Michaelis - Menten Equation and Lineweaver derivation and Inhibition

Steps to derive MM equation

1) k1 [E][S] = k-1[ES] + k2[ES]

2) [E_T] = [E] + [ES], so —> [E] = [E_T] - [ES]

3) Plug in [E] into 1)

4) k1([E_T] - [ES])[S] = k-1[ES] + k2[ES]

5) Find K_M= ([E_T] - [ES])[S] / [ES]

6) Now solve for [ES]

7) [ES] = [E_T][S] / K_M + [S]

8) Incorporate in V₀= k2[ES]

9) V₀= k2[E_T][S] / K_M + [S]

10) V_max= k2[E_T] —> Substitute into previous

11) V₀= V_max[S] / K_M + [S] —> MM Equation

What is Km

• Vmax/2, when the substrate concentration at which the reaction velocity is half maximal 

• Indicates Affinity 

• Lower Km = Higher Affinity 

Vmax

• Indicates Chemistry

• The theoretical maximal velocity

• Vmax is asymptotically approached

• 0th order: independent of [S]

Vmax / Km

• 1st order reaction

• only depends on [S]

• indicates Binding

kcat

• Vmax/[E_T]

• 1st order rate constant: only dependent on the Enzyme

• The number of substrate molecules converted to product per enzyme per unit of time, when E is fully saturated 

• High kcat: high number of substrate to product 

kcat/Km

• The specificity constant

• 2nd order rate constant

• measure of the specificity of the enzyme at low substrate concentrations

• [S]«Km

• How “perfect” and enzyme can be

• Find S, bind S, ES —> P

• High number = High productivity

Lineweaver - Burk plot

Vmax:

Km:

Vmax/Km:

Vmax: Chemistry

Km: Affinity

Vmax/Km: Binding

Lineweaver - Burk plot:

Slope:

y-int

x-int:

Km/Vmax

1/Vmax

1/Km

Km app means

the presence of an inhibitor, not the true Km

Inhibitors alter the activity of ___ by combining with it in a way that influences ______ and ______

enzymes

the binding of substrates

the turnover number

Irreversible inhibitor

substance that causes inhibition that cannot be reversed: Inactivators

• Usually forming or breaking covalent bonds

Reversible Inhibitor 

A substance that binds to an enzyme to inhibit it, but can be released 

• formation of non covalent bonds

Types of inhibition

• Competitive

• Uncompetitive

• Mixed or Noncompetitive (same thing)

May bind at the active site or alternative binding sit e

Competitive Inhibition

Competes with substrate for binding site

What does K_I measure

The dissociation constant for enzyme inhibitor binding

The presence of I make [S] appear to be _____ so Km appears _____ than normal. This “new” Km is called ____. This can also be known as ___Km

less

larger

K_M^app

alpha

A competitive inhibitor _____ the amount of free enzyme available for substrate binding thus _____ the K_M for the substrate

reduces

increasing

The effect of a competitive inhibitor can be overcome with ____ concentrations of _____

(alpha effect of inhibitor)

high

substrate

Competitive inhibitors _____ structure of substrates with ______ that prevent _____ from occurring

mimic

modifications

chemistry

Competitive inhibitors affect

K_M—> affinity

Vmax/Km —> Binding

But not Vmax—> chemistry

Why does Competitive Inhibition not affect Vmax

Inhibitors do not effect E’s ability to catalyze a reaction