Reaction Mechanism, Bioreaction and Bioreactors
Transcript of Reaction Mechanism, Bioreaction and Bioreactors
Reaction Mechanism, Bioreaction and Bioreactors
Lecture 9
Active Intermediates
• Many reaction proceed via formation of active intermediate by collision or interaction with other molecules
A M A M∗+ → +
• The idea was suggested in 1922 by F.A.Lindermann , acitveintermediates were experimentally observed using femtosecond spectroscopy by A.Zewail (Nobel Prize 1999)
cyclobutane x2 ethylene
Pseudo –Steady-State Hypothesis (PSSH)
• Active intermediates react as fast as they are formed, so their net rate of formation is zero:
* *1
0N
A iAi
r r=
= ≡∑
Pseudo –Steady-State Hypothesis (PSSH)
• Gas-phase decomposition of azomethane( )3 2 2 6 22CH N C H N→ +
• experimentally found to follow
– 1st order at pressures above 1atm
– 2nd order below 50mmHg
2 6C H AZOr C∝
2 6
2C H AZOr C∝
Pseudo –Steady-State Hypothesis (PSSH)• Suggested mechanism:
( ) ( ) ( ) ( )1 *3 2 3 2 3 2 3 22 2 2 2
*AZOkCH N CH N CH N CH N⎡ ⎤+ ⎯⎯⎯→ + ⎣ ⎦
( ) 3 *3 2 2 6 22
* AZOkCH N C H N⎡ ⎤ ⎯⎯⎯→ +⎣ ⎦
( ) ( ) ( ) ( )2 *3 2 3 2 3 2 3 22 2 2 2
* AZOkCH N CH N CH N CH N⎡ ⎤ + ⎯⎯⎯→ +⎣ ⎦
21 * 1 *AZO AZO AZOr k C=
• the rate laws
2 * 2 * *AZO AZO AZO AZOr k C C= −
3 * 3 * *AZO AZO AZOr k C= −
* 1 * 2 * 3 * 0AZO AZO AZO AZOr r r r= + + ≡
Pseudo –Steady-State Hypothesis (PSSH)• solving for Cazo* and finding the rate of formation of product:
6
21 3
2 3r
AZOC H
AZO
k k Crk C k
=+
• at low concentrations
6
22 3 1rAZO C H AZOk C k r k C=
6
1 32 3
2rAZO C H AZO AZO
k kk C k r C kCk
= =
• at high concentrations
Pseudo –Steady-State Hypothesis (PSSH)• Experimentally finding the mechanism:
6
21
1r
AZOC H
AZO
k Crk C
=′ +
• Rule of thumb for developing the mechanism:– species having the concentration appearing in the denominator
probably collide with the active intermediate – species having the concentration appearing in the numerator probably
produce the active intermediate
Enzymatic reactions
• lower activation energies for enzymatic pathways lead to enormous enhancement in reaction rates
• enzymes are highly specific: one enzyme can usually catalyze only one type of reaction
• enzymes usually work at mild conditions; at extreme temperatures or pH may unfold losing its activity
Enzymatic reactions
• Two models for enzyme-substrate interaction: the lock-and-key and the induced fit:
both the enzyme molecule and the substrate molecule are distorted thereforstressing and weakining the bond for rearrengement
Michaelis-Menten equation
• kcat (s-1)– the turnover number: the number of substrate molecules converted in a given time on a single enzyme molecule when saturated with the substrate
• Km (mol/l) – Michaelis constant or affinity constant: measure of attraction of the enzyme to the substrate
( )( )( )cat t
SM
k E Sr
S K− =
+
( )( )
maxS
M
V Sr
S K− =
+
Evaluation of Michaelis-Menten parameters
• Michaelis-Menten plot • Lineweaver-Burk plot
• Hanes-Woolf plot (better Vmax)
• Eadie-Hofstee plot(doesn’t bias low concentraion points
( )( )
maxS
M
V Sr
S K− =
+
( )maxS
S Mrr V KS
⎡ ⎤−− = − ⎢ ⎥
⎣ ⎦
( )max max
1 1 1M
S
Kr V V S
⎡ ⎤− = + ⎢ ⎥
⎣ ⎦
( ) ( )max max
1M
S
S K Sr V V
− = +
Batch reactor calculations
• after integration, in terms of conversion
ureaurea
dN r Vdt
− = −urea
ureadC r
dt− = −
in liquid
max ureaurea
urea M
V CrC K
− =+
0 0
max
urea urea
urea urea
C Curea urea M
ureaurea ureaC C
dC C Kt dCr V C
+= =
−∫ ∫
0
max max
1ln1
ureaM C XKtV X V
= +−( )0 1urea ureaC C X= −
• combining with the Michaelis-Menten law
• mole balance on urea:
Effect of Temperature
• catalytic breakdown of H2O2 vs temperature
temperature inactivationdue to enzyme denaturation
rise due to Arrhenius law
Inhibition of Enzyme reactions• Competitive inhibition
Inhibition of Enzyme reactions• Uncompetitive inhibition
Inhibition of Enzyme reactions• Non-competitive inhibition
Bioreactors
• Cells consume nutrients to grow, to produce more cells and to produce the product in question:– (I) fueling reactions (nutrient degradation)– (II) synthesis of small molecules (amino acids)– (III) synthesis of large molecules (proteins, DNA, RNA)
• Cell growth and division
• Advantages of bioconversion:– mild reaction conditions– high yields approaching 100%– stereospecific synthesis
Bioreactors• Growth in the reactor
Substrate More Cells ProductCells⎯⎯⎯→ +
e.g. CO2, water, proteins etc.• Batch bioreactor
Bioreactors• Cell growth in bioreactors
adjusting pathways to the new conditions
exp growth: dividing at max rate
stationary phase: lack of some nutriotients limits cell growth;many important products (e.g. antibiotics) produced at this phase.
Bioreactors: Rate laws
• Monod equation
Substrate More Cells ProductCells⎯⎯⎯→ +
g cr Cµ=
maxs
s s
CK C
µ µ=+
• Specific growth rate
max s cg
s s
C CrK Cµ
=+
• In many systems the product can inhibit cells growth (e.g. wine making)
max s cg obs
s s
C Cr kK Cµ
=+ *1
n
pobs
p
Ck
C⎛ ⎞
= −⎜ ⎟⎜ ⎟⎝ ⎠ product concentration
where metabolism ceases
• e.g. glucose-to-ethanol: n=0.5, Cp*=93g/l
Bioreactors: Rate laws• Other growth equations:
– Tessier equation
– Moser equation
max 1 exp sg c
Cr Ck
µ ⎡ ⎤⎛ ⎞= − −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦
( )max
1s c
gs
C CrkC λ
µ−
=+
usually give better fit in the beginning and in the end of fermentation
• Cell death rate (due to harsh environment, mixing shear forces, local depletion in nutrients, toxic substances)
( )d d t t cr k k C C= +
• Temperature effect: similar curve with max
Bioreactors: Stoichiometry
• Yield coefficient for cells and substrate
Substrate More Cells ProductCells⎯⎯⎯→ +
/Mass of new cells formed
Mass of substrate consumedC
c sS
CYC
∆= = −
∆
• Yield coefficient for product in the exponential phase
/Mass of product formed
Mass of new cells formedP
p cC
CYC
∆= =
∆
max/
s cp p c
s s
C Cr YK Cµ
=+
Bioreactors: StoichiometrySubstrate More Cells ProductCells⎯⎯⎯→ +
• Yield coefficient for product in the stationary phase
/Mass of product formed
Mass of substrate condumedP
p sS
CYC
∆= = −
∆
max/
s cp p c
s s
C Cr YK Cµ
=+
• Maintenance utilization term, typically m=0.05 h-1.
Mass of substrate consumed for maintenanceMass of cells Time
m =⋅
Physiologically based pharmacokinetics (PBPK)
• Chemical reaction engineering approach can be applied to pharmacokinetics
Physiologically based pharmacokinetics (PBPK)
• Chemical reaction engineering approach can be applied to pharmacokinetics
Problem• P7-9: