Enzymatic reactions involving more than one substrate

Most reactions involve more than one substrate. These are called bisubstrate reactions and, in general, these reactions can be written as: A + B → P + Q where A and B are the substrates; P and Q are the products.

There are two types of bisubstrate reactions:

1. Single displacement reactions. The enzyme must bind all substrates before a reaction occurs and products are released.

2. Double displacement reactions. Some products are released before all substrates bind the enzyme. This is also called a “ping-pong” reaction mechanism.

Single displacement reactions

1. Ordered mechanism. The substrates must bind the enzyme in an ordered way. This also is called sequential mechanism. In the Cleland notation this can be written:

A B P Q

k1 k-1 k2 k-2 k4 k-4 k5 k-5 k3 k E EA EAB -3 EPQ EQ E

A and B are the leading and following substrates, respectively.

Example: reduction of NAD+ by alcohol dehydrogenase to yield NADH and acetaldehyde:

+ NAD + CH3CH2OH ↔ NADH + CH3CHO

A B P Q

How would you confirm that the leading substrate is NAD+?

1 Single displacement reactions - ordered mechanism rate equation

The derivation of the ordered bisubstrate-biproduct (ordered Bi-Bi) rate equation is done in a similar sway to the derivation of the rate equation for single substrates. The resulting reciprocal rate equation is

1 1 KA KB KAKB = + M + M + S S v0 Vmax Vmax [A] Vmax[B] Vmax [A][B]

where v0 is the initial velocity of the reaction, Vmax is the€ maximal velocity of the reaction A K M is the KM for A in the presence of saturating amounts of B B K M is the KM for B in the presence of saturating amounts of A A B K S and K S are the dissociation constants of A and B from the enzyme, respectively.

Single displacement reactions - ordered mechanism rate equation

A B X-intercept is -1/K M(apparent). Y intercept is (1/Vmax)(1+K M/[B]). In all these cases the A apparent KM is extracted from the graphs. The actual K M is obtained in the presence of a A saturating concentration of B. How is the apparent K M changing as [B] is increasing?

2 Single displacement reactions - random binding

2. Random single displacement reactions occur when both reactants must be bound to the enzyme at the same time for a reaction to occur, but the order in which they bind is not important.

A B P Q

EA EQ

E EAB EPQ E EB EP

B A Q P

Single displacement reactions - random binding

Example of a random, single displacement mechanism:phosphorylation of creatine by creatine kinase.

Creatine + ATP ↔ Creatine-P + ADP

How would you confirm that this is a random, single displacement mechanism?

3 Single displacement reactions - random mechanism rate equation

For the derivation of the simplest form of the rate equation within this mechanism, one must assume that both substrates are at independent and rapid equilibrium with the enzyme.

A corollary of this is that the EAB → EPQ conversion is rate-limiting. When these assumptions are met, the Lineweaver-Burke equation is:

A B B A B 1 1 KS KM KM KS KM = + B + + v0 Vmax VmaxKS [A] Vmax[B] Vmax [A][B] where all the terms have been defined above. €

Single displacement reactions -random binding mechanism

A Why doesn’t the apparent K M value change as the concentration of B increases?

4 Double displacement (ping pong) reaction mechanism

A P B Q

E EA ↔ E’P E’ E’B ↔ EQ E

Note that E’ sometimes is designated F. E’ can be a covalent or a non-covalent modification of the enzyme.

Overall, this scheme yields A + B ↔ P + Q which sometimes is written

P-X + B ↔ P + B-X

Double displacement (ping pong) reaction mechanism: glutamate:aspartate aminotransferase

5 Double displacement (ping pong) reaction rate equation 1 1 KA KB = + M + M v0 Vmax Vmax [A] Vmax[B]

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Differentiating among reaction mechanisms The indicative Lineweaver-Burke equations can be used to elucidate the reaction mechanism. Nevertheless, it is very useful to have another way of corroborating a mechanism by using a method that does not rely on kinetic data.

Single-displacement ordered and double displacement (ping-pong) mechanisms can be differentiated by isotope exchange experiments.

P-X + B ↔ P + B-X

6 Differentiating reaction mechanisms

P-X P B B-X

E EP-X ↔ EXP EX EXB ↔ EB-X E

P-X + B ↔ P + B-X Assume a ping-pong reaction mechanism where A = P-X and Q = B-X , and X is the group that is transferred from P to B.

In the first step of the reaction P-X + E ↔ EX + P And in the second step EX + B ↔ B-X + E In the absence of B only the first step will occur. If a small amount of exogenous, labeled X is added, and if X is exchanged from solution with the bound X (EX is NOT a covalent modification), then reversal of the first step will yield EX* + P ↔ P-X* + E. The substrate will become labeled. This is indicative of a double-displacement mechanism.

More useful is the addition of P-X and P* (where P* is radioactive) to the enzyme in the absence of B. What is the predicted result in the case of a double displacement mechanism? Does this outcome require a non-covalent interaction of the enzyme with the transferred group?

Differentiating reaction mechanisms

A + B ↔ P + Q

or

P-X + B ↔ P + B-X

Consider the same reaction above, only now using a single displacement, ordered mechanism.

A = P-X; B-X = Q.

In the first step, P-X + E ↔ EP-X

And in subsequent steps EP-X + B ↔ EBP-X ↔ EPB-X ↔ E + P + B-X

If labeled X is added, and B is omitted, the reversal of the first step does not result in the formation of a labeled substrate because P-X is not changed by the enzyme until B has been bound.

7 Differentiating reaction mechanisms Example: sucrose phosphorylase

Sucrose phosphorylase catalyzes the reaction:

glucose-fructose + phosphate ↔ glucose-1-phosphate + fructose

If a labeled fructose is included and a phosphate is omitted from the reaction, the following is observed: glucose-fructose + fructose* ↔ glucose-fructose* + fructose

If glucose-1-phosphate and labeled phosphate, but not fructose, are incubated with the enzyme, the following is observed:

glucose-1-phosphate + phosphate* ↔ Glucose-1-phosphate* + phosphate

In contrast, maltose phosphorylase does not transfer the labels as given above. So sucrose phosphorylase works through a double displacement (ping-pong) mechanism, whereas maltose phosphorylase works through a sequential (ordered) single displacement mechanism.

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