John 1. Hogg University of Kansas Lowrence. 66044
Computer Programs for Chemical Kinetics An annotated bibliography
The following compilation consists of references to computer programs which are available for treating various types of chemical kinetics systems. Most of these programs are easily obtainable from t h e authors and many are ~ u b l i s h e din c o m ~ l e t edetail i n the references. These references were obtained, for the most part, in a literature search usina Chemical Abstracts a s the information source. ~ y ~ c subjects a l searched include computer programs, kinetics, least-squares, enzyme kinetics, etc. The list should include references to all of the computer programs of the desired type t o which specific reference was made u p through the January 29, 1973 issue of Chemical Abstracts. For convenience, t h e programs have been listed in the following categories depending on the function of the program Treatment of Ex~erimentalData for Internal-Order Reactions
Mathematical Simulation of Enzyme Systems Other General Programs Treatment of Experimental Data for Integral Order Reactions (1) Casanova, J-ph Jr , end Weaver, E. R.. '4nhductbn to Computer Use. RopamsforFirsf-OrderRat. Canatants," J. CmM. EDUC.. 42 (3). 137 (1965).
The article presents a simple hut versatile computer program for the calculation qf first-order and pseudo-first-order rate constants and least-squares. The instructions have been based on the general partial chemiNB where A is the reactant of the rate-contrdlcal equation A ling step, B is the product, and N is the integer required by the stoiehiometry. Neither A nor B need actually he concentrations, but may be any variables related to the compounds of interest. Computations of the rate constant, k, are based on the integrated form of the rate expression
-
whereAo is the concentration ofA at t = 0. Five cases are considered so that many types of data may be analyzed. The cases are: Variable A is directly measurable; Variable B is directly measurable; Variable A is indirectly measurable; Variable B is indirectly measurable; and Least-squares ealculation only.
(2) &tar. Dclos F.. "Computer Programs for Chemistry," Vol. 1, W. A. Benjamin, Inc.. NcwYork. 1968.
A computer program, LSKINI, accepts experimental data and calculates the best values of the tint-order rate parameters. The program makes least-squares adjustments of all parameters or, if desired. anv or all oarameters can he held unehaneed. Various
+
A = A. (A, - A.)eCA' The program has Guggenheirn capabilities also. The program is discussed in great detail in chapter 6 of the above reference. A completelisting of the program is published. (3) K u n d d . Fnderiek A,. Svirbely. W. J.. and Stewart, J. M.. "Kinetics 68: Program for the Solution of Camptitive-Conrccutive, Second-Order ~ i n e t i e a%(esetionr." U.S. Atomic Energy Comm., 1468,TR-68-69,80pp.
A Fortran system designed to solve competitive-consecutive seeond-orderkinetics has been written. (4) Munuiim, Boris, ,'A Computer Program for CHEM. EDUC.. 46,109 (1969).
Thrs program, awilahle from the repnairorv or chemical eaperirnents at Southern 1.linnis Un~verirty,has hrrn urittrn to process dara iorserund-order nlkyl acerate saponification (51 Neimo. Lao,"Qusntitative Determination af Component* af Mixtures Basad on DiifDmntial Second~OrderReaction Ratrj." Suomen Kemlafilehti, 8. 41, I47 (1968).
This program, available from the author, is presented for processing kinetic data for the quantitative determination of components in multicomponent mixtures that react simultaneously with a given reagent in accordance with seeond-order kinetics. The individual rate constants of the reacting species are computed. Speetmphotometnc Mcaauremcnts to Compute Chemical RLaetion Rstes and comtete Them to a RsfD Equation: A Computer Pmpam."NASA Contract R e p , 1969. NASA-CR-lW672, U p p .
(6) Rheio, Robert A,, "Proeeising
A program and two subroutines was designed for processing spectrapbatametric transmittance data for the computation of himolecular initial reaction rates, and the correlation of the rates to eipressions. Input and output are shown. (7)
Wer!&ma. G.J.. "Forkan N Pmgram
for F&duelion of Spedmphotomefric Reaction Kinetics Dafa,"Atomic Energ. Comm., 1965,RFD-629. 17 pp.
The program described computes first., second., and thirdorder reaction rate constants from spectropbotometrie absorbance data.
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(8) Taylor. Jampi W., and Williams, Fabe* C.. "Computer Celeulafionsof Fkt-Order RateConsfsnts,"J.CHEM. EDUC .47(2I,lW(1970l.
The authors discuss a program for calculating first-order rate constants. A listing of the program is not published but may he obtained from the authors. The program accepts an4 data which are linear in or inversely proportional to concentration, as well as %T. Provision is made for using other types of data also. Rate constants may he calculated using time units other than those given as input data. If desired, the infinity value which best fits the data is calculated and used in the calculation of the rate constant. A specified percent Confidence limit is calculated, and, if desired, those points exceeding this limit may be discarded. If desired, the program will calculate the rate constant by comparison with the known rate constant of a standard, against which the unknown is measured. If desired, the pMgram can d o a Guggenheim-type calculation a t the same time that it does a least-squares fit. Various weighting options are also available. The name of the program is KINDAT. (9) Wiherg,'K.nncth B., "Computer programming for Chemisfs." W. A. Benjamin. Inc,NewYork, 1365.
This book contains many computer programs for chemical kinetics. On page 27 is a linear least-squares program and on page 41 is a simple program for calculating first-order rate constants using the least-squares method. Chapter nine, entitled "Examples af Computer Programs," contains, on pages 172-3, a program for finding the rate constant for either a first- or second-order reaction. The program calculates the rate constants through one, two, and three half-lives and compares the data (observed versus calculated) through each of these periods. Pages 176-81 contain another first-order program in which the infinity point is varied to obtain a better fit of the experimental data. Pages 184-7 contain a program for consecutive first-order reactions. Pages 241 and 244 contain two different versions of a program for second-order reactions.
Treatment of Experimental Data for Enzyme Kinetics (11 Abrash. Henry I., Kunz, Abraham
N., and Niemann, Carl, "Calculation of Kinetic Conatanta of Enzyme-Catalyzed Reeetions Using Digllal Computers," Biochim. Biaphys. Ada. 45.378 (1960).
A program for a Datatron 220 digital computer far calculation of kinetic constants of enzyme-catalyzed reactions is available.
(61 WieLer. H.. Jahannpi, K. J., and Hem. B.:ISA Computer R o s a m for the Determination of Kinetic Parameters fmm Sigmoidal Steady-State Kinetics." FEES Left.. 8, 17Sl1970l.
A computer program is described which serves the parameter fitting of sigmoidal and hyperbolic initial velocity versus substrate concentration characteristics, excluding any parameter interpretation based on models. (7) Williams, Andrew, (Calculation of Miehaelis-Menten Parameten), "Inkduction to the Chemisfryaf Enzyme Action," MeGrsar-Hill, landon, 1569.
The calculation of KM and ko is carried out by fitting the kinetic data directly to the hyperbolic Michaelis-Menten function using a least-squares procedure. The complete Algol program which uses the method of Wilkinson [Biochern. J.,80, 324 (1961)l is presented.
Determination of Activation Parameters (1) Isenhour. Thoma. L.. and Jurs. Peter C., (Thermdynsmic Parameters). "lntmduction to Computer Prwamming for Chemists." Allyn and Bacon. Inc.. Boston, 1972,.
For an ~ s o t h e m aprocess l
AG
=
AH
- TAS
Since AG" = -RTlnKalso it is easily seen that
Using the above equation one can calculate AH and AS from data on K a s a function of temperature. Program 26 in the above reference determines the best linear least-squares fit of 1nK versus 1/T, the slope of which is -AH/R and intercept is ASIR. The standard deviations of the values are also determined. (2) Wdd, svante, "Estimation of Advation parameters from o n e Kinetic Erwrimeot (varytemp Method). E m r A n d p i s and Revised Computer Pmgram." Acfa. Chem. Scnnd., 25. 336 (1971): and Wold. Svante. and Ablberg, Per. "Evaluation of Activetion parameters tor a Fimt.Ordor Readion from One Kinetic Experiment. Theory. Numerical Mefhoda. and Computer Pmgrsm." Ado. Chem. Scond., 24.618 (19701.
A new method (Varytemp) has been applied to pseudo-firstorder reactions using the polarimeter technique for the determination of activation parameters. The method consists of varying the temperature of the sample while continuously measuring a property of the sample. These data are then used to evaluate the activation parameters using the computer program, Varytemp.
Mathematical Simulation of Kinetic Systems (1) Dsuidson. Smtt, and Baammb, Jack. '"Promam for Studying a Second-Order ReaetionSequonc%"J. CHEM. EDUC..48.830(19711.
A digital computer program for the Michaelis-Menten equation is presented. The method of non-linear regression analysis is used.
A program is available from the authors for studying the kinetics of the sequence
(3) Cleland. W. W.. "The Stetlatical Anslyais of Enzyme Kinetic Data." Aduan. Euymoi, 29. 1 (1967); and "Computer Bograms for P r a c ~ ~ i nEnzyme g Kinefie Data. Noturn, 138,463(19631.
A program is discussed in the first reference which uses values of u and substrate concentration as input parameters to determine, by an iterative fit, the least-square values of KM, V , , l/VM, KM/VMand their standard errors. The paper has an excellent discussion on the statistical analysis of enzyme kinetic data in general.
X + B
A Y
The student types m values of Bo, k, and kl/kz. For each 1% increment of reactant A from 100-0 the printout tabulates values of A, B, X, and Y,average rate, time, and elapsed time. Adjustment of parameters permits study of consecutive first-order reactions.
(4) Mares-Guis. Mareos, "The Cslevlation of The Enzyme Inhibitor D i d a t i o n Conatant, K,. Using sDigital Computel.l'An. Acod B m ! l Ciene.. 40.51 (1961).
(2) Detsr, Delos F.. "Simplified Computer Pxograms for Treating Camplex Reaction
A Fortran IV program for us6 in an IBM 1130 computer for a least-squares treatment of the calculation of enzyme-inhibitor dissociation constants, Ki, has been written.
This is e program whrch can he used to drscriht romplex reac. tion mechaniimr u,hwh do nor invulve srcndy state inrrrmedmes nor cqurlibria. It r~ nrressar). ru supply initial renrmrmrionr and rate constants as input.
( 5 ) Hulfin, Eskil, Lillequiat. Gisele, lundhlad, Gunnar Psdw Sucn, and Sfahl. Gunnar. "Enwme Activity Calculations by Curvilinear Reprersion Analysis. A ~ ~Desk~ Top~Cal&lator. t i Umd ~ ing ;he Study af CytoProgram for 8 ~ chrome ~ReductaaesndHyslumnidaae."Acto Chem. Scond.. 23,3426 119691.
(3) Msnoek, John J., and Haopor, David L., "Camputer Rogram for Simulation of any Complex FkbOrder Chemical Reaction? I . CHEM. EDUC.. 48. 530
A program for doing numerical calculations of reaction rates, particularly extrapolation of enzymic activities to zero time, is presented. The program uses curvilinear regression analysis and was designed for use on an Olivetti Programma 101 desk top ealeuiatw.
A general computer program is described which uses the Monte Carlo Method to simulate the course of any reaction system consisting of first-order and pseudo-first-order reactions. The student supplies only relative rate constants and initial concentrations. It includes optional graphical output.
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Journalof Chemical Education
Mechanisma,"J.C~M.EDUC..44, 191 (19671.
(1971).
141 MeLaughlin. Eileen. and Rozeft. R. W.."Kinetics of Complex Syatema Tending to Equilibilum." Chem. Tech.. 120 (1971) and J. CHEM. EDUC. 4917). 482 11972).
pH, substrate concentration, time, temperature, and inhibitor
Exact integrated rate expressions for systems of linked equilibria are derived via the Laplace-Carson transform. Results have been obtained for all kinetic situations linking up to four components by first-order reversible reactions. Any initial concentration of each component is allowed. The program calculates the concentrations of reactants and products of systems of this type given the rate constants, times, and initial concentrations.
IS1 Snyder. Floyd A., Henderson, J. Rank, and Cook. David A,. "Inhibition of Purine Metabolism. Camputer-Assisted Analysis of h u g Effects." Bioehem. Phormaeol., 21.2351 (1972).
Mathematical Simulation of Enzyme Systems
concentration.
Procedures using an APL/360 computer program are described for calculating the apparent rates of eight enzymes and three additional parameters of purine rihonucleotide metabolism far total reactivity data obtained using intact Ehrlich ascites tumor cells, and for determining the effects of drugs oneaeh separate enzyme.
Other General Programs
(1) Bums, Jsmm A,. "Steady S t a t e of General Multionzyme Networks and Thcb Aasacisbd Pmprties. Campufstional Approaches," FEES Left., 2lsupplementl. S30(19691.
(11 Bahn, Gilbert S., "Aurilian, Activities in the Area of Finite-Kinetics Calcdatiom." WesiStotesSeer.. Combust. lnst (Pnp).WSSICI, 68119681.
A program for the analysis of enzyme networks containing up to 30 enzymes is discussed.
Computer handling of reaction rates and kinetics is discussed. Programs considered are: CHEMREAC, SWISH, GENCOM, RATERANK, and FINEK.
(2) Detar. Delos F.. "A Computer Pmgram for Making Steady State Calculations. Ndfes on Effective Pmgnmmiw Techniques." J. CHEM EDUC.. 44(41. 193 (1967); end "Computer Pmgrams far Chemistry." Vol. 2. W. A. Benjamin, In% New York. 1970.
A complete listing of this program is available in both references listed above. The program, RMCHSS, treats a variety of complex reaction mechanisms including those with steady state intermediates. I t is useful far enzyme problems where there is a single enzyme and a single level of protonation. Several enzyme complexes may he present. A given equation may have a t most two reactants and two products. Input parameters include the number of compounds, the number of steady state intermediates, the number of reaction, the identity of reactants and products for each step, rate constants for each resction, and initial concentrations. The output consists of the concentrations of the various species as a function of time. (4) Hanson, Kenneth R.. Ling, Robert, snd Havir. Evelyn. "A Computer Pmgram for Fitting Data to the Michaelis-Menten Equation." Biaebm. Eiophys. Rer. Commu"., 29. 194i1967).
This program is used to fit data to the Michaelis-Menten equation with the following assumptions being implicit: the data are a sample of a population whose mean values correspond to MichaelisMenten kinetics; for all practical purposes (substrate) is free of error and the error in V for a given (substrate) is normally distributed about a true mean; and the variance in V is constant and independent of its mean values or of (substrate). Using the above assumptions maximum likelihood estimates for the eonstants of the equation are calculated by iteration. The calculations are based on the normal Michselis-Menten equation. The input parameters are a rough value for K M ,values af students' T for various confidence limits and decrees of freedom. values of i u b . t ~ a l e c o n c c . n ~ m t i o n , and t h e rorreipmdinp. \,nlur of \: The progmm is most useful fur t h e iritlnl: 01 t h w r e t ~ r a model* l uf enzyme systems ~
~~
~
~
( 5 ) Humt, R. 0.."A Computer Pmgram for Writing the Stesdy-Stale Rete Equation
for a Multisubatrate EnzymicRosction." Can. J Bioehsm., 47.941 (1969).
The determinant procedure for deriving the rate equation for an enzymic mechanism has been converted into Fortran IV language for use with a digital computer. The distribution equations far three t o nine enzyme species, which may interact along all possible pathways, can he determined readily. The method permits several mechanisms to be analyzed in a matter of a few minutes. (61 Lasch. J.. "Maximum Likelihood Esfimsfes of Enzyme Kinetic Parameters Based Upon theTheory ofLinear Models,"Aefo. B i d Msd. Gar, 23.747 (19691.
The analysis of enzyme kinetics data using digital computers is reported. Programs for obtaining maximum likelihood estimates of enzyme kinetic parameters of steady-state (least-square fit) were written. 171 Wolf, Walter A,, "A Computer Model of An Enzyme." J. CHEM. EDUC., 19, 546 11972).
This program is useful for running model enzyme assays on enzymes obeying "ideal" Michaelis-Menten kinetics. It is designed to be used on a time-sharing-termind. The simulated reaction is hased on the use of a radioactive substrate with a fixed enzyme concentration. The student supplies the assay conditions such as
A general program is descrihed for complex homogeneous idealgas reactions. (3l Detar, Delas F.. "Computer P r w a m e for Chemistry." Vol. 1. W. A. Benjamin. Inc.. New York, 1968.
The program LSG provides a fairly general least-squares program. It has the capability to adjust any or all of the values 00, u., and k. It has a weightingaption. (4) Dye. James L.. end Nicdy, Vincent A,. "A General Purpose Curve-FittinpPmgrsm forclass andRorsrch Use." J. CHEM. EDUC.. d8.443 (19711.
This program, available from the Program Library a t the Michigan State University Computer Library, is a general purpose curue-fitting program which is designed to handle functions which are either linear or non-linear in the adjustable parameter.
A linear least-sauares oromam for the evaluation of eauilihrium constants from s&tras&& data was developed. The'system is limited to systems with two unknown absorhing species. (61 Isenhour. Thomas L., and Jurs, Peter C., (Statistical Data Evaluation). "Introduction to Computor Pmgramming far Chemista." Allyn and Bacon. Ine.. Boston 1972.
Program 30 in this hook is a simple program to take a set of data, figure the mean and standard deviation, and the 95% and 99% confidence limits. (71 Isenhour, Thomas L., and Jurs, Peter C., (Chemical Kinetics), "Introduction ta CompuferPlogrammingforChemlsts."Allyn and Bamn, hc..Boaton 1912.
Program 31 in the above reference uses a linear least-squares treatment t o determine which values of n give the best fit of the experimental data to the equation below -dW -= h(X)n dt where n can take on the values 0.. K.-.. 1., %. .-, or 2. Values of k are calculated simultaneously. If values of k are known a t different temperatures the activation energy can be determined also. ~
~
IS1 Isenhoui. Thomas L., and Jurr, Peter C., (Linear Lesst-Squares Fit). '.Intmduction toComputer Programmingfor Chcmisa,"Allyn and Bacm, lnc. Boston. 1972.
Program 22 of the above reference uses a linear least-squares technique to fit data to an equation y = oo + alx'where aa is the intercept and o~ is the' slope. The program has the capability to employ weighting factors. Standard deviations are calculated. I91 Itskovich, I. A,. and Spiuak. S. I.. "Anslyais of tho Use of Linear Pmgramming Methods During the Construction af a Kinetic Model of a Complex Chemical Reaction,' Upr. SGL.4-5.142(19701. Russian.
A program for the determination of rates via linearly independent paths was written far the "Minsk 20" computer. 110) Lyndrup, Mark L., "Computer Pmgram for the Treatment of Date f o r e Kinetic Study of tho Parsulfate~lodideCloek Resetion." J. CHEM. EDUC.. 49, 30 (19711.
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A computer program written in Basic treats data collected for a kinetic study of the clock reaction between persulfate and iodide ions. The program allows calculation of the reaction order, specific rate constants at different temperatures, and the activation energy. (11) Ncilen, Walter B., "lterativ. Computer Pmgrsms for Equilibrium and Kinetics: J.CHEM. EDUC., 48.414l1971l.
A set of interactive computer programs is available from the author. Students describe chemical systems to the programs which calculate the equilibrium state or time development of the system. Students may immediately determine the effect of changing parameters an the system. The program EQUIL solves general ionic and gas phase equilihrium problems. GlBBS salves equilibrium problems by minimizing free energy. BALAN balances the free energy of reactants and products in each reaction. RATES solves general kinetics problems using a fourth-order Runge-Kutta algorithm with varying step size. (12) Roddy. P.J., and Murti. P. S., "Least-squareparameto. Eatimstian in C h e m i d Kinetin: Computer Pmgremme."lndionJ. Technoi., 9.161 (15711.
This program, available from the authors on request, uses a combination of linear multiple regression analysis and non-linear least-squares to estimate chemical kinetics by an iterative procedure. The method ensures a fast rate of convergence. (131 Sharma. V. S.. and Leussing,D. L.. "A General Computer Appmach for Caleulatin8 Fato Constants from Near Equilibrium Kinetic Studies." Talanta. 18. 1137 (19711.
A general computer program far estimating rate constants from relaxation times is described. The program CORNEK is essentially a least-squares refinement program applied ta non-linear systems. It uses directly the differential forms of the first derivatives of mass-balance and rate equations, thus avoiding the timeconsuming derivations of near-equilibrium rate equations. A listing of the program is published. (14) Virapaa, Asko. "Tape Preparation P m s a m s far Msfhatron Digital Computer Swterns. IV. l b c t i o n Kinetics Caleuiations: V d t h Tok. mikimusioifos, Julk, 142 (19691.
112 )I Journalof Chemical Education
Thirty-three programs concerned with reaction kinetics are discussed. (151 Williams, Anhew. (Csleulation of Initial Rates), "lnfmduction to the Chemistry ofE~z~meActian."M~Graw-Hiil, NewYork, 1965.
A least-squares procedure is used to calculate the best polynomial to fit the data points. This Algol program is based on the methad of Booman and Niemann [J.Arner. Chern. Soe.. 78, 3642 (1956)). (161 Williams, Anhew, (Estimafiao of pK. Value). "Intmduefian to the Chemistry of Enzyme Action." McGraw-Hill. New York, 1969.
An ALGOL computer program is presented in which an initial guess for a suitable range of values for K, and kit, is used to find a set where the sum of the sauares of observed minus calculated values is a minimum. A complete listing is presented (171 Williams, Andrew, (Estimation of pK. Value). "Intraductian to the Chemistry of Enzyme Anion." McGrsw-Hill. New York, 1969.
An ALGOL program for the estimation of the three disposable parameters ( K I , K2, and kt,,) in bell-shaped pH profiles is presented.
Several other programs dealing with various aspects of chemical kinetics are i n current use a t the University of Kansas. These programs deal with t h e following subjects: Arrhenius parameters for competitive reactions; calculation of pseudo Nth-order rate constants; calculation of kinetic order; calculation of buffer component concentrations; relative reactivities; iterative non-linear leastsquares program for first-order reactions; and linear leastsquares program for first-order reactions. Information about these programs may he obtained by corresponding with the author. The references are listed in alphabetical order according t o the last name of t h e author. The author apologizes for any omissions or misrepresentations of the programs.
