- Email: [email protected]
MSR—A program for kinetic analysis of enzyme modification data on PC
MSR-A PROGRAM FOR KINETIC ANALYSIS ENZYME MODIFICATION DATA ON PC CHUN LIU and National
Laboratory
(Received
BAO-HE
OF
Quc
of Biomacromolecules. Institute of Biophyslca. 100101. P. R. China
Academia
Sinica. Beiling
1.5 September 1992; in reoised form 4 Februury 1993; received for publication IS Februarv 1993)
Abstract-A computer program has been written for the kinetic method of substrate reaction (MSR) in enzyme modification studies. The program analyses a series of progress curves that continuously record signals (absorbance. fluorescence emission. etc.) reflecting the concentration changes of substrate or product during enzyme modification in the presence of substrate. After the apparent kinetic parameters are calculated by graphdrawing or curve-fitting method. a series of relevant plots is shown, from which information about the enzyme-inhibitor interaction can be deduced and microscopic kinetic constants calculated. Program Data analysis
Kinetics Substrate
Inhibition reaction
Enzyme
modification
INTRODUCTION Some years ago, a systematic study on kinetics of both reversible and irreversible modification of enzyme activity was presented [ 11. Based on a unified scheme of enzyme activity modification, it was shown that the concept of substrate competition applies to both reversible and irreversible inhibitions. Kinetic criteria were proposed to distinguish between competitive, noncompetitive and uncompetitive irreversible inhibitions. From the equations derived for the substrate reaction in the presence of modifier. it was also shown that the apparent rate constants for the irreversible modification of enzyme activity can often be obtained in a single experiment. By plotting the apparent rate constants against reactant concentrations in suitable forms, microscopic kinetic constants can be calculated. A great number of applications has been made in this and other laboratories during the past few years [2,3]. So far, studies using this method have included chemical modification [4], simple competitive inhibition [5,6], complexing inhibition [4,7], reactivation of inhibited enzyme [HI, inhibition of two substrate enzymes [9], slow binding reversible inhibition [lo], enzyme inhibition monitored by a coupling enzyme system [ 111, inhibition of receptor-bound urokinase [ 121, enzyme inactivation by urea [13], activity change during association and dissociation [14], inactivation by metal chelators [15] and conformational change before enzyme modification [16]. A common feature in all these applications is that the exponential part of the progress curve has to be first determined by certain graphical methods such as the semi-log plots. This kind of data treatment is not only laborious but also error prone. Furthermore, pre-existing assumptions will give people propensities that will affect the objectiveness of the result and make it somewhat difficult to use the kinetic criteria in real circumstances. MSR was developed to ease the work of data treatment and facilitate the use of kinetic criteria.
* Author
Cal 23:4-t
to whom correspondence
should be addressed.
CHAINLIU and BAO-HE @I
302
THEORETICAL
BACKGROUND
Detailed discussion of the theory of substrate reaction during modification of enzyme activity can be found in the literature. Here, only a brief review of certain typical cases will be presenfed. The reaction scheme for the inhibition of a single substrate enzyme is: Y x.&l + S+E=ES--i Y
k-t,; k,o S+EY=
k’ E+P
I’ 011k’.,/ h”,,, ESY
where E, Y, S and P represent enzyme, modifier, substrate and product, respectively. The rate of decrease of the total unmodified forms of enzyme ET which includes both E and ES can be given in the following form:
4ETI - - dt =(4-f] + B)[E,l- B[E,,], where [E,,] = [ET],_,,. By integration and rearrangement, [p] = u-_ A[Y]+B where
the product
Bt+
at time t can be shown to be:
formed
A’Y1
A,y,+B(l-exp((-AIYl+~)r))
u = k, [(E,,][S]/( Knr + [S]), and A = k+,&,
For those inhibitors before the irreversible
.B=
which form a noncovalent, modification step: E+I
k’,,[S]
k-&I,+
+ k’+,,[Sl
KM+[S]
Kb+[S]
.
dissociable
complex
with the enzyme
K, =E+-+EI*
it can be shown that the product formation case, except that u and A are as follows:
k&JPl ’ = 1+ [S]IK,+ [Y]IKy’
versus
time has similar
form to the above
k.ilK, A = 1 + [S]IK,
+ [Y]IKy
Thus, the complexing and noncomplexing types can be differentiated by plotting I/A against [Y], since such a plot gives a straight line with positive slope for the complexing type and a straight line parallel to the x-axis for the noncomplexing type. Similarly. the competitive and uncompetitive types can be differentiated by l/A against [S] and l/A constants can also be against l/[S] plots [l, 21, as shown in Table 1. The microscopic calculated by such plots. The equations for other types of enzyme modification are slightly different and some other plots can be chosen to differentiate types or to calculate the microscopic constants. Detailed discussions of the mathematical aspect can be found in references [l-3, 14, 16, 181. HARDWARE
REQUIREMENT
MSR runs on PC and compatibles with MS-DOS 2.1 or later versions. It requires 640 K memory and EGA or VGA graphics adaptor. Installing it on a hard disk will accelerate the speed, but a 360 K floppy disk is enough for the program to operate properly.
Kinetic Table Irreversible r- (1)
[P-l - I/[11 [I]/r--[I] [11/r-- [S] [II/r - I/[S]
1. Plotsformechanism
analysis
analysis
of enzyme
data
and calculation
303
of the microscopic
constants
Straight line passing through origin [2,3] Pass through origin for single-step and complexing types. has positive conformational type [ 161 Horizontal line for one-step inhibition has positive slope for complexing type Straight line for competitive type. k,,,, KM can be calculated from slope and Straight line for uncompetitive type, K,,,. Knr can bs calculated from slope and
y-intercept [4] intercept intercept
for
[ 1.21 [ 1,2]
Reversible r-111 I/X, -[I] k,lh
- li[I]
l/A --[I]
l/A--IS] I/A -- l/[S]
Straight line with slope, A, and y-intercept. B 12.31 The reciprocal of the residual activity, increases with increase of [I] for reversible inhibition, does not change if the inhibited enzyme has activity [ 1, IO) Straight line for noncomplexing type. apparent forward rate. A. and backward rate. B, of the inhibition can be calculated from slope and intercept [lo] Horizontal line for one-step inhibition has positive slope for complexing type [ 1,2,4] Straight line for competitive type, k,,, K,u can be calculated from slope and intercept Straight line for uncompetitive type. k +,,. KM can be calculated from slope and intercept
Two e.rponential case From these two plots. four microscopic constants r,.r? -- [I] r, + r! - [I] constants as K, is predetermined IlO]
DESCRIPTION
OF THE
can be calculated
if other
related
PROGRAM
MSR was written in PASCAL. The “pull-down” menus control all the processes from data input to result output. The conceptual flow of the program is summarized in Fig. 1. Main
1
Edit Data
Menu
/7
r
Specify Group to be analyzed
I
Plot
I
I Built-in
I
I
Reversible
[II
User-define
[Sl
Fig. 1. Flow chart of MSR
Irreversible
III
[Sl
304
CIILIN
1.1~1and
BAwH~
0~1
The editor unit allows the user both to type in his experimental data and to adapt data files obtained from other programs to the format of MSR’s data file. Since MSR analyses a series of reaction curves of changing substrate or inhibitor concentration, each data file must specify its specific concentrations of [S] and [I]. Once the data files have been adapted to the proper format. analysis can be started. The user first instructs the program as to the type of analysis to be performed. i.e. whether [S] or [I] is changing among different progress curves. Then the program searches the current directory for data files of this type. It prompts the user to select one group among the found ones. At this moment, the user can either view his data graphically or begin analysis. The tirst step of analysis is to resolve the progress curves into linear and exponential components. Two graphical methods are supplied to resolve the progress curve, the linear component subtracting method (LCS) and the Guggenheim method. The LCS is based on widely used hand-drawing practice (see Appendix). This method is suitable for those cases in which steady state is established at the end of the recording of progress curves, so that a straight line (asymptote) overlaying the ending part of the reaction curve can be drawn. The program’s LCS method draws curves on the screen instead of on paper. The user guides the ruler by pressing arrow keys on the keyboard, leaving the calculations and plotting to the program. The result is displayed on the screen and memorized for later use. In order to analyse curves for which steady state had not been achieved completely, a Guggenheim plot is also supplied [ 171. A regression method is also provided to make the process of data treatment easier. With this method, the only thing the user has to do is to select a kinetic equation. The program will estimate initial values of the variables and refine them by damping Gauss-Newton algorithm. Although regression analysis does not require the steady state to be reached, analysing only a small part of a reaction curve will lead to an erroneous result, or even result in the unconvergence of the calculation. Using simulated data, it is demonstrated that the regression method gives a more accurate result than the graphical methods, and shows less dependence on the extent to which steady state is reached. With 50 data points or more. data with 5% random errors can be treated to give a virtually unbiased result. Once the apparent kinetic parameters are determined. the program provides a series of relevant plots. Some of these are summarized in Table 1. In addition to the various supplied plots. MSR can use the user-defined expression to calculate x and y and plot them on the rectangular coordinates. This feature allows the program to be used for variations of the theory in different circumstances. The analysed result. i.e. the apparent kinetic parameters of the selected group, can be displayed on the screen as a summary table. They also can be exported to a disk file in ASCII format, which can be imported during a later session. or used by other programs as well. At any time. a graph displayed on the screen can be sent to an online printer by pressing the [F8] key on the keyboard. A context-sensitive help can be called by pressing [Fl] in most circumstances. DISCUSSION The study of enzyme kinetics is characterized by extensive data treatment, thus offering a pressing demand for new ways of handling the experimental data. The old method of hand-drawing curves on paper is inadequate not only because it is laborious and time consuming, but also because manually data reading is so rough that it may hide valuable information that may otherwise be extracted by using more delicate methods. The LCS and Guggenheim method in MSR use the same principles that the classical method of hand-drawing does, but the data reading is done by computer. If the original data were directly transferred through A/D interface from instrument, much greater precision could be obtained by using MSR than by using the classical hand-drawing methods. Study of enzyme modification by measuring the substrate consumption or product formation has several advantages. Instead of taking dispersed measurements, it records a
Kinetic analysis of enzyme data
305
curve for one enzyme-inhibitor-substrate mixture. Much information is carried with this progress curve. By measuring progress curves at different substrate and inhibitor concentrations more information is recorded. Some of this information is beyond the ability of the “incubate and assay” method. Although MSR was developed for the easy extraction of information from such progress curves, we do not intend to turn MSR into a program to do automatic analysis. MSR is highly interactive. In the two graphical methods for analysing apparent kinetic parameters, it is the user not the program that calculate the values. What is different from a conventional graphical practice is that it is much faster and easier. After the apparent kinetic parameters are determined, MSR provides instant presentations of many useful secondary plots. These plots give only the factual information. Although suggestions can be obtained by calling the help facility, the conclusion is left for the user to make. All these features make MSR ;I program able to handle different types of data treatment in different situations. A free copy of the compiled program is available to anyone who sends us a blank diskette (3hOKB or I .2MB 5.2.5”. 1MB or 2MB 3.25”) plus return postage.
continuous
progress
SUMMARY In this paper. we reported the development of a computer program for the kinetic method of substrate reaction in enzyme modification studies. The program analyses a series of progress curves, data of which can be either transferred directly to the computer from instruments through A/D interfaces. or typed in by the built-in file editor of the program. The apparent kinetic parameters can then be calculated by automatic curvefitting or by graph-drawing on the screen. After the apparent kinetic parameters are calculated. a series of relevant plots is shown. from which information about the enzyme-inhibitor interaction can be deduced and microscopic kinetic constants calculated. The user can also formulate his own mathematical expressions, the program will then use the user-defined expressions to calculate values of Y and X variables and plot them on the rectangular coordinates. .4ckri~,k,ledq~,nlent--W~
thanh Dr Y,\N(~ How,
for writing the graphics hardcopy subroutine.
REFERENCES 1. 2. 3.
4. 5.
6.
7. 8. 9. 10. II.
12.
13. 1-t.
C L. Twu. Kinetic\ of lrreversiblc modification of enzyme activity. .~CIU Riochim. Biophys. Sinica 5. 3’)X-317 (1965). C. L. Tsou. Kinetics of substrate reaction during ~rrevcrslblc modifcation of enzyme activity, Ado. En-_wnol. 61, x-4.x (198X). C L. Tsou. Theory and applications of the kinetics ot substrate reaction during Irreversible modification of enzyme xtiwty, Bio~vzrrge/ics: Molt~ulur Bio/o,qy. Biorhcvnis~rv and Puthoiog~. Symposium in Honor of k’qi’s 71)1/l Birth&y. pp. 275-N-l. 7‘. Oziwa and C. H. Kim. Eds (1YYO). W. X. Tian and C. L. Taou. Determination 01 rate constant of enzyme modification by measuring the sllbstratc reaction in the presence of the modifier. Rioc~hc,mr.srr~ 21. 101X-1032 (1982). P. S. Gravett. C. C. Viljoen and M. M. J. Oosthuizrn. Inactivation of arginine esterase E-I of Bitis ~~&wricu venom by irreversible inhibitors including a water-soluble carbodiimide, a chloromathyl ketone and isatoic anhydrldc, Iu/. .I. Biochtvn. 23. 1101-l I IO ( lY9! )_ S. R. Stone and J. Hofsieenge. Speciliclty of actlvatcd human protein C. Hiochem. J. 230. 497-502 (1985). hi. Silverberg, J. Long0 and A. P. Kaplan. Stu,dy of the effect of high molecular weight kininogen upon the fluid-phase inactivation of kallikein hy Cl inhlhltor. J. hrrd. C‘hc~m. 261. 14965- 14968 (1986). W. Liu, K. Y. Zhao and C. L. Thou. Reactivation kinetic\ of drethylphosphoryl acetylcholine estcrase, E.ur. J. Niochern. 151. 52%S2Y (19X5). 2’. X. Wang. B. Prices and C. L. Tsou. tiinrtlcs (11inactivation 01 crcatinc kinase by modification of its thiol groups, Rioclwmistr~ 27. SO95- 5 I00 ( 19Xx). J M. Zhou. c‘. Liu and (‘. L. Tsou. Kinetics of trypsin Inhibition hy Its specific inhibitors, Biochunisrry 28. 1~170-1076 (19X9). J A. Tcruel, J. Tuc:rla. F. F. Belda, F. G. Carmona. .I. C.
CHVN LIU and BAO-HE Qu
306
15. 2. X. Wang, H. B. Wu, X. C. Wang, H. M. Zhou and C. L. Tsou. Kinetics of the course of inactivation of aminoacylase by l,lO-phenanthroline, B&hem. J. 281, 285-290 (1992). 16. L. Chun and C. L. Tsou. Kinetic differentiation between enzyme inactivation involving complex formation with the inactivator and that involving a conformation change step. Biochem. .I. 282. 501-504 (1992). 17. H. Gutfreund, Enzymes: Physical Principles, p. 202. Wiley. New York (1972). 18. K. Y. Zhao and C. L. Tsou. Kinetics of substrate reaction during irreversible modification of enzyme activity where the modifier is not in great excess of the enzyme, J. Theor. Biol. 157, 505-521 (1992).
About the Author-&UN LICKreceived his B.S. degree from Jilin University, Changchun, P. R. China, in 1986 and Ph.D degree from the Institute of Biophysics. Academia Sinica in 1991. He is on the faculty of National Laboratory of Biomacromolecules. Institute of Biophysics. Academia Sinica and is currently a Fogarty Visiting Fellow at the National Institutes of Health, Bethesda. His current research interests include enzyme regulation kinetics, hormone and neuromediator function, biochemistry of the development and differentiation of nervous systems and also computer applications in these fields.
About the Author-l&o-Hk Qu graduated from Tsinghua University (Beijing, P. R. China) with a B.S. degree in 1989. and is now pursuing his Ph.D. degree at the Institute of Biophysics, Academia Sinica, directed by Prof. Chen-Lu Tsou. His major is enzyme kinetics. enzyme structure and function.
APPENDIX:
LINEAR
A curve represented
COMPONENT
by multiexponential
SUBTRACTING
METHOD
terms can be resolved as follows:
[P]=a+h.r+A,.exp(-r,.t)+
..
+A,.exp(-r,.t).
When 1 is sufficiently large, [P+p1=a + b.y. This corresponds to the part of straight line on the recorded curve when the reaction reached steady state at sufficiently large t. Thus subtracting the asymptote from the recorded curve will give: [PI-[P@]=A,.exp(-r,.t)+
..
+A,,.exp(-r,.t),
where r, > r,,_, > . > r2 > r, > 0. The plot of log([P] - [P@]) against time has an asymptote at large t, since [P] - [P$J] - >A, .exp( - r,. t) at large t. The slowest exponential term can be determined from such a plot. Subtracting A,.exp( - r,.t) from [P] - [P@], we have: [PI-[Pq5-A,.exp(-r,.t)=A,.exp(-r?.t)+
. . +A,,.exp(-r,,.t).
Plotting the logarithm against time will give the rate and the amplitude of the second slowest exponential term as the slope and Y-intercept of the curve asymptote. This procedure can be repeated until the fastest exponential term has been calculated.
Laboratory
(Received
BAO-HE
OF
Quc
of Biomacromolecules. Institute of Biophyslca. 100101. P. R. China
Academia
Sinica. Beiling
1.5 September 1992; in reoised form 4 Februury 1993; received for publication IS Februarv 1993)
Abstract-A computer program has been written for the kinetic method of substrate reaction (MSR) in enzyme modification studies. The program analyses a series of progress curves that continuously record signals (absorbance. fluorescence emission. etc.) reflecting the concentration changes of substrate or product during enzyme modification in the presence of substrate. After the apparent kinetic parameters are calculated by graphdrawing or curve-fitting method. a series of relevant plots is shown, from which information about the enzyme-inhibitor interaction can be deduced and microscopic kinetic constants calculated. Program Data analysis
Kinetics Substrate
Inhibition reaction
Enzyme
modification
INTRODUCTION Some years ago, a systematic study on kinetics of both reversible and irreversible modification of enzyme activity was presented [ 11. Based on a unified scheme of enzyme activity modification, it was shown that the concept of substrate competition applies to both reversible and irreversible inhibitions. Kinetic criteria were proposed to distinguish between competitive, noncompetitive and uncompetitive irreversible inhibitions. From the equations derived for the substrate reaction in the presence of modifier. it was also shown that the apparent rate constants for the irreversible modification of enzyme activity can often be obtained in a single experiment. By plotting the apparent rate constants against reactant concentrations in suitable forms, microscopic kinetic constants can be calculated. A great number of applications has been made in this and other laboratories during the past few years [2,3]. So far, studies using this method have included chemical modification [4], simple competitive inhibition [5,6], complexing inhibition [4,7], reactivation of inhibited enzyme [HI, inhibition of two substrate enzymes [9], slow binding reversible inhibition [lo], enzyme inhibition monitored by a coupling enzyme system [ 111, inhibition of receptor-bound urokinase [ 121, enzyme inactivation by urea [13], activity change during association and dissociation [14], inactivation by metal chelators [15] and conformational change before enzyme modification [16]. A common feature in all these applications is that the exponential part of the progress curve has to be first determined by certain graphical methods such as the semi-log plots. This kind of data treatment is not only laborious but also error prone. Furthermore, pre-existing assumptions will give people propensities that will affect the objectiveness of the result and make it somewhat difficult to use the kinetic criteria in real circumstances. MSR was developed to ease the work of data treatment and facilitate the use of kinetic criteria.
* Author
Cal 23:4-t
to whom correspondence
should be addressed.
CHAINLIU and BAO-HE @I
302
THEORETICAL
BACKGROUND
Detailed discussion of the theory of substrate reaction during modification of enzyme activity can be found in the literature. Here, only a brief review of certain typical cases will be presenfed. The reaction scheme for the inhibition of a single substrate enzyme is: Y x.&l + S+E=ES--i Y
k-t,; k,o S+EY=
k’ E+P
I’ 011k’.,/ h”,,, ESY
where E, Y, S and P represent enzyme, modifier, substrate and product, respectively. The rate of decrease of the total unmodified forms of enzyme ET which includes both E and ES can be given in the following form:
4ETI - - dt =(4-f] + B)[E,l- B[E,,], where [E,,] = [ET],_,,. By integration and rearrangement, [p] = u-_ A[Y]+B where
the product
Bt+
at time t can be shown to be:
formed
A’Y1
A,y,+B(l-exp((-AIYl+~)r))
u = k, [(E,,][S]/( Knr + [S]), and A = k+,&,
For those inhibitors before the irreversible
.B=
which form a noncovalent, modification step: E+I
k’,,[S]
k-&I,+
+ k’+,,[Sl
KM+[S]
Kb+[S]
.
dissociable
complex
with the enzyme
K, =E+-+EI*
it can be shown that the product formation case, except that u and A are as follows:
k&JPl ’ = 1+ [S]IK,+ [Y]IKy’
versus
time has similar
form to the above
k.ilK, A = 1 + [S]IK,
+ [Y]IKy
Thus, the complexing and noncomplexing types can be differentiated by plotting I/A against [Y], since such a plot gives a straight line with positive slope for the complexing type and a straight line parallel to the x-axis for the noncomplexing type. Similarly. the competitive and uncompetitive types can be differentiated by l/A against [S] and l/A constants can also be against l/[S] plots [l, 21, as shown in Table 1. The microscopic calculated by such plots. The equations for other types of enzyme modification are slightly different and some other plots can be chosen to differentiate types or to calculate the microscopic constants. Detailed discussions of the mathematical aspect can be found in references [l-3, 14, 16, 181. HARDWARE
REQUIREMENT
MSR runs on PC and compatibles with MS-DOS 2.1 or later versions. It requires 640 K memory and EGA or VGA graphics adaptor. Installing it on a hard disk will accelerate the speed, but a 360 K floppy disk is enough for the program to operate properly.
Kinetic Table Irreversible r- (1)
[P-l - I/[11 [I]/r--[I] [11/r-- [S] [II/r - I/[S]
1. Plotsformechanism
analysis
analysis
of enzyme
data
and calculation
303
of the microscopic
constants
Straight line passing through origin [2,3] Pass through origin for single-step and complexing types. has positive conformational type [ 161 Horizontal line for one-step inhibition has positive slope for complexing type Straight line for competitive type. k,,,, KM can be calculated from slope and Straight line for uncompetitive type, K,,,. Knr can bs calculated from slope and
y-intercept [4] intercept intercept
for
[ 1.21 [ 1,2]
Reversible r-111 I/X, -[I] k,lh
- li[I]
l/A --[I]
l/A--IS] I/A -- l/[S]
Straight line with slope, A, and y-intercept. B 12.31 The reciprocal of the residual activity, increases with increase of [I] for reversible inhibition, does not change if the inhibited enzyme has activity [ 1, IO) Straight line for noncomplexing type. apparent forward rate. A. and backward rate. B, of the inhibition can be calculated from slope and intercept [lo] Horizontal line for one-step inhibition has positive slope for complexing type [ 1,2,4] Straight line for competitive type, k,,, K,u can be calculated from slope and intercept Straight line for uncompetitive type. k +,,. KM can be calculated from slope and intercept
Two e.rponential case From these two plots. four microscopic constants r,.r? -- [I] r, + r! - [I] constants as K, is predetermined IlO]
DESCRIPTION
OF THE
can be calculated
if other
related
PROGRAM
MSR was written in PASCAL. The “pull-down” menus control all the processes from data input to result output. The conceptual flow of the program is summarized in Fig. 1. Main
1
Edit Data
Menu
/7
r
Specify Group to be analyzed
I
Plot
I
I Built-in
I
I
Reversible
[II
User-define
[Sl
Fig. 1. Flow chart of MSR
Irreversible
III
[Sl
304
CIILIN
1.1~1and
BAwH~
0~1
The editor unit allows the user both to type in his experimental data and to adapt data files obtained from other programs to the format of MSR’s data file. Since MSR analyses a series of reaction curves of changing substrate or inhibitor concentration, each data file must specify its specific concentrations of [S] and [I]. Once the data files have been adapted to the proper format. analysis can be started. The user first instructs the program as to the type of analysis to be performed. i.e. whether [S] or [I] is changing among different progress curves. Then the program searches the current directory for data files of this type. It prompts the user to select one group among the found ones. At this moment, the user can either view his data graphically or begin analysis. The tirst step of analysis is to resolve the progress curves into linear and exponential components. Two graphical methods are supplied to resolve the progress curve, the linear component subtracting method (LCS) and the Guggenheim method. The LCS is based on widely used hand-drawing practice (see Appendix). This method is suitable for those cases in which steady state is established at the end of the recording of progress curves, so that a straight line (asymptote) overlaying the ending part of the reaction curve can be drawn. The program’s LCS method draws curves on the screen instead of on paper. The user guides the ruler by pressing arrow keys on the keyboard, leaving the calculations and plotting to the program. The result is displayed on the screen and memorized for later use. In order to analyse curves for which steady state had not been achieved completely, a Guggenheim plot is also supplied [ 171. A regression method is also provided to make the process of data treatment easier. With this method, the only thing the user has to do is to select a kinetic equation. The program will estimate initial values of the variables and refine them by damping Gauss-Newton algorithm. Although regression analysis does not require the steady state to be reached, analysing only a small part of a reaction curve will lead to an erroneous result, or even result in the unconvergence of the calculation. Using simulated data, it is demonstrated that the regression method gives a more accurate result than the graphical methods, and shows less dependence on the extent to which steady state is reached. With 50 data points or more. data with 5% random errors can be treated to give a virtually unbiased result. Once the apparent kinetic parameters are determined. the program provides a series of relevant plots. Some of these are summarized in Table 1. In addition to the various supplied plots. MSR can use the user-defined expression to calculate x and y and plot them on the rectangular coordinates. This feature allows the program to be used for variations of the theory in different circumstances. The analysed result. i.e. the apparent kinetic parameters of the selected group, can be displayed on the screen as a summary table. They also can be exported to a disk file in ASCII format, which can be imported during a later session. or used by other programs as well. At any time. a graph displayed on the screen can be sent to an online printer by pressing the [F8] key on the keyboard. A context-sensitive help can be called by pressing [Fl] in most circumstances. DISCUSSION The study of enzyme kinetics is characterized by extensive data treatment, thus offering a pressing demand for new ways of handling the experimental data. The old method of hand-drawing curves on paper is inadequate not only because it is laborious and time consuming, but also because manually data reading is so rough that it may hide valuable information that may otherwise be extracted by using more delicate methods. The LCS and Guggenheim method in MSR use the same principles that the classical method of hand-drawing does, but the data reading is done by computer. If the original data were directly transferred through A/D interface from instrument, much greater precision could be obtained by using MSR than by using the classical hand-drawing methods. Study of enzyme modification by measuring the substrate consumption or product formation has several advantages. Instead of taking dispersed measurements, it records a
Kinetic analysis of enzyme data
305
curve for one enzyme-inhibitor-substrate mixture. Much information is carried with this progress curve. By measuring progress curves at different substrate and inhibitor concentrations more information is recorded. Some of this information is beyond the ability of the “incubate and assay” method. Although MSR was developed for the easy extraction of information from such progress curves, we do not intend to turn MSR into a program to do automatic analysis. MSR is highly interactive. In the two graphical methods for analysing apparent kinetic parameters, it is the user not the program that calculate the values. What is different from a conventional graphical practice is that it is much faster and easier. After the apparent kinetic parameters are determined, MSR provides instant presentations of many useful secondary plots. These plots give only the factual information. Although suggestions can be obtained by calling the help facility, the conclusion is left for the user to make. All these features make MSR ;I program able to handle different types of data treatment in different situations. A free copy of the compiled program is available to anyone who sends us a blank diskette (3hOKB or I .2MB 5.2.5”. 1MB or 2MB 3.25”) plus return postage.
continuous
progress
SUMMARY In this paper. we reported the development of a computer program for the kinetic method of substrate reaction in enzyme modification studies. The program analyses a series of progress curves, data of which can be either transferred directly to the computer from instruments through A/D interfaces. or typed in by the built-in file editor of the program. The apparent kinetic parameters can then be calculated by automatic curvefitting or by graph-drawing on the screen. After the apparent kinetic parameters are calculated. a series of relevant plots is shown. from which information about the enzyme-inhibitor interaction can be deduced and microscopic kinetic constants calculated. The user can also formulate his own mathematical expressions, the program will then use the user-defined expressions to calculate values of Y and X variables and plot them on the rectangular coordinates. .4ckri~,k,ledq~,nlent--W~
thanh Dr Y,\N(~ How,
for writing the graphics hardcopy subroutine.
REFERENCES 1. 2. 3.
4. 5.
6.
7. 8. 9. 10. II.
12.
13. 1-t.
C L. Twu. Kinetic\ of lrreversiblc modification of enzyme activity. .~CIU Riochim. Biophys. Sinica 5. 3’)X-317 (1965). C. L. Tsou. Kinetics of substrate reaction during ~rrevcrslblc modifcation of enzyme activity, Ado. En-_wnol. 61, x-4.x (198X). C L. Tsou. Theory and applications of the kinetics ot substrate reaction during Irreversible modification of enzyme xtiwty, Bio~vzrrge/ics: Molt~ulur Bio/o,qy. Biorhcvnis~rv and Puthoiog~. Symposium in Honor of k’qi’s 71)1/l Birth&y. pp. 275-N-l. 7‘. Oziwa and C. H. Kim. Eds (1YYO). W. X. Tian and C. L. Taou. Determination 01 rate constant of enzyme modification by measuring the sllbstratc reaction in the presence of the modifier. Rioc~hc,mr.srr~ 21. 101X-1032 (1982). P. S. Gravett. C. C. Viljoen and M. M. J. Oosthuizrn. Inactivation of arginine esterase E-I of Bitis ~~&wricu venom by irreversible inhibitors including a water-soluble carbodiimide, a chloromathyl ketone and isatoic anhydrldc, Iu/. .I. Biochtvn. 23. 1101-l I IO ( lY9! )_ S. R. Stone and J. Hofsieenge. Speciliclty of actlvatcd human protein C. Hiochem. J. 230. 497-502 (1985). hi. Silverberg, J. Long0 and A. P. Kaplan. Stu,dy of the effect of high molecular weight kininogen upon the fluid-phase inactivation of kallikein hy Cl inhlhltor. J. hrrd. C‘hc~m. 261. 14965- 14968 (1986). W. Liu, K. Y. Zhao and C. L. Thou. Reactivation kinetic\ of drethylphosphoryl acetylcholine estcrase, E.ur. J. Niochern. 151. 52%S2Y (19X5). 2’. X. Wang. B. Prices and C. L. Tsou. tiinrtlcs (11inactivation 01 crcatinc kinase by modification of its thiol groups, Rioclwmistr~ 27. SO95- 5 I00 ( 19Xx). J M. Zhou. c‘. Liu and (‘. L. Tsou. Kinetics of trypsin Inhibition hy Its specific inhibitors, Biochunisrry 28. 1~170-1076 (19X9). J A. Tcruel, J. Tuc:rla. F. F. Belda, F. G. Carmona. .I. C.
CHVN LIU and BAO-HE Qu
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15. 2. X. Wang, H. B. Wu, X. C. Wang, H. M. Zhou and C. L. Tsou. Kinetics of the course of inactivation of aminoacylase by l,lO-phenanthroline, B&hem. J. 281, 285-290 (1992). 16. L. Chun and C. L. Tsou. Kinetic differentiation between enzyme inactivation involving complex formation with the inactivator and that involving a conformation change step. Biochem. .I. 282. 501-504 (1992). 17. H. Gutfreund, Enzymes: Physical Principles, p. 202. Wiley. New York (1972). 18. K. Y. Zhao and C. L. Tsou. Kinetics of substrate reaction during irreversible modification of enzyme activity where the modifier is not in great excess of the enzyme, J. Theor. Biol. 157, 505-521 (1992).
About the Author-&UN LICKreceived his B.S. degree from Jilin University, Changchun, P. R. China, in 1986 and Ph.D degree from the Institute of Biophysics. Academia Sinica in 1991. He is on the faculty of National Laboratory of Biomacromolecules. Institute of Biophysics. Academia Sinica and is currently a Fogarty Visiting Fellow at the National Institutes of Health, Bethesda. His current research interests include enzyme regulation kinetics, hormone and neuromediator function, biochemistry of the development and differentiation of nervous systems and also computer applications in these fields.
About the Author-l&o-Hk Qu graduated from Tsinghua University (Beijing, P. R. China) with a B.S. degree in 1989. and is now pursuing his Ph.D. degree at the Institute of Biophysics, Academia Sinica, directed by Prof. Chen-Lu Tsou. His major is enzyme kinetics. enzyme structure and function.
APPENDIX:
LINEAR
A curve represented
COMPONENT
by multiexponential
SUBTRACTING
METHOD
terms can be resolved as follows:
[P]=a+h.r+A,.exp(-r,.t)+
..
+A,.exp(-r,.t).
When 1 is sufficiently large, [P+p1=a + b.y. This corresponds to the part of straight line on the recorded curve when the reaction reached steady state at sufficiently large t. Thus subtracting the asymptote from the recorded curve will give: [PI-[P@]=A,.exp(-r,.t)+
..
+A,,.exp(-r,.t),
where r, > r,,_, > . > r2 > r, > 0. The plot of log([P] - [P@]) against time has an asymptote at large t, since [P] - [P$J] - >A, .exp( - r,. t) at large t. The slowest exponential term can be determined from such a plot. Subtracting A,.exp( - r,.t) from [P] - [P@], we have: [PI-[Pq5-A,.exp(-r,.t)=A,.exp(-r?.t)+
. . +A,,.exp(-r,,.t).
Plotting the logarithm against time will give the rate and the amplitude of the second slowest exponential term as the slope and Y-intercept of the curve asymptote. This procedure can be repeated until the fastest exponential term has been calculated.