Bio307 Lecture 7 (enzyme Kinetics Iii).ppt

Michaelis-Menten Model accounts for the kinetic properties of many enzymes Primary function of enzymes is to enhance the rates of reactions V 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 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.

V0

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

reverse reaction preferred

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

ES

KM is equal to the dissociation constant of the ES complex if k-1 is much larger than k2. 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 forward rate 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

Example RuBisCO is an enzyme in the Calvin cycle that fixes atmospheric carbon and has a turnover rate of 3.3 s-1. How long does it take RuBisCO to fix one molecule of carbon dioxide?

Turnover rate = [S] = 3.3s-1 time

Time = 1 = 0.30s 3.3s-1

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

Taking the reciprocal gives:

Eadie-Hofstee Linearization Invert and multiply with Vmax

Vmax = Vmax (KM+[S]) = V Vmax[S]

KM + [S] [S]

rearrange

Vmax = VKM + V[S] = VKM + V [S] [S]

isolate v

V = -KM V + Vmax [S] V [S]

V

Sources of errors Lineweaver Burke Linearization

Small substrate concentrations determine the Linearization Most error prone

-1 KM

Sources of errors Eadie Hofstee Linearization

Vmax

Lesser error prone