4 Noggle, J H (1993) Practical Curve Fitting and Data Analysis: Software and Self-lnstruction for ... kinetics is to learn how to plot data for correctly calculating Km ...
35 the scatter of points is too great for meaningful analysis. 'Linear plots may be usefully applied for diagnostic purposes and to calculate initial estimates of Vmax and Km.1"3"4 Systematic deviation of data from an expected line may indicate the model mechanism is wrong or reveal inadequacy of the assay method, allosteric interactions, substrate inhibition or the presence of impurities. 3 Furthermore, such plots are still useful for visualisation and communication of results. 2'3 The discussion above is based on certain widely held assumptions with respect to the experimental data, for example that initial velocities are measured where the concentration of enzyme is far less than that of the substrate. Recent advances make it possible to apply numerical integration to analysis of other situations such as where the concentrations of enzyme and substrate are similar, s Non-linear analysis may also be applied to a variety of other biochemical data, which in some cases cannot be linearised by transformation, for example pH profiles,I ligand binding e'4 or growth models. 4 The textbooks examined included "standard" textbooks, practical textbooks and problem-oriented texts. All included initial estimation of Vmax and K m from plots of v vs [S], followed by Lineweaver-Burk plots. 9-19 Many, though not all, included some discussion of distortion of errors by the transformation. Two texts 14"t7 simply mentionied that other t y p e s of linearised plots existed, while others included details of E a d i e - H o f s t e e plots,7" 12.13.15.19H a n e s - W o o l f plots 7"t5.19 or Direct Linear plots. 7ASA6 Non-linear analysis of untransformed data was briefly mentioned in some texts, 7'l°A2"14`t8 with a more detailed treatment in only one. ~5 The practical texts 9A6 did not have the most comprehensive coverage. Furthermore, in a compilation of practical biochemistry experiments from Biochemical Education, only one enzymology practical included determination of kinetic parameters by non-linear regression, 2° while seven others included analysis by L i n e w e a v e r - B u r k plots. Thus there seems to be a gap between our practical teaching and current experimental methodology. In conclusion it seems that while the traditional analyses of enzyme kinetics still have value, we must be prepared to update our teaching in this area to reflect changes in professional practice.
Perspectives on Computing in Medical Education This is a new quarterly column in the journal Academic Medicine. The column is edited by Dr Charles P Friedman of the University of North Carolina School of Medicine. The aim of the column is to stimulate debate and general discussion of fundamental issues, such as how to integrate computer-based activities into the curriculum, or whether computer simulation should (or in fact really can) replace dissection. Issue- and policy-oriented essays are used to inspire collective thinking about the roles and uses of computers in medical education.
0307-4412(94)00159-6
ENZYPLOT: A Microcomputer Assisted Program for Teaching Enzyme Kinetics F A LEONE, J A BARANAUSKAS and P CIANCAGLINI
References ~Cleland, W W (1979) Meth Enzymol 63, 103-138 2Leatherbarrow, R J (1990) TIBS 15,455-458 3Henderson, P J F (1991) in Enzyme Assays -- A Practical Approach, Eisenthal, R and Danson, M (Eds) Oxford University Press, Oxford, 277-316 4 Noggle, J H (1993) Practical Curve Fitting and Data Analysis: Software and Self-lnstruction for Scientists and Engineers, Ellis Horwood, PTR Prentice Hall, New Jersey. Reviewed in Biochem Educ 21, 210-211 (1993) 5Duggleby, R G (1991) TIBS 16, 51-52 ~Cognet, J A H, Pothier, J, Leseney, A M and Marion, C (1994) Biochem Educ 22, 146-149
BIOCHEMICAL
7Kuchel, P W and Ralston, G B, Coordinating Authors (1988) Schaum's Outline of Theory and Problems in Biochemistry, McGraw Hill, New York, 225-269. 8Frieden, C (1993) TIBS 18, 58-60 '~Plummer, D T (1987) An Introduction to Practical Biochemistry, 3rd Edition. McGraw Hill, London, 225-234 I"Magill, J M (1988) Problem Solving in Biochemistry: A Practical Approach, MacMillan, New York, 81-91 t~Stryer, L (1988) Biochemistry, 3rd Edition, W H Freeman and Company, New York, 187-195 ~2Rawn, J D (1989) Biochemistry, Neil Patterson, North Carolina, 166186 t3Matthews, C K and van Holde, K E (1990) Biochemistry, Benjamin Cummings, California, 357-365 I~Voet, D and Voet, J G (1990) Biochemistry, John Wiley and Sons, New York, 335-344 15Smith, C A and Wood, E J (1991) Molecular and Cell Biochemistry: Biological Molecules, Chapman and Hall, London, 87-100 16Boyer, R F (1993) Modern Experimental Biochemistry, 2nd Edition. Benjamin Cummings, California, 299-306 ~TLehninger, A L, Nelson, D L and Cox, M M (1993) Principles of Biochemistry, 2nd Edition. Worth Publishers, New York, 213-221 ~Zubay. G (1993) Biochemistry, 3rd Edition. Wm C Brown, Iowa, 205217 t'Garrett, R H and Grisham, C M (1995) Biochemistry, Saunders College Publishing, Fort Worth, 360-374 -'"Busquets, M and Franco, R (1989) in Practical Biochemistry for Colleges, Edited by Wood, E J, Pergamon Press, Oxford, 21-23
E D U C A T I O N 23(1) 1995
Departamento de Quimica Faculdade de Filosofia Ci~ncias e Letras de Ribeirdo Preto Universidade de Sdo Paulo 14049 Ribeirdto Preto SP, Brazil
Introduction The somewhat enigmatic relationship between reaction rate and substrate concentration makes enzyme kinetics a
36 subject difficult to comprehend and to apply for many .undergraduate students. The abstract manner of teaching and the scant importance given to the contribution of mathematical formulas are, in our opinion, legitimate criticisms of the teaching of this subject. As a result the student becomes apprehensive and does not acquire a reasonable background. The aim of enzyme kinetics obtained under steady-state conditions is to estimate the values of K m and V~ by fitting sets of initial reaction rate and substrate concentration to the Michaelis-Menten equation: I v -
Wm IS] Kn, + IS]
(1)
Enzyme catalyzed reactions show a first-order dependence of rate at low concentrations of substrate. However, instead of increasing indefinitely as the substrate concentration rises, the reaction rate approaches a limit known as the limiting rate or enzyme saturation, but eqn 1 shows, this limiting rate is not reached at any finite substrate concentration. Thus, for practical reasons, good estimates of K m and Vm are often carried out by varying substrate concentration to obtain initial rates between 10 and 90% Vm. A n o t h e r important aspect of good practice of enzyme kinetics is to learn how to plot data for correctly calculating Km and V~, as well as to gauge the limitations of each plot. The plot of v against [S] is the easiest way of representing steady-state kinetic data. However, it does not permit accurate determination of the values of K m and Vm. Several equivalent plots 2-6 of the Michaelis-Menten equation have been used but none of them is fully satisfactory for calculating K m and Vm values. In this paper we describe a program, E N Z Y P L O T , in which the microcomputer serves as a personal tutor which allows the user to acquire a reasonable background in enzyme kinetics. Software E N Z Y P L O T is a program for fitting steady-state kinetic data from "Michaelian" enzymes. It can be used for teaching activities, either to present information in lectures or during experimental sections. E N Z Y P L O T runs well in any 640 Kbyte IBM Personal Computer or compatible running MS-DOS or PC-DOS version 3.0 or better. It also requires an IBM Color Graphics Adapter and an optional line printer. E N Z Y P L O T works with four main sections which can be accessed from the main menu: FILE, D A T A , G R A P H , PRINT. When selected, each option will appear highlighted, that is, it will appear in reverse video. After selecting the option, a window menu will show several subjects and the selected one will also appear highlighted. Within FILE window, the user can select to Load a file, to Save data or results, to Visit DOS or to Quit E N Z Y P L O T . From D A T A window, the user can Edit or Display the results on the screen. By using the G R A P H B I O C H E M I C A L E D U C A T I O N 23(1) 1995
window, up to six basic curves can be plotted, named: Lineweaver-Burk plot (1/v against 1/[S]), Eadie-Hofstee plot (v against v/[S], Hanes plot ([S]/v against [S]), semilogarithmic plot (v against log [S]), MichaelisMenten plot (v against [S]) and direct linear plot (v against - [ S ] , see Figure 1). Two boxes are displayed on the screen beside each plot, the Regression and Cursor boxes, respectively. The Regression box contains the values of K m , V m as well as the statistical analysis of the curve fitting. The Cursor box gives the user the instantaneous coordinates of the cursor at any position of the graph (Figure 1). An important feature of E N Z Y P L O T is that if the substrate concentrations were not varied enough to obtain initial rates varying from 10 to 90% of Vm, the user will be warned. In that case, a third box will appear and E N Z Y P L O T will suggest to the user how to proceed to obtain good results to calculate correctly Km and Vm. Finally, by selecting the P R I N T window, the user can print just one or all of the results obtained. A complete Readme file provides useful information about ENZYPLOT. Discussion Currently there are sound reasons for using inexpensive microcomputers as an educational resource in Biochemistry. With E N Z Y P L O T , any student can use the microcomputer as a personal tutor to learn to appreciate the qualitative and the quantitative relationships between substrate concentration and the rate of enzyme-catalyzed reactions. An important characteristic of E N Z Y P L O T is that it allows the user to observe the variations occurring in the calculated values of K m and Vm when the same result is plotted using the six equivalent representations of the Michaelis-Menten equation. In addition, the program allows the user to modify the data, simulating errors in the experimental results. This constitutes an additional advantage for E N Z Y P L O T since the user will be able to recognize, in the different plots, the appearance of distortions caused by experimental errors. A n o t h e r important aspect built-in to E N Z Y P L O T concerns the determination of Vm. While the concept of Vm is widespread in Biochemistry textbooks, eqn 1 clearly shows that this limiting rate is not reached at any finite concentration of substrate. By using simulations of their experiments, the students will observe that even at very high concentrations of substrate this value will not be reached. Finally, E N Z Y P L O T has a feature which allows the user to manipulate the mathematical formulas of each plot, leading not only to a better learning of enzyme kinetics but also to eliminating the fear of computers and of mathematics. For this, through the cursor movement, the student will have instantaneously (in the Cursor box) the coordinate values of each point in the graph which can be used in the corresponding mathematical formula to extrapolate any value of the plot.
37 (a)
Lineweaver-Burk
(e)
plot
Michaelis-Menten
plot
Vm
Rel[ression
Regression
V m = 5.320E+01 K m = 1.608E-03 R = 9.996E-01 R2 = 9.992E-01 SE = 4.698E-03
V m = 5.320E+01 K m = 1.608E-03 R = 9.996E-01 R2 = 9.992E-01 SE = 4.698E-03
>_.
Vm/2 Cursor X = 1.818E+04 Y = 1.076E-01
Cursor Y
1/[S]
(b)
Eadie-Hofstee
Km
8.265E+00
IS]
plot
(f) Resression V m = 5.343E+01 K m = 1.607E-03 R = -9.903E-01 R2 = 9.806E-01 SE = 2.294E+00
o
Median V m = 5.298E+01 K m = 1.603E-03
Insufficient Data points at I High Substrate concentration
V o
D i r e c t )lot V
o
Cursor X = -1.378E-02 Y = 2.304E+02
I
Cursor X = 3.178E+04 Y = 8.265E+00
I
I
v/Is]
Km
I
I
-[s] (c)
Hanes plot Resression V m = 5.204E+01 K m = 1.505E-03 R = 9.995E-01 R2 = 9.990E-01 SE = 3.470E-06
Figure 1 (a) Lineweaver-Burk plot, (b) Eadie-Hofstee plot, (c) Hanes plot, (d) Semilogarithmic plot, (e) Michaelis-Menten plot, (f) Direct linear plot Persons interested in receiving a copy of the program should write to Dr F A Leone at the above address or Internet address: F D A L E O N E @ B R U S P . A N S P . B R .
Cursor
+ I
I
I
Y = 7.174E-05
I
IS] (d) Semi-logarithmic Vm ..................................
Acknowledgements We thank Hector F Terenzi and Joseph Miller for their helpful suggestions and careful reading of the manuscript. We also thank FAPESP, CNPq and FINEP for the continuous support given for our laboratory.
plot .4~ Resression V m = 5.320E+011 K m = 1.608E-03 R = 9.996E-01 R2 = 9.992E-01 SE = 4.698E-03
References LM i c h a e l i s ,
3Eadie, 4Hofstee, "Hanes,
Vm/2
L and Menten,
2Lineweaver,
M L ( 1 9 1 3 ) Biochem Zeit 49, 3 3 3 - 3 6 9
N a n d B u r k , D ( 1 9 3 4 ) J A m Chem Soc 5 6 , 6 5 8 - 6 6 6
G S ( 1 9 4 2 ) J Biol Chem 146, 8 5 - 9 3 B H J ( 1 9 5 2 ) J Biol Chem 199, 3 5 7 - 3 6 7 C S ( 1 9 3 2 ) Biochem J 2 6 , 1 4 0 6 - 1 4 2 1
~'Eisenthal, R and Cornish-Bowden,
Cursor X = -1.818E+00 Y = 8.265E+00
Log IS]
B I O C H E M I C A L E D U C A T I O N 23(1) 1995
A ( 1 9 7 4 ) Biochem J 139, 7 1 5 - 7 2 0
