Computer Assisted Reaction-Rate Analyses Gerald E. James’ and Harry L. Pardue Department of Chemistry, Purdue University, Lafayette, Ind. 47907 A small general purpose digital computer has been used for on-line processing of reaction-rate data for quantitative analyses. The detector signal is entered via an analog to digital converter into computer memory, where it is stored as a function of time. These data are processed and concentration data are printed on teletype. Important features of the program include the following: Preliminary rate measurements are utilized to adjust data acquisition rates and other operating parameters to be optimum for each experiment, regardless of the reaction rate. As a consequence, a wide dynamic range of analyses can be performed without making any changes in hardware. Multiple rate measurements are performed on each experiment, resulting in a highly precise average rate for each analysis. The program and hardware system is versatile, permitting signals of many types to be utilized. Different kinetic systems can be utilized by adjusting the detector signal to be compatible with the analog to digital converter and providing yes, no, and decimal number answers to questions printed on teletype by the computer during setup. Results are reported for the determination of alkaline phosphatase activity in reconstituted serum and saline, and for the determination of osmium at concentrations between 10-9 and 1 0 - W . Relative standard deviations and deviations from linearity are below 1% for normal conditions and range between 1% and 5% for very adverse conditions.
FROM THE POINTof view of the analytical chemist, kinetic data can serve several useful functions. These include providing a more complete understanding of the reactions with which he is working than would be possible otherwise, indicating how important parameters must be controlled to provide the desired results in a particular application and providing quantitative analyses based upon kinetic measurements. Whatever the intended use of the data, it will be served best by data of the highest reliability collected with minimal effort in the shortest period of time. A survey of literature concerned with chemical kinetic measurements shows that it is not uncommon practice to consider data with precision no better than 5-lOZ as acceptable ( I ) . Furthermore, the procedures utilized for collecting these data frequently are laborious and time-consuming. Aside from detracting from the attractiveness of these types of studies, it is probable that such measurement procedures impede the progress of experimental studies and obscure important information which would be accessible with improved technique. These observations point to the need for continuing effort directed at improving instrumentation for kinetic studies. In recent years, significant effort has been devoted to the development and evaluation of automated methods for obtaining and processing kinetic data for quantitative analyses (2-5). Important developments include complete automa1
Present address, Shell Development Co., Emeryville, Calif.
(1) G . A. Rechnitz, ANAL.CHEM., 38, 513R, (1966). (2) H. L. Pardue, Rec. Chem. Prog., 27, 151 (1966). (3) W. J. Blaedel and G. P. Hicks in “Advances in Analytical Chemistry and Instrumentation,” Vol. 3, Wiley, New York,
1964, pp 105-42. (4) E. M. Cordos, S. R. Crouch, and H. V. Malmstadt, ANAL. CHEM., 40, 1812 (1968). ( 5 ) G. E. James and H. L. Pardue, ibid., p 796. 1618
ANALYTICAL CHEMISTRY
tion of the data collection and processing steps, reduction of measurement times to a few seconds, and demonstration that the reliability of kinetic methods can be better than 1 %. In most cases reported to date, the control and computational processes have been performed using analog instrumentation. Instrument systems reported have several limitations in common. Because of the limited dynamic range of the analog systems used, high reliability results are seldom obtained for concentration ranges greater than about tenfold without major changes in instrumental parameters or reagent conditions, or both. The instrument systems have generally been designed for use in performing routine analyses where all reaction characteristics have been determined, and chemical and instrumental conditions have been established. In most cases, the final result is based upon a two point measurement scheme with no averaging except that provided by analog filters in the detector and computer circuits. In most cases, no provision has been made for providing multiple measurements on a single sample or for providing a comparison between measurements made at different times. There are other limitations which are dependent upon the specific approach taken to the rate measurement step. Instruments which measure the signal change over a preselected time interval [constant time method (31 require that the signal change linearly with time. Also, a very slow reaction, relative to the optimal rate, may yield a signal change which is too small to be measured accurately during the preselected time interval and conversely a very fast reaction may generate a change which is outside the linear response range of the system (chemical and/or instrumental) during the reaction time. Instruments which measure the time required for the signal to change from one preset level to another [variable time method (3)]eliminate the requirements of a linear signal-time relationship and ensure that the reliability in measuring the signal is the same for all concentration levels. However, this method introduces the complications that a very slow reaction may require an excessively long measurement time which certainly can be inconvenient and may exceed the operating range established for the instrument, while a very fast reaction may overcome the preset interval so quickly that a reliable steady rate is not achieved or an inaccurate measurement of the reaction time is obtained. Instrumentation which measures the slopes of response curves (6> can reduce some of the problems characteristic of the constant time and variable time methods if it is designed to respond rapidly. However, such an instrument is extremely susceptible to signal noise and the analog damping required to yield a meaningful output for most practical signals reduces the response speed and limits the applicable range of such a system. Most of the problems outlined above can be reduced or eliminated by proper use of a system with a very fast response speed, data storage capability and the ability to make preliminary measurements and adjust operating parameters to optimize conditions for the current problem. While all of these requirements are fully within the capability of analog
(6) H. L. Pardue and W. E. Dahl, J. Electroanal. Chem., 8, 268
(1964).
systems, they are more easily implemented in a digital system. This report describes results of an evaluation of a small general purpose digital computer for on-line processing of reaction-rate data for quantitative analyses. A general description of the program is included. Some of the more important features of the system are summarized here. The program is a flexible one allowing for different data rates, different mathematical manipulation of the raw data prior to the final computational step, computation by the constant time and variable time methods, different proportionality constants, and different numbers of measurements on each sample. The desired mode($ of operation are selected by providing simple answers to questions presented on a teletype by the computer at the beginning of a set of experiments. A filtering routine is included which provides high accuracy results for rate signals with a poor signal to noise ratio. The program provides for preliminary and approximate rate measurements early in the reaction with subsequent adjustment of parameters to optimize the operating conditions for each specific situation encountered. The final experimental conditions for any run will be based upon decisions made on that run just seconds or fractions of a second earlier. This approach allows a signal-time profile to be established in computer memory in which the time scale is automatically selected to yield optimal data. This technique permits analytical results of high reliability to be obtained from a very wide range of reaction rates with no decisions or changes required of the operator. The program provides for multiple measurements on each sample. The measurements may be made on overlapping or separate portions of the response curve. This can be an important feature in averaging results as well as in deciding if and when a reaction has reached the limiting rate. All of these features combine to provide analytical results with relative standard deviations well within 1%. The precision of individual rate measurements is such that reliable analyses were performed on reactions in which a kinetic blank existed which was an order of magnitude larger than the rate because of the sought-for constituent. For the results shown and discussed later, the output was taken from a teletype which contained printout of multiple computations on each sample by the constant time and variable time approaches, Z T us. time and absorbance us. time. Results are presented for the determination of the activity of the enzyme alkaline phosphatase and for the determination of osmium using the Ce(1V)-As(II1) reaction. Alkaline phosphatase results show relative standard deviations of about 0.3 % and linearity (rate us. activity) of about 1 %. Osmium is determined down to 1O-I1M, with relative standard deviations of about 1.5% at 10-lOM and 5 % at 10-l1M. The relative standard deviation of all results from linearity for concentrations between 10-9Mand 10-llMis 1 . 3 z . Results are also presented for rate measurements on a precise electronically generated signal ramp upon which a very high noise signal was superimposed to produce a signal to noise ratio of less than 2. These results show that accuracy and precision of better than 0.5 % in the presence of over 50 % 60-Hz noise.
system, an analog to digital converter (ADC) and the digital computer with a suitable complement of peripheral equipment. PHOTOMETER. The photometer used was that described by Pardue and Rodriguez (7). The photometer employs optical feedback to yield photometric drift of less than 0.02 % T per hour. Wavelength selection is made with interference filters with a band width of less than 20 nm. The photometer cell is thermostated to within h0.02 "C and is equipped with a rotary stirrer to provide rapid mixing of reagents. The amplifier system permits any fraction of the total photometer signal to be bucked out and the remainder to be amplified by variable amounts to yield the correct amplitude and polarity to be compatible with the ADC utilized. In a typical situation, the 100% T phototube current may be 1 X A, and it is desirable to have the range 30% T to 40% T represented by full range of a 0 to 10 V ADC. In this case, a 0.3 X A current of polarity opposite to that of the phototube current is summed with a phototube current. A feedback resistor of lo7 ohms in the first amplifier followed by a gain of 100 would give an output of 0 V at 30% T and 10 V at 40% T . In the work reported here, the signal conditioning circuit had a time constant of about 0.1 sec. ANALOGTO DIGITAL CONVERTER.The ADC used was unipolar 0 V to -10.23 V converter with a maximum conversion rate (for 10 bits) of 30 KHz (Model C002, Digital Equipment Corp., Waltham, Mass.). COMPUTER.The digital computer utilized in this work is the Hewlett Packard 2115A equipped with 8K of core memory (Hewlett Packard, Inc., Palo Alto, Calif.). Peripherals included a teletype, a paper tape punch, and a fast paper tape reader. Procedures. ALKALINE PHOSPHATASE. The measurement of alkaline phosphatase activity was based on the hydrolysis of p-nitrophenyl phosphate to p-nitrophenolate ion at pH 10.5, using conditions similar to those described by Bowers and McComb (8). The course of the reaction was followed by monitoring the change in absorbance of the p-nitrophenolate ion at 407 nm. Enzyme activity was determined in Versatol E reconstituted serum (General Diagnostic Division, Warner Chilcott, Morris Plains, N. J.), diluted with 0.9% saline. In some cases purified alkaline phosphatase from E . coli (Type 1114, Sigma Chemical Co., St. Louis, Mo.) was added to increase the range of activities examined. In other experiments, the purified enzyme was diluted with saline solution and activity measurements were made. The photometer and amplifier system was adjusted to give 1000-mV output for the reaction mixture at the point of initiating the reaction. Measurements were to be made between 80 and 100% T . ?he photometer signal over this range was made compatible with the ADC by bucking out 800 mV of the signal and amplifying the resultant by 50.0. The signal presented to the ADC is 0.00 V at 80% T and -10.00 V at 100% T . The first rate approximation is made between 96.00 and 95.00% T and quantitative rate measurements are made at selected intervals between 95 and 80% T . The measurement procedure consists of adding 2.00 ml of substrate, activating the computer, and adding 1.00 ml of buffered enzyme solution to the well stirred substrate solution in the cell. Results are printed on the teletype. OSMIUM.The determination of osmium is based on its catalysis of the oxidation of As(II1) to As(V) by Ce(IV) (9-I]), in 5 M H2S04. Osmium solutions were prepared by repeated dilutions of a 3 X 10-aM solution prepared by dissolving an appropriate quantity of osmium tetroxide in de-
EXPERIMENTAL
The apparatus and experimental conditions utilized for the determination of alkaline phosphatase and osmium are described below. Apparatus. The principal instruments utilized in this work were a highly stable photometer with a flexible amplifier
(7) H. L. Pardue and P. A. Rodriguez, ANAL. CHEM., 39,901 (1967). (8) G. N. Bowers and R. B. McComb, Clin. Chern., 12,70 (1966). (9) C. Surasiti and E. B. Sandell, Anal. Chim. Acta, 22,261 (1960). (10) H. L. Pardue and R. L. Habig, ibid., 36, 383 (1966). (11) R. L. Habig, H. L. Pardue, and J. B. Worthington, ANAL. CHEM.,39, 600 (1967). VOL. 41, NO. 12, OCTOBER 1969
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PROGRAM DESCRIPTION
Q Photometer
Analog
7 1 , I Acquisition
-
1-1
General Description. The principal functions the program is designed to perform are represented in Figure 1. This diagram is intended to indicate what is done and not necessarily how or in what order the different functions are performed. Initially data are taken at a rate selected to be fast compared to the fastest reaction rate anticipated. An approximate rate measurement is made to determine the data sampling rate for subsequent measurements. The data entered into an arithmetic register in the computer are treated simultaneously by two independent methods, the variable time method and a hybrid of the variable and constant time methods. The transmittance data are converted into absorbance for computational purposes, but this and all but the simplest mathematical manipulators are performed either prior to or after the data acquisition process in order not to limit the data acquisition rate. In the variable time method, the objective is to measure the time required for the reaction to proceed to a preselected extent or for the indicator signal to change over a preselected interval. The resulting time is inversely proportional to the concentration of the rate determining species (2). In the constant time method, the objective is to measure the total concentration or signal change over a preselected time interval. Preliminary work with this method demonstrated that its major limitation is the limited dynamic range. A reaction which is too fast will exceed the maximum limit of the measurement system before the selected time interval is expired, and a reaction which is too slow will generate a signal change which is too small to be resolved accurately. The effective dynamic range for good accuracy using the constant time approach appears to be about 10-fold for the system used here. It is probable that the ten-bit A/D converter with a maximum resolution of about 0.1 % (1 part in 1024) is the limiting factor in this system. To reduce this problem and still evaluate this general approach, a modified constant time approach was introduced. In this approach, a preliminary approximation of the reaction rate is used to determine how frequently the signal should be measured to obtain the desired number of measurements, over the available signal range of the ADC. The program includes an averaging routine so that the signal recorded at any time is the average of several values on either side of that point, the averaging being performed over a time period corresponding to one tenth of the time interval over which the signal change is measured. After the reactants in the cell have reached a steady state, a preliminary computation of the reaction rate is made by the variable time method. The resulting information is utilized to adjust parameters in the data acquisition subroutine to provide a suitable rate of collecting data for the rate in question. During the early stages of this work, it was observed that occasionally sharp noise spikes occurred. These noise pulses could cause serious errors in the variable time method. To eliminate this problem, a digital filtering subroutine was included in the program. The filter routine was written such that these noise pulses would be rejected by the computer. The time constant of this filter also is adjusted on the basis of the preliminary rate measurement. In the present work, this preliminary measurement step was performed only once for each sample run. However, in some applications, in particular where the reaction rate or rate of signal change varies with time, it may be advantageous to repeat this operation with time. It should be emphasized that this preliminary computation and the resulting parameter adjustments require a time period which is short compared to the observation time for any reaction considered in this work. After the preliminary computations are completed and appropriate parameters are adjusted, then a series of independent measurements are made on each reaction. The
Adjustments
Tim Constant
Ccnversion : D
I
,
I
Digital Filtering Preliminary Computation
i Variable Time
Result Averaging
Pseudo Constant Time
Result Averaging
ionized water. All other reagents were prepared as described earlier (7), except that the As(II1) solution contained 10-4M HgC12to reduce the potential problems resulting from contamination of the samples or reaction mixture with iodide. The transmittance of the reaction mixture at the time the reaction is initiated is 31.80% relative to deionized water. The signal was made compatible with the ADC by bucking out 300.0 mV (30 %) of the photometer signal and amplifying the resultant by 100. The signal presented to the ADC is 0.00 V at 30 % T and - 10.00 V at 40% T. The first rate approximation is made over the interval of 32.50 to 32.52% T . The quantitative rate measurements were made on overlapping intervals of 0.70% T between 32.50 and 34.00% T. These small % T intervals were selected so that measurement times for the very low concentrations determined would not be excessively long. The procedure consists of adding 2.00 ml of 2.5 X 10-2M As(II1) to the reaction cell followed by 1.00 ml of 2 X 10-aM Ce(1V) and 0.100 ml of Os(VII1) in that order. Results are printed on the teletype. The rate of the uncatalyzed reaction between CeOV) and As(II1) was measured at various points during a series of determinations and the resulting values were subtracted from the values measured with osmium present to provide a kinetic blank correction. MEASUREMENTS ON SIGNAL RAMP. An analog signal ramp, the slope of which could be precisely set and reproduced, was obtained by electronic integration of a precisely measured dc signal. The slope of the ramp was set by adjusting the input signal to the integrator. Before being fed to the input of the ADC, the ramp signal was summed at the input of an operational amplifier with a 4V peak to peak 60-Hz signal which was obtained from a sine wave generator. The ramp signal went from 0 V to - 10 V with the rate of change being measured over eight overlapping 1.OO-V intervals from 2.00 to 9.50 V. The noise thus was over 50% as large as the total measurement interval and 400% as large as the 1-V measurement intervals. 1620
ANALYTICAL CHEMISTRY
results are averaged and the individual results along with the average are presented on the teletype. Program Setup. Since the program is a general program for kinetic measurements, it must be made compatible with each chemical system being measured and with the transducer system being used. The program setup consists of entering information into the computer in the form of decimal numbers or yes-no type answers to a series of questions printed on the teletype by the stored program. The information required includes factors necessary for the computer to correctly translate the ADC data into the appropriate transducer signal, the number of measurements to be made and information necessary to set up the signal intervals over which the measurements are to be made, the direction of signal change, the proportionality constant between the reciprocal time computed for an interval and the units into which that value is to be converted, and a trigger level. In many cases the reaction rates are fast enough that there is not enough time to activate the computer after injection of the last constituent into the cell. Therefore, a section of the program was written so that the computer could be activated prior to the addition of the reaction initiator. Since the addition of the last constituent produces either a decrease or increase in the transducer signal which will reach some reproducible initial value, the program anticipates the attainment of this value, the trigger level, and will not allow access to the measurement routine until this event has occurred. In cases where the signal does not traverse the measurement intervals during the addition of the last constituent, this trigger is not necessary. Variable Time Section. A flow diagram for the variable time portion of the program is represented in Figure 2. The numerical values in the diagram are representative of the alkaline phosphatase determination. In this diagram, S represents the output from the ADC which is the digital equivalent of the photometer signal. The symbol, Tn, represents the digital equivalent of a reference level, resident in the computer for the nth interval, to which the input signal is compared. The program is inactive until the signal rises above the trigger level (sample added to substrate in cell). After the program is activated, the computer enters into a wait loop where it remains until the transmittance falls to the initial value of 96.00%. When this level is reached, the reference is decremented by 100 (1.00% T ) and the input signal is compared at regular intervals (determined by the clock frequency) to this new reference T2. For all analyses performed here, the initial sampling rate was 1 kHz. The digital filter was set to reject signal levels which were below threshold for less than 0.01 sec. After each interval during which S remains greater than T2, a counter is incremented. When S falls below Tz, the counts accumulated in the counter are utilized to evaluate the rate of change of the signal. This information is utilized to compute a count rate such that 10,000 counts will be accumulated over the largest interval for which a rate measurement will be made. A down counter, driven by the system clock, is set to control the frequency with which the signal is compared with the reference in the computer and the frequency with which the data counter is advanced. In this fashion the same resolution is obtained for all reactions, regardless of their rate. The preliminary estimate of reaction rate is also utilized to modify the time constant of the digital filter. The criterion utilized here is that to be recognized, a signal must remain below threshold for a time equal to or greater than 0.001 times the time change per signal interval. When these preliminary adjustments are completed, the computer proceeds with the collection of quantitative data. This process is initiated by setting T, equal to 9600 - 100 or 9500 and comparing the ADC signal to this. Each time the signal is observed to be greater than the reference level,
S < T,
Activate Program
Increment Cwnter
Counter
Counter
Counter
Value
AE /At
Desired Count Rate
Rates or
Rates
Figure 2. Flow chart for variable time program T,, the data counter is incremented. If the signal is observed to be below the reference level, the filter counter is decremented at a constant rate, such that the total time required to decrease the contents of the counter to zero is equal to 0.01 times the previously approximated time per signal interval. Each time the filter counter is decremented, the signal is reexamined. If it no longer is below T,, (noise pulse), then the data counter is incremented and the filter counter is reset to its initial value. However, if it remains below Tn for the period represented by the filter counter, then it is assumed to be a real value and the data counter contents are stored in memory. This process is repeated until all data are collected. Then the data are processed, concentrations are computed and averaged, and results are printed out. RESULTS AND DISCUSSION
Alkaline Phosphatase. Results for the determination of alkaline phosphatase activity in reconstituted serum are reported in Tables I and 11. The data in Table I show typical results obtained for a single run. In this case the final result is the average of seven independent rate measurements. The separate measurements within the run by both computational methods agree closely, and the averaged results by the two methods agree to within 0.08%. The data in Table I1 represent the averages of repeat determinations on several dilutions of reconstituted serum. The results reported represent the equivalent of 0.1 ml of serum of the reported activity added to 2.9 ml of buffer-substrate solution in the cell. The results are averaged and normalized to the highest concentration examined to account for dilution factors. The maximum deviation of any normalized result from the average is 1.25% throughout the tenfold concentration range with most deviations being well below this level. Relative standard deviations are all below 0.6 %. These data represent the upper portion of the range of VOL. 41, NO. 12, OCTOBER 1969
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Table I. Repetitive Computations of Alkaline Phosphatase Activity for Single Run for Reconstituted Serum Per cent T Enzyme concn (mU/ml) Deviation from mean, % intervalu Var. time Const. time Var. tiHe Const. time 94-90 102.99 103.46 +O. 15 +0.69 93-89 103.88 102.24 +1.01 -0.50 92-88 103.79 104.36 +0.91 $1.57 91-87 102.71 101.87 -0.13 -0.86 86-83 102.28 101.58 -0.54 -1.14 85-82 101.93 103.67 $0.89 +0.90 84-81 102.23 102.10 -0.50 -0.63 Av. 102.84 102.75 0.63 1.14 Rel. std. dev. (%) Difference between averages (mU/ml> 0.9 (0.088%) a Per cent transmittance interval for variable time method measured to 10.02 % T. Table 11. Repetitive Determinations of Alkaline Phosphatase Activity in Reconstituted Serum by Variable Time Method Relative concn taken 10 6 4 2 1
Enzyme activity found,. mU/ml I 255.4 150.9 102.8 51.18 25.65
I1
111
IV
255.8 152.3 102.5 51.25 25.55
256.7 152.7 103.0 51.22 25.75
103.7
Av. 256.0 152.0 103.0 51.22 25.65
Normalized activityb 256.0 253.3 257.5 256.1 256.5 Av. 256.5
Rel. std. dev., ,Z 0.26 0.62 0.50
0.07 0.39
Dev. norm. values from mean, % -0.19 -1.25 +0.39 0.16 +0.00
= Each result reported is average of seven computations made on each run. b All activities normalized to relative value of 10.
Table 111. Repetitive Measurements of Purified Alkaline Phosphatase in Saline Solution by Variable Time Method with Electrical Noise on Signal' Relative concn taken
Enzyme activitv foundb mU/ml I1 I11 IV 10 1295.6 1282.6 1297.6 1282,3 8 1026.4 1025.4 1019.8 6 734.7 735.0 736.6 4 483.1 486.6 485.8 483.3 2 245.9 246.6 246.5 1 120.7 120.6 120.7 The photometer signal had IWmV, WHz noise superimposed on it at the ADC input. * Each result reported is average of five computations made on each run. c All activities normalized to relative concentration value of 1. I
Av. 1289.5 1023.9 735.4 484.7 246.3 120.7
Normalized activityc 129.0 127.9 122.6 121.2 123.1 120.7
Rel. std. dev., % 0.64 0.35 0.14 0.36 0.15 0.05
Table IV. Quantitative Data for Ultra Trace Amounts of Osmium Osmium concn, (moles/l. x 10")
Dev. norm. Normalized Rel. std. values from Rate data corrected" for uncatalyzed reaction Average rates* dev., % mean, % 100 2366 2437 2389 2333 2342 2373 2373 1.76 +O. 64 50 1186 1194 1196 1208 1196 2392 0.76 +1.44 234.2 2342 1.46 -0.68 10 234.2 230.8 237.6 2323 5.09 -1.48 23.23 1 21.89 23.66 24.13 a All data corrected for an uncatalyzed reaction rate of about 185. Each correction determined repeatedly during series of analyses. 6 All values normalized to that of 10-gM solution.
clinical interest (8). As it was of interest to demonstrate the dynamic range of the total system, measurements were performed o n higher concentrations of a purified enzyme preparation in saline solution. Results of this study are reported in Table 111. In addition to the increased concentration range, the signal from which these computations were made had a lOO-mV, 60-Hz noise signal superimposed o n it at the ADC input in order to demonstrate the effectiveness of the 1622
e
ANALYTICAL CHEMISTRY
filter routine. No other changes were made in either hardware or software in obtaining these data. The repeatability of the results, compared to those in Table 11, is not effected by either the increased reaction rate or the noise o n the signal. On the other hand, the measured rate is not a linear function of added enzyme. Independent experiments demonstrated that this nonlinearity is not a function of the measurement system, but rather is a function of the chem-
ical system. The reason(s) for this nonlinearity was not determined. A second reaction, the osmium catalyzed Ce(1V)-As(II1) reaction, was selected to demonstrate the wide dynamic range of the system. Experimental data covering a 100-fold concentration range are reported in Table IV. The data were printed out as reciprocal time but could have been calibrated in concentration units. In evaluating these data, several points should be noted. The first is the absolute values of the concentrations involved which are 10-QM down to 10-IIM. Second, this 100-fold concentration range was covered with good accuracy without making any changes in the hardware or mode of handling the samples. All necessary modifications to handle the significant changes in reaction rate were made by software in the computer. The total signal change for these measurements represented only 1.5% T . This range was selected to avoid excessively long measurement times for the very slow reactions of interest here. Measurement times for these analyses were 1.5 min at 10-QM osmium and 30 min at 10-llM osmium. The rate of the uncatalyzed reaction between Ce(1V) and As(I1) is significant compared to the rate of the catalyzed reaction for the concentrations presented in Table IV. For example, at 10-IoM osmium, the rates of the catalyzed and uncatalyzed rates are about equal and at 10-IIM osmium, the uncatalyzed rate is about ten times larger than the catalyzed rate. In addition, the uncatalyzed rate decreased with time and was redetermined at frequent intervals. Therefore, the data in Table IV at lower concentrations represent differences between relatively large numbers. When all the above factors are considered, it becomes clear that the problem was selected to submit the system to a rather severe test. The data demonstrate that the test was passed in admirable fashion. The data have reliability comparable to that being reported currently for much less demanding circumstances. Measurements on Signal Ramp. In Table V results are shown for rate measurements by the variable time method on an electrically generated signal when the signal to noise (Sjlv) was reduced to less than 2 by a superimposed 60-Hz sine wave. The relative rate or slope of the ramp was varied over an 80-fold range by precisely adjusting the input to the ramp generator to give measurement times of from 2.5 sec to 200 sec. Measurements of the rate of signal change at relative rate 500 with no noise resulted in a value of 232.1 with a relative standard deviation of 0.003z. It can be seen that the high noise levels have only a minimal effect of the reproducibility and accuracy of the rate measurements. The rate measurements shown are linear with relative rate with a relative standard deviation of less than 0.5 %. The minimizing of the effects of noise is due to the combination of the digital noise rejection filter and the averaging of several rate measurements on each run. The rejection filter will reject any signal pulse which has a half-cycle time of less than 0.01 of the time estimated for the true signal to traverse one of the measurement intervals. Thus, only noise resulting in rates of signal changes on the same order of magnitude as the true signal is likely to produce significant errors. The averaging of several measurements reduces the effects of low frequency noise and, of course, reduces the effect of a single erroneous measurement. That simple averaging would not work satisfactorily in the presence of noise was made evident by the fact that the constant time method yielded only nonsense values for the same measurements shown in Table V. The noise levels set for the measurements reported in Table V are not likely to be encountered in a real situation, but the
Table V. Rate Measurements on an Electrically Generated Signal Ramp with High Noise Level. Rel. Relative Measured ratesc std. dev., rateb I 11 I11 Average 0.82 46.67 46.23 45.98 46.05 100 91.00 91.28 0.37 91.66 91.17 200 115.5 0.53 114.8 115.6 250 116.0 232.6 0.26 232.6 231.8 5Wd 233.5 460.2 0.15 460.9 460.2 1000 459.6 0.12 923.7 923.8 924.9 922.6 2000 1860 0.41 1868 1853 4000 1858 1.63 3663 3111 3116 8000 3694 a The signal ramp was generated by electronically integrating a precisely measured dc current. A 4-V, 60-Hz signal was superimposed on the ramp signal to give a signal to noise ratio of 2. b Values represent input current to electronic integrator. c Each value is an average of eight rate measurements made on each run by variable time method. d Rate measurements made on this signal with no noise was 232.1 with a rel. std. dev. of 0.003z. data indicate that the measurement technique can tolerate high noise levels, and that under normal conditions the effects of random noise and sharp spikes would be minimal. This study has demonstrated that the on-line digital computer is a very effective tool collecting and processing kinetic data for quantitative analyses. One important feature is its capability of making repeated measurements and computations on each experimental run. This capability coupled with high stability detection equipment can generate data with very high reliability. The repeatability of the data reported in Tables I-IV is equivalent to that for the best data reported for analog instrumentation and is superior to most. The data in Tables IV and V were collected under very adverse conditions. A second important feature of the computer is its ability to use current information to adjust operational parameters to optimum values for the current experiment. This capability permits a dynamic range of analyses which has not been demonstrated for analog instrumentation to date. The program described provides a dynamic range of l o 4 with a time resolution of 0.1 %, and the range could easily be extended to lo6if desired. One objective of this work was to compare the constant time and variable time methods for collecting and processing kinetic data. It is concluded that if analyses are to be performed over a relatively small dynamic range (< 10-fold concentration range), then the two approaches can be made to work equally well in most cases. However, if a dynamic range greater than about tenfold is desired, then the variable time approach is superior. This results primarily from the fact that it is much easier to resolve time as a variable over wide ranges than to resolve transducer signals over comparable ranges. It should not be concluded from these observations that the analog systems should be completely replaced by the digital computer. Such factors as cost and size still render the analog systems, or miniature hybrid systems, attractive. However, in addition to indicating several important advantages of the digital computer over previously reported analog techniques, the present work also suggests directions which can be followed in developing the digital computer into an incomparable tool for kinetic measurements.
RECEIVED for review June 16, 1969. Accepted July 18, 1969. Work supported by PHS Grant Number GM 13326-03 from the National Institutes of Health. VOL. 41, NO. 12, OCTOBER 1969
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