Bio307 Lecture 6 (enzyme Kinetics Ii).ppt

Michaelis-Menten Model accounts for the kinetic properties of many enzymes Primary function of enzymes is to enhance the rates of reactions V0 is reaction velocity or rate of catalysis: Number of moles product/second Vmax: maximal velocity Km: Michaelis-Menten constant = substrate concentration at which there is half of max. velocity

The extent of product formation is determined as a function of time for a series of substrate concentrations

Changes in concentration of all reaction partners V0: the rate of increase in product with time when product concentration is still low (pre-steady state)

V0

linear proportional to substrate concentration

V0 is determined for each substrate concentration by measuring the rate of product formation at early times before product accumulates

The Michaelis – Menten Model The model proposed, which is the simplest one that accounts for the kinetic properties of many enzymes, is

We want an expression that relates the rate of catalysis to the concentrations of substrate and enzyme and the rates of the individual steps. Our starting point is that the catalytic rate is equal to the product of the concentration of the ES complex and k2.

The Michaelis – Menten Model cont. Now we need to express [ES] in terms of known quantities. The rates of formation and breakdown of ES are given by:

Assumption: steady – state = concentration of ES intermediates stays the same even when substrate and product concentration changes

The Michaelis – Menten Constant Km

KM has the units of a concentration!

Km = [E] [S] / [ES]

The Michaelis – Menten Constant Km contin.

or

The Michaelis – Menten Constant Km contin.

Insert ES concentration into:

The Michaelis – Menten equation Term for V0 What about Vmax? (ESconc.=Etotal conc. Each active site exists as ES complex)

Analogous to:

Michaelis – Menten - Equation

When [S] is much less than KM: V0 = (Vmax/KM)[S]; that is, the rate is directly proportional to the substrate concentration. When [S] is much greater than KM: V0 = Vmax; that is, the rate is maximal, independent of substrate concentration. When [S] is KM: V0 = Vmax/2

The meaning of KM

1) KM is the concentration of substrate at which half of the active sites are filled

2) KM is related to the rate constants of individual steps in the catalytic scheme

If k-1 >>>>k2

The meaning of KM cont. The dissociation constant of the ES complex is given by:

KM is equal to the dissociation constant of the ES complex if k2 is much smaller than k-1. When this condition is met, KM is a measure of the strength of the ES complex: a high KM indicates weak binding; a low KM indicates strong binding. It must be stressed that KM indicates the affinity of the ES complex only when k-1 is much greater than k2.

The meaning of Vmax The maximal rate, Vmax, reveals the turnover number of an enzyme, which is the number of substrate molecules converted into product by an enzyme molecule in a unit time when the enzyme is fully saturated with substrate. It is equal to the kinetic constant k2, which is also called kcat.

The maximal rate, Vmax, reveals the turnover number of an enzyme if the concentration of active sites [E]T is known, because

Lineweaver – Burk Plot The plot provides a useful graphical method for analysis of the Michaelis – Menten equation:

Taking the reciprocal gives:

Linearisation methods

Protein-Ligand interaction

v/[S] als Funkt. von v.