• 검색 결과가 없습니다.

NNonsegrregated Seggregatedd .

N/A
N/A
Protected

Academic year: 2022

Share "NNonsegrregated Seggregatedd ."

Copied!
23
0
0

로드 중.... (전체 텍스트 보기)

전체 글

(1)

6 3 Quantifying Growth Kinetics 6.3. Quantifying Growth Kinetics

ƒ Model

ƒ Model

Unstructured Structured .

N

Most idealized case

Cell population treated as Multicomponent

Nonsegr

Balanced Growth

one component solute average cell description

regated

(approximation)

Average cell Average cell

single component Multicomponent

Seg Balanced

approximation approximation

g p p

heterogeneous description of cell-to-cell

individual cells heterogeneity

gregated

Growth (approximation)

Actual case

d .

(2)

6.3.2. Using Unstructured Nonsegregated Models to Predict Specific Growth Rate

ƒ 6 3 2 1 Substrate-limited growth

ƒ 6.3.2.1. Substrate-limited growth

ƒ Monod equation

ƒ Monod equation

µ = _____

µm S

µ

Ks + S

µm : maximum specific growth rate Ks : saturation constant

ƒ Other equations

(3)

Other equations

for substrate-limited growth

(4)

When more than one substrate is growth rate limiting

ƒ Interactive or multiplicative

µ/µ = [µ(s )] [µ(s )] [µ(s )]

µ/µm = [µ(s1)] [µ(s2)] … [µ(sn)]

ƒ AdditiveAdditive

µ/µm = w1 [µ(s1)] + w2 [µ(s2)] + … + wN [µ(sn)]

ƒ Noninteractive

( ) ( ) ( )

µ = µ(s1) or µ(s2) or … µ(sn)

where the lowest value of µµ(s( ii) is used.)

(5)

6 3 2 2 Models with growth inhibitors 6.3.2.2. Models with growth inhibitors

ƒ The inhibition pattern of microbial growth is analogous to enzyme inhibition.

a a ogous to e y e b t o

ƒ Substrate inhibition

ƒ Product inhibition

ƒ Inhibition by toxic compound

(6)

Substrate Inhibition of Cell Growth

(7)

Enzyme Inhibition Enzyme Inhibition

N titi i hibiti

Noncompetitive inhibition

Competitive inhibition

(8)

Product Inhibition of Cell Growth Product Inhibition of Cell Growth

(9)

Cell Growth in Ethanol Fermentation Cell Growth in Ethanol Fermentation

(10)

Inhibition by Toxic Compounds Inhibition by Toxic Compounds

(11)

Enzyme Inhibition Enzyme Inhibition

Competitive inhibition Competitive inhibition

Noncompetitive inhibition Noncompetitive inhibition

(12)

Enzyme Inhibition Enzyme Inhibition

Uncompetitive inhibition

(13)

Inhibition by Toxic Compounds Inhibition by Toxic Compounds

(14)

6 3 2 3 The logistic equation 6.3.2.3. The logistic equation

dX/dt X

dX/dt = µ X

dX/dt k (1 X/X ) X X(0) X dX/dt = k (1-X/X) X, X(0)=X0

X0 ekt X

=

X0 e

1- (X0 /X) (1 - ekt)

______________

Sigmoidal

(stationary phase involved)

(15)

6.3.2.4. Growth model

for filamentous organisms

ƒ In suspension culture : formation of microbial pellet

ƒ On solid medium : colony (long and highly branched cellsy ( g g y

ƒ In the absence of mass transfer limitations

R ∝ t R: radius of a microbial pellet R t R: radius of a microbial pellet

radius of a mold colony dR/dt = kp = constant Eq(1)

(16)

Growth model for filamentous organisms Growth model for filamentous organisms

ƒ M : mass of pellet

dM/dt (4 R2) (dR/dt) dM/dt = ρ (4πR2) (dR/dt)

= kpp ρ (4πRρ ( 2) (by Eq(1))) ( y q( ))

= kp (36πρ)1/3 (4/3 πR3ρ)2/3

= γ M2/3 Eq(2)

where γ = kp (36πρ)1/3 M = 4/3 πR3ρ

(17)

Growth model for filamentous organisms Growth model for filamentous organisms

E (2)

ƒ Eq(2)

dM/dt = γγ M2/3 Eq(2)q( ) M-2/3 dM = γ dt

3 [M1/3] = γ t

M = (M 1/3 + (γ t)/3)3

M M0

M = (M01/3 + (γ t)/3)3

≈ (γ t /3)3

M0 (the initial biomass) is usually very small compared to M

compared to M.

(18)

6 3 3 Chemically Structured Model 6.3.3. Chemically Structured Model

ƒ Since it is not practical to write material balances on every cell

component, we must select skillfully the key variables and processes of major interest in a particular application when formulating a

of major interest in a particular application when formulating a structured kinetic model.

ƒ Mass balance inside the cell

ƒ Batch

ƒ VR : total volume of liquid in the reactor

ƒ C : extrinsic concentration of component i

ƒ Ci : extrinsic concentration of component i

ƒ X : extrinsic concentration of biomass

(19)

Intrinsic and Extrinsic Concentrations Intrinsic and Extrinsic Concentrations

ƒ Intrinsic concentration

ƒ The amount of a compound per unit cell mass (or cellThe amount of a compound per unit cell mass (or cell volume)

ƒ Extrinsic concentration

ƒ The amount of a compound per unit reactor volumeThe amount of a compound per unit reactor volume

(20)

Intrinsic and Extrinsic Concentrations Intrinsic and Extrinsic Concentrations

(21)

Intrinsic and Extrinsic Concentrations Intrinsic and Extrinsic Concentrations

(22)

Single-cell model for E. coli by Shuler and colleagues

ƒ Fig. 6.14

ƒ The model contains the order of 100

stoichiometric and kinetic parameters almost all stoichiometric and kinetic parameters, almost all of which can be determined from previous

literature an the biochemistry of E coli growth literature an the biochemistry of E. coli growth.

(23)

Single-cell model for E. coli by Shuler and colleagues

참조

관련 문서

- flux of solute mass, that is, the mass of a solute crossing a unit area per unit time in a given direction, is proportional to the gradient of solute concentration

 Engineering stress - The applied load, or force, divided by the original cross-sectional area of the material..  Engineering strain - The amount that a material deforms per

• position: fractional multiples of the unit cell edge lengths ) P:..

 The inverse pole figure gives the probability of finding a given specimen direction parallel to crystal (unit cell) directions.  By collecting data for several reflections

Correlation of automated red cell count (aRBC) and mean of manual red cell counts (mRBC).. Correlation of estimated red cell count (eRBC) and mean of manual red

• Specific heat (capacity): the measure of the heat energy required to increase the temperature of a unit mass of a required to increase the temperature of a unit mass of a

Figure.11 1 1 1.The cell growth, soluble glucan producti .The cell growth, soluble glucan producti .The cell growth, soluble glucan producti .The cell growth, soluble glucan

– Established the fundamentals of high temperature fuel cells such as the molten carbonate and solid oxide fuel cell.. – In 1958, he demonstrated an alkali cell using a