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: