Bi-Bi Reactions 2 substrates, 2 products Kinetics of Multisubstrate - - PowerPoint PPT Presentation
4. Kinetics of Multisubstrate Reactions Bi-Bi Reactions 2 substrates, 2 products Kinetics of Multisubstrate Reactions Contents Terminology Kinetic Mechanisms Ordered sequential Random sequential Ping-pong Effects of [S]
Contents Terminology Kinetic Mechanisms
Ordered sequential Random sequential Ping-pong
Effects of [S] in Bi-Bi Systems
Sequential enzymes Ping-pong enzymes
Determination of kinetic parameters Inhibition patterns of Bi-Bi Reactions
Symbols
Substrates: A, B Products: P, Q Enzyme forms: E (free enzyme), F
Transitory Complexes
Enzyme-substrate: EA, EB, EAB Enzyme-product: EP, EQ, EPQ Enzyme-substrate-product: EAP, EBQ
Central Complexes
Transitory complex that is full (binding site) (EAB), (EPQ)
[E] + n x [S] [ESn] [E] + n x [P]
k1 k-1 kcat
Assumptions and Givens: d[ESn]/dt = O (Steady state) [P] = 0 at t = 0 V = d[P]/dt = n x kcat [ES] [E]t = [E] + [ESn] Vmax = n kcat[E]t Km = {k-1 + kcat}/k1 = [S]½ at V0 = ½Vmax V0 = Vmax [S]h = kcat[E]t[S]h where h = Hill coefficient Km
h + [S]h Km h + [S]h h = 1 for a MM enzyme
Cannot measure
Bi-Bi reactions Sequential
Both A and B must add to E before either P or Q is released
Non-Sequential 3:Ping-Pong
Single binding site P is released before both A and B have bound
2:Random
2 binding sites No specified order of A,B addition and P, Q release
1:Ordered
2 binding sites Compulsory order of A,B addition and P ,Q release
Steady state ordered
No assumptions made about relative rates of various steps
Rapid Equilibrium
Kia >> V/Et
A B P Q E E EA EQ
EAB EPQ
A:Steady state ordered B:Equilibrium Ordered v = VAB KiaKb + KaB + KbA + AB
E E EA EAB+EPQ+EQ
v = VAB KiaKb + KbA + AB
E EA EAB+EPQ+EQ
A must bind first
E and A in thermodynamic eq. Kia >> V/Et Ka 0, KaB = 0
E.G.: NAD(P)H- dependent
A A B B P P Q Q E E EA EB EQ EP
EAB EPQ
Kia Kib Kb Ka
Distribution of Et in its different forms
2 distinct binding sites Rapid equilibrium: KiaKb = KaKib Catalysis is rate-limiting
EAB EPQ [EP] and [EQ] 0 [Et] = [E] + [EA] + [EB] + [EAB]
E EB EA EAB
If A binds first
E.G.: kinases and some dehydrogenases
A has a donor group which is transferred to a group on the enzyme (E-form) The enzyme with the donor group covalently bound to it forms a new stable enzyme form F P is release from FP B binds to the site vacated by P Donor moiety is transferred to B Q is release from EQ
A B P Q E E EA FP F FB EQ
E F EA,FP,FB,EQ
The enzyme travels back and forth between the 2 stable forms E and F like a ping-pong ball
E.G. aminotransferases, serine proteases
1: [EA]. Polypeptide S binds noncovalently with E. 2: [FP]. H+ is transferred from Ser to His. S forms tetra hedral transition state with E 3: F + P. H + is transferred to C-terminal fragment, which is released by cleavage of the C-N bond. The N-terminal fragment is bound through acyl linkage to Ser. 4:[FB]. H2O (B)binds to F in place of polypeptide 5: [EQ]. H2O transfers H + to His 57 and its –OH to the remaininf S
state complex is formed. 6: E + Q. The 2nd peptide fragment (Q) is released. The acyl bond is cleaved, H + is transferred from His back to Ser, and E returns to initial state.
To study the kinetics of enzymes with 2 substrates: Vary the [A] at different fixed concentrations of B Measure the resulting initial velocities
The data are plotted as 1/v versus 1/[A] A separate plot is made for each level of the second substrate B Example: A was used as variable substrate and B as the fixed substrate
INITIAL VELOCITY PATTERN is obtained
This initial velocity pattern will vary according to the kinetic mechanism of the enzyme This enables us to distinguish between sequential and Ping- pong mechanisms
Vmax
A change in Vmax indicates the effect of a change in the [fixed substrate] (B) on reaction velocity v at high [variable substrate] (A)
Slope
A change in the slope indicates the effect of a change in the [fixed substrate] (B) on reaction velocity v at very low [variable substrate] (A)
Ka is the MM constant for A at saturation with B Kb is the MM constant for B at saturation with A V is the maximum velocity at saturation with both substrates A and B At lower concentration than saturation of the second substrate, the app Km and app V max differ from the true Km and true Vmax The relationships between the app Km and Vmax and the true Km and Vmax depend on: Kinetic mechanism of the enzyme Which substrate is varied
Ordered Random
A B P Q E E EA EQ
EAB EPQ
A A B B P P Q Q E E EA EB EQ EP
EAB EPQ
B4 B3 B2 B1
1/v 1/A
1/V(1-Ka/Kia)
A = Variable substrate B = fixed substrate B = Variable substrate A = fixed substrate
Vmax
with in [B]
Ka with in [B] Vmax
with in [A]
Kb with in [A]
Slopes and Intercepts change
1/v 1/B
1/V(1-Kb/Kib)
B4 B3 B2 B1
1/v 1/A
1/V(1-Ka/Kia)
A4 A3 A2 A1
1/v 1/B
1/V(1-Kb/Kib)
Initial velocity patterns are the same regardless of which reciprocal substrate concentration is plotted on the horizontal axis ( 1/A or 1/B ) The cross-over point can be above, below or on the horizontal axis If Kia > Ka: Cross-over point = y + If Kia = Ka: Cross-over point = y 0 If Kia < Ka: Cross-over point = y -
B4 B3 B2 B1
1/v 1/A
1/V(1-Ka/Kia) Slopes = (KiaKb/V)(1/B) + Ka/V Intercepts = (Kb/V)(1/B) + 1/V Slopes 1/B KiaKb/V Ka/V
Slope of intercepts plot Intercept of intercepts plot
Slope of intercepts plot Slope of slopes plot
Kia=
Intercept of slopes plot Intercept of intercepts plot
Ka=
Intercepts (I/Vapp) 1/B Kb/V 1/Vtrue
Reaction FP F + P is irreversible
Initial velocity: [P] = 0 Irreversibility of reaction isolates the rate limiting step EA E+A from the influence of B A change in [B] has no effect at low [A] Slopes of LB (Km/Vmax) remain unchanged A B P Q E E EA FP F FB EQ
1/v 1/A
B4 B3 B2 B1
Ka /V
A4 A3 A2 A1
1/v 1/B
Kb/V
A = Variable substrate B = fixed substrate B = Variable substrate A = fixed substrate
Intercepts change, Slopes constant
Intercepts = (Kb/V)(1/B) + 1/V
Slope of intercepts plot Intercept of intercepts plot
Kb=
Intercept of intercepts plot Slope of parallel reciprocal plot
Ka=
1/v 1/A
B4 B3 B2 B1
Ka /V
Intercepts (I/Vapp) 1/B Kb/V 1/Vtrue
The type of inhibition pattern obtained with an inhibitory substrate analogue depends on:
The kinetic mechanism the substrate that is varied
The initial velocity equation for an inhibited enzyme reaction can be derived readily by
multiplying with the factor (1 + I / Ki ) the terms in the denominator of the rate equations that represent the form of the enzyme with which the inhibitor react
Slopes of reciprocal plot varies with I : I is a competitive inhibitor of the substrate that is varied. Slopes and intercepts of reciprocal plot varies with I : I is a noncompetitive inhibitor of the substrate that is varied. Intercepts of reciprocal plot varies with I : I is an uncompetitive inhibitor of the substrate that is varied.
1/v 1/A 1/A 1/A I4 I3 I2 I1 I4 I3 I2 I1 I4 I3 I2 I1
The directly determined inhibition constant can be an apparent rather than a true inhibition constant. The directly determined inhibition constant depends on
The kinetic mechanism The concentration of the fixed substrate
The true inhibition constant must be calculated by using
the relationship between the true and app inhibition constants for a particular mechanism The concentration of the fixed substrate and the value
A A B B P P Q Q E E EA EB EQ EP
EAB EPQ
Kia Kib Kb Ka
A B P Q E E EA EQ
EAB EPQ
Inhibitor of A (SA) reacts only with E : Competitive w.r.t. A and noncompetitive w.r.t. B Inhibitor of B (SA) reacts only with EA : Competitive w.r.t. B and uncompetitive w.r.t. A
A B P Q E E EA FP F FB EQ
Substrate analogues react with stable forms of enzyme (E,F) Inhibitor of A (SA) reacts only with E : Competitive w.r.t. A and uncompetitive w.r.t. B Inhibitor of B (SA) reacts only with F : Competitive w.r.t. B and uncompetitive w.r.t. A Can get SA of both A and B which binds to E and F: Noncompetitive w.r.t. A and B