Enzyme kinetics- the Michaelis-Menten equation PDF

Preview

Summary

Download Enzyme kinetics- the Michaelis-Menten equation PDF

Description

Enzyme'Kine*cs'in'the'Steady'State:''A'Straigh6orward' Deriva*on'of'the'Michaelis>Menten'Equa*on'

Rate Equations--

k1 (1) E

+

S

Note: If k1 and k-1 are fast, compared to k2, then k-1/k1 ! KS, where KS is the dissociation constant for the binding of S to the enzyme.

E•S k-1

k2 (2) E•S

E

+

P

Conservation Equations--

Note: Under standard enzyme assay conditions, substrate is present in large excess over enzyme. Thus, very little of ST is present as the E•S complex. Furthermore, measurements are made of initial rate (during the early linear phase of the reaction), i.e. under conditions where very little of ST has been converted to P. Hence, ST ! S. In contrast, the amount of E•S complex is a significant fraction of the total enzyme present.

(3) ST = S + P + E•S (4) ET = E + E•S

Steady-State Assumption-(5) d[E•S]/dt = k1[E][S] — k-1[E•S] — k2[E•S] = 0

Note: This expression states that the rate of formation of the E•S complex and its rate of destruction are equal.

Velocity Equation-(6) v = —d[S]/dt = d[P]/dt = k2[E•S]

Arithmetic Rearrangements--

Note: This expression means that the rate of product formation by an enzyme is directly proportional to the amount of E•S complex present. Note: These manipulations are designed to allow us to express the rate of reaction, i.e. the velocity, in terms of the one variable that it is possible for us to measure & control conveniently, namely the substrate concentration, [S].

From eqn. (4), E = ET — E•S, which we can substitute into eqn. (5), yielding: k1 [ET] [S] — k1 [E•S] [S] — k-1 [E•S] — k2 [E•S] = 0, which reduces to: k1 [ET] [S] [E•S] = k-1 + k2 + k1 [S] We can now substitute this expression for [E•S] into eqn. (6), v = k2 [E•S], which yields: k2 k1 [ET] [S] v =

k2 [ET] [S]

Vmax [S]

= k-1 + k2 + k1 [S]

= k-1 + k2

Km + [S] + [S]

k1 where Km = (k-1 + k2 ) / k1 & Vmax = k2[ET] (k2 is also called kcat or the “turnover number”)....