multiplicity of steady states in continuous culture of mammalian cells
DESCRIPTION
MULTIPLICITY OF STEADY STATES IN CONTINUOUS CULTURE OF MAMMALIAN CELLS . Andrew Yongky , Tung Le, Simon Grimm, Wei-Shou Hu Department of Chemical Engineering and Materials Science, University of Minnesota . Major incentives for continuous operations. Reduced turn around time - PowerPoint PPT PresentationTRANSCRIPT
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MULTIPLICITY OF STEADY STATES IN CONTINUOUS CULTURE OF MAMMALIAN CELLS
Andrew Yongky, Tung Le, Simon Grimm, Wei-Shou HuDepartment of Chemical Engineering and Materials Science,
University of Minnesota
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Major incentives for continuous operations
• Reduced turn around time• Steady state operation (a continuous operation need not to be at a steady state)
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Continuous Process with recycle
F, s0(1+α) F, s, x
V, s, xF, s, x2
αF, s, cx
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F, s0
F, s, x, xd
V, s, x
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F, s0
F, s, x, xd
V, s, x
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What is a steady state
• Has meaningful solution(s) when the system’s equations are set to 0
• Sometimes a system has a unique steady state for a set of operating conditions
• Other times, has mutliple steady state
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Stead State Concentrations in Continuous Culture with Cell Recycle
0.0 1.0 2.0 3.0 4.0 5.0 6.00.0
0.5
1.0
1.5
2.0
2.5
3.0
Dilution RateCell
and
Subs
trat
e Co
ncen
trati
ons
With Cell Recycle
Simple Continuous CultureWashout
SubstrateSubstrate
Washout
Cell
Cell
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0100
200300
400500
600700
800900
10000
20
40
60
80
100
120
140
0
0.01
0.02
0.03
0.04
0.05
0.06
Time (hr)
Flux
(mM
/h)
Grow
th R
ate
(hr-
1)
0 100 200 300 400 500 600 700 800 90010000
2
4
6
8
10
0
2
4
6
8
10
Time (hr)
Conc
entr
ation
(mM
)
Cell
Conc
(x10
6 ce
lls/m
L)
Lac
Glc
Cell conc
JLac
Growth Rate
JGlc
What is a steady state from an operational perspective
D = 0.033; Glc = 7 mM
Under one set of conditions (dilution rate, feed concentration), the state reaches constant valuesKey physiological parameters: growth rate, metabolism are constant
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0100
200300
400500
600700
800900
10000
20
40
60
80
100
120
140
Time (hr)
Flux
(mM
/h)
0 100 200 300 400 500 600 700 800 90010000
2
4
6
8
10
0
2
4
6
8
10
Time (hr)
Conc
entr
ation
(mM
)
Cell
Conc
(x10
6 ce
lls/m
L)
Lac
Glc
Cell conc
JLac
Growth Rate
JGlc
What is a steady state from an operational perspective
D = 0.033; Glc = 7 mM
The same data if obtained from perfusion culture, may not be SSgrowth rate, metabolism may not be constant
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Continuous Process with recycle
F, s0(1+α) F, s, x
V, s, xF, s, x2
αF, s, cx
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The Theme
• Multiple metabolic state when cells grow at one set of growth rate, glucose and lactate concentrations
• The metabolic steady state multiplicity leads to cell concentration multiplicity
• If we ensure the same steady state is achieved in different runs, process will be more robust
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Glucose
Pyruvate
Glutamine
TCA cycle
Lactate
Cell Mass
Amino Acids
AcetylCoA
NH3
CO2
O2
High flux state
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Glucose
Pyruvate
Glutamine
TCA cycle
Lactate
Cell Mass
Amino Acids
AcetylCoA
NH3
CO2
O2
Low flux state
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Glucose
Pyruvate
Glutamine
TCA cycle
Lactate
Cell Mass
Amino Acids
AcetylCoA
NH3
CO2
O2
Low flux state
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0
2
4
6
Cel
l Con
c. (1
09 /L)
Fed-batch
Batch
0
1
2
3
0 100 200 300Time (hr)
DL/
DG
(mol
/mol
)
0
1
2
3
4
Glu
cose
(g/L
)
0
1
2
0 100 200 300Time (hr)
Lact
ate
(g/L
)
Continuous Culture with Metabolic Shift
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Distinct Steady States Corresponding to Different Metabolic States
0
2
4
6
0 100 200 300Time (hrs)
Cel
l Con
c (1
06 /mL)
DL/DG0.030.050.150.300.50
1.50
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The system: A ballA contour of surface on which it can move
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Steady State, where “things” can be “steady”, “at equilibrium”
Stable steady state
Unstable steady state
No steady state
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The system: A ballA contour of surface that it can move
Force: gravitational force, external force, friction force
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The system: A ballA contour of surface that it can move
Force: gravitational force, external force, friction force
The stability of the system can be shown mathematically using equations describing the system
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Stable steady state
Unstable steady state
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When the “state” of a system changes, it moves along where the system has stable steady state.
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Stability analysis can be applied to chemical reaction systems
The kinetic equations for all glycolysis, PPP and TCA cycle enzymes are all very well characterized
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Allosteric Regulations in Glycolysis PathwayGlucose
Fructose-6-Phosphate
Pyruvate
Fructose-1,6-Bisphosphate
Fructose-2,6-Bisphosphate
Glucose-6-Phosphate
Phosphoenol PyruvatePyruvate Kinase
PFK2
Hexokinase
…
Lactate
InhibitionActivation
Phosphofructokinase
Pyruvatemito
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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
30
50
70
Extracellular Glucose (mM)
Glyc
olys
is Fl
ux (m
M/h
)
Stable, low flux state
Unstable steady state, unrealizable
Stable, high flux state
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When the “state” of a system changes, it moves along where the system has stable steady state.
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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
30
50
70
Extracellular Glucose (mM)
Glyc
olys
is Fl
ux (m
M/h
)
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Allosteric Regulations in Glycolysis PathwayGlucose
Fructose-6-Phosphate
Pyruvate
Fructose-1,6-Bisphosphate
Fructose-2,6-Bisphosphate
Glucose-6-Phosphate
Phosphoenol PyruvatePyruvate Kinase
PFK2
Hexokinase
…
Lactate
InhibitionActivation
Phosphofructokinase
Pyruvatemito
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Akt Down-regulated and p53 Up-regulated in Late Stage
Glucose
Fructose-6-Phosphate
Pyruvate
Fructose-1,6-Bisphosphate
Fructose-2,6-Bisphosphate
PFK1
Glucose-6-Phosphate
Phosphoenol Pyruvate
Pyruvate Kinase
PFK2p53
PGAM
Glucose
GLUT1
AktAMP
K
InhibitionActivation
HK
Myc Hif1a
PFK2
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0 1 2 3 4 510
30
50
70
Extracellular Glucose (mM)
Glyc
olys
is Fl
ux (m
M/h
)Bistabilty in Central Metabolism
Unstable Steady States
High Flux State
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Effect of Lactate on Glycolytic Flux
02
46
810
0
10
20
30
40
500
20
40
60
80
Lactate (mM) Glucose (mM)
Glyc
olys
is Fl
ux (m
M/h
)
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Effect of Lactate on Glycolytic Flux
Lactate (mM) Glucose (mM)
Glyc
olys
is Fl
ux (m
M/h
)
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Lactate (mM) Glucose (mM)
Glyc
olys
is Fl
ux (m
M/h
)
Effect of Lactate on Glycolytic Flux
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Effect of AKT on Glycolytic Activity
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Trajectory of Cells in Shifting to Low Flux State
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Trajectory of Cells in Shifting to Low Flux State
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Trajectory of Cells in Shifting to Low Flux State
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Figure 6: Transient behavior demonstrating effect of glucose concentration perturbations on cellular metabolic state
50 40 20 10 0
Lac (mM)0
10
15 0
20
40
60
80
30
Glc (mM)
Glyc
olys
is Fl
ux (m
M/h
)
5
B
AC
D
E
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F, s0
F, s, x, xd
V, s, x
Multi-scale Model: Metabolism Model in Continuous Culture
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0 0.01 0.02 0.03 0.04 0.050
5
10
15
20
Dilution Rate (hr-1)
Cell
Conc
(x10
6 ce
lls/m
L)
0 0.01 0.02 0.03 0.04 0.050
20
40
60
80
Dilution Rate (hr-1)
JGlc
(mM
/hr)
Bistability in Continuous Culture
0 0.01 0.02 0.03 0.04 0.050
1
2
3
4
5
Dilution Rate (hr-1)
Gluc
ose
(mM
)
Multiscale model simulationGlc = 8 mM
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0 0.5 1 1.5 2 2.50
20
40
60
80
Glucose (mM)
JGlc
(mM
/hr)
0 0.5 1 1.5 2 2.50
2
4
6
8
10
12
Glucose (mM)Ce
ll Co
nc (x
106
cells
/mL)
Bistability in Continuous Culture
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0 0.01 0.02 0.03 0.04 0.050
5
10
15
20
Dilution Rate (hr-1)
Cell
Conc
(x
106
cells
/mL)
0 0.01 0.02 0.03 0.04 0.050
5
10
15
20
Dilution Rate (hr-1)
Cell
Conc
(x
106
cells
/mL)
0 0.01 0.02 0.03 0.04 0.050
20
40
60
80
Dilution Rate (hr-1)JG
lc (m
M/h
r)
0 0.01 0.02 0.03 0.04 0.050
20
40
60
80
Dilution Rate (hr-1)
JGlc
(mM
/hr)
0 0.01 0.02 0.03 0.04 0.050
5
10
15
20
Dilution Rate (hr-1)
Cell
Conc
(x
106
cells
/mL)
0 0.01 0.02 0.03 0.04 0.050
20
40
60
80
Dilution Rate (hr-1)
JGlc
(mM
/hr)
Effect of Glucose FeedGlc = 15 mM
Glc = 8 mM
Glc = 5 mM
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Distinct Steady States Corresponding to Different Metabolic States
0
2
4
6
0 100 200 300Time (hrs)
Cel
l Con
c (1
06 /mL)
DL/DG0.030.050.150.300.50
1.50
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0 200 400 600 800 10000
20
40
60
80
100
120
140
0
0.01
0.02
0.03
0.04
0.05
0.06
Time (hr)
Flux
(mM
/h)
Grow
th R
ate
(hr-
1)
0 200 400 600 800 10000
2
4
6
8
10
0
2
4
6
8
10
Time (hr)
Conc
entr
ation
(mM
)
Cell
Conc
(x10
6 ce
lls/m
L)
D = 0.033; Glc = 7 mM
Lac
GlcCell conc
JLac
Growth Rate
JGlc
Transient Trajectory of Culture with High Metabolic Flux
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0100
200300
400500
600700
800900
10000
20
40
60
80
100
120
140
0
0.01
0.02
0.03
0.04
0.05
0.06
Time (hr)
Flux
(mM
/h)
Grow
th R
ate
(hr-
1)
0 100 200 300 400 500 600 700 800 90010000
2
4
6
8
10
0
2
4
6
8
10
Time (hr)
Conc
entr
ation
(mM
)
Cell
Conc
(x10
6 ce
lls/m
L)
Lac
Glc
Cell conc
JLac
Growth Rate
JGlc
Transient Trajectory of Culture with Low Metabolic Flux
D = 0.033; Glc = 7 mM
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Benefit of slow growth rate?
Transcriptome analysis – effect of culture age?
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Conclusion• Physiological steady state
- truly benefit continuous operation• Metabolic regulation and growth
causes metabolic steady state multiplicity
• Continuous cell culture reactor – multiple steady state
• Different trajectories lead to different steady state
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Thank you!