- Email: [email protected]
The use of Michaelis-Menten Kinetics in cell biology and physiology teaching laboratories
26
The Use of Michaelis-Menten Kinetics in Cell Biology and Physiology Teaching Laboratories RALPH SORENSEN
and NICOLE NOVAK
Biology Department Gettysburg College, Gettysburg, PA 17325,
USA
Introduction The analysis of enzyme behavior using Michaelis-Menten kinetics is a staple of the biochemistry laboratory. By analysing enzyme activity as a function of substrate concentration, students can indirectly observe the saturation of the active site, measure the maximal velocity of a given enzyme concentration, and compare the relative affinity of an enzyme for different substrates. By using double-reciprocal plots (Lineweaver-Burk, EadieHofstee), students can measure these kinetic properties of enzymes with precision and distinguish between competitive, non-competitive, and uncompetitive inhibition. The simple mechanism of Michaelis and Menten E+S$ES>E+P k,
(I)
establishes several important premises: that the enzyme combines directly with the substrate, that the binding of the substrate is not always productive, and that enzyme is not consumed in the process (ie the enzyme acts as a true catalyst). A relatively-straightforward set of algebraic manipulations leads to the Michaelis-Menten equation:
v, = (Vmax[WWm + [Sl>
(2)
This equation describes the initial velocity of any enzyme (self-evidently less than the maximal velocity, V,,,) as a function of two parameters: substrate concentration, [S], and the Michaelis-Menten constant, K,. From eqn 2, the initial velocity is one-half of the V,,, when the substrate concentration is equal to the K,. K, is also defined in terms of the first and second-order rate constants for the breakdown and formation of the ES complex. Assuming that k3 is much less than kZ, K, is equal to the dissociation constant of the ES complex (k2/kl). As such, K, is a useful measure of the binding affinity of the substrate for the active site: a high K, indicates a low binding affinity and vice versa. Empirical verification of this formula by these techniques establishes the accuracy of the theoretical premises. Students learn this information in biochemistry classes in the context that Michaelis and Menten derived it: enzyme activity. Practical experience in the laboratory is, therefore, typically limited to well-studied systems such as the measurement of K, for bacterial P-galactosidase using the substrate o-nitrophenyl P-D-galactoside’ and the demonstration of competitive inhibition of mitochondrial succinate dehydrogenase by malonate.’ BIOCHEMICAL
EDUCATION
24( 1) 1996
The tools employed by Michaelis and Menten have been employed, of course, in broader contexts. Students, through lack of practical application, often fail to appreciate the general utility of this approach outside the analysis of enzyme behavior. It seems axiomatic that students could use profitably their appreciation of MichaelisMenten kinetics to explore biological phenomena involving the interaction of two entities other than enzyme and substrate. Thus the combination of a substrate molecule with an enzyme is not unlike, for example, the combination of a photon with the reaction center of photosystem II or a hormone with a cell-surface receptor. We have used precisely these two examples in cell biology and physiology courses. Through these exercises, students gain a greater appreciation of the molecular mechanics of these phenomena precisely because of their previous study of enzyme kinetics. I describe these two examples as an argument for the greater use of Michaelis-Menten kinetics in practical courses following basic biochemistry. The Hill Reaction
The Hill reaction is the laboratory equivalent of the light reaction of photosynthesis. Using light energy and isolated chloroplasts, photosystem II splits water and passes the electrons through the electron transfer chain in the thylakoid membrane to an artificial electron acceptor. An artificial electron acceptor such as 2,6-dichlorophenolindophenol (DCIP) loses color upon reduction allowing a simple spectrophotometric analysis of the rate of electron transfer. Students can easily measure the rate of the Hill reaction as a function of light intensity. Changing the distance of the light source varies the intensity of light striking the chloroplast preparation. The reaction center of photosystem II can be saturated with photons of red light just like the active site of an enzyme can be saturated with substrate molecules. By plotting initial velocity against light intensity (numerically equal to the reciprocal of the squared distance), the saturation point, or maximal velocity (If,,,), is suggested by the flattening of the curve (Fig 1). Students attempt to extrapolate this curve to its asymptote in order to estimate the If,,,,,. This procedure, however, is quite inaccurate. A Lineweaver-Burk doublereciprocal plot (Fig 2) allows the precise calculation of the value of V,,,. Students can use this value to return to the Michaelis-Menten graph and redo the asymptote. The Neuromuscular
Junction
The physiology of muscle contraction is commonly studied in student laboratories in animal physiology by using the frog gastrocnemius muscle and the sciatic nerve. Students connect the preparation to a mechanical transducer with the output recorded by a polygraph. Students explore the relationship between the strength of electrical stimuli delivered via the exposed sciatic nerve and the force of As the stimulation consequent muscle contraction. voltage increases, so does the contraction until a maximal contraction force is approached (Fig 3). In a Michaelis-
27
0
a
Y
r-4
Stimulus(volts)
Light intensity (l/cm2)
Figure I A Michaelis-Menten plot of DCIP reduction (absorbance units per minute) as a function of light intensity (expressed as the reciprocal of the distance of the light source) by isolated spinach chloroplasts. The secondorder curve was drawn by hand
Ez
-8
5 -
8 c-4
8
l/light intensity (cm2)
Figure 2 A Lineweaver-Burk double-reciprocal plot of the data presented in Fig 1. Linear regression was performed using the CA-Cricket Graph III program (Computer Associates). The formula for the regression line is: y = 0.002x + 2.097. v,,, is calculated from the reciprocal of the y-intercept to be 0.477 Almin. This value may be used to extrapolate the asymptote in Fig I BIOCHEMICAL
EDUCATION
24(l)
1996
Figure 3 A Michaelis-Menten plot of the contraction force (in grams) exerted by curare-treated (0) and untreated (0) frog gastrocnemius preparations as a function of the applied stimulus voltage (in volts). A sub-threshold voltage is identified. The second-order curves were drawn by hand Menten sense, the muscle becomes saturated as the contraction approaches its maximum. In this example, the stimulus voltage is treated as an analog to substrate concentration. Muscle contraction is propagated across the neuromuscular synapse by the neurotransmitter acetylcholine. Acetylcholine leaves the presynaptic membrane by exocytosis, interacts with receptors at the postsynaptic membrane, and triggers depolarization of the post-synaptic membrane. The magnitude of the stimulus voltage mimics, therefore, acetylcholine concentration. Curare (D-tubocurarine) is structurally similar to acetylcholine and would be expected to competitively inhibit the interaction of acetylcholine with its receptor. By remeasuring muscle contraction force in muscle preinjected with 2 ml of D-tubocurarine (0.1 Kg/ml), the effects of curare on contraction force are observed (Fig 3). Analysis of these data by use of a Lineweaver-Burk double-reciprocal plot (Fig 4) shows that curare increased the K, of the post-synaptic acetylcholine receptors (the negative reciprocal of the x-intercept). By competing with acetylcholine binding, the curare decreased the affinity of the receptors for acetylcholine. At the same time, curare did not significantly change the V,,,,, (the reciprocal of the y-intercept). High stimulating voltage, functioning like a saturating substrate concentration, abolished the curare inhibition. These two kinetic properties are, of course, the hallmarks of competitive inhibition. The hypothesis that curare competitively inhibits acetylcholine is thus supported. In the construction of the double reciprocal plot, we subtracted a ‘sub-threshold voltage’ of 0.5 volt from each stimulus value. This operation threshold is a combination
Proposal for a Regional Organisation of Biochemists in Africa The Federation of African Biochemical Societies (FABS)
I N
l/Stimulus
(volts-l)
Figure 4 A Lineweaver-Burk double-reciprocal plot of the data presented in Fig 3. Sub-threshold voltage has been subtracted. Linear regression was performed on data from the curare-treated (0) and untreated (0) preparations of curare using the CA-Cricket Graph III program (Computer Associates). The formulae for the regression lines are: y = 0.0036x + 0.0093 (curare-treated) and y = 0.0009x + 0.0099 (untreated). The calculated K,,, and V,,,, for the curare-treated preparation are 0.387 volt and 107 grams, respectively, and for the untreated preparation, 0.091 volt and 101 grams
of the physiological requirement for the generation of an action potential and the inherent insensitivity of the transducer. This threshold phenomenon can be observed from the Michaelis-Menten plot (Fig 3).
Conclusion Michaelis and Menten’s mathematical description of enzyme behavior is a powerful tool useful in the analysis of enzyme activity. By making an analogy of substrate concentration to, for example, light intensity or stimulus voltage, students can focus the analytical power of this tool on diverse biological examples. To the extent that students are well-grounded in the basics of MichaelisMenten theory, this strategy capitalizes on their background in very helpful ways.
References ‘Clark, J M and Switzer, Freeman, San Francisco
R L (1977) Experimental
‘Bregman, A A (1987) Laboratory Second edition, Wiley, New York
BIOCHEMICAL
Biochemiswy, W H
Investigations in Cell Biology,
EDUCATION
24(l) 1996
Following the formation of FEBS in 1964 other regional organisations of biochemists emerged. These were the Pan American Association of Biochemical Societies, PAABS, and the Federation of Asian and Oceanian Biochemists, FAOB. A region that has not previously been covered is Africa. A major reason for this was the political troubles in southern Africa but now that biochemists and others can move freely throughout Africa it is timely that a regional organisation should be set up which will enhance the development of biochemistry through the support of local biochemical societies. It is proposed to hold the first Pan African Conference on Biochemistry and Molecular Biology entitled Health, Food Production, Environmental Protection and Industrial Development in Nairobi, 2nd to 6th September, 1996. During this conference the formation of FABS will be proposed and a draft constitution is being prepared. The International Union of Biochemistry and Molecular Biology (IUBMB) has lent its support both in terms of the conference and the launch of FABS as has FEBS. The support of other organisations is now being sought. An International Organising Committee under the Chairmanship of Professor D W Makawiti, Chairman of the Biochemical Society of Kenya, is being formed. Anyone able to assist in the launch of FABS is invited to contact either Professor Makawiti, Department of Biochemistry, University of Nairobi, Nairobi, Kenya, email Dominic_ Makawiti@Ken. Healthnet.Org, or Peter N Campbell, Department of Biochemistry and Molecular Biology, University College London, Gower Street, London WClE 6BT, UK fax 44-171-7293.
Book Review in Brief Essays in Biochemistry
Volume 30
Edited by D K Apps and K F Tipton. pp 157. Portland Press, London. 1995. &17._50/$30 ISBN l-85578-018-6 This latest volume of Essays contains nine fairly short chapters on a wide range of topics. It will enable students and graduate students to update on key areas of modern biochemistry and cell biology. The chapters are written in a clear way providing an authoritative view on the topics under discussion. The chapters are on: contact sites and transport in mitochondria, tyrosine hydroxylase, antizyme/ornithine decarboxylase, the chloroplast genome, lectins, exocytosis, intracellular calcium channels, diphtheria toxin, and thyrotropin-releasing hormone. The chapters offer students the chance to become familiar with a topic ‘at one sitting’: they will also be useful to those preparing lectures. The style includes the use of a second colour in the diagrams making them on the whole more attractive and easier to comprehend. Mary Humphries
The Use of Michaelis-Menten Kinetics in Cell Biology and Physiology Teaching Laboratories RALPH SORENSEN
and NICOLE NOVAK
Biology Department Gettysburg College, Gettysburg, PA 17325,
USA
Introduction The analysis of enzyme behavior using Michaelis-Menten kinetics is a staple of the biochemistry laboratory. By analysing enzyme activity as a function of substrate concentration, students can indirectly observe the saturation of the active site, measure the maximal velocity of a given enzyme concentration, and compare the relative affinity of an enzyme for different substrates. By using double-reciprocal plots (Lineweaver-Burk, EadieHofstee), students can measure these kinetic properties of enzymes with precision and distinguish between competitive, non-competitive, and uncompetitive inhibition. The simple mechanism of Michaelis and Menten E+S$ES>E+P k,
(I)
establishes several important premises: that the enzyme combines directly with the substrate, that the binding of the substrate is not always productive, and that enzyme is not consumed in the process (ie the enzyme acts as a true catalyst). A relatively-straightforward set of algebraic manipulations leads to the Michaelis-Menten equation:
v, = (Vmax[WWm + [Sl>
(2)
This equation describes the initial velocity of any enzyme (self-evidently less than the maximal velocity, V,,,) as a function of two parameters: substrate concentration, [S], and the Michaelis-Menten constant, K,. From eqn 2, the initial velocity is one-half of the V,,, when the substrate concentration is equal to the K,. K, is also defined in terms of the first and second-order rate constants for the breakdown and formation of the ES complex. Assuming that k3 is much less than kZ, K, is equal to the dissociation constant of the ES complex (k2/kl). As such, K, is a useful measure of the binding affinity of the substrate for the active site: a high K, indicates a low binding affinity and vice versa. Empirical verification of this formula by these techniques establishes the accuracy of the theoretical premises. Students learn this information in biochemistry classes in the context that Michaelis and Menten derived it: enzyme activity. Practical experience in the laboratory is, therefore, typically limited to well-studied systems such as the measurement of K, for bacterial P-galactosidase using the substrate o-nitrophenyl P-D-galactoside’ and the demonstration of competitive inhibition of mitochondrial succinate dehydrogenase by malonate.’ BIOCHEMICAL
EDUCATION
24( 1) 1996
The tools employed by Michaelis and Menten have been employed, of course, in broader contexts. Students, through lack of practical application, often fail to appreciate the general utility of this approach outside the analysis of enzyme behavior. It seems axiomatic that students could use profitably their appreciation of MichaelisMenten kinetics to explore biological phenomena involving the interaction of two entities other than enzyme and substrate. Thus the combination of a substrate molecule with an enzyme is not unlike, for example, the combination of a photon with the reaction center of photosystem II or a hormone with a cell-surface receptor. We have used precisely these two examples in cell biology and physiology courses. Through these exercises, students gain a greater appreciation of the molecular mechanics of these phenomena precisely because of their previous study of enzyme kinetics. I describe these two examples as an argument for the greater use of Michaelis-Menten kinetics in practical courses following basic biochemistry. The Hill Reaction
The Hill reaction is the laboratory equivalent of the light reaction of photosynthesis. Using light energy and isolated chloroplasts, photosystem II splits water and passes the electrons through the electron transfer chain in the thylakoid membrane to an artificial electron acceptor. An artificial electron acceptor such as 2,6-dichlorophenolindophenol (DCIP) loses color upon reduction allowing a simple spectrophotometric analysis of the rate of electron transfer. Students can easily measure the rate of the Hill reaction as a function of light intensity. Changing the distance of the light source varies the intensity of light striking the chloroplast preparation. The reaction center of photosystem II can be saturated with photons of red light just like the active site of an enzyme can be saturated with substrate molecules. By plotting initial velocity against light intensity (numerically equal to the reciprocal of the squared distance), the saturation point, or maximal velocity (If,,,), is suggested by the flattening of the curve (Fig 1). Students attempt to extrapolate this curve to its asymptote in order to estimate the If,,,,,. This procedure, however, is quite inaccurate. A Lineweaver-Burk doublereciprocal plot (Fig 2) allows the precise calculation of the value of V,,,. Students can use this value to return to the Michaelis-Menten graph and redo the asymptote. The Neuromuscular
Junction
The physiology of muscle contraction is commonly studied in student laboratories in animal physiology by using the frog gastrocnemius muscle and the sciatic nerve. Students connect the preparation to a mechanical transducer with the output recorded by a polygraph. Students explore the relationship between the strength of electrical stimuli delivered via the exposed sciatic nerve and the force of As the stimulation consequent muscle contraction. voltage increases, so does the contraction until a maximal contraction force is approached (Fig 3). In a Michaelis-
27
0
a
Y
r-4
Stimulus(volts)
Light intensity (l/cm2)
Figure I A Michaelis-Menten plot of DCIP reduction (absorbance units per minute) as a function of light intensity (expressed as the reciprocal of the distance of the light source) by isolated spinach chloroplasts. The secondorder curve was drawn by hand
Ez
-8
5 -
8 c-4
8
l/light intensity (cm2)
Figure 2 A Lineweaver-Burk double-reciprocal plot of the data presented in Fig 1. Linear regression was performed using the CA-Cricket Graph III program (Computer Associates). The formula for the regression line is: y = 0.002x + 2.097. v,,, is calculated from the reciprocal of the y-intercept to be 0.477 Almin. This value may be used to extrapolate the asymptote in Fig I BIOCHEMICAL
EDUCATION
24(l)
1996
Figure 3 A Michaelis-Menten plot of the contraction force (in grams) exerted by curare-treated (0) and untreated (0) frog gastrocnemius preparations as a function of the applied stimulus voltage (in volts). A sub-threshold voltage is identified. The second-order curves were drawn by hand Menten sense, the muscle becomes saturated as the contraction approaches its maximum. In this example, the stimulus voltage is treated as an analog to substrate concentration. Muscle contraction is propagated across the neuromuscular synapse by the neurotransmitter acetylcholine. Acetylcholine leaves the presynaptic membrane by exocytosis, interacts with receptors at the postsynaptic membrane, and triggers depolarization of the post-synaptic membrane. The magnitude of the stimulus voltage mimics, therefore, acetylcholine concentration. Curare (D-tubocurarine) is structurally similar to acetylcholine and would be expected to competitively inhibit the interaction of acetylcholine with its receptor. By remeasuring muscle contraction force in muscle preinjected with 2 ml of D-tubocurarine (0.1 Kg/ml), the effects of curare on contraction force are observed (Fig 3). Analysis of these data by use of a Lineweaver-Burk double-reciprocal plot (Fig 4) shows that curare increased the K, of the post-synaptic acetylcholine receptors (the negative reciprocal of the x-intercept). By competing with acetylcholine binding, the curare decreased the affinity of the receptors for acetylcholine. At the same time, curare did not significantly change the V,,,,, (the reciprocal of the y-intercept). High stimulating voltage, functioning like a saturating substrate concentration, abolished the curare inhibition. These two kinetic properties are, of course, the hallmarks of competitive inhibition. The hypothesis that curare competitively inhibits acetylcholine is thus supported. In the construction of the double reciprocal plot, we subtracted a ‘sub-threshold voltage’ of 0.5 volt from each stimulus value. This operation threshold is a combination
Proposal for a Regional Organisation of Biochemists in Africa The Federation of African Biochemical Societies (FABS)
I N
l/Stimulus
(volts-l)
Figure 4 A Lineweaver-Burk double-reciprocal plot of the data presented in Fig 3. Sub-threshold voltage has been subtracted. Linear regression was performed on data from the curare-treated (0) and untreated (0) preparations of curare using the CA-Cricket Graph III program (Computer Associates). The formulae for the regression lines are: y = 0.0036x + 0.0093 (curare-treated) and y = 0.0009x + 0.0099 (untreated). The calculated K,,, and V,,,, for the curare-treated preparation are 0.387 volt and 107 grams, respectively, and for the untreated preparation, 0.091 volt and 101 grams
of the physiological requirement for the generation of an action potential and the inherent insensitivity of the transducer. This threshold phenomenon can be observed from the Michaelis-Menten plot (Fig 3).
Conclusion Michaelis and Menten’s mathematical description of enzyme behavior is a powerful tool useful in the analysis of enzyme activity. By making an analogy of substrate concentration to, for example, light intensity or stimulus voltage, students can focus the analytical power of this tool on diverse biological examples. To the extent that students are well-grounded in the basics of MichaelisMenten theory, this strategy capitalizes on their background in very helpful ways.
References ‘Clark, J M and Switzer, Freeman, San Francisco
R L (1977) Experimental
‘Bregman, A A (1987) Laboratory Second edition, Wiley, New York
BIOCHEMICAL
Biochemiswy, W H
Investigations in Cell Biology,
EDUCATION
24(l) 1996
Following the formation of FEBS in 1964 other regional organisations of biochemists emerged. These were the Pan American Association of Biochemical Societies, PAABS, and the Federation of Asian and Oceanian Biochemists, FAOB. A region that has not previously been covered is Africa. A major reason for this was the political troubles in southern Africa but now that biochemists and others can move freely throughout Africa it is timely that a regional organisation should be set up which will enhance the development of biochemistry through the support of local biochemical societies. It is proposed to hold the first Pan African Conference on Biochemistry and Molecular Biology entitled Health, Food Production, Environmental Protection and Industrial Development in Nairobi, 2nd to 6th September, 1996. During this conference the formation of FABS will be proposed and a draft constitution is being prepared. The International Union of Biochemistry and Molecular Biology (IUBMB) has lent its support both in terms of the conference and the launch of FABS as has FEBS. The support of other organisations is now being sought. An International Organising Committee under the Chairmanship of Professor D W Makawiti, Chairman of the Biochemical Society of Kenya, is being formed. Anyone able to assist in the launch of FABS is invited to contact either Professor Makawiti, Department of Biochemistry, University of Nairobi, Nairobi, Kenya, email Dominic_ Makawiti@Ken. Healthnet.Org, or Peter N Campbell, Department of Biochemistry and Molecular Biology, University College London, Gower Street, London WClE 6BT, UK fax 44-171-7293.
Book Review in Brief Essays in Biochemistry
Volume 30
Edited by D K Apps and K F Tipton. pp 157. Portland Press, London. 1995. &17._50/$30 ISBN l-85578-018-6 This latest volume of Essays contains nine fairly short chapters on a wide range of topics. It will enable students and graduate students to update on key areas of modern biochemistry and cell biology. The chapters are written in a clear way providing an authoritative view on the topics under discussion. The chapters are on: contact sites and transport in mitochondria, tyrosine hydroxylase, antizyme/ornithine decarboxylase, the chloroplast genome, lectins, exocytosis, intracellular calcium channels, diphtheria toxin, and thyrotropin-releasing hormone. The chapters offer students the chance to become familiar with a topic ‘at one sitting’: they will also be useful to those preparing lectures. The style includes the use of a second colour in the diagrams making them on the whole more attractive and easier to comprehend. Mary Humphries