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Cells Growth in Continuous Culture Continuous culture: fresh nutrient medium is continually supplied to a well-stirred culture and products and cells are simultaneously withdrawn. At steady state, concentrations of cells, products and substrates are constant. In batch culture: the culture environment changes continually. growth, product formation and substrate utilization terminate after a certain time interval. A continuous-culture laboratory setup medium Products, cells Ideal Chemostat Same as perfectly mixed continuous-flow, stirred-tank reactor (CFSTR). - Control elements: pH, dissolved oxygen, temperature - Fresh sterile medium is fed to the completely mixed and aerated (if required) reactor. - Suspension is removed at the same rate. - Liquid volume in the reactor is kept constant. Cell Growth in Ideal Chemostat A material balance on the cell and substrate concentration around the chemostat yields, FX 0 FX VR g X VR kd X VR 1 FS0 FS VR g X M Y dX dt VR q p X 1 Yp / s VR dS dt X /S F is the volumetric flowrate of nutrient solution (l/h); VR is the culture volume (l) (constant); X is the cell concentration (g/l); P is the extracellular product (g/l); µg and kd are growth rate and endogenous rate constant, respectively (h-1). qp is the specific rate of extracellular product formation (g P/g cells-h) Yp/s is the product yield coefficient (g P/g S). Subscript 0 denotes the parameters at the feed medium. Cell Growth in Ideal Chemostat At steady state, X0=0, kd ≈ 0, qp=0 , Monod equation applied, 0 0 0 dX FX 0 FX VR g X VR kd X VR dt 0 1 FS0 FS VR g X dS VR q p X VR Yp / s dt M Y X /S g m S KS S 1 0 Cell Growth in Ideal Chemostat At steady state, X0=0, kd ≈ 0, qp=0 , Monod equation applied, g D m S S KS S M K D S m D Assign. Q 6.13, qo 2 M Ks D X Y ( S0 S ) Y ( S0 ) m D X /S X /S Cell Productivity: DX Dopt d ( DX ) 0 Dopt dD Ks m (1 ) K s S0 X opt Y X / S ( S 0 K s ( K s S 0 ) K s ) M D=F/VR, is dilution rate (1/time), the reciprocal of residence time. Cell Growth in Ideal Chemostat Washed out: If D is set at a value greater than µm (D > µm), the culture cannot reproduce quickly enough to maintain itself. 4 0.3 DX µm = 0.2 hr-1 3.5 0.25 0.2 2.5 X 2 S 0.15 1.5 0.1 1 0.05 0.5 0 0 0.05 0.1 0.15 D (1/hr) 0.2 0 0.25 DX (g/L-hr) S, X (g/L) 3 Determination of Monod Parameters In Chemostat: µg=D, varying D obtains D~S g D m S KS S S K D S m D m 1 1 1 ( Lineweaver - Burk) S KS D KS Chemostat technique: reliable, constant environment, operation may be difficult. Determination of Monod Parameters Batch: X, S, t → lnX ~ t , get µm (slope) from data in exponential phase. X ln μnet t μm t X0 m S dX g , Xdt KS S 1 g S g Kd 0 KS 1 1 ( Lineweaver - Burk) m S m KS m S m (Hanes - Woolf) Cell Growth in Ideal Chemostat At steady state, X0=0, kd > 0, qp=0 , Monod equation applied, 0 0 dX FX 0 FX VR g X VR kd X VR dt 0 1 FS0 FS VR g X dS VR q p X VR Yp / s dt M Y X /S g m S KS S 1 0 Cells Growth in Continuous Culture Ideal Chemostat Endogenous metabolism (X0=0, kd > 0, qp=0) is considered Equation summary net g k d m S kd Ks S Ks ( D k d ) g D kd ; S m D kd X Y M (S0 S ) D X /S D kd Productivities: DX 1 AP Y 1 M Y X /S X /S ms D kd ms M Y X /S Cells Growth in Continuous Culture Ideal Chemostat Endogenous metabolism (X0=0, kd > 0, qp=0) is considered 1 AP Y 1 M Y X /S ms D X /S Y M and ms can be obtained from chemostat experiemnt s X /S X AP AP by plotting1/Y (Y ) against1/D. X /S X /S S S 0 kd Then k d can be obtained from ms M Y X /S Cells Growth in Continuous Culture Ideal Chemostat Endogenous metabolism (X0=0, kd > 0, qp=0) is considered. Ks and m can be determined . Ks( D k d ) S m D kd m 1 1 S Ks( D k d ) Ks 1 1 Plot versus S (D kd ) m 1 slope , y intercept Ks Ks Cell Growth in Ideal Chemostat At steady state, X0=0, kd >0, qp>0 , Monod equation applied, 0 dX0 FX 0 FX VR g X VR kd X VR dt 1 FS0 FS VR g X M Y g m S KS S 0 dS VR q p X VR Yp / s dt 1 X /S The mass balance on product formation : dP dP V R q p X FP V R q p X DP dt dt at steady state, DP q p X Cells Growth in Continuous Culture Ideal Chemostat Endogenous metabolism (kd > 0, qp > 0) is considered Equation summary: g D kd Ks ( D kd ) S m D kd X Y M ( S0 S ) X /S D YXM/ S D kd q p Yp / s DP q p X Productivities: DP, DX Use graphical method to determine the optimum DP, DX. Summary of Growth Kinetics - Autocatalytic reaction: The rate of growth is directly related to cell concentration Net specific growth rate (1/time): 1 dX net X dt net g kd - Cell concentration determination - Growth patterns and kinetics in batch culture - lag phase X - logrithmic or exponential growth phase: ln X μnet t , d 0 - deceleration phase - stationary phase: endogenous metabolism dX kd X dt - death phase Summary of Growth Kinetics - Effect of factors: - Dissolved oxygen: oxygen consumption rate : g X YX / O 2 oxygen transfer rate : k L a(C * C ) - Temperature, pH, ionic strength, substrate concentration. - Heat evolution: H s 1 H c YX /S YH Summary of Growth Kinetics - Monod equation: g m S KS S -Cell growth in continuous culture: qp=0, kd ≈0, X0=0, Monod equation is applied: g D X Y M X /S Productivity: DX m S S KS S (S0 S ) X Y X /S Dopt m (1 X opt Y M M X /S K D S m D ( S0 S ) Y M X /S ( S0 Ks ) K s S0 (S0 K s ( K s S0 ) K s ) Ks D ) m D Summary of Growth Kinetics -Cell growth in continuous culture: qp=0, kd >0, X0=0, Monod equation is applied: m S net g k d kd Ks S Ks ( D k d ) g D kd ; S m D kd X Y M (S0 S ) D X /S D kd Productivities: DP, DX 1 AP Y 1 M Y X /S X /S ms D Summary of Growth Kinetics -Cell growth in continuous culture: qp>0, kd >0, X0=0, Monod equation is applied: DP q p X X Y M ( S0 S ) X /S D YXM/ S D kd q p Yp / s g D kd Ks ( D kd ) S m D kd Productivities: DP, DX