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

Major incentives for continuous operations

• Reduced turn around time• Steady state operation (a continuous operation need not to be at a steady state)

Continuous Process with recycle

F, s0(1+α) F, s, x

V, s, xF, s, x2

αF, s, cx

F, s0

F, s, x, xd

V, s, x

F, s0

F, s, x, xd

V, s, x

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

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

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

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

Continuous Process with recycle

F, s0(1+α) F, s, x

V, s, xF, s, x2

αF, s, cx

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

Glucose

Pyruvate

Glutamine

TCA cycle

Lactate

Cell Mass

Amino Acids

AcetylCoA

NH3

CO2

O2

High flux state

Glucose

Pyruvate

Glutamine

TCA cycle

Lactate

Cell Mass

Amino Acids

AcetylCoA

NH3

CO2

O2

Low flux state

Glucose

Pyruvate

Glutamine

TCA cycle

Lactate

Cell Mass

Amino Acids

AcetylCoA

NH3

CO2

O2

Low flux state

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

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

The system: A ballA contour of surface on which it can move

Steady State, where “things” can be “steady”, “at equilibrium”

Stable steady state

Unstable steady state

No steady state

The system: A ballA contour of surface that it can move

Force: gravitational force, external force, friction force

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

Stable steady state

Unstable steady state

When the “state” of a system changes, it moves along where the system has stable steady state.

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

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

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

When the “state” of a system changes, it moves along where the system has stable steady state.

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

)

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

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

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

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

)

Effect of Lactate on Glycolytic Flux

Lactate (mM) Glucose (mM)

Glyc

olys

is Fl

ux (m

M/h

)

Lactate (mM) Glucose (mM)

Glyc

olys

is Fl

ux (m

M/h

)

Effect of Lactate on Glycolytic Flux

Effect of AKT on Glycolytic Activity

Trajectory of Cells in Shifting to Low Flux State

Trajectory of Cells in Shifting to Low Flux State

Trajectory of Cells in Shifting to Low Flux State

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

F, s0

F, s, x, xd

V, s, x

Multi-scale Model: Metabolism Model in Continuous Culture

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

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

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

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

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

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

Benefit of slow growth rate?

Transcriptome analysis – effect of culture age?

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

Thank you!