1. Architecture, networks, and complexity John Doyle John G Braun Professor Control and dynamical systems BioEngineering, Electrical Engineering Caltech

2. NRC theory report: Bad news and good news Bad: Attempts to connect with theory Topology, modularity, information,… Good: Biology motivation Diversity Metabolism Cell interior Architecture (is not topology) Robustness Decision Behavior

3. Alternative: Essential ideas Listening to physicians, biologists, and engineers Robust yet fragile (RYF) “Constraints that deconstrain” (G&K) Unity creating diversity Network architecture Layering Control and dynamics (C&D) Hourglasses and Bowties

4. Collaborators and contributors (partial list) Biology: Csete,Yi, El-Samad, Khammash, Tanaka, Arkin, Savageau, Simon, AfCS, Kurata, Smolke, Gross, Kitano, Hucka, Sauro, Finney, Bolouri, Gillespie, Petzold, F Doyle, Stelling, Caporale,… Theory: Parrilo, Carlson, Murray, Vinnicombe, Paganini, Mitra Papachristodoulou, Prajna, Goncalves, Fazel, Liu, Lall, D’Andrea, Jadbabaie, Dahleh, Martins, Recht, many more current and former students, … Web/Internet: Li, Alderson, Chen, Low, Willinger, Kelly, Zhu,Yu, Wang, Chandy, … Turbulence: Bamieh, Bobba, McKeown, Gharib, Marsden, … Physics: Sandberg, Mabuchi, Doherty, Barahona, Reynolds, Disturbance ecology: Moritz, Carlson,… Finance: Martinez, Primbs, Yamada, Giannelli,… Current CaltechFormer CaltechOtherLongterm Visitor

5. Thanks to you for inviting me, and NSF ITR AFOSR NIH/NIGMS ARO/ICB DARPA Lee Center for Advanced Networking (Caltech) Boeing Pfizer Hiroaki Kitano (ERATO) Braun family

6. Multiscale Physics Systems Biology & Medicine Network Centric, Pervasive, Embedded, Ubiquitous Core theory challenges My interests Sustainability?

7. Systems Biology & Medicine Bacterial networks Necessity in chemotaxis Design principles in heat shock response Architecture of metabolism Origin of high variability and power laws Architecture of the cell Control of core metabolism and glycolytic oscillations SBML/SBW SOSTOOLS Wildfire ecology Physiology and medicine (new) Publications: Science, Nature, Cell, PNAS, PLOS, Bioinfo., Trends, IEEE Proc., IET SysBio, FEBS, PRL,…

8. Wilbur Wright on Control, 1901 “We know how to construct airplanes.” (lift and drag) “Men also know how to build engines.” (propulsion) “Inability to balance and steer still confronts students of the flying problem.” (control) “When this one feature has been worked out, the age of flying will have arrived, for all other difficulties are of minor importance.”

9. Feathers and flapping? Or lift, drag, propulsion, and control?

10. Recommendations (Obviously…) More and better theory Need an “architecture” for research that is as networked as biology and our best technologies Create the right “waist” of the research hourglass E.g. find the constraints that deconstrain

11. RobustYet Fragile Human complexity Efficient, flexible metabolism Complex development and Immune systems Regeneration & renewal  Complex societies  Advanced technologies  Obesity and diabetes  Rich microbe ecosystem  Inflammation, Auto-Im.  Cancer  Epidemics, war, …  Catastrophic failures Evolved mechanisms for robustness allow for, even facilitate, novel, severe fragilities elsewhere often involving hijacking/exploiting the same mechanism There are hard constraints (i.e. theorems with proofs)

12. food intake Glucose Oxygen Amino acids Fatty acids Organs Tissues Cells Molecules Universal metabolic system Blood Peter Sterling and Allostasis

13. VTA Prefrontal cortex Accumbens dopamine Universal reward systems sports music dance crafts art toolmaking sex food Dopamine, Ghrelin, Leptin,…

14. VTA Prefrontal cortex Accumbens dopamine Universal reward systems sports music dance crafts art toolmaking sex food Glucose Oxygen Organs Tissues Cells Molecules Universal metabolic system Blood food

15. VTA Prefrontal cortex Accumbens dopamine work family community nature Universal reward systems Robust and adaptive, yet … food sex toolmaking sports music dance crafts art

16. VTA Prefrontal cortex Accumbens dopamine work family community nature Universal reward systems Robust and adaptive, yet … food sex toolmaking sports music dance crafts art

17. sex food toolmaking sports music dance crafts art VTA Prefrontal cortex Accumbens dopamine work family community nature

18. work family community nature sex food toolmaking sports music dance crafts art VTA Prefrontal cortex Accumbens dopamine Vicarious money salt sugar/fat nicotine alcohol industrial agriculture market/ consumer culture

19. work family community nature sex toolmaking sports music dance crafts art VTA Prefrontal cortex Accumbens dopamine Vicarious money salt sugar/fat nicotine alcohol cocaine amphetamine

20. Vicarious money salt sugar/fat nicotine alcohol high sodium obesity overwork smoking alcoholism drug abuse hyper- tension athero- sclerosis diabetes inflammation immune suppression coronary, cerebro- vascular, reno- vascular cancer cirrhosis accidents/ homicide/ suicide

21. Vicarious money salt sugar/fat nicotine alcohol high sodium obesity overwork smoking alcoholism drug abuse hyper- tension athero- sclerosis diabetes inflammation immune suppression coronary, cerebro- vascular, reno- vascular cancer cirrhosis accidents/ homicide/ suicide VTA dopamine Glucose Oxygen

22. RobustYet Fragile Human complexity Efficient, flexible metabolism Complex development and Immune systems Regeneration & renewal  Complex societies  Advanced technologies  Obesity and diabetes  Rich microbe ecosystem  Inflammation, Auto-Im.  Cancer  Epidemics, war, …  Catastrophic failures Evolved mechanisms for robustness allow for, even facilitate, novel, severe fragilities elsewhere often involving hijacking/exploiting the same mechanism There are hard constraints (i.e. theorems with proofs)

23. Robust yet fragile Systems can have robustness of –Some properties to –Some perturbations in –Some components and/or environment Yet fragile to other properties or perturbations. Many issues are special cases, e.g.: Efficiency: robustness to resource scarcity Scalability: robustness to changes in scale Evolvability: robustness of lineages on long times to possibly large perturbations

24. Case studies Today (primary): Cell biology Today (secondary): Internet Toy example: Lego Wildfire ecology Physiology Power grid Manufacturing Transportation Other possibilities: Turbulence Statistical mechanics Physiology (e.g. HR variability, exercise and fatigue, trauma and intensive care) RYF physio (e.g. diabetes, obesity, addiction, … ) Disasters statistics (earthquakes)

25. Bio and hi-tech nets Exhibit extremes of Robust Yet Fragile Simplicity and complexity Unity and diversity Evolvable and frozen Constrained and deconstrained What makes this possible and/ or inevitable? Architecture

26. We use this word all the time. What do we really mean by it? What would a theory look like? Architecture

27. RobustYet Fragile Human complexity Efficient, flexible metabolism Complex development and Immune systems Regeneration & renewal  Complex societies  Advanced technologies  Obesity and diabetes  Rich microbe ecosystem  Inflammation, Auto-Im.  Cancer  Epidemics, war, …  Catastrophic failures It is much easier to create the robust features than to prevent the fragilities. There are poorly understood “conservation laws” at wor k

28. Robust yet fragile Most essential challenge in technology, society, politics, ecosystems, medicine, etc: Managing spiraling complexity/fragility Not predicting what is likely or typical But understanding what is catastrophic (though perhaps rare) What community will step up and be central in this challenge?

29. Components and materials Systems requirements: functional, efficient, robust, evolvable, scalable Robust yet fragile System and architecture Perturbations

30. Component System-level EmergentProtocols Architecture= Constraints Aim: a universal taxonomy of complex systems and theories Describe systems/components in terms of constraints on what is possible Decompose constraints into component, system- level, protocols, and emergent Not necessarily unique, but hopefully illuminating nonetheless Contraints that deconstrain

31. fan-in of diverse inputs fan-out of diverse outputs universal carriers Diverse function Diverse components Universal Control Universal architectures Hourglasses for layering of control Bowties for flows within layers

32. Evolution of theory Verbal arguments (stories, cartoons, diagrams) Data and statistics (plots, tables) Modeling and simulation (dynamics, numerics) Analysis (theorems, proofs) Synthesis (hard limits on the achievable, reverse engineering good designs, forward engineering new designs) All levels interact and iterate

33. Example: Theory of planetary motion Verbal (Ptolemy, Copernicus) Data & stats (Brahe, Galileo, Kepler) Model & sim (Newton, Einstein) Analysis (Lagrange, Hamilton, Poincare) Synthesis (NASA/JPL) All levels interact and iterate

34. Drill down Describe theory Show some math Just to give a flavor You can ignore details Always return to verbal descriptions and hand- waving summaries Verbal Data/stat Mod/sim Analysis Synthesis

35. Synthesis theories: Limits and tradeoffs On systems and their components Thermodynamics (Carnot) Communications (Shannon) Control (Bode) Computation (Turing/Gödel) Assume different architectures a priori. No networks

36. Hard limits and tradeoffs On systems and their components Thermodynamics (Carnot) Communications (Shannon) Control (Bode) Computation (Turing/Gödel) Fragmented and incompatible Cannot be used as a basis for comparing architectures New unifications are encouraging No dynamics or feedback

37. Hard limits and tradeoffs 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 Robust/ fragile is unifying concept

38. Why glycolytic oscillations? Various answers depend on meaning of “why” Will go deeper into “why” using stages… Start with simplest possible models Motivate generalizable and scalable methods Extremely familiar and “done” problem in biology and dynamics at the small circuit level Convenient to introduce new theory and thinking using the most familiar possible examples

39. Basics of glyc-oscillations Verbal arguments (stories, cartoons, diagrams) Data and statistics (plots, tables) Result: Cells and extracts show oscillatory behavior. Why?

40. Why? Modeling and simulation Verbal arguments (stories, cartoons, diagrams) Data and statistics (plots, tables) Modeling and simulation (dynamics, numerics) Why = propose mechanism, model, simulate, compare with data Has been done extensively for this problem What’s new? Simplicity and robustness

41. y x Control Autocatalytic reaction metabolite consumption

42. Catabolism Precursors Carriers Co-factors Fatty acids Sugars Nucleotides Amino Acids Core metabolism

43. Catabolism Precursors Carriers

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

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

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

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

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

49. TCA Gly G1P G6P F6P F1-6BP PEPPyr Gly3p 13BPG 3PG 2PG ATP NADH Oxa Cit ACA If we drew the feedback loops the diagram would be unreadable.

50. Stoichiometry or mass and energy balance Nutrients Products Interna l Biology is not a graph.

51. Stoichiometry plus regulation Matrix of integers “Simple,” can be known exactly Amenable to high throughput assays and manipulation Bowtie architecture  Vector of (complex?) functions  Difficult to determine and manipulate  Effected by stochastics and spatial/mechanical structure Hourglass architecture Can be modeled by optimal controller (?!?)

52. TCA Gly G1P G6P F6P F1-6BP PEPPyr Gly3p 13BPG 3PG 2PG ATP NADH Oxa Cit ACA Stoichiometry matrix S

53. Regulation of enzyme levels by transcription/translation/degradation TCA Gly G1P G6P F6P F1-6BP PEPPyr Gly3p 13BPG 3PG 2PG Oxa Cit ACA

54. TCA Gly G1P G6P F6P F1-6BP PEPPyr Gly3p 13BPG 3PG 2PG ATP NADH Oxa Cit ACA Allosteric regulation of enzymes

55. TCA Gly G1P G6P F6P F1-6BP PEPPyr Gly3p 13BPG 3PG 2PG ATP NADH Oxa Cit ACA Allosteric regulation of enzymes Regulation of enzyme levels

56. TCA Gly G1P G6P F6P F1-6BP PEPPyr Gly3p 13BPG 3PG 2PG ATP NADH Oxa Cit ACA Allosteric regulation of enzymes Regulation of enzyme levels Fast response Slow

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

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

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

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

61. y x Control Autocatalytic

62. y x Control Autocatalytic

63. y x

64. y x

65. time 101520 -0.5 0 0.5 1 x error

66. time 05101520 -0.5 0 0.5 1 V=3 V=10 V=1.1

67. Why? Modeling and simulation Why = propose mechanism, model, simulate, compare with data Scalable to larger systems? Yes Nonlinear? Yes Explore parameter space? Awkward Explore sets of uncertain models? Awkward

68. Why: Analysis Verbal arguments (stories, cartoons, diagrams) Data and statistics (plots, tables) Modeling and simulation (dynamics, numerics) Analysis (theorems, proofs) Why = parameter regimes of instability, global results with nonlinearities

69. Explicit regions of (in)stability Easy to compare with experiments Oscillations caused by nonzero q (autocatalytic) small k (low enzyme) large V (high flux) large h (strong inhibition) Slow response caused by large q (autocatalytic) small V (low flux) small h (wea k inhibition) oscillationsslow

70. 05101520 -0.5 0 0.5 1 oscillations

71. 05101520 -0.5 0 0.5 1 0102030405060 0 0.5 1 1.5 Nonlinear

72. 05101520 -0.5 0 0.5 1

73. 05101520 -0.5 0 0.5 1 Conservation law?

74. Analysis issues Why = parameter regimes of instability, global results with nonlinearities Scalable to larger systems? Less than sim Nonlinear? Yes Explore parameter space? Better than sim Explore sets of uncertain models? Better than sim Prove what models can’t do? Yes Major research frontier

75. Why: Synthesis Are there intrinsic tradeoffs or is this a “frozen accident”? (The former.) What are the relevant engineering principles? How to separate necessity from accident? Are there hard limits or conservation laws that apply? (Yes) Is biology near these limits? (Apparently) Why does autocatalysis and other efficiency issues aggravate regulation? (Stay tuned)

76. 05101520 -0.5 0 0.5 1 x time Spectrum freq 012345 -2 0 1 2 3

77. 05101520 -0.5 0 0.5 1 x time freq 012345 -2 0 1 2 3 Theorem:

78. x time freq Theorem: 05101520 -0.5 0 0.5 1 012345 -2 0 1 2 3

79. Why: Synthesis There are too many hard limits on achievable performance to show in one hour… Most are aggravated by –large q (more autocatalysis) –small V and k (less enzyme) Thus tradeoffs between control response and efficiency Can summarize with hand-waving argument. Why = it’s an inevitable consequence of engineering tradoffs.

80. y x

81. Why: Synthesis (to do) There are hard contraints and tradeoffs Biology is hard up against these limits Yet there remains “design freedom” Why these particular “choices”? What has evolution optimized? Robustness (and evolvability)?

82. 05101520 0.8 0.85 0.9 0.95 1 1.05 Time (minutes) [ATP] h = 3 h = 0 0246810 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Frequency Log(Sn/S0) h = 3 h = 0 Spectrum Time response Robust Yet fragile

83. 0246810 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Frequency Log(Sn/S0) h = 3 h = 0 Robust Yet fragile

84. 0246810 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Frequency Log(Sn/S0) h = 0 Robust Yet fragile

85. 0246810 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Frequency Log(Sn/S0) h = 3 h = 2 h = 1 h = 0 Tighter steady-state regulation Transients, Oscillations Theorem

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

87.  benefitscosts benefits = attenuation of disturbance goal: make this as negative as possible cost = amplification goal: make this small Constraint:

88. - e=d-u Control u Plant d Bode  What helps or hurts this tradeoff? Helps: advanced warning, remote sensing Hurts: instability, remote control

89. Control demo Note: assumes continuous time A classic illustration of instability and control, the simple inverted pendulum experiment, illustrates the essential point. Here the pendulum is the plant, and the human is the controller. The experiment can be done with sticks of different lengths or with an extendable pointer, holding the proximal tip between thumb and forefinger so that it is free to rotate but not otherwise slip. Unstable plants are intrinsically more difficult to control than stable ones, and are generally avoided unless the instability confers some great functional advantage, which it often does.

90. With the controlling hand fixed, this system has two equilibria, down and up, which are stable and unstable, respectively. By watching the distal tip and controlling hand motion, the up case can be stabilized if the stick is long enough. For an external disturbance, imagine that someone is throwing objects at the stick and you are to move so that the stick remains roughly vertical and avoids the thrown object. Alternatively, imagine that the distal tip is to track some externally driven motion. You will soon find that it is much easier to control the distal tip down than up, even though the components in both cases are the same. Because the up configuration is unstable, certain hand motions are not allowed because they produce large, unstable tip movements. This presents an obstacle in the space of dynamic hand movements that must be avoided, making control more difficult.

91. If you make the stick shorter, it gets more unstable in the up case, evident in the short time it takes the uncontrolled stick to fall over. Shorter pendulums get harder and ultimately impossible to control in the up case, while length has little such effect on the down case. Also, the up stick cannot be stabilized for any length if only the proximal tip is watched, so the specific sensor location is crucial as well. This exercise is a classical demonstration of the principle that the more unstable a system the harder it is to control robustly, and control theory has formally quantified this effect in several ways.

93. - e=d-u Control u Plant d  Freudenberg and Looze, 1984

94. - e=d-u Control u Plant d Bode  benefitscosts stabilize

95. - e=d-u Control u Plant d Bode  benefitscosts stabilize Negative is good

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

97. Variety of producers Electric power network Variety of consumers Good designs transform/manipulate energy Subject to hard limits

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

99. Good designs transform/manipulate robustness Subject to hard limits Unifies theorems of Shannon and Bode (1940s) Claim: This is the most crucial (known) limit against which network complexity must cope Disturbance - e=d-u Control Sensor Channel Encode Plant Remote Sensor d Control Channel benefits feedback stabilize remote sensing remote control costs Robust Fragile

100. - e=d-u Control u Plant d Bode  benefitscosts stabilize

101. - e=d-u Control u Plant d Bode  benefitscosts stabilize Negative is good

102.  benefitscosts Robust Yet fragile Bode’s integral formula

103.  benefitscosts Disturbance - e=d-u Control u Plant d Cost of control Cost of stabilization

104. - e=d-u Control Plant Control Channel Cost of remote control benefitscosts

105. Disturbance - e=d-u Control Plant d Control Channel benefits feedback stabilize remote control costs

106. Disturbance - e=d-u Control Sensor Channel Encode Plant Remote Sensor d Control Channel benefits feedback stabilize remote sensing remote control costs

107. Benefit of remote sensing benefitscosts Disturbance - e=d-u Control Sensor Channel Encode Plant Remote Sensor d Control Channel

108. Disturbance - e=d-u Control Sensor Channel Encode Plant Remote Sensor d Control Channel benefits feedback stabilize remote sensing remote control costs

109. Disturbance - e=d-u Control Sensor Channel Encode Plant Remote Sensor d Control Channel Bode/Shannon is likely a better p-to-p comms theory to serve as a foundation for networks than either Bode or Shannon alone.

110. Variety of producers Electric power network Variety of consumers Good designs transform/manipulate energy Subject to hard limits

111. Good designs transform/manipulate robustness Subject to hard limits Unifies theorems of Shannon and Bode (1940s) Claim: This is the most crucial (known) limit against which network complexity must cope Disturbance - e=d-u Control Sensor Channel Encode Plant Remote Sensor d Control Channel benefits feedback stabilize remote sensing remote control costs Robust Fragile

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

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

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

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

116. Robust designs transform/manipulate robustness Subject (and close) to hard limits Fragile designs are far away from hard limits and waste robustness. Disturbance - e=d-u Control Sensor Channel Encode Plant Remote Sensor d Control Channel Robust Fragile Control Channel

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

118. Questions? End of part 1