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TCA

Gly. G1P. G6P. F6P. F1-6BP. Gly3p. ATP. 13BPG. 3PG. TCA. Oxa. ACA. 2PG. PEP. Pyr. NADH. Cit. F6P. F1-6BP. Gly3p. ATP. 13BPG. 3PG. Gly. G1P. G6P. F6P. F1-6BP. Gly3p. ATP. 13BPG. 3PG. TCA. Oxa. ACA. 2PG. PEP. Pyr. NADH. Cit. Autocatalytic. x. Control. y.

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TCA

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  1. Gly G1P G6P F6P F1-6BP Gly3p ATP 13BPG 3PG TCA Oxa ACA 2PG PEP Pyr NADH Cit

  2. F6P F1-6BP Gly3p ATP 13BPG 3PG Gly G1P G6P F6P F1-6BP Gly3p ATP 13BPG 3PG TCA Oxa ACA 2PG PEP Pyr NADH Cit

  3. Autocatalytic x Control y F6P F1-6BP Gly3p ATP 13BPG 3PG

  4. F6P F1-6BP Gly3p ATP 13BPG 3PG Autocatalytic x Control y

  5. Autocatalytic x Control y Minimal metabolism model • x = ultimate product (ATP) • y = intermediate metabolite • Two feedbacks of x: • Autocatalytic • Control

  6. RHP z and p Hard limits

  7. Autocatalytic x Control y

  8. x produced y consumed

  9. Autocatalytic x Control y consumed produced

  10. x consumed

  11. Autocatalytic x y

  12. Autocatalytic x Control y

  13. Autocatalytic x Control y

  14. 1.05 h >>1 h = 1 0.8 h >>1 0.6 Spectrum 0.4 0.2 h = 1 Log(|Sn/S0|) 0 -0.2 -0.4 -0.6 -0.8 0 2 4 6 8 10 Frequency Ideal [ATP] 1 0.95 Time response 0.9 0.85 0.8 0 5 10 15 20 Time (minutes)

  15. 1.05 Yet fragile Robust [ATP] 1 h >> 1 0.95 Time response 0.9 0.85 h = 1 0.8 0 5 10 15 20 Time (minutes) 0.8 h >>1 0.6 Spectrum 0.4 0.2 h = 1 Log(Sn/S0) 0 -0.2 -0.4 -0.6 -0.8 0 2 4 6 8 10 Frequency

  16. Yet fragile 0.8 h = 3 0.6 Robust 0.4 0.2 h = 0 Log(Sn/S0) 0 -0.2 -0.4 -0.6 -0.8 0 2 4 6 8 10 Frequency

  17. Yet fragile 0.8 0.6 Robust 0.4 0.2 h = 0 Log(Sn/S0) 0 -0.2 -0.4 -0.6 -0.8 0 2 4 6 8 10 Frequency

  18. This tradeoff is a law. Transients, Oscillations log|S|  Biological complexity is dominated by the evolution of mechanisms to more finely tune this robustness/fragility tradeoff. Tighter regulation

  19. Hard limits RHP p RHP z Benefits must be “paid for” within bandwidth z

  20. “Optimal” controller x “Optimal” enzyme y Necessity, not accident

  21. q=α=0 q=α=1 Necessity, not accident 0 10 0 10

  22. Necessity or accident? • Alternative designs Synthesis challenges • Other rates and uncertainty • Computational complexity • Higher order dynamics • Global, nonlinear • Comparisons with data • Robustness is key

  23. Hard limits and tradeoffs Robust/ fragile is unifying concept On systems and their components • Thermodynamics (Carnot) • Communications (Shannon) • Control (Bode) • Computation (Turing/Gödel) • Include dynamics and feedback • Extend to networks • New unifications are encouraging

  24. cost = amplification goal: make this small  • benefits = attenuation of disturbance • goal: make this as negative as possible Constraint: benefits costs

  25. Bode d e=d-u - u Plant  Control stabilize benefits costs

  26. Bode d e=d-u - u Plant  Control Negative is good stabilize benefits costs

  27. Disturbance - e=d-u d Remote Sensor Plant Control Channel Sensor Channel Control Encode Nuno C Martins and Munther A Dahleh, Feedback Control in the Presence of Noisy Channels: “Bode-Like” Fundamental Limitations of Performance. Nuno C. Martins, Munther A. Dahleh and John C. Doyle Fundamental Limitations of Disturbance Attenuation in the Presence of Side Information (Both in IEEE Transactions on Automatic Control) http://www.glue.umd.edu/~nmartins/

  28. Electric power network Variety of producers • Good designs transform/manipulate energy • Subject (and close)to hard limits Variety of consumers

  29. 110 V, 60 Hz AC (230V, 50 Hz AC) Gasoline ATP, glucose, etc Proton motive force Standard interface Constraint that deconstrains Variety of consumers Variety of producers Energy carriers

  30. Robust Fragile Disturbance - e=d-u d Remote Sensor Control Channel Plant Sensor Channel Control Encode remote control benefits stabilize remote sensing feedback costs • Robust designs transform/manipulate robustness • Subject (and close) to hard limits • Fragile designs are far away from hard limits and waste robustness.

  31. Hard limits and tradeoffs Robust/ fragile is unifying concept On systems and their components • Thermodynamics (Carnot) • Communications (Shannon) • Control (Bode) • Computation (Turing/Gödel) • Include dynamics and feedback • Extend to networks • New unifications are encouraging

  32. [a system] can have [a property] robust for [a set of perturbations] Fragile Yet be fragile for Robust [a different property] Or [a different perturbation]

  33. [a system] can have [a property] robust for [a set of perturbations] Fragile • Some fragilities are inevitable in robust complex systems. Robust • But if robustness/fragility are conserved, what does it mean for a system to be robust or fragile?

  34. Emergent Fragile • Some fragilities are inevitable in robust complex systems. Robust • But if robustness/fragility are conserved, what does it mean for a system to be robust or fragile? • Robust systems systematically manage this tradeoff. • Fragile systems waste robustness.

  35. Sugars Diverse Fatty acids Precursors Co-factors Catabolism Universal Control Amino Acids Diverse Nucleotides Genes Proteins Carriers Trans* DNA replication Systems requirements: functional, efficient, robust, evolvable Hard constraints: Thermo (Carnot) Info (Shannon) Control (Bode) Compute (Turing) Protocols Constraints Components and materials: Energy, moieties

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