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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

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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, s 0 (1+α) F, s, x V, s, x F, s, x 2 αF, s, cx

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F, s 0 F, s, x, x d V, s, x

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F, s 0 F, s, x, x d 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 Dilution Rate Cell and Substrate Concentrations With Cell Recycle Simple Continuous Culture Washout Substrate Washout Cell

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Lac Glc Cell conc J Lac Growth Rate J Glc 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 values Key physiological parameters: growth rate, metabolism are constant

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Lac Glc Cell conc J Lac Growth Rate J Glc 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 SS growth rate, metabolism may not be constant

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Continuous Process with recycle F, s 0 (1+α) F, s, x V, s, x F, s, x 2 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 NH 3 CO 2 O2O2 High flux state

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Glucose Pyruvate Glutamine TCA cycle Lactate Cell Mass Amino Acids AcetylCoA NH 3 CO 2 O2O2 Low flux state

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Glucose Pyruvate Glutamine TCA cycle Lactate Cell Mass Amino Acids AcetylCoA NH 3 CO 2 O2O2 Low flux state

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Continuous Culture with Metabolic Shift

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Distinct Steady States Corresponding to Different Metabolic States Time (hrs) Cell Conc (10 6 /mL) ΔL/ΔG 0.03 0.05 0.15 0.30 0.50 1.50

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The system: A ball A 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 ball A contour of surface that it can move Force: gravitational force, external force, friction force

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The system: A ball A 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 Pathway Glucose Fructose-6-Phosphate Pyruvate Fructose-1,6- Bisphosphate Fructose-2,6- Bisphosphate Glucose-6- Phosphate Phosphoenol Pyruvate Pyruvate Kinase PFK2 Hexokinase … Lactate Inhibition Activation Phosphofructokinase Pyruvate mito

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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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Allosteric Regulations in Glycolysis Pathway Glucose Fructose-6-Phosphate Pyruvate Fructose-1,6- Bisphosphate Fructose-2,6- Bisphosphate Glucose-6- Phosphate Phosphoenol Pyruvate Pyruvate Kinase PFK2 Hexokinase … Lactate Inhibition Activation Phosphofructokinase Pyruvate mito

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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 PFK2 p53 PGAM Glucose GLUT1 Akt AMPK Inhibition Activation HK Myc Hif1a PFK2

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Bistabilty in Central Metabolism Unstable Steady States High Flux State

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Effect of Lactate on Glycolytic Flux Lactate (mM) Glucose (mM) Glycolysis Flux (mM/h)

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Effect of Lactate on Glycolytic Flux Lactate (mM) Glucose (mM) Glycolysis Flux (mM/h)

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Lactate (mM) Glucose (mM) Glycolysis Flux (mM/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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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) Glycolysis Flux (mM/h) 5 B AC D E

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F, s 0 F, s, x, x d V, s, x Multi-scale Model: Metabolism Model in Continuous Culture

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Bistability in Continuous Culture Multiscale model simulation Glc = 8 mM

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Bistability in Continuous Culture

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Effect of Glucose Feed Glc = 15 mM Glc = 8 mM Glc = 5 mM

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Distinct Steady States Corresponding to Different Metabolic States Time (hrs) Cell Conc (10 6 /mL) ΔL/ΔG 0.03 0.05 0.15 0.30 0.50 1.50

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D = 0.033; Glc = 7 mM Lac Glc Cell conc J Lac Growth Rate J Glc Transient Trajectory of Culture with High Metabolic Flux

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Lac Glc Cell conc J Lac Growth Rate J Glc 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!

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