biocatalysis
→ biological molecule acts as catalyst (= enhances rate of reaction without being destroyed
or incorporated in product)
catalyst in same form after catalyzation; small amount required to transform many molecules
catalysis; no effect on equilibrium position
Ea (activation energy) obtained from kinetic energy of reactant(s)
kinetic energy depends on vibrational, translational and rotational energy
increased vibrational energy → may weaken interatomic bonds
a: stabilization of transition state b: destabilization of ground state of reactants
homogeneous: freely dissolved in solution
→ organic catalyst; organometallic complex; enzyme in water
heterogeneous: solid in liquid/gas environment
→ inorganic catalyst; immobilized enzyme; enzyme in organic solvent
advantages enzymes:
- environmentally acceptable (natural) → biodegradable
- operate under mild conditions → less waste and energy requirements
- accept unnatural substrates
- enzymes are selective (chemo-, regio-, stereo-)
- can be made by fermentation
- can be modified
catalysis by complexation doesn’t influence activation energy; brings reactants together in
optimum orientation; way to decrease energy of activation by destabilization of ground state
catalysis by temporary formation of covalent intermediates; one reaction step is split up in
several steps with low activation energy
catalysis by general acid/base → selective (de)protonation
catalysis by distortion of conformation substrate → destabilization ground state
,cofactors: helper molecules assisting enzymes; (in)organice
coenzymes: specific type of organic cofactor; low molecular weight organic compounds
1. kinetic data and their interpretation
if reaction runs via intermediate; rate determined by slowest step
bimolecular: 2 molecules collide and react
monomolecular: 1 molecule dissociates or reacts
determination of reaction rates: concentration as function of time with chromatography
1st order reactions
rate depends on concentration of reactant
[𝐴]
rate: −
𝑑[𝐴]
𝑑𝑡
= 𝑘1 [𝐴] → 𝑙𝑛 [𝐴] 𝑡 = −𝑘1 𝑡
0
[A]0 is constant; 𝑙𝑛[𝐴]𝑡 = −𝑘1 𝑡 + 𝐶
plotting 𝑙𝑛[𝐴]𝑡 against t gives slope equal to −𝑘1
𝑡1/2 = halflife = time needed to reduce concentration reactant to 50%
𝑙𝑛2
𝑡1/2 =
𝑘1
2nd order reactions
rate depends on concentration of reactants
𝑑[𝐴] 𝑑[𝐵] 𝑑[𝑃]
− =− =+ = 𝑘2 [𝐴][𝐵]
𝑑𝑡 𝑑𝑡 𝑑𝑡
pseudo-first order kinetics
[𝐴]0 >> [𝐵]0
𝑑[𝐴] 𝑑[𝐵] 𝑑[𝑃]
− 𝑑𝑡 = − 𝑑𝑡 = + 𝑑𝑡 = 𝑘2 [𝐴][𝐵] = 𝑘1 ′[𝐵] with 𝑘1 ′ = 𝑘2 [𝐴]
water: 1000 g/L and 18 g/mol → [H2O] = 55.6 M
reversible reactions
, 𝑑[𝐴] 𝑑[𝐵]
A → B rate: − 𝑑𝑡
= 𝑑𝑡
= 𝑘1 [𝐴]
𝑑[𝐵] 𝑑[𝐴]
B → A rate: − 𝑑𝑡 = 𝑑𝑡
= 𝑘−1 [𝐵]
preequilibria
𝑑[𝐴⋅𝐵]
steady state approach: assume [A⋅B] is constant during large part of reaction ( = 0)
𝑑𝑡
→ 𝑘1 [𝐴][𝐵] = 𝑘−1 [𝐴 ⋅ 𝐵] + 𝑘2 [𝐴 ⋅ 𝐵]
𝑘1 𝑘2 [𝐴][𝐵]
→ 𝑣 = 𝑘2 [𝐴 ⋅ 𝐵] =
𝑘−1 +𝑘2
𝑘1
slow breakdown of A⋅B: 𝑘2 << 𝑘1 , 𝑘−1 → 𝑣 = 𝑘2 [𝐴][𝐵]
𝑘−1
rapid breakdown of A⋅B: 𝑘2 >> 𝑘−1 → 𝑣 = 𝑘1 [𝐴][𝐵]
Michaelis-Menten model for enzyme kinetics of one-substrate reaction
𝐾𝑀 : ratio of rate of breakdown and formation of enzyme-substrate complex
small value → stable tight complex
𝑘−1 + 𝑘2 [𝐸][𝑆]
𝐾𝑀 = =
𝑘1 [𝐸 ⋅ 𝑆]
[E⋅S] and [E] often not measurable, [𝐸] 𝑇 is known (total concentration enzyme)
[𝐸] 𝑇 = [𝐸] + [𝐸 ⋅ 𝑆]
[𝐸]𝑇 [𝑆]
[𝐸 ⋅ 𝑆] = now contains only measurable parameters
𝐾𝑀 +[𝑆]
𝑑[𝑃] 𝑘2 [𝐸]𝑇 [𝑆] 𝑉𝑚𝑎𝑥 [𝑆]
rate: 𝑣 = = 𝑘2 [𝐸 ⋅ 𝑆] = =
𝑑𝑡 𝐾𝑀 +[𝑆] 𝐾𝑀 +[𝑆]
𝑑[𝑃] 𝑉𝑚𝑎𝑥
first order; [S] is small; 𝑣 = = [𝑆]
𝑑𝑡 𝐾𝑀
𝑑[𝑃]
zero order; [S] is large; 𝑣 = = 𝑉𝑚𝑎𝑥
𝑑𝑡
Arrhenius equation
𝐸𝑎
Arrhenius equation: 𝑘𝑜𝑏𝑠 = 𝐴 ⋅ 𝑒 −𝑅𝑇
A = pre-exponential factor
𝐸
− 𝑎
𝑘𝑜𝑏𝑠 = 𝑃𝑍𝑒 𝑅𝑇
P = probability factor (bc not every collision is effective); Z = collision number (/s)
, determine activation energy by measuring k(obs) at 2 not too diff. temperatures and dividing
𝑘 𝐴𝑒−𝐸𝑎/𝑅𝑇1
(A cancels out) → 𝑘1 = −𝐸 /𝑅𝑇
2 𝐴𝑒 𝑎 2
1 𝑘1
𝐸𝑎 = 𝑅𝑙𝑛
1 1 𝑘2
( − )
𝑇2 𝑇1
activation energy is always positive because 𝑘1 < 𝑘2
transition state theory
Eyring equations
𝛥𝐺∓ 𝛥𝐻∓ 𝛥𝑆∓
𝑘𝐵 𝑇 𝑘𝐵 𝑇
𝑘= 𝑒 − 𝑅𝑇 and 𝑘= 𝑒 − 𝑅𝑇 𝑒− 𝑅 because G = H - TS
ℎ ℎ
𝑑𝑙𝑛(𝑘/𝑇) 𝛥𝐻 ∓
𝑑(1/𝑇)
=− 𝑅
(slope of graph)
solvation
bimolecular reaction: solvent has huge influence on rate
because both reactants are surrounded by solvent molecules, which must be pushed aside
so reactants are able to react
in water is more solvation than in DMF, due to strong dipole-dipole interactions; in DMF is
ground state destabilization
→ biological molecule acts as catalyst (= enhances rate of reaction without being destroyed
or incorporated in product)
catalyst in same form after catalyzation; small amount required to transform many molecules
catalysis; no effect on equilibrium position
Ea (activation energy) obtained from kinetic energy of reactant(s)
kinetic energy depends on vibrational, translational and rotational energy
increased vibrational energy → may weaken interatomic bonds
a: stabilization of transition state b: destabilization of ground state of reactants
homogeneous: freely dissolved in solution
→ organic catalyst; organometallic complex; enzyme in water
heterogeneous: solid in liquid/gas environment
→ inorganic catalyst; immobilized enzyme; enzyme in organic solvent
advantages enzymes:
- environmentally acceptable (natural) → biodegradable
- operate under mild conditions → less waste and energy requirements
- accept unnatural substrates
- enzymes are selective (chemo-, regio-, stereo-)
- can be made by fermentation
- can be modified
catalysis by complexation doesn’t influence activation energy; brings reactants together in
optimum orientation; way to decrease energy of activation by destabilization of ground state
catalysis by temporary formation of covalent intermediates; one reaction step is split up in
several steps with low activation energy
catalysis by general acid/base → selective (de)protonation
catalysis by distortion of conformation substrate → destabilization ground state
,cofactors: helper molecules assisting enzymes; (in)organice
coenzymes: specific type of organic cofactor; low molecular weight organic compounds
1. kinetic data and their interpretation
if reaction runs via intermediate; rate determined by slowest step
bimolecular: 2 molecules collide and react
monomolecular: 1 molecule dissociates or reacts
determination of reaction rates: concentration as function of time with chromatography
1st order reactions
rate depends on concentration of reactant
[𝐴]
rate: −
𝑑[𝐴]
𝑑𝑡
= 𝑘1 [𝐴] → 𝑙𝑛 [𝐴] 𝑡 = −𝑘1 𝑡
0
[A]0 is constant; 𝑙𝑛[𝐴]𝑡 = −𝑘1 𝑡 + 𝐶
plotting 𝑙𝑛[𝐴]𝑡 against t gives slope equal to −𝑘1
𝑡1/2 = halflife = time needed to reduce concentration reactant to 50%
𝑙𝑛2
𝑡1/2 =
𝑘1
2nd order reactions
rate depends on concentration of reactants
𝑑[𝐴] 𝑑[𝐵] 𝑑[𝑃]
− =− =+ = 𝑘2 [𝐴][𝐵]
𝑑𝑡 𝑑𝑡 𝑑𝑡
pseudo-first order kinetics
[𝐴]0 >> [𝐵]0
𝑑[𝐴] 𝑑[𝐵] 𝑑[𝑃]
− 𝑑𝑡 = − 𝑑𝑡 = + 𝑑𝑡 = 𝑘2 [𝐴][𝐵] = 𝑘1 ′[𝐵] with 𝑘1 ′ = 𝑘2 [𝐴]
water: 1000 g/L and 18 g/mol → [H2O] = 55.6 M
reversible reactions
, 𝑑[𝐴] 𝑑[𝐵]
A → B rate: − 𝑑𝑡
= 𝑑𝑡
= 𝑘1 [𝐴]
𝑑[𝐵] 𝑑[𝐴]
B → A rate: − 𝑑𝑡 = 𝑑𝑡
= 𝑘−1 [𝐵]
preequilibria
𝑑[𝐴⋅𝐵]
steady state approach: assume [A⋅B] is constant during large part of reaction ( = 0)
𝑑𝑡
→ 𝑘1 [𝐴][𝐵] = 𝑘−1 [𝐴 ⋅ 𝐵] + 𝑘2 [𝐴 ⋅ 𝐵]
𝑘1 𝑘2 [𝐴][𝐵]
→ 𝑣 = 𝑘2 [𝐴 ⋅ 𝐵] =
𝑘−1 +𝑘2
𝑘1
slow breakdown of A⋅B: 𝑘2 << 𝑘1 , 𝑘−1 → 𝑣 = 𝑘2 [𝐴][𝐵]
𝑘−1
rapid breakdown of A⋅B: 𝑘2 >> 𝑘−1 → 𝑣 = 𝑘1 [𝐴][𝐵]
Michaelis-Menten model for enzyme kinetics of one-substrate reaction
𝐾𝑀 : ratio of rate of breakdown and formation of enzyme-substrate complex
small value → stable tight complex
𝑘−1 + 𝑘2 [𝐸][𝑆]
𝐾𝑀 = =
𝑘1 [𝐸 ⋅ 𝑆]
[E⋅S] and [E] often not measurable, [𝐸] 𝑇 is known (total concentration enzyme)
[𝐸] 𝑇 = [𝐸] + [𝐸 ⋅ 𝑆]
[𝐸]𝑇 [𝑆]
[𝐸 ⋅ 𝑆] = now contains only measurable parameters
𝐾𝑀 +[𝑆]
𝑑[𝑃] 𝑘2 [𝐸]𝑇 [𝑆] 𝑉𝑚𝑎𝑥 [𝑆]
rate: 𝑣 = = 𝑘2 [𝐸 ⋅ 𝑆] = =
𝑑𝑡 𝐾𝑀 +[𝑆] 𝐾𝑀 +[𝑆]
𝑑[𝑃] 𝑉𝑚𝑎𝑥
first order; [S] is small; 𝑣 = = [𝑆]
𝑑𝑡 𝐾𝑀
𝑑[𝑃]
zero order; [S] is large; 𝑣 = = 𝑉𝑚𝑎𝑥
𝑑𝑡
Arrhenius equation
𝐸𝑎
Arrhenius equation: 𝑘𝑜𝑏𝑠 = 𝐴 ⋅ 𝑒 −𝑅𝑇
A = pre-exponential factor
𝐸
− 𝑎
𝑘𝑜𝑏𝑠 = 𝑃𝑍𝑒 𝑅𝑇
P = probability factor (bc not every collision is effective); Z = collision number (/s)
, determine activation energy by measuring k(obs) at 2 not too diff. temperatures and dividing
𝑘 𝐴𝑒−𝐸𝑎/𝑅𝑇1
(A cancels out) → 𝑘1 = −𝐸 /𝑅𝑇
2 𝐴𝑒 𝑎 2
1 𝑘1
𝐸𝑎 = 𝑅𝑙𝑛
1 1 𝑘2
( − )
𝑇2 𝑇1
activation energy is always positive because 𝑘1 < 𝑘2
transition state theory
Eyring equations
𝛥𝐺∓ 𝛥𝐻∓ 𝛥𝑆∓
𝑘𝐵 𝑇 𝑘𝐵 𝑇
𝑘= 𝑒 − 𝑅𝑇 and 𝑘= 𝑒 − 𝑅𝑇 𝑒− 𝑅 because G = H - TS
ℎ ℎ
𝑑𝑙𝑛(𝑘/𝑇) 𝛥𝐻 ∓
𝑑(1/𝑇)
=− 𝑅
(slope of graph)
solvation
bimolecular reaction: solvent has huge influence on rate
because both reactants are surrounded by solvent molecules, which must be pushed aside
so reactants are able to react
in water is more solvation than in DMF, due to strong dipole-dipole interactions; in DMF is
ground state destabilization
