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] in Bi-Bi Systems  Sequential enzymes  Ping-pong enzymes  Determination of kinetic parameters  Inhibition patterns of Bi-Bi Reactions

Terminology  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)

Steady State Models for n S, n P k cat k 1 [E] + n x [S] [ES n ] [E] + n x [P] k - 1 Assumptions and Givens:  d[ES n ]/dt = O (Steady state)  [P] = 0 at t = 0 Cannot  V = d[P]/dt = n x k cat [ES] measure  [E] t = [E] + [ES n ]  V max = n k cat [E] t  K m = {k -1 + k cat }/k 1 = [S] ½ at V 0 = ½V max  V 0 = V max [S] h = k cat [E] t [S] h where h = Hill coefficient K m h + [S] h K m h + [S] h h = 1 for a MM enzyme

Kinetic Mechanisms Bi-Bi reactions Sequential Non-Sequential Both A and B must add to E before either P or Q is released 1:Ordered 3:Ping-Pong 2:Random 2 binding sites 2 binding sites Single binding site Compulsory order of A,B No specified order of A,B P is released before both addition and P ,Q release addition and P, Q release A and B have bound Steady state ordered Rapid Equilibrium ordered No assumptions made about relative rates of various steps K ia >> V/E t

1:Ordered Sequential Mechanism E.G.: NAD(P)H- dependent oxidoreductases A B P Q E EA EQ E EAB EPQ  A:Steady state ordered VAB v = K ia K b + K a B + K b A + AB A must bind first E E EA EAB+EPQ+EQ  B:Equilibrium Ordered VAB v = K ia K b + K b A + AB E and A in thermodynamic eq. K ia >> V / E t E EA EAB+EPQ+EQ K a 0, K a B = 0

E.G.: kinases 2: Random Sequential Mechanism and some dehydrogenases A B P Q K ia K b EA EQ E EAB EPQ E EP EB K ib K a B A Q P  2 distinct binding sites VAB v =  Rapid equilibrium: K ia K b = K a K ib K ia K b + K a B + K b A + AB  Catalysis is rate-limiting If A binds  EAB EPQ E EB EA EAB first  [EP] and [EQ] 0 Distribution of E t in  [E t ] = [E] + [EA] + [EB] + [EAB] its different forms

3: Ping-Pong Mechanism E.G. aminotransferases, serine proteases A P B Q E EA F FB E FP EQ VAB  A has a donor group which is v = transferred to a group on the K a B + K b A + AB enzyme (E-form)  The enzyme with the donor group E F EA,FP,FB,EQ covalently bound to it forms a new stable enzyme form F  P is release from FP The enzyme travels back and forth  B binds to the site vacated by P between the 2 stable forms E and F like a ping-pong ball  Donor moiety is transferred to B  Q is release from EQ

 ANIMATION:

FIG. 11.13 (Mathews): Action of chymotrypsin 1: [EA]. Polypeptide S binds 2: [FP] . H + is transferred from Ser 3: F + P . H + is transferred to C-terminal noncovalently with E. to His. S forms tetra hedral fragment, which is released by cleavage of transition state with E the C-N bond. The N-terminal fragment is bound through acyl linkage to Ser. 4: [FB] . H 2 O (B)binds to F in 5: [EQ] . H 2 O transfers H + to His 6: E + Q . The 2 nd peptide fragment (Q) place of polypeptide 57 and its – OH to the remaininf S is released. The acyl bond is cleaved, H + fragment. A tetrahedral transition is transferred from His back to Ser, and state complex is formed. E returns to initial state.

Effects of [S] in Bi-Bi Systems 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

Effects of [S] in Bi-Bi Systems  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  Parameters in Initial Velocity Pattern Graphs that are considered:  V max  A change in V max 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)

Effect of A and B on K a , K b and V  K a is the MM constant for A at saturation with B  K b 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 K m and app V max differ from the true K m and true V max  The relationships between the app K m and V max and the true K m and V max depend on:  Kinetic mechanism of the enzyme  Which substrate is varied

Initial Velocity Patterns: Sequential Enzymes  Ordered A B P Q E EA EQ E EAB EPQ  Random A B P Q EA EQ E E EAB EPQ EP EB B A Q P

Initial Velocity Patterns: Ordered Sequential B 1 B 2 B 3 1/ v 1/ v B 4 1/ V (1- K a / K ia ) 1/ V (1- K b / K ib ) -1/ K ia 1/ A -1/ K ib 1/ B A = Variable substrate B = Variable substrate B = fixed substrate A = fixed substrate V max with in [B] V max with in [A] K a with in [B] K b with in [A] Slopes and Intercepts change

Initial Velocity Patterns: Random Sequential B 1 A 1 B 2 A 2 B 3 A 3 1/ v 1/ v B 4 A 4 1/ V (1- K a / K ia ) 1/ V (1- K b / K ib ) -1/ K ia 1/ A -1/ K ib 1/ B 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 K ia > K a : Cross-over point = y + If K ia = K a : Cross-over point = y 0 If K ia < K a : Cross-over point = y -

Determination of Kinetic Constants: Sequential Enzymes Slopes = ( K ia K b / V )(1/ B ) + K a / V B 1 B 2 B 3 Slopes 1/ v K ia K b / V B 4 K a / V 1/ V (1- K a / K ia ) 1/ B -1/ K ia 1/ A Intercepts = (K b /V)(1/B) + 1/V Slope of intercepts plot K b = Intercept of intercepts plot Slope of slopes plot Intercepts K ia = Slope of intercepts plot K b / V (I/V app ) Intercept of slopes plot 1/V true K a = Intercept of intercepts plot -1/K b 1/ B

Initial Velocity Patterns: Ping-Pong Enzymes A P B Q E EA F FB E FP EQ 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 (K m /V max ) remain unchanged

Initial Velocity Patterns: Ping-Pong Enzymes A 1 A 2 A 3 B 1 A 4 B 2 1/ v B 3 B 4 1/ v K b / V 1/ B 1/ A A = Variable substrate B = Variable substrate K a / V B = fixed substrate A = fixed substrate Intercepts change, Slopes constant

Determination of Kinetic Constants: Ping-Pong Enzymes B 1 B 2 Intercepts = (K b /V)(1/B) + 1/V B 3 B 4 1/ v Intercepts K a / V K b / V (I/V app ) 1/ A 1/V true -1/K b Slope of intercepts plot 1/ B K b = Intercept of intercepts plot Slope of parallel reciprocal plot K a = Intercept of intercepts plot

Inhibition patterns of Bi-Bi Reactions  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 / K i ) the terms in the denominator of the rate equations that represent the form of the enzyme with which the inhibitor react

Dead-end Inhibition Patterns for Bi-Bi Reaction Mechanisms  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. I 4 I 4 I 4 I 3 I 3 I 3 I 2 I 2 I 2 1/ v I 1 I 1 I 1 1/ A 1/ A 1/ A

True and Apparent Inhibition Constants  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 of the kinetic parameter associated with that substrate  The type of inhibition obtained with an inhibitory substrate analogue (SA) depends on which substrate is varied

1: Rapid equilibrium, random mechanism A B P Q K ia K b EA EQ E EAB EPQ E EP EB K ib K a B A Q P  Inhibitor of A (SA) reacts with E and EB : Competitive w.r.t. A and noncompetitive w.r.t. B  Inhibitor of B (SA) reacts with E and EA : Competitive w.r.t. B and noncompetitive w.r.t. A