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LECTURE 3: ENZYME KINETICS
LECTURE OUTCOMES
After mastering the present lecture materials, students will be able to to explain enzyme substrate interaction in the conversion of substrate to product to explain enzyme kinetics including the rate of reactions as a function of substrate concentration to calculate Km and Vmax of reactions catalyzed by enzymes
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LECTURE FLOW
Enzyme-Substrate Interaction 1. Lock and Key" Hypothesis 2. The "Induced Fit" Hypothesi
Enzyme Kinetics Michalis-Menten
Equation Double-reciprocal or Lineweaver-Burk Eadie-Hofstee Hanes-Woolf
INTRODUCTION
http://www.demochem.de/kinetics.htm
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Enzyme-Substrate Interaction 1. Lock and Key" Hypothesis 2. The "Induced Fit" Hypothesis 1.
"Lock and Key" Hypothesis Emil Fischer in 1890 proposed "Lock and Key" Hypothesis
active site
substrates
The shape, or configuration, of the active site is especially designed for the specific substrate involved.
Because the configuration is determined by the amino acid sequence of the enzyme, the native configuration of the entire enzyme molecule must be intact for the active site to have the correct configuration. In such a case, the substrate then fits into the active site of the enzyme in much the same way as a key fits into a lock.
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2. The "Induced Fit" Hypothesis
Enzymes are highly flexible, conformationally dynamic molecules, and many of their remarkable properties, including substrate binding and catalysis, are due to their structural pliancy.
Transition conformation
Realization of the conformational flexibility of proteins led Daniel Koshland to hypothesize that the binding of a substrate (S) by an enzyme is an interactive process. The shape of the enzyme's active site is actually modified upon binding S, in a process of dynamic recognition between enzyme and substrate aptly called induced fit.
ATP
ATP lyase or ATPase
Mg(2+)
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In essence, substrate binding alters the conformation of the protein, so that the protein and the substrate "fit" each other more precisely. The process is truly interactive in that the conformation of the substrate also changes as it adapts to the conformation of the enzyme.
Induced Fit Model
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Enzyme Kinetics
Basic Prinsiple
Enzyme kinetics is the study of the chemical reactions that are catalyzed by enzymes or the study of the rates of enzymecatalyzed reactions This study provides information on enzyme specificities and mechanisms The formation of ES complex is the base of enzymic reactions
E+S
ES
E+P
What is the rate of reaction (V) if Case 1 [S] increases [E] is constant
Case 1 [S] is constant [E] increases
V = δP/δt Zero order SP
V
S P k t t
S kt
S kt C
S t S k t S 0 0
Why are enzyme kinetics important? 1. 2.
3.
It provides valuable information for enzyme mechanism It gives an insight into the role of an enzyme under physiological conditions It can help show how the enzyme activity is controlled and regulated
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The influence of [E] These reactions are said to be "zero order" because the rates are independent of substrate concentration, and are equal to some constant k
V
[S] is constant
[E]
Order zero first second
Rate k
Comments
rate is independent of substrate concentration rate is proportional to the first power of k[S] substrate concentration rate is proportional to the square of the k[S][S]=k[S]2 substrate concentration rate is proportional to the first power of k[S1][S2] each of two reactants
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Enzyme Kinetics
Enzymes follow zero order kinetics when substrate concentrations are high.
Zero order means there is no increase in the rate of the reaction when more substrate is added.
Given the following breakdown of sucrose to glucose and fructose Sucrose + H20
→
Glucose + Fructose H
H
H O HO
H
OH
OH
H OH
H OH
H HO
H
H
O
HO H
HO H H
OH OH
The reaction is reversible which means some substance can be synthesized from the substrate in the reaction If environmental factors are constant, the rate of product formation (reaction velocity, V) is dependent upon the concentration of enzyme and substrate [E] = enzyme concentration [S] = substrate concentration
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The influence of [S] The concentration of substrate [S] greatly influences the rate of product formation (the velocity of a reaction, V)
Studying the effects of [S] on the velocity of a reaction is complicated by the reversibility of enzyme reactions, e.g. conversion of product back to substrate To overcome this problem, initial velocity (vo) measurements are used. At the start of a reaction, [S] is in large excess of [P], thus the initial velocity of the reaction will be dependent on substrate concentration
When initial velocity is plotted against [S], a hyperbolic curve results, where
Vmax represents the maximum reaction velocity This occurs at [S] >> E, and all available enzyme is "saturated" with bound substrate, meaning only the ES complex is present.
High [S] Saturating [E] Low [S]
50% [S] Km
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MICHAELIS-MENTEN MODEL
1.
Lenore Michaelis and Maud L. Menten proposed a general theory of enzyme action in 1913 The formation of ES Complex
Their theory was based on the assumption that the enzyme (E) and its substrate (S) associate reversibly to form an enzyme-substrate complex, ES
E+S
k1 k2
ES
k3 k4
E+P
E = Enzyme, S = Substrate, P = Product ES = Enzyme-Substrate complex , and k1, k2, k3 & k4 = rate constants. k4 is very small and ignored
This association/dissociation is assumed to be a rapid equilibrium, and Ks is the enzyme : substrate dissociation constant. At equilibrium, k2[ES] = k1[E][S] and [E][S] k 2 KS [ES ] k 1
2.
Steady-State Assumption
The interpretations of Michaelis and Menten were refined and extended in 1925 by Briggs and Haldane, by assuming [ES] quickly reaches a constant value in such a dynamic system.
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That is, ES is formed as rapidly from E + S, and disappears by its two possible fates
This assumption is termed the steady-state assumption and is expressed as [ES ] 0 t
3.
dissociation to regenerate E + S, and reaction to form E + P
Initial Velocity Assumption
Because enzymes accelerate the rate of the reverse reaction as well as the forward reaction, the conversion of E+P to ES, and k4(E][P] = 0
E+S
4.
k1 k2
ES
k3
E+P
However, if we observe only the initial velocity for the reaction immediately after E and S are mixed in the absence of P, the rate of any back reaction is negligible because its rate will be proportional to [P], and [P] is essentially 0 Given such simplification, we now analyze the system described by equation above in order to describe the initial velocity v as a function of [S] and amount of enzyme.
Total Enzyme
The total amount of enzyme is fixed and is given by the formula [E] = free enzyme and [ES] = the amount of [E]0 = [E] + [ES] enzyme in the enzyme-substrate complex.
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The rate of product formation is dependent upon [ES] and k3
dP v k 3 ES dt
[ES] is the difference between the rates of ES formation minus the rates of its disappearance.
dES k 1 E S k 2 ES k 3 ES dt The assumption of steady state gives The rate of [ES] formation = The rate of [ES] formation ES = k1[E][S] = ES = (k2 + k3) (ES) Michaelis-Menten Cosntant KM = (k2 + k3 )/k1
Michaelis-Menten Equation
Vmax
Vmax[S] V KM [S]
½Vmax
V
KM
[S]
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The best substrate for enzyme is that which has the highest Vmax/KM Enzyme Chymotrypsin Carbonic Anhydrase
1.
Vmax KM 100 5000 600,000 8000
Vmax/KM 1/50 600/8
KM Michaelis-Menten Equation:
V = Vmax[S]/(KM+[S])
2.
If V = ½Vmax ½Vmax = Vmax[S]/(KM+[S]) ½(KM+[S]) = [S]KM+[S] = 2[S] KM = [S]
KM = (k2 + k3)/k1
E+S
This means that KM is equal to the substrate concentration at V = ½ Vmax
k1 k2
ES
k3
E+P
The rate-determining step of the reaction is k3, for the formation of product so if k2 >> k3 KM = k2/k1 k2/k1 is known as a dissociation constant for the ES complex k2/k1 reflects a tendency of ES complex to dissociate to be E and S, KM = k2/k1 can be used as a relative measure of the affinity of a substrate for an enzyme
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Low KM high apparent affinity of a substrate for an enzyme High KM low apparent affinity of a substrate for an enzyme Enzyme Pyruvate carboxylase 3.
Substrate pyruvate HCO3ATP
Km (μM) 400 1000 60
Turnover number k3 = Vmax/[E]0 Moles of substrate transformed per second per mole of active site, or the number of substrate molecules converted to P by an E molecule in a unit time when E is fully saturated.
Penetuan KM dan Vmax
Harga KM bervariasi sangat besar, tapi dari kebanyakan enzim berkisar diantara 10-1 - 10-6 M (Tabel 2.1) tergantung substrat dan lingkungan seperti suhu dan kuantitas ion Untuk mendapatkan harga KM dan Vmax, analisis langsung persamaan diatas dapat dilakukan, tapi cara ini membutuhkan waktu yang lama, dan bantuan komputer sangat penting untuk mengoptimasi harga parameter persamaan dengan cepat.
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Tabel 2.1 Parameter beberapa enzim
PENDEKATAN LAIN
Linierisasi persamaan Modifikasi persamaan ke bentuk linier sehingga dapat dianalisis dengan mudah 1. Persamaan “double-reciprocal” atau “Lineweaver-Burk” 2. Persamaan “Eadie-Hofstee” 3. Persamaan “Hanes-Woolf”
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Persamaan “double-reciprocal” atau “Lineweaver-Burk” Vmax[S] KM [S] Jika ruas kiri dibalik dan demikian juga ruas kanan, maka V
1 KM 1 1 . V Vmax [S] Vmax
Sekarang persamaan ini akan mudah dianalisis dengan metode linier sedehana
Sekarang y = 1/V ; x = 1/[S] a = 1/Vmax ; b = KM/Vmax dapat dianalisis dengan y = a + bx Jika 1/V dihubungkan dengan 1/[S], suatu garis lurus akan dihasilkan yang memotong sumbu y pada 1/Vmax dan sumbu x pada -1/KM serta membentuk sudut terhadap sumbu x sebesar KM/Vmax.
1/V KM/Vmax
-1/KM
1/Vmax
1/[S]
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Persamaan “Eadie-Hofstee” V
Vmax[S] KM [S]
V ( K M [ S ]) V max [ S ] V [ S ] VK M V max [ S ] V
VK M V max [ S ] [S ]
V K M
V Vmax [S]
Sekarang y = V ; x = V/[S] a = Vmax ; b = -KM dapat dianalisis dengan y = a + bx Jika V dihubungkan dengan V/[S], suatu garis lurus akan dihasilkan yang memotong sumbu y pada Vmax dan sumbu x pada Vmax/KM serta membentuk sudut terhadap sumbu x sebesar KM
Vmax V KM
Vmax/KM
V/[S]
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Persamaan “Hanes-Woolf” V
Vmax [S] KM [S]
V (K
M
[ S ]) V max [ S ]
[S ] K M [S ] V V max [S ] K M V V max
1 V max
.[ S ]
[S] K M 1 .[S] V Vmax Vmax
Sekarang y = [S]/V ; x = [S] a = KM/Vmax ; b = 1/Vmax dapat dianalisis dengan y = a + bx
Jika [S]/V dihubungkan dengan [S], suatu garis lurus akan dihasilkan yang memotong sumbu y pada KM/Vmax dan sumbu x pada -KM serta membentuk sudut terhadap sumbu x sebesar 1/Vmax.
[S]/V 1/Vmax
KM/Vmax -KM [S]
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STEPS OF MODEL DERIVATION
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STEPS OF MODEL DERIVATION 1.
Pembentukan ES adalah inti dari hipotesis tersebut
E+S 1.
2.
4.
5.
6.
k1 k2
ES
k3 k4
E+P
(1)
Reaksi E dengan S terjadi dengan kecepatan k1 dan menghasilkan kompleks ES (enzimsubstrat) Kompleks ES dapat berubah menjadi E dan S bebas kembali dengan kecepatan k2, atau menjadi E dan P dengan kecepatan k3.
Jika k3 k4 , maka reaksi bersifat “irreversible”, sehingga produk P tidak ada yang diubah kembali menjadi substrat asal dan k4 dapat diabaikan. Suatu hal penting yang perlu diingat adalah bahwa konstanta k1, k2, k3 dan k4 proporsional dengan G aktivasi substrat dari reaksi yang bersangkutan Pada [S] yang rendah, kebanyakan enzim berada dalam bentuk bebas, sehingga penambahan S akan langsung terikat dengan E dan diubah menjadi P dengan demikian kecepatan awal proporsional dengan peningkatan [S]
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7.
8.
9.
Pada [S] yang lebih tinggi, kecepatan reaksi bervariasi dengan peningkatan [S] karena enzim mulai mengalami kejenuhan Pada [S] yang tinggi, semua enzim dijenuhi oleh substrat dan karenanya berada dalam bentuk kompleks ES Jadi enzim dalam suatu reaksi dapat berada dalam keadaan bebas dan terikat dengan substrat, sehingga total enzim secara matematis adalah
[E]0 = [E]+[ES]
10.
11.
12.
(2)
Penurunan persamaan Michaelis-Menten tergantung pada asumsi yang disebut ”Briggs-Haldane Steady-State” Keadaan "steady state" adalah suatu keadaan dimana konsentrasi intermediat (perantara) ES tetap konstan, sementara konsentrasi substrat dan produk berubah Keadaan demikian terjadi apabila kecepatan pembentukan ES sama dengan kecepatan peruraian ES
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13.
Keadaan “steady” dapat dinyatakan secara matematis seperti dengan persamaan berikut
[ES]/t = 0
(3)
dimana t = waktu (menit) 14.
Pernyataan [ES]/t dapat ditulis dari sudut konstanta dan konsentrasi pers (1) yaitu Kecepatan pembentukan ES
ES = k1[E][S]
(4a)
Kecepatan peruraian ES
ES = (k2 + k3) (ES) 15.
(4b)
Dalam keadaan "steady state" kedua persaman (4a) dan (4b) adalah sama, sehingga
[ES]/t = k1[E][S]-(k2+k3)(ES) = 0 (5)
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16.
Subsitusi E dari pers (2) kedalam pers (5) menghasilkan (2) [E]0 = [E]+[ES] [E] = [E]0-[ES] (5) [ES]/t = k1[S][E]-(k2+k3)(ES) k1[S][E] = k1[S]([E]0-[ES]) = k1[S][E]0-k1[S][ES] Hence k1[S][E]0-k1[S][ES] - (k2+k3)(ES) = 0 k1[S][E]0–(k1[S]+k2+k3)[ES]=0
17.
(6)
Pengaturan persamaan lebih lanjut (k1[S]+k2+k3)[ES] = k1[S][E]0 (7)
18.
Persamaan ini dapat dimodifikasi dengan cara ruas kanan dibagi dengan k1[S], [ES]
19.
[E]0 1 (k 2 k3 ) / k1[S]
(8)
Karena k1, k2, dan k3 adalah konstanta, maka ketiga konstanta ini dapat dijadikan satu konstanta yaitu (k2 + k3 )/k1 = KM yang dikenal sebagai konstanta Michaelis-Menten
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20.
21.
Untuk kebanyakan enzim k3 k2, sehingga KM akan mendekati (k2 + k1), sedang (k2 + k3 )/ k1 adalah Ks (konstanta dissosiasi kompleks enzim-substrat). Jika KM, yang merupakan ukuran affinitas enzim akan substrat, disubsitusikan kedalam pers (8), maka
[ ES ] 22.
[ P ] k 3 [ ES ] t
(10)
Subsitusi [ES] dari pers. (10) ke dalam pers (9) memberikan
V 24.
(9)
Kecepatan reaksi katalisis dapat dinyatakan dengan jumlah produk yang tebentuk per satuan waktu yaitu produk dari konsentrasi kompleks ES dengan kapasitas katalisis enzim k3 (turnover number).
V
23.
[ E ]0 1 ( K M /[ S ])
k 3 [ E ]0 1 ( K M /[ S ])
(12)
Pada keadaan E dijenuhi S yang berarti semua enzim terikat dengan substrat dalam kompleks ES, maka V = Vmax = k3[E]0. Kemudian persamaan diatas dapat ditulis dalam bentuk berikut.
V
Vmax Vmax[S] 1 (KM / [S]) atau V K [S] M
(13)
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25. 26.
Persamaan diatas dikenal sebagai persamaan Michaelis-Menten yang digunakan secara luas Stoikiometri pers (13) didasarkan atas satu substrat dan satu produk (uni-uni), sementara banyak reaksi enzimatis yang melibatkan stoikiometri yang lebih kompleks seperti berikut;
S P1 + P2 (Ui-Bi) S1 + S2 P (Bi-Uni) S1 + S2 P1 + P2 (Bi-Bi) 27.
Tetapi, persamaan Michaelis-Menten berlaku untuk reaksi yang lebih kompleks sekalipun dengan mekanisme yang berbeda.
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FIG. 2. Overall structure of Rubisco from C. reinhardtii. The view is down the local 4-fold axis. The L subunits are depicted in two shades of gray, and the S subunits are in yellow. The S subunit A-B loops are shown in red. The inset shows a close-up view of the same region in the Spinacia enzyme with the same color coding. Pictures were produced with MOLSCRIPT (41) modified by Esnouf (42) and rendered with RASTER3D (43). Taylor et al., 2001, J. Biol. Chem., 276: 48159–48164
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Web Figure 8.3.A A model for the structure of rubisco in chloroplasts from higher plants. Rubisco consists of 8 large (L) and 8 small (S) subunits arranged as 4 dimers. Small subunits are shown in red (only four of the small subunits are seen), large subunits are shown in blue and green, in order to show the boundaries of the dimers. (From Malkin and Niyogi 2000.) (Click image to enlarge.)
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