MULTIPLICITY OF STEADY STATES IN CONTINUOUS CULTURE OF MAMMALIAN CELLS

1. 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

2. Major incentives for continuous operations • Reduced turn around time • Steady state operation (a continuous operation need not to be at a steady state)

3. Continuous Process with recycle F, s0 (1+α) F, s, x F, s, x2 V, s, x αF, s, cx

4. F, s0 F, s, x, xd V, s, x

5. F, s0 F, s, x, xd V, s, x

6. 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

7. Stead State Concentrations in Continuous Culture with Cell Recycle Cell and Substrate Concentrations Cell With Cell Recycle Cell Simple Continuous Culture Washout Substrate Substrate Washout Dilution Rate

8. What is a steady state from an operational perspective D = 0.033; Glc = 7 mM Cell conc Growth Rate Lac JGlc JLac Glc Under one set of conditions (dilution rate, feed concentration), the state reaches constant values Key physiological parameters: growth rate, metabolism are constant

9. What is a steady state from an operational perspective D = 0.033; Glc = 7 mM Cell conc Growth Rate Lac JGlc JLac Glc The same data if obtained from perfusion culture, may not be SS growth rate, metabolism may not be constant

10. Continuous Process with recycle F, s0 (1+α) F, s, x F, s, x2 V, s, x αF, s, cx

11. 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

12. Glucose High flux state Lactate Pyruvate Cell Mass AcetylCoA CO2 TCA cycle O2 NH3 Amino Acids Glutamine

13. Glucose Low flux state Lactate Pyruvate Cell Mass AcetylCoA CO2 TCA cycle O2 NH3 Amino Acids Glutamine

14. Glucose Low flux state Lactate Pyruvate Cell Mass AcetylCoA CO2 TCA cycle O2 NH3 Amino Acids Glutamine

15. Continuous Culture with Metabolic Shift

16. Distinct Steady States Corresponding to Different Metabolic States ΔL/ΔG 0.03 0.05 0.15 Cell Conc (106/mL) 0.30 0.50 1.50 Time (hrs)

17. The system: A ball A contour of surface on which it can move

18. Steady State, where “things” can be “steady”, “at equilibrium” Unstable steady state No steady state Stable steady state

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

20. 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

21. Unstable steady state Stable steady state

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

23. 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

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

25. Stable, high flux state

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

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

29. Akt Down-regulated and p53 Up-regulated in Late Stage Glucose GLUT1 Glucose Akt AMPK HK Glucose-6-Phosphate PFK2 PFK2 Fructose-6-Phosphate Myc Hif1a Fructose-2,6-Bisphosphate p53 PFK1 Fructose-1,6-Bisphosphate PGAM Inhibition Phosphoenol Pyruvate Activation Pyruvate Kinase Pyruvate

30. Bistabilty in Central Metabolism High Flux State Unstable Steady States

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

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

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

34. Effect of AKT on Glycolytic Activity

35. Trajectory of Cells in Shifting to Low Flux State

36. Trajectory of Cells in Shifting to Low Flux State

37. Trajectory of Cells in Shifting to Low Flux State

38. Figure 6: Transient behavior demonstrating effect of glucose concentration perturbations on cellular metabolic state 80 C A B 60 Glycolysis Flux (mM/h) 40 20 E 15 0 10 Glc (mM) D 5 0 10 0 20 30 40 50 Lac (mM)

39. F, s0 F, s, x, xd V, s, x Multi-scale Model: Metabolism Model in Continuous Culture

40. Bistability in Continuous Culture Multiscale model simulation Glc = 8 mM

41. Bistability in Continuous Culture

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

43. Distinct Steady States Corresponding to Different Metabolic States ΔL/ΔG 0.03 0.05 0.15 Cell Conc (106/mL) 0.30 0.50 1.50 Time (hrs)

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

45. Transient Trajectory of Culture with Low Metabolic Flux D = 0.033; Glc = 7 mM Cell conc Growth Rate Lac JGlc JLac Glc

46. Benefit of slow growth rate? Transcriptome analysis – effect of culture age?

47. 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

48. Thank you!