Bioprocess Engineering

Transcription

1 1 Bioprocess Engineering Chap. 3 Enzymes I. Introduction 1. Enzymes are usually proteins of high MW (15000<MW<several million Daltons) that act as catalysts 2. More than 2000 enzymes are known 3. Enzymes are named by adding ase to the end of S (urease) or the rxn catalyzed (alcohol dehydrogenase) 4. Some enzymes need nonprotein group for their activity (1) cofactor: metal ions like Mg, Zn, Mn, Fe (2) coenzymes: NAD, FAD, CoA, and some vitamins (3) Holoenzyme: an enzyme containing a nonprotein group (4) Apoenzyme: protein part of the holoenzyme (5) Holoenzyme=Apoenzyme + Cofactor 5. Isozymes: enzymes that occur in different molecular forms, but catalyze same rxn. 6. Enzymes are substrate specific II. How Enzymes Work 1. Enzymes lower the activation energy of rxn by binding S and forming E-S complex by weak interactions (mostly van der Waals forces & H-bonding) 2. Enzymes do not affect free-energy change or equilibrium constant 3. Active site: the specific site of S binding 4. E-S binding described by lock and key model, lock: E; key: S 5. Proximity effect: in multisubstrate rxns, E holds S close to each other and to the E active site 6. Orientation effect: E hold S at certain position & angles to improve rxn rate 7. The formation of E-S complex may cause slight changes in the 3D structure of E III Enzyme Kinetics 1. Michaelis-Menton kinetics (saturation kinetics)

2 2 k 1 k 2 2. E + S ===== ES E + P k Two major approaches used in developing a rate expression for E-catalyzed rxns: (1) rapid equilibrium approach (2) quasi-steady-state approach 4. v= d[p]/dt = k 2 [ES] (1) v = rate of product formation or substrate comsumption in moles/l-s 5. d[es]/dt = k 1 [E][S]-k -1 [ES]-k 2 [ES] 6. [E 0 ] = [E]+[ES] (conservation equation on E) 7. The rapid equilibrium assumption: (Henri, Michaelis, Menton) (1) assuming a rapid equilibrium between E and S to form ES (2) equilibrium constant: K m = k -1 /k 1 = [E][S]/[ES] (3) [ES] = [E 0 ][S]/((k -1 /k 1 )+[S]) = [E 0 ][S]/(K m +[S]) where K m = k -1 /k 1 (4) v = d[p]/dt = k 2 [E 0 ][S]/(K m +[S]) = V m [S]/(K m +[S]) where V m = k 2 [E 0 ] (5) A low value of K m suggests that the E has a high affinity for the S 8. The quasi-steday-state assumption (GE Briggs and JBS Haldane) (1) assumption: d[es]/dt 0 (2) [ES] = k 1 [E][S]/(k -1 +k 2 ) (3) [E 0 ]=[E]+[ES] [ES]=k 1 ([E 0 ]-[ES])[S]/(k -1 +k 2 ) [ES]=[E 0 ][S]/((k -1 +k 2 )/k 1 +[S]) (4) v = dp/dt = k 2 [ES] = k 2 [E 0 ][S]/((k -1 +k 2 )/k 1 +[S]) = V m [S]/(K m +[S]) (5) K m =(k -1 +k 2 )/k 1 and K m = k 2 [E 0 ] 9. Experimental determining rate parameters for Michaelis-Menton type kinetics (1) experimental data obtained from initial-rate experiments (2) Double-reciprocal plot (Lineweaver-Burk plot) a. 1/v = 1/V m + (K m /V m )(1/[S]) b. good estimates on V m, but not on K m (3) Eadie-Hofstee plot a. v = V m -K m (v/[s]) (4) Hanes-Woolf plot a. [S]/v = K m /V m +[S]/V m 10. Models for more complex enzyme kinetics (1) some E have more than one S binding sites (2) Allostery or cooperate binding: the binding of one S facilitates binding of other S molecules a. Rate expression in this case: v=-d[s]/dt=v m [S] n /(K m +[S] n ) b. n=cooperativity coefficient

3 3 c. n>1 : positive cooperativity (p.68 Fig.3.8) d. ln(v/(v m -v))=nln[s]-lnk m (4) Inhibited enzyme kinetics: a. enzyme inhibitors: bind to E and reduce their activity, may be irreversible or reversible (i) irreversible inhibitors such as heavy metals form a stable complex with E, may be reversed only by using chelating agents such as EDTA (ethylenediaminete-traacetic acid) and citrate (ii) reversible inhibitors may dissociate more eisaly from E (a) competitive usually S analogs compete with S for the active site of E mechanism (p.69) v = V m [S]/{K m (1+[I]/K I )+[S]} = V m [S]/(K m, app +[S]) K m, app = K m (1+[I]/K I ) K m increased and v reduced (b) noncompetitive not S analogs inhibitors bind on sites other than the active site and reduce E activity to S mechanism (p.69) v = V m /{(1+[I]/K I )(1+K m /[S])} = V m, app /(1+K m /[S]) V m, app = V m /(1+[I]/K I ) V m reduced (c) uncompetitive bind to ES complex and have no affinity for E mechanism (p.71) v ={V m [S]/(1+[I]/K I )}/{K m /(1+[I]/K I )+[S]}=V m, app /(K m, app +[S]) both V m and K m reduced Lineweaver-Burk plots (p.70 Fig.3.10) (d) S inhibition High S conc. may cause inhibitions in some E rxns (p.72, Fig3.11) mechanism (p71) K SI = [S][ES]/[ES 2 ], K m = [E][S]/[ES] v =V m [S]/{K m +[S]+[S] 2 /K SI } v= V m /(1+K m /[S]) when [S] is low and inhibition effect is not observed

4 4 (1) Effect of ph v =V m /(1+[S]/K SI ) when [S] is high and inhibition is dominant The S conc. resulting in the max. rxn. Rate is: [S] max =(K m K SI ) 1/2 a. variations in the ph of the medium result in changes in the ionic form of the active site and change the activity of E b. changes in ph may also alter the 3D structure of E c. E are only active over a certain ph range d. ph of the medium may affect V max, K M, and the stability of E e. the scheme of ph dependence of E rxn rate for ionizing E (Eq.3.40, p.75) K M, K1, K2 and [E 0 ] (Eq.3.41, p.75) v = (Eq.3.42, p.76) or (Eq.3.43, p.76) K M, app =1 + K2/[H+] + [H+]/K1 The ph optimum of E is between pk1 and pk2 f. for the ionizing S, the scheme is (Eq.3.44, p.76) v= (Eq.3.45, p.76) g. the prediction of ph optimum of E requires a knowledge of the active site characteristics of E, usually determined experimentally (Fig.3.14, p.76) (2) Temp effects a. the rate of E-catalyzed rxn increases with temp up to a certain limit b. above a certain temp, E activity decreases with temp due to E denaturation (Fig.3.15, p.77) (temp activation & temp inactivation) c. Arrhenius eq: v = k 2 [E], k 2 = Ae -Ea/RT, Ea = activation energy (kcal/mol) d. d[e]/dt = k d [E], [E] = [E 0 ]e- kdt, k d = A d e- Ed/RT = denaturation const E d = deactivation energy (kcal/mol) e. v = Ae -Ea/RT [E 0 ]e- kdt f. 4 < Ea < 20 kcal/mol ; 40 < Ed < 130 kcal/mol (E denaturation by temp is much faster than E activation) rise in temp from 30 o C to 40 o C results in a 1.8-fold increase in E activity, but a 41-fold increase in E denaturation g. variations in temp affect both V max and K M of E III. Immobilized Enzyme Systems 1. advantages: E reutilization and elimination of E recovery and purification processes, and may provide a better environment for E activity 2. Methods of immobilization: (1) entrapment a. physical enclosure of E in a small space

5 5 b. matrix entrapment and membrane entrapment, including microencapsulation, are two major methods of entrapment c. matrix are usually polymeric materials, such as Ca-alginate, agar, k-carrageenin, polyacrylamide and collagen d. matrix can be a particle, a membrane, or a fiber e. E soln mixed with polymer soln before polymerization takes place f. mostly, a semipermeable membrane is used to retain high MW E, while allowing small MW S or P access to the E g. microencapsulation: microscopic hollow spheres are formed, the spheres contain E soln and enclosed within a porous membrane h. problems: E leaking into soln, diffusional limitations, reduced E activity and stability, lack of control of microenvironmental conditions (2) Surface immobilization a. two major types: adsorption and covalent binding b. adsorption: (i) attachment of E on surfaces of support particles by weak physical forces, such as van der Waals or dispersion forces (ii) desorption of E is a common problem (iii) adsorption may be stabilized by cross-linking with glutaraldehyde, which may denature some proteins (iv) the surface of the support materials may need to be pretreated c. covalent binding: (i) retention of E on support surfaces by covalent bond formation (ii) E bind to support material via certain functional groups, such as amino, carboxyl, hydroxyl, and sulfhydryl groups (iii) other agents such as glutaraldehyde, bis-diazobenidine, and 2,2-disulfonic acid are usually used for cross-linking of E (3) criteria for selection of support materials: a. the binding capacity of support material, which is a function of charge density, functional groups, porosity, and hydrophonicity b. stability and retention of E activity, which is a function of functional groups and microenvironmental conditions 3. Diffusion limitations in immobilized E systems (1) Damkohler number a. Da = max. rate of rxn/max. rate of diffusion = V m /k L [S b ] [S b ] = S conc in th bulk liquid (g/cm 3 ) k L = mass transfer coefficient (cm/s)

6 6 b. Da<<1 : reaction rate is limiting Da ~ 1 : diffusion and rxn resistances are comparable Da>>1 : diffusion rate is limiting (2) Diffusion effects in surface-bound E on nonporous support materials a. Scheme (Fig.3.17, p.84) b. at steady state, the rxn rate is equal to the mass-transfer rate: Js = k L ([S b ]-[S s ]) = V m [S s ]/(K M +[S s ]) V m = max rxn rate per unit of external surface area k L = liquid mass transfer coefficient c. when the system is strongly mass transfer limited, [S s ]~0 v = k L [S b ] (for Da>>1, pseudo first order) d. when the system is reaction limited (Da<<1) v = V m [S b ]/(K M, app +[S b ]) K M, app = K M {1+V m /(k L [S b ]+K M )} (a function of stirring speed) (3) Diffusion effects in E immobilized in a porous matrix a. Scheme (Fig.3.19, p.86) (diffusion and rxn are simultaneous) b. at steady state, diffusion rate is equal to rxn rate: D e (d 2 [S]/dr 2 + (2/r)(d[S]/dr)) = V m [S]/(K M +[S]) V m = max rxn rate per unit volume of support D e = effective diffusivity of S within the porous matrix With BCs: r=r, [S]=[Ss] ; r=0 d[s]/dr=0 c. (p.87, eq.3.56a; 3.56b) d. the rate of S comsumption is equal to the rate of S transfer through the external surface of the support particle at steady state: r s = N s = -4ΠR 2 D e d[s]/dr r=r e. under diffusion limitations, the rate is usually expressed as: r s = η(v m [S s ]/(K M +[S s ])) η = effectiveness factor = the ratio of rxn rate with diffusion limitation to the rxn rate with no diffusion limitation (i) η<1, conversion is diffusion limited (ii) η~1, conversion is limited by ran rate and diffusion limitations are negligible (iii) η is a function of φ and β (Fig.3.20, p.88) (iv) for a zero-order rxn rate (β 0), η~1 for a large range of φ (v) for a first-order rxn rate (β ), η =(3/φ)[1/tanhφ - 1/φ] f. to obtain true intrinsic rate const in immobilized E, diffusion resistances should be eliminated by using small particle sizes, a high degree of turbulence abound the particles, and high S conc.

7 7 g. for max conversion rates, particle size should be small (D p 10µm) and E loading should be optimized (Fig.3.21, p.88) (4) electrostatic and steric effects in immobilized E systems a. for an E immobilized onto a charge support, the shift in the ph-activity profile is given by: ph = ph i ph e = 0.43(zFψ/RT) ph i = internal ph value ph e = external ph value z = charge on the S F = Faraday constant (96500 coulomb/eq.g) ψ = electrostatic potential R = gas constant b. the activity of E toward a high MW S is usually reduced upon immobilization to a much greater extent than for a low MW S due to steric hindrance by the support c. Thermal stability of E often increases upon immobilization due to the presence of thermal diffusion barriers and the constraints on protein unfolding d. The ph stability of E usually increases upon immobilization too. V. Large Scale Production of Enzymes 1. Mostly, E are produced by using overproducing strain of certain organisms 2. Separation and purification usually involves: (1) cultivation of the organisms (2) separation of cells by filtration or centrifugation (if E is extracellular) (3) cell disruption (if E is intracellular) (4) removal of cell debris and nucleic acids (5) precipitation of proteins (6) ultrafiltration of the desired E (7) chromatography (8) crystallization (9) drying