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However, given the proper approach to software design and implementation, powerful analyses programs supported by interactive graphics displays can be designed to run on the minicomputers used in the laboratory or pilot plants for experimental control and data acquisition. One such program was described and three examples were presented. This program is currently being used on a routine basis to analyze data sets-from varied experiments ranging from chemistry to electrical engineering. The program can be run on any PDP-11 or LSI-11 with 32K of memory, a floppy disk, and a graphics terminal.
LITERATURE CITED (1) Frazer, Jack W. Anal. Chem. 1980,52, 1205A. (2) Frazer, Jack W.; Brand, Hal R. Anal. Chem. 1980, 52, 1730-1738. (3) Frazer, Jack W.; Rigdon, Lester P.; Brand, Hal R.; Pomernacki, Charles L.; Brubaker, Thomas A. Anal. Chem. 1980, 57,1748-1754. (4) Frazer, Jack W.; Rlgdon, Lester P.; Brand, Hal R.; Pomernackl, Charles L. Anal. Chem. 1980, 51, 1739-1747. (5) Frazer, Jack W. Am. Lab. (Falrfleld, Conn.) 1081, 13 (4), 60-78. (6) Herget, Charles J.: Pomernacki, Charles L.; Frazer, Jack W. Anal. Chlm. Acta Comp. Technlq. Optlmlz. 1980, 122,403-419. (7) Herget, Charles J.; Frazer, Jack W. “Incorporatlon of Chemical KinetIC Models Into Process Control”, to be submitted for publication. (8) DATAPLOT; National Technlcal Informatlon Service (NTIS), U S . Department of Commerce: Sprlngfleld, VA.
(9) Brand, Hal R. “DIGLIB”; Lawrence Llvermore National Laboratory, L311, Llvermore, CA.
RECEIVED for review October 12,1982. Accepted January 10, 1983. Work performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under Contract No. W-7405-ENG-48. This document was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the University of California nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial products, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government thereof, and shall not be used for advertising or product endorsement purposes.
Simulation as an Aid to Experimental Design Jack W. Frazer,*‘ David J. Balaban, and Juila L. Wang Lawrence Llvermore National Laboratoty, P.O.
Box 808 L-3 11, Llvermore, California 94550
A slmulator of chemlcal reactlons can ald the sclentist In the design of experlmentatlon. They are of great value when studying enzymatlc klnetlc reactions. One such slmulator is a numerical ordinary differential equatlon solver which uses lnteractlve graphlcs to provlde the user wlth the capablilty to slmulate an extremely wlde range of enzyme reaction conditions for many types of slngle substrate reactions. The concentratlon vs. tlme profiles of any subset or all nlne states of a complex reaction can be dlsplayed wlth and without simulated Instrumental nolse. Thus the user can estlmate the practicality of any proposed experlmentatlon given known Instrumental noise. The experimenter can readily determine whlch state provldes the most lnformatlon related to the proposed kinetic parameters and mechanlsm. A general dlscusdon of the program lncludlng the nondlmensionallzatlon of the set of dlfferential equations Is Included. Flnaily, several slmuiatlon examples are shown and the results discussed.
In most laboratories experimentation and computer modeling are activities which are often treated as if they are unrelated. Experimentalists design experiments, take data, and analyze the data. People doing computer modeling run simulations to understand the behavior of chemical systems. When these scientific endeavors are conducted as independent activities, neither group can fully benefit from the intuition, experience, and results obtained by the other group. Present address: Keithley Instruments, Inc., 28775 Aurora Road, Cleveland, Ohio 44139.
There are several reasons for this separation of effort. The primary reason is the outdated belief that the computers which are useful for doing automated data acquisition are too small to be used for complex data analysis and simulation. Recent computer hardware advances have produced computers that can perform equally well for data acquisition, complex analysis, and simulation. Here the point is not that everything should be done on the same machine, but that there is no longer any reason to consider the activities of computer modeling and experimentation to be independent of each other. Many types of scientific and engineering endeavors require computer-controlled execution of complex experiments. Two examples of such endeavors are research conducted in pilot plants and the automation of an existing manufacturing facility. Such projects can often be more easily accomplished when computer modeling in the form of simulation is conducted concurrently with the experimentation. This paper discusses the use of simulation as an aid to experimental design. Before discussing the specific example that will be used, a few important remarks are in order. Simulation and its application to experimental design are really only a small part of the much larger field of the automation of scientific research. It makes little sense to consider simulation independently of on-line use of instrumentation, control transducers, and computers for experimentation or independently of interactive graphics for complex data analysis. A written attempt to keep this idea in perspective continually would obscure the specific points of the paper, but the reader should keep the idea in mind while reading this paper. The example to be discussed is the design of experiments to elucidate the dynamics of a complex set of chemical re-
0003-2700/83/0355-0904$01.50/00 1983 Amerlcan Chemlcal Society
ANALYTICAL CHEMISTRY, VOL. 55, NO. 6, MAY 1983
actions. Specifically, the discussion will be directed toward the study of complex enzyme-catalyzed reactions. When designing an experiment to determine the concentration of a reactant or iintermediate as a function of time, it is often not obvious which reactant will best provide the information needed to choose the most appropriate of two or more chemical models under consideration. A further complication is the fact that data taken at the wrong time during the course of the reaction may provide little or no information even if the data are relatively free of noise. Furthermore, the researcher's ability to mentally estimate when and from what state variable the desired information is to be found can be greatly reduced when only moderate levels of noise are introduced via the system control functions or instruments. In summary, intuition supported by a few simple calculations often does not provide the information required to design the most meaningful experiment. However, with the aid of a fully automated experimental apparatus designed for easy use, one can often concurrently utilize a graphically oriented simulation to aid in the design of effective experiments.
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THEORY Consider a study of enzyme-catalyzed reactions in order to provide sufficient data for the estimation of rate constants as one example of complex experimentation. The instrumentation is usually selected to measure changes in one or more of the staite variables of interest, e.g., the disappearance of substrate or free inhibitor or the appearance of product or an enzyme complex. From preliminary studies during the isolation and purification stages of research on a new enzyme, the researcher acquires "rough" data which can be used to estimate bounds on equilibrium and rate constants for various reaction mechanisms. Given a good interactive simulation program with gaphics support, these estimates can be utilized together with known instrument and other "noise" to assess different experimental designs. In addition, the scientist can examine various state variable time profiles as a function of changes in parameter values, Le., estimates of rate or equilibrium constants. Tho most appropriate variable to follow can be selected ,dong with the time interval providing the most significant information. The following is a discussion of one simulator designed to run on the connputers incorporated in the enzyme experimentation app,aratus built at LLNL (1-5). It is a program utilizing interactive graphics and was designed for easy use in the support of experimental designs. In addition, it is useful as a tool to help the researcher develop insight and intuition with regard to complex sets of reactions. The remainder of t h i g theory section will have the following form: The chemical model will be defined. The concept of fluxes will be introduced and defined. The chemical model will be transformed to a mathematical model using fluxes. The conservation of mass laws will be written down as a system of algebraic equations. The process of nondimensionalization will be described. The final noindimensional model will be written down. The Chemical Model. The chemical model for the partial or mixed enzyme kinetic system being studied is given in Figure 1. The rate constants for the various reactions are labeled next to the reaction they govern. A number of constraints are associated with the rate constants of the model. The constraints are determined by several things. First, if a reaction in one direction is cut off by setting a rate constant to zero, then the reaction in the opposite direction is also cut off. The constraint b@ I1 is given since we are studying partial or mixed inhibition systems. The CY = y constraint is determined by the Onsager microscopic reversibility principle.
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