable or constant weight and log-log or semi-log transformation, maximum t
5
e.s+
11111.eee*
^. ._
UC SO4 *q mL)L)a I.,.*“-” DILUTION FRCTOR l.BBBS ENTER WGT IF CON STRNTI 8 IF NOT 1.540* IF LOG-LOG ENTER 1, e IF NOT 1.eeet MRXIMUM T FOR FL 2.8481 POINTS/GROUP s. eee* STD. POTENCY 1.e00* LINE NUllBER e.eee* NO. OF POINTS 20. BBB? CPfl---SET FLRG FOR TAPE 7975. eee 6535. BBU 798?.8BB 8035. eee 7365.080 8287.900
TOTRL
BACKGROUND
I.%! CPN 36.800+ 40. me* STRNDRRD CPN 11235.eee*
VALUE
VALUE
18.r
73.*
12.r
B6I.i
HININUM
NO.
MAXIMUM
DATE
ASSRY
1.047
0.932 ERROR 8.814
iLOPE
iTD CONC ;ET FLAG IONE---OR ‘EST CONC
iTRNDRRD
IERN
STRNDRRD
IERN
STRNDRRD
IERN
STRNDRRD
1ERN
8.354
9.114
2.898
1.004 ERROR 8.829 NU.S, UHEN 0 FOR
8.034
0.909 ERROR
8.781 ERROR 8.825
e.e11
eem eeei
0.812 ERROR
28. 48.
s.eee+ 1e.eetw
CONCENTRATIONS
11167.eee 9388.009
13ss7.eeB 12362. Bllfd
18112.808
8368.089 8252. BBB i213e.eee 7865. BIB
6777.
BBR .___ 564s.eee
7662. BBB sss2.eee 6488. OeB 7342.069 INTERCEPT 8.918
0.477
_..
DF a; 121 1.888 12.800 T SLOPE, DF 8.366 13.888 T PRRRLLELITY~DF 8.800 26. BBB StI 1.888 FIDUCIRL LIMITS 1.219 6.820 TEST CONC NO.S, SET FLAG UHEN DONE---OR e FOR NEW LIME 2.099 3.688 4.088 SLOPE 8.369 INTERCEPT 0.417 ZORRELRTION 8.836 F LINEARITY, DF 8.213 1.800 12.800 r SLOPE, DF s.495 13. eee I PRRRLLELITY,DF 8.292 26. eee :H e. 778 :IDUCIRL LIMITS 1.913 8. see
F LINERRITY,
CORRELRTIOH
2:
eee
ITRNDRRD
IERN
ZRNDRRD
)ERN
ZTRNDRRD
IERN
mei
8.929 ERROR 8.819
8.865 ERROR 0.814
6.774 ERROR 8.821
28; eBe* 48. eeef
ie.eee+
5.
13167.088 ,311QW a’98 ALVZ”.“. DONCENTRRTION! B
12388.
8857. Bee 8738. eee 8898.888 9332. B.BB 9865.818
7932.eei
2%:
CPM---SET2k.. FOR TAPE 6315.888 7812.eee 5785.880
SET FLRG FOR NEU LINE---OR e FOR REPERT RNRLYSIS LINE NUNBER 2.8681 NO. OF POINTS
FIG. 3. Partial printout tapes from the bioassay shown in Fig. 2 (lines 0, I, and 2).
%b::s 7612:eee
ERROR 0.823 .INE NUMBER I. eeec IO. OF POINTS 28. eee+ PI+--SET FLAG OR TRPE 7397. eee 7198.888
;TRNDRRD
IERN
iTRNDRRD
IERN
8.815
;gBgB
91e7:eee ieess.eee 12627.8e0 lesB7.eee 11277.888 13187.eee 14385.eee :ONCENTRRTIONS s.eeet 18.8881 20. eeei 40.8881 IERN 8.831 jTRNDRRD ERROR 8.017 IERN 0.034 iTRNDRRD ERROR
fXxr :;3;:
7180.881 7993. eee
7627.008 1.863 ERROR 8.809 NO.St WHEN 6 FOR
8.943
e.ss2
8.389
3.880 4.880
1.143 3i.eee l.lSB
DF
LIMITS 1.392 0.944 SET FLRB FOR NEU LINE---OR 0 FOR REPERT h4RLYSiS LINE NUMBER 3.eeet NO. OF POINTS 28. Beet
FIDUCIRL
SM
1.674 2.000 16.088 T SLOPE, DF 12.847 18.888 T PRRRLLELITY~DF
F LINERRITY~
CORRELRTION
INTERCEPT
SLOPE
STD CONC SET FLAG DONE---OR TEST CONC TEST CONC NO.S, SET FLAG WHEN DONE---OR B FOR NEW LINE 1.880 2.000
STRNDRRD
MEAN
368
PHILLIPS AND HERINGTON
value for fiducial limits calculation (for minimum tz and chosen probability), the number of points per group (a constant), and the potency of the standard are entered manually at the beginning of the program. Data for each sample are then entered, in sequence. The line number and total number of points are entered manually, followed by the uncorrected CPM in sequence (entered manually or by tape). If the weight is constant, it is processed automatically; if variable, weights are requested and must be entered manually, in sequence. Concentrations for each sample are entered manually, in sequence. The full dose-response line is plotted (Fig. 2) as the series of means and standard errors are printed. For parallel-line analysis, the standard line must be entered prior to the test lines. After inspection of the full dose-response lines, concentration numbers are chosen for a trial pair of standard and test lines, selecting portions which appear to be linear and parallel. (If the previous standard line appears reasonable, repeat selection of the standard may be omitted. If the test line is obviously unsatisfactory, analysis may be omitted entirely and a new test sample requested). In Fig. 2, the last three concentrations (numbers 2,3, and 4) for both the standard (line number 0) and the first test sample (line number 1) yield satisfactory lines: insignificant F(linearity), significant t (slope), and insignificant f (parallelity) as shown in the printout in Fig. 3. All four concentrations may be used for the second test sample (line number 2). If the trial comparison is unsatisfactory, analysis may be repeated using different concentration numbers to form the standard and test lines. After the best possible comparison has been made, a new test sample is requested. With the option for CPM entry by paper tape, a 180-point variable-weight assay may be calculated in 60 min and a 450-point constant-weight assay in 90 min. COMMENT
This program is designed to process dose-response data containing responses of the form: z = k,k,[(x - kJy]. (For somatomedin bioassays, k, represents specific activity, k, the dilution factor, k, the background CPM, x the uncorrected response CPM, and 3’ the cartilage weight.) The program is suitable for any assay system in which responses are of the above form, and in which dose-response relationships are linear after semi-log or log-log transformation. (Other simple transformations could be substituted if desired.) The Hewlett-Packard 9800 system memory limits dose-response lines to ~5 concentrations and ~30 points, or other combinations with a total of 35. This is adequate for most biological assay systems, and all conventional somatomedin bioassays may be analyzed with this program. Since raw responses are corrected and expressed in standard units, the responses in a series of similar assays may be compared for quality control analysis. The program was written specifically for a desktop computer which was small
GENERAL BIOSSAY PROGRAM
enough to permit the investigator and large enough to perform the gator’s choice will be based mainly determined by experience with the allows the analysis to be repeated data.
369
to choose the optimal parallel-line analysis, required operations conveniently. The investion the calculated F and t values, but will also be particular bioassay system in use. This program until satisfactory, without tedious reentry of raw
ADDENDUM
The analysis employed here follows conventional parallel-line statistics (I, 2). A list of specific equations and a copy of the program may be obtained by writing L. S. Phillips. ACKNOWLEDGMENT The authors express their gratitude to Dr. Laurence S. Jacobs for his encouragement and suggestions. REFERENCES 1. FINNEY,
D. J. “Statistical Method in Biological Assay,” 2nd Ed. Griffin, London, 1971.
ARMITAGE, P. “Statistical Methods in Medical Research.” Wiley, New York, 1971. HALL, K. Acta Endocrinoi., Suppl. 163, (1972). DAUGHADAY, W. H. Adu. Znt. Med. 17,237 (1971). DAUGHADAY, W. H., HALL, K., RABEN, M. S., SALMON, W. D., JR., VAN DEN BRANDE, AND VAN WYK, J. J. Nature 235,107 (1972). 6. DAUGHADAY, W. H., PHILLIPS, L. S., AND HERINGTON, A. C. Methods in Enzymology. 2. 3. 4. 5.
93, (1975).
J. L.,
37-B,
AND
BIOMEDICAL
RESEARCH
A General Bioassay Application
8,362-369
(1975)
Program for Desktop Computer: to Somatomedin Bioassay*
L. S. PHILLIPS? AND A. C. HERINGTON: Metabolism Division, Department of Medicine, Washington University School of Medicine, St. Louis, Missouri 63110 Received May 14,1974 This program for desktop computer processes general bioassay data where responses are of the form: z = kl k2 [(x - k&l, Designed for the Hewlett-Packard 9800 computer system with specific application to somatomedin bioassays, the program contains options for manual or paper tape data entry, for variable or constant amount of substrate, for log-log or semi-log transformation, and for computer plotting of dose-response lines. Parallel-line analysis includes calculation of index of precision (A), F (linearity), t (slope), t (parallelity), potency and fiducial limits. This convenient system allows easy examination of the full dose-response lines and rapid selection of the portions appropriate for analysis, which can then proceed without tedious reentry of raw data. INTRODUCTION
Biological assays are frequently required during the isolation and characterization of natural products. These assay systems measure potency by comparing the responses generated by test samples to those generated by a given standard. Since biological systems may be affected by a variety of extraneous factors, the measured responses must be shown to be qualitatively similar for the standard and the unknowns. Dose-response lines are calculated for each substance tested, and assays are accepted as valid only if the lines satisfy predetermined criteria for linearity and parallelity (I, 2). If the paired standard and test substances do not have dose?e?ionse lines which are satisfactory over the full dose range, valid potency ratios * This study was supported in part by Research Grant 5 ROl AM01526 and Training Grant 2 TO1 AM05027 from the National Institute of Arthritis, Metabolism, and Digestive Diseases, Bethesda, Maryland. (William H. Daughaday, M.D., Principal Investigator). t Trainee in Metabolism, supported by Training Grant 2 TO1 AM05027 from the National Institute of Arthritis, Metabolism, and Digestive Diseases, Bethesda, Maryland. Current address: Northwestern University Medical School, Ward Memorial Building, 303 East Chicago Avenue, Chicago, Illinois 60611. Reprint requests to Dr. Phillips. 2 Senior Fulbright-Hays Scholar. Current address: Medical Research Centre, Prince Henry’s Hospital, St. Kilda Road, Melbourne, Australia. Copyright Q 1975 by Academic Press, Inc. 362 All rigbts of reproduction Printed in Great Britain
in any form reserved.
GENERALBIOASSAYPROGRAM
363
may be calculated only for the portions of the lines which meet the criteria for parallel-line assays. The appropriate portions of the lines are not known in advance, and a desirable analytic system must provide for selection of the proper portions of the lines after computation of the full dose-response lines. Manual statistical analysis is prohibitively laborious for assayswith a large number of samples, and existing computer programs often require elaborate hardware or expensive terminals which may not be easily adapted to laboratory needs (3). Desktop computers are readily available, relatively inexpensive, and may be programmed without special training. They are especially well-suited for analysis of biological assays, since they can allow the investigator to examine the full doseresponse lines and to choose those portions appropriate for quantitative comparison. Somatomedin, a polypeptide which is thought to mediate the action of growth hormone in promoting skeletal growth (4,5), is measured in bioassays by the stimulation of sulfate incorporation by cartilage in vitro (6). Tracer (35S)S0, is used to monitor incorporation of sulfate, and results are expressed as pg SO4 incorporated per 100 mg (dry weight of cartilage). In current somatomedin bioassays, pieces of cartilage may be of variable or constant weight, and dose-response lines are calculated after either log-log or semi-log transformation. We report here a general bioassay program for desktop computer, with specific application to somatomedin bioassays. Designed for the Hewlett-Packard 9800 computer system, the program contains options for manual or paper tape data entry, for variable or constant cartilage weight, for log-log or semi-log transformation, and for computer plotting of dose-response lines. Parallel-line analysis includes calculation of index of precision (A), F (linearity), t (slope, t (parallelity), potency and fiducial limits. This convenient system allows easy examination of the full dose-response lines and rapid selection of the portions appropriate for analysis, which can then proceed without reentry of raw data. SYSTEM
This program was originally written for a Hewlett-Packard 9800 desktop computer system, which consists of the 9810A calculator with option 001 (111 datastorage registers), option 003 (2036 program steps), and option 004 (printer). Plug-in instruction blocks ROM 11211A (printer) and 11214A (statistics) are also required. Programming requires direct instructions, without a special language such as FORTRAN; the computer may be programmed manually or by magnetic cards. The statistics block performs simple arithmetic operations and statistical analysis. The optional 9863A tape reader and 9862A calculator plotter (with ROM 11215A) allow data entry by paper tape (teletype) and automatic plot of doseresponse lines, respectively. Using this program, the 9800 computer system will accept dose-response lines composed of ~30 total points at ~5 concentrations; the number of points for each concentration must be constant.
364
PHILLIPS AND HERINGTON PROGRAM
A major feature of this program is the maintenance of accessto the complete dose-responsedata for both standard and test samplesuntil a satisfactory comparison has been made. To accomplish this, the standard dose-responseline is assigned a “line number” of 0 and test samplesare assignedline numbers with values >O. Standard or test dose-responsedata are given different storage locations depending on the assignedline number. Responsesand doses(concentrations) are stored in sequence, separately. Each concentration is designated by its “concentration
FIG. 1. Programflow-chart.A, B, C, D, andE denoteimportantlocationswithin the program.
GENERAL
BIOASSAY
PROGRAM
365
number” (1,2. . . 5 for the first, second. . . fifth concentration entered). The combination of line number and concentration number allows access to any selected concentration with its corresponding group of points. The dose-response data are not erased until new data are entered. A flow-chart is shown in Fig. 1. Data Entry and Line Plot. Unless the plotter option is omitted, graph axes are
RSSRY
ea
I.
IX-Its.-73.
? 1 .L-l
I .3
I .r
1.1
I .a
q .m
8.R
PI. I .
I.7
a.
E.5 1:::
J3.
1:::::::::::::::::::::::
FIG. 2. Computer plot of axes and of full dose-response lines from a representative bioassay. The ordinate (log pg SO,/100 mg dry weight) has been scaled according to the expected maximum and minimum responses. The abscissa has been incremented by one unit for each successiveconcentration (in this assay, 5,10,20, and 40% for each line). The “line number” is automatically printed below each dose-response line. 14
366
PHILLIPS AND HERINGTON
drawn and the ordinate scaled according to the highest and lowest expected responses. Data are then entered for background correction of raw CPM, and for calculation of specific activity. Options are selected for variable or constant weight, and for log-log or semi-log transformation. The standard potency, maximum t for fiducial limit calculations, and number of points for each concentration (all constant) are entered and stored. The line number and total number of points for that line are entered, followed by the uncorrected CPM in sequence. Optional data entry by paper tape is determined by a keyboard signal, “FLAG.” Variable weights are then entered manually unless a constant weight was previously entered, and the data arc stored as “tS0,” (pg SO, incorporated per 100 mg of cartilage). If the log-log option was previously selected, each value is restored as its logarithm. The concentrations are then entered and stored in sequence as their logarithms. The mean response (with SEM) is printed for each concentration. With the plotter option. the full dose-response line (Fig. 2) is plotted by incrementing the abscissa by one unit for each successive concentration and scaling the mean responses by their relation to the highest and lowest expected responses (stored earlier). If a standard line has been entered, a new (test) line is requested: if a test line has been entered, analysis follows. Analysis
From the full standard and test dose-response lines. portions of each line are selected for trial parallel-line analysis. The portion of the standard line is chosen first, by selection of the appropriate concentration numbers. After a set of concentra tions has been chosen, actual line analysis (regression analysis; 3.: test of slope, linearity, and parallelity; potency; and fiducial limits) is signaled from the keyboard by “FLAG.” (The standard is compared to itself for calculation of its fiducial limits). An option allows the use of the portion of the standard line selected previously, omitting the selection of a new line. The concentration numbers for a trial portion of the test line are chosen after the standard line has been selected; an option allows the omission of analysis of the test line (if obviously nonlinear and/or nonparallel) and leads to the request for a new line. After completion of the comparison of trial portions of the standard and test lines, the analysis may be repeated with selection ofdifferent concentrations, or a new sample (line number) is requested.
A partial printout tape from a sample assay is shown in Fig. 3. To minimize operator error, specific instructions appear prior to each separate entry of data. Assay number, date, estimated maximum and minimum responses, background CPM and standard CPM (a dilution of total CPM/tube), total /leg SO, per tube (a constant), dilution factor (to convert specific activity to chosen units), options for variable or constant weight and log-log or semi-log transformation, maximum t
5
e.s+
11111.eee*
^. ._
UC SO4 *q mL)L)a I.,.*“-” DILUTION FRCTOR l.BBBS ENTER WGT IF CON STRNTI 8 IF NOT 1.540* IF LOG-LOG ENTER 1, e IF NOT 1.eeet MRXIMUM T FOR FL 2.8481 POINTS/GROUP s. eee* STD. POTENCY 1.e00* LINE NUllBER e.eee* NO. OF POINTS 20. BBB? CPfl---SET FLRG FOR TAPE 7975. eee 6535. BBU 798?.8BB 8035. eee 7365.080 8287.900
TOTRL
BACKGROUND
I.%! CPN 36.800+ 40. me* STRNDRRD CPN 11235.eee*
VALUE
VALUE
18.r
73.*
12.r
B6I.i
HININUM
NO.
MAXIMUM
DATE
ASSRY
1.047
0.932 ERROR 8.814
iLOPE
iTD CONC ;ET FLAG IONE---OR ‘EST CONC
iTRNDRRD
IERN
STRNDRRD
IERN
STRNDRRD
IERN
STRNDRRD
1ERN
8.354
9.114
2.898
1.004 ERROR 8.829 NU.S, UHEN 0 FOR
8.034
0.909 ERROR
8.781 ERROR 8.825
e.e11
eem eeei
0.812 ERROR
28. 48.
s.eee+ 1e.eetw
CONCENTRATIONS
11167.eee 9388.009
13ss7.eeB 12362. Bllfd
18112.808
8368.089 8252. BBB i213e.eee 7865. BIB
6777.
BBR .___ 564s.eee
7662. BBB sss2.eee 6488. OeB 7342.069 INTERCEPT 8.918
0.477
_..
DF a; 121 1.888 12.800 T SLOPE, DF 8.366 13.888 T PRRRLLELITY~DF 8.800 26. BBB StI 1.888 FIDUCIRL LIMITS 1.219 6.820 TEST CONC NO.S, SET FLAG UHEN DONE---OR e FOR NEW LIME 2.099 3.688 4.088 SLOPE 8.369 INTERCEPT 0.417 ZORRELRTION 8.836 F LINEARITY, DF 8.213 1.800 12.800 r SLOPE, DF s.495 13. eee I PRRRLLELITY,DF 8.292 26. eee :H e. 778 :IDUCIRL LIMITS 1.913 8. see
F LINERRITY,
CORRELRTIOH
2:
eee
ITRNDRRD
IERN
ZRNDRRD
)ERN
ZTRNDRRD
IERN
mei
8.929 ERROR 8.819
8.865 ERROR 0.814
6.774 ERROR 8.821
28; eBe* 48. eeef
ie.eee+
5.
13167.088 ,311QW a’98 ALVZ”.“. DONCENTRRTION! B
12388.
8857. Bee 8738. eee 8898.888 9332. B.BB 9865.818
7932.eei
2%:
CPM---SET2k.. FOR TAPE 6315.888 7812.eee 5785.880
SET FLRG FOR NEU LINE---OR e FOR REPERT RNRLYSIS LINE NUNBER 2.8681 NO. OF POINTS
FIG. 3. Partial printout tapes from the bioassay shown in Fig. 2 (lines 0, I, and 2).
%b::s 7612:eee
ERROR 0.823 .INE NUMBER I. eeec IO. OF POINTS 28. eee+ PI+--SET FLAG OR TRPE 7397. eee 7198.888
;TRNDRRD
IERN
iTRNDRRD
IERN
8.815
;gBgB
91e7:eee ieess.eee 12627.8e0 lesB7.eee 11277.888 13187.eee 14385.eee :ONCENTRRTIONS s.eeet 18.8881 20. eeei 40.8881 IERN 8.831 jTRNDRRD ERROR 8.017 IERN 0.034 iTRNDRRD ERROR
fXxr :;3;:
7180.881 7993. eee
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3.880 4.880
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LIMITS 1.392 0.944 SET FLRB FOR NEU LINE---OR 0 FOR REPERT h4RLYSiS LINE NUMBER 3.eeet NO. OF POINTS 28. Beet
FIDUCIRL
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1.674 2.000 16.088 T SLOPE, DF 12.847 18.888 T PRRRLLELITY~DF
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STD CONC SET FLAG DONE---OR TEST CONC TEST CONC NO.S, SET FLAG WHEN DONE---OR B FOR NEW LINE 1.880 2.000
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MEAN
368
PHILLIPS AND HERINGTON
value for fiducial limits calculation (for minimum tz and chosen probability), the number of points per group (a constant), and the potency of the standard are entered manually at the beginning of the program. Data for each sample are then entered, in sequence. The line number and total number of points are entered manually, followed by the uncorrected CPM in sequence (entered manually or by tape). If the weight is constant, it is processed automatically; if variable, weights are requested and must be entered manually, in sequence. Concentrations for each sample are entered manually, in sequence. The full dose-response line is plotted (Fig. 2) as the series of means and standard errors are printed. For parallel-line analysis, the standard line must be entered prior to the test lines. After inspection of the full dose-response lines, concentration numbers are chosen for a trial pair of standard and test lines, selecting portions which appear to be linear and parallel. (If the previous standard line appears reasonable, repeat selection of the standard may be omitted. If the test line is obviously unsatisfactory, analysis may be omitted entirely and a new test sample requested). In Fig. 2, the last three concentrations (numbers 2,3, and 4) for both the standard (line number 0) and the first test sample (line number 1) yield satisfactory lines: insignificant F(linearity), significant t (slope), and insignificant f (parallelity) as shown in the printout in Fig. 3. All four concentrations may be used for the second test sample (line number 2). If the trial comparison is unsatisfactory, analysis may be repeated using different concentration numbers to form the standard and test lines. After the best possible comparison has been made, a new test sample is requested. With the option for CPM entry by paper tape, a 180-point variable-weight assay may be calculated in 60 min and a 450-point constant-weight assay in 90 min. COMMENT
This program is designed to process dose-response data containing responses of the form: z = k,k,[(x - kJy]. (For somatomedin bioassays, k, represents specific activity, k, the dilution factor, k, the background CPM, x the uncorrected response CPM, and 3’ the cartilage weight.) The program is suitable for any assay system in which responses are of the above form, and in which dose-response relationships are linear after semi-log or log-log transformation. (Other simple transformations could be substituted if desired.) The Hewlett-Packard 9800 system memory limits dose-response lines to ~5 concentrations and ~30 points, or other combinations with a total of 35. This is adequate for most biological assay systems, and all conventional somatomedin bioassays may be analyzed with this program. Since raw responses are corrected and expressed in standard units, the responses in a series of similar assays may be compared for quality control analysis. The program was written specifically for a desktop computer which was small
GENERAL BIOSSAY PROGRAM
enough to permit the investigator and large enough to perform the gator’s choice will be based mainly determined by experience with the allows the analysis to be repeated data.
369
to choose the optimal parallel-line analysis, required operations conveniently. The investion the calculated F and t values, but will also be particular bioassay system in use. This program until satisfactory, without tedious reentry of raw
ADDENDUM
The analysis employed here follows conventional parallel-line statistics (I, 2). A list of specific equations and a copy of the program may be obtained by writing L. S. Phillips. ACKNOWLEDGMENT The authors express their gratitude to Dr. Laurence S. Jacobs for his encouragement and suggestions. REFERENCES 1. FINNEY,
D. J. “Statistical Method in Biological Assay,” 2nd Ed. Griffin, London, 1971.
ARMITAGE, P. “Statistical Methods in Medical Research.” Wiley, New York, 1971. HALL, K. Acta Endocrinoi., Suppl. 163, (1972). DAUGHADAY, W. H. Adu. Znt. Med. 17,237 (1971). DAUGHADAY, W. H., HALL, K., RABEN, M. S., SALMON, W. D., JR., VAN DEN BRANDE, AND VAN WYK, J. J. Nature 235,107 (1972). 6. DAUGHADAY, W. H., PHILLIPS, L. S., AND HERINGTON, A. C. Methods in Enzymology. 2. 3. 4. 5.
93, (1975).
J. L.,
37-B,