1. Local Error/flow control Relay/MUX Global E/F control Relay/MUX Physical Application E/F control Relay/MUX Complex Network Architecture Flow Reactions Protein level Flow Reactions RNA level Flow Reactions DNA level John Doyle John G Braun Professor Control and Dynamical Systems BioEngineering, Electrical Engineering Caltech

2. Theory Data Analysis Numerical Experiments Lab Experiments Field Exercises Real-World Operations First principles Rigorous math Algorithms Proofs Correct statistics Only as good as underlying data Simulation Synthetic, clean data Stylized Controlled Clean, real-world data Semi- Controlled Messy, real-world data Unpredictable After action reports in lieu of data Doyle Architecture of complex networks

3. Robust yet fragile Constraints that deconstrain Essential ideas: Architecture Question Answer

4. The Conversation “APPLICATIONLAYER” SPECIALIZED - Collaboration - Sit Awareness - Command/Control - Integration/Fusion SPECIALIZED - Collaboration - Sit Awareness - Command/Control - Integration/Fusion “NETWORKLAYER” “PHYSICALLAYER” VIDEO/IMAGERY - VTC - GIS - Layered Maps VIDEO/IMAGERY - VTC - GIS - Layered Maps VOICE - Push-to-talk - Cellular - VoIP - Sat Phone - Land Line VOICE - Push-to-talk - Cellular - VoIP - Sat Phone - Land Line TEXT - email - chat - SMS TEXT - email - chat - SMS WIRED - DSL - Cable WIRED - DSL - Cable WIRELESS LOCAL - WiFi - PAN - MAN WIRELESS LOCAL - WiFi - PAN - MAN WIRELESS LONG HAUL - WiMAX - Microwave - HF over IP WIRELESS LONG HAUL - WiMAX - Microwave - HF over IP REACHBACK - Satellite Broadband - VSAT - BGAN REACHBACK - Satellite Broadband - VSAT - BGAN POWER - Fossil Fuel - Renewable POWER - Fossil Fuel - Renewable HUMAN NEEDS - Shelter - Water - Fuel - Food HUMAN NEEDS - Shelter - Water - Fuel - Food PHYSICAL SECURITY - Force Protection - Access Authorization PHYSICAL SECURITY - Force Protection - Access Authorization OPERATIONS CENTER - NetSec - Command/Control - Leadership OPERATIONS CENTER - NetSec - Command/Control - Leadership HUMAN / COGNITIVE LAYER Social/Cultural Organizational Political Economic A Layered View of HFN Architecture Layering? Robust yet fragile? Constraints that deconstrain?

5. Infrastructure networks? Water Waste Food Power Transportation Healthcare Finance All examples of “bad” architectures: Unsustainable Hard to fix Where do we look for “good” examples?

6. Robust yet fragile Constraints that deconstrain Essential ideas: Architecture Question Answer Simplest case studies InternetBacteria

7. Simplest case studies Successful architectures Robust, evolvable Universal, foundational Accessible, familiar Unresolved challenges New theoretical frameworks Boringly retro? InternetBacteria

8. Universal, foundational Techno- sphere InternetBacteria Bio- sphere

9. Universal, foundational Techno- sphere Internet Bio- sphere Bacteria Spam Viruses

10. Two lines of research: 1.Patch the existing Internet architecture so it handles its new roles Techno- sphere Internet Real time Control over (not just of) networks Action in the physical world Human collaborators and adversaries Net-centric everything

11. Techno- sphere Internet Real time Control over (not just of) networks Action in the physical world Human collaborators and adversaries Net-centric everything Two lines of research: 1.Patch the existing Internet architecture 2.Fundamentally rethink network architecture

12. Two lines of research: 1.Patch the existing Internet architecture 2.Fundamentally rethink network architecture Techno- sphere InternetBacteria Bio- sphere Case studies

13. Robust yet fragile* Essential ideas: Architecture Question * Carlson

14. 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

15. Assume different architectures a priori. No networks New unifications are encouraging, but not yet accessible Hard limits. Hard constraints: Thermo (Carnot) Info (Shannon) Control (Bode) Compute (Turing)

16. Physical Thermodynamics Communications Control Computation Cyber Thermodynamics Communications Control Computation InternetBacteria Case studies

17. [a system] can have [a property] robust for [a set of perturbations] Robust Fragile Robust Yet Fragile (RYF) Yet be fragile for [a different property] Or [a different perturbation] Proposition : The RYF tradeoff is a hard limit that cannot be overcome.

18. Robust Fragile Theorems : RYF tradeoffs are hard limits Physical Thermodynamics Communications Control Computation Cyber Thermodynamics Communications Control Computation

19. Robust yet fragile Biology and advanced tech nets show extremes Robust Yet Fragile Simplicity and complexity Unity and diversity Evolvable and frozen What makes this possible and/ or inevitable? Architecture (= constraints) Let’s dig deeper.

20. Constraints that deconstrain* Essential ideas: Architecture Answer * Gerhart and Kirschner

21. Constraints that deconstrain* Essential ideas: Architecture Answer Bad architecture: Things are broken and you can’t fix it Good architecture: Things work and you don’t even notice

22. Components and materials: Energy, moieties Systems requirements: functional, efficient, robust, evolvable Protocols Are there universal architectures?

23. Pathways (Bell) Layers (Net) Ancient network architecture: “Bell-heads versus Net-heads” Operating systems Phone systems

24. HTTP TCP IP my computer Wireless router Optical router Physical web server MAC Switch MAC Pt to Pt Layering?

25. HTTP my computer web server Applications Browsing the web

26. Wireless router Optical router Physical my computer web server The physical pathway

27. Wireless router Optical router Physical HTTP my computer web server Applications

28. Wireless router Optical router Physical HTTP my computer web server Applications Diverse Resources Diverse Applications Share?

29. Resources TCP IP Error/flow control Relaying/Multiplexing (Routing) Applications

30. TCP IP Error/flow control Relaying/Multiplexing (Routing)

31. Error/flow Relay/MUX Resources Applications Control

32. Resources Applications diverse and changing

33. Error/flow Relay/MUX Control Fixed and universal

34. Resources Deconstrained Applications Deconstrained Constraints that deconstrain Gerhart and Kirschner

35. my computer Wireless router Physical TCP IP

36. my computer Wireless router Physical MAC Switch TCP IP

37. my computer Wireless router Physical MAC Error/flow control Relaying/Multiplexing Switch

38. Resources MAC Error/flow control Relaying/Multiplexing Switch Applications Wireless router Local

39. my computer Wireless router Physical MAC Switch TCP IP Error/flow control Relaying/Multiplexing Error/flow control Relaying/Multiplexing Local Global Differ in Details Scope

40. Wireless router Optical router Physical web server TCP IP

41. Wireless router Optical router Physical web server MAC Pt to Pt TCP IP

42. Wireless router Optical router Physical web server MAC Pt to Pt Error/flow control Relay/MUX Local TCP IP Error/flow control Relay/MUX Global

43. HTTP TCP IP my computer Wireless router Optical router Physical web server MAC Switch MAC Pt to Pt

44. Local Global Physical Application Recursive control structure Local Scope

45. Error/flow control Relay/MUX Physical Application Recursive control structure

46. Local Error/flow control Relay/MUX Global E/F control Relay/MUX Physical Application E/F control Relay/MUX Recursive control structure Recursion

47. Architecture is not graph topology. Architecture facilitates arbitrary graphs.

48. Resources Deconstrained Applications Deconstrained Constraints that deconstrain Generalizations Optimization Optimal control Robust control Game theory Network coding

49. Each layer is abstracted as an optimization problem Operation of a layer is a distributed solution Results of one problem (layer) are parameters of others Operate at different timescales Layering as optimization decomposition application transport network link physical Application: utility IP: routing Link: scheduling Phy: power

50. r Each layer is abstracted as an optimization problem r Operation of a layer is a distributed solution r Results of one problem (layer) are parameters of others r Operate at different timescales Minimize response time, … Maximize utility Minimize path cost Maximize throughput, … Minimize SINR, maximize capacities, … Layering and optimization* IP TCP/AQM Physical Application Link/MAC *Review from Lijun Chen and Javad Lavaei

51. Protocol decomposition: TCP/AQM TCP/AQM as distributed primal-dual algorithm over the network to maximize aggregate utility (Kelly ’98, Low ’99, ’03) router TCPAQM my PC source algorithm (TCP) iterates on rates link algorithm (AQM) iterates on prices Primal: Dual horizontal decomposition

52. Generalized utility maximization r Objective function: user application needs and network cost r Constraints: restrictions on resource allocation (could be physical or economic) r Variables: Under the control of this design r Constants: Beyond the control of this design Application utility IP: routing Link: scheduling Phy: powerNetwork cost

53. Layering as optimization decomposition r Networkgeneralized NUM r Layerssub-problems r Interfacefunctions of primal/dual variables r Layeringdecomposition methods Vertical decomposition: into functional modules of different layers Horizontal decomposition: into distributed computation and control IP TCP/AQM Physical Application Link/MAC

54. Case study I: Cross-layer congestion/routing/scheduling design Rate controlScheduling Routing Rate constraint Schedulability constraint

55. Cross-layer implementation  Rate control:  Routing: solved with rate control or scheduling  Scheduling: Network Transport Physical Application Link/MAC A Wi-Fi implementation by Warrier, Le and Rhee shows significantly better performance than the current system. Rate controlScheduling Routing

56. Case study II: Integrating network coding r Optimization based model for rate control: back- pressure based scheme (1,1,1) S d2d2 d1d1 (1,0,1) (1,1,0) (1,0,1) (1,1,0) coding subgraph information flow physical flow Constraint from NC

57. Case study II: Integrating network coding r Optimization based model for rate control: back- pressure based scheme Rate control Session scheduling Congestion price update Backpressure in congestion

58. S1S1 2 d2d2 b1 b1+b2 S2S2 2 d1d1 b2 b1+b2 b1 b2 a new optimization approach to inter-session network coding three sessions: (s 1 ;d 1 ), (s 2 ;d 2 ), (s 1,s 2 ;d 1,d 2 ) 1 2 A B 3 A B B A+B 1 2 A 3 forwarding network coding physical network coding correlated data gathering in senor networks LZ coder input data coded data coding matrix 0.9 0.5 0.2 compression/link aware opportunistic routing distributed source coding (LZ+NC) throughput-optimal scheduling dual scheduling algorithm wireless scheduling s(t)=arg max{p s (t)c s (t)} BSMS Other case studies

59. Dual dynamics: TCP/AQM router TCPAQM my PC source algorithm (TCP) iterates on rates link algorithm (AQM) iterates on prices Primal: Dual horizontal decomposition

60. Dual dynamics Vector notation Controller is fully decentralized Globally stable to optimal equilibrium Generalizations to delays, other controllers

61. What else is this good for? Controller is fully decentralized Globally stable to optimal equilibrium Generalizations to delays, other controllers Views TCP as solving an optimization problem Clarifies tradeoff at equilibrium Generalizes to other strategies, other layers Framework for cross layering

62. But are the dynamics optimal? Controller is fully decentralized Globally stable to optimal equilibrium Generalizations to delays, other controllers Optimal controller? Dynamic tradeoffs? Routing, other layers? Framework for cross layering?

63. State weight Control weight dynamics Inverse optimality toy example What is this controller optimal for? dynamics controller Optimal control

64. State weight Control weight dynamics Inverse optimality review Optimal control What is this controller optimal for? Integral quadratic penalty Deviation from equilibrium Balance state versus control penalty Well-known and “ancient” literature

65. State weight Control weight dynamics Simple change Optimal control

66. What is this controller optimal for? IQ penalty on deviation from equilibrium Balance state versus control penalty

67. Simple change Optimal control

68. State weight Control weight dynamics What is this controller optimal for? IQ penalty on deviation from equilibrium Balance state versus control penalty

69. Optimal control Network

70. Vector notation

71. State weight Control weight dynamics What is this controller optimal for? IQ penalty on deviation from equilibrium Balance state versus control penalty Optimal controller is decentralized

72. What else is this result good for? Elegant proofs of stability Clarifies the tradeoff in dynamics Insights about joint congestion control and routing Can derive more general control laws

73. Finite horizon version Terminal cost is lagrangian

74. 74 An additional constraint: energy aware design r Energy has become a key issue in systems design r Tradeoff between energy usage and traditional performance metrics such as throughput and delay r Challenges:  How to leverage existing energy aware technologies such as speed scaling  What are fundamental limits on various tradeoffs  The impact of energy aware design on the system architecture r Our current focus is on wireless networks

75. 75 Case study: wireless downlink scheduling “natural” speed scaling weighted sum of response time and energy  Developed an online algorithm with a competitive ratio of  Extending to other scenarios such as time-varying channels and finite energy budget, etc. 1 N B

76. 76 Generalization to game theory r Developed to study strategic interactions r Provides a series of equilibrium solution concepts r Considers informational constraints explicitly  Equilibria arise as a result of adaptation and learning, subject to informational constraint r Provides a basis for designing systems to achieve the given desired goals (e.g., mechanism design) Player i payoff function Player i strategy Player i strategy space

77. Game theory: Engineering perspective r Network agents are willing to cooperate, but only have limited information about the network state  E.g., may not have access to the information/signaling required by an optimization-based design  The best is to optimize some local or private objective and adjust its action based on limited information about the network state r Non-cooperative game can be used to model such a situation  Let network agents behave 'selfishly' according to the game that is designed to guide individual agents to seek an equilibrium achieving the systemwide objective 77

78. 78 Game theory based decomposition system-wide performance objective design agent utility and define game look for distributed converging algorithm protocol design: protocols as distributed update algorithms to achieve equilibira must respect informational constraints

79. Eco vs. Eng r Economic (traditional perspective): incentive is a hard constraint that must be taken into account in the design  The agent utility is given  Some possibility results exist Mechanism design Cooperative game r Engineering: the focus is on the implementation in practical systems  Respect informational constraint of the system  The challenge: to what extend we can program network agents to achieve desired systemwide objectives r Tradeoff among computational, informational, and incentive issues 79

80. 80 Case study: Throughput optimal channel access scheme to achieve maximum throughput under weighted fairness constraint utility distributed converging algorithm can be seen as an axiomatic approach

81. Biology versus the Internet Similarities Evolvable architecture Robust yet fragile Layering, modularity Hourglass with bowties Dynamics Feedback Distributed/decentralized Not scale-free, edge-of-chaos, self- organized criticality, etc Differences Metabolism Materials and energy Autocatalytic feedback Feedback complexity Development and regeneration >3B years of evolution >4B

82. Biology versus the Internet Similarities Evolvable architecture Robust yet fragile Layering, modularity Hourglass with bowties Dynamics Feedback Distributed/decentralized Not scale-free, edge-of-chaos, self- organized criticality, etc Differences Metabolism Materials and energy Autocatalytic feedback Feedback complexity Development and regeneration >3B years of evolution

83. Control of the Internet sourcereceiver Packets control packets

84. sourcereceiver signaling gene expression metabolism lineage Biological pathways

85. sourcereceiver control energy materials signaling gene expression metabolism lineage More complex feedback

86. sourcereceiver control energy materials Autocatalytic feedback

87. sourcereceiver control energy materials signaling gene expression metabolism lineage More complex feedback What theory is relevant to these more complex feedback systems?

88. RNA DNA Protein Pathways Metabolic pathways “Central dogma” Network architecture? Layers?

89. Catabolism Precursors Carriers Co-factors Fatty acids Sugars Nucleotides Amino Acids Metabolism energy materials

90. Catabolism Precursors Carriers Co-factors Fatty acids Sugars Nucleotides Amino Acids Core metabolism Inside every cell (  10 30 )

91. Genes Co-factors Fatty acids Sugars Nucleotides Amino Acids Proteins Precursors Autocatalytic feedback Nutrients Core metabolism DNA replication Trans* Catabolism Carriers Environment Huge Variety Huge Variety Bacterial cell

92. Co-factors Fatty acids Sugars Nucleotides Amino Acids Catabolism Precursors Taxis and transport Nutrients Carriers Core metabolism Huge Variety Same 12 in all cells Same 8 in all cells  100  same in all organisms

93. Genes Co-factors Fatty acids Sugars Nucleotides Amino Acids Polymerization and complex assembly Proteins Precursors Autocatalytic feedback Taxis and transport Nutrients Core metabolism DNA replication Trans* Catabolism Carriers  100  10 4 to  ∞ in one organisms Huge Variety 12 8

94. Polymerization and complex assembly Autocatalytic feedback Genes Proteins DNA replication Trans*  10 4 to  ∞ in one organisms Huge Variety Few polymerases Highly conserved

95. Co-factors Fatty acids Sugars Nucleotides Amino Acids Catabolism Polymerization and complex assembly Proteins Precursors Autocatalytic feedback Taxis and transport Nutrients Regulation & control Carriers Core metabolism Genes DNA replication Regulation & control Trans* The bowtie architectu re of the cell. Flow/error Reactions Proteins Flow/error Reactions RNA level Flow/error Reactions DNA level Translation Transcription Carriers The hourglass architectur e of the cell. Need a more coherent cartoon to visualize how these fit together.

96. Catabolism Precursors Carriers

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

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

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

100. Enzymatically catalyzed reactions TCA Gly G1P G6P F6P F1-6BP PEPPyr Gly3p 13BPG 3PG 2PG Oxa Cit ACA

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

102. TCA Pyr Oxa Cit ACA Gly G1P G6P F6P F1-6BP PEP Gly3p 13BPG 3PG 2PG ATP Autocatalytic NADH produced consumed Rest of cell

103. Carriers TCA Pyr Oxa Cit ACA Gly G1P G6P F6P F1-6BP PEP Gly3p 13BPG 3PG 2PG ATP NADH Reactions Proteins Control?

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

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

106. 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.

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

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

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

110. TCA Gly G1P G6P F6P F1-6BP PEPPyr Gly3p 13BPG 3PG 2PG ATP NADH Oxa Cit ACA Level Error/flow Reaction

111. TCA Gly G1P G6P F6P F1-6BP PEPPyr Gly3p 13BPG 3PG 2PG ATP NADH Oxa Cit ACA Flow/error Reactions Protein level

112. TCA Gly G1P G6P F6P F1-6BP PEPPyr Gly3p 13BPG 3PG 2PG ATP NADH Oxa Cit ACA Flow/error Reactions Protein level Fast response Slow Layered architecture

113. Flow/error Reactions Protein level Flow/error Reactions RNA level Flow/error Reactions DNA level

114. Flow/error Reactions Protein level Flow/error Reactions RNA level Flow/error Reactions DNA level Protein RNA DNA Translation Transcription

115. Flow/error Reactions Protein level Flow/error Translation RNA level Flow/erro r Transcription DNA level Recursion

116. Flow/error Reactions Protein level RNA Flow React DNA Flow React DNA Flow React DNA Scope

117. Diverse Reactions DNA Diverse Genomes

118. Diverse Reactions DNA Diverse Genomes Flow/error Protein level Flow/error Reactions RNA level Flow/error Reactions Translation Transcription Conserved core control

119. Flow/error Protein level Flow/error Reactions RNA level Flow/error Reactions Translation Transcription

120. Flow/error Reactions Protein level TCA Pyr Oxa Cit ACA Gly G1P G6P F6P F1-6BP PEP Gly3p 13BPG 3PG 2PG ATP NADH

121. Flow/err or Reactions Protein level TCA Pyr Oxa Cit ACA Gly G1P G6P F6P F1-6BP PEP Gly3p 13BPG 3PG 2PG ATP NADH Layering revisited Flow/err or Reactions ProteinsCarriers More complete picture

122. Flow/error Protein level Catabolism Precursors Carriers Co-factors Fatty acids Sugars Nucleotides Amino Acids RNA DNA

123. Precursors Co-factors Fatty acids Sugars Nucleotides Amino Acids RNA DNA Biosynthesis

124. RNA level/ Transcription rate DNA level Biosynthesis RNA Gene Transc. xRNA RNAp Precursors Co-factors Fatty acids Sugars Nucleotides Amino Acids

125. Catabolism AA RNA RNAp Precursors Nucl. AA Gene Transc. xRNA

126. Catabolism AA tRNA Ribosome RNA RNAp transl. Enzymes Precursors Nucl. AA Gene Transc. xRNA mRNA ncRNA

127. AA Ribosome RNA RNAp transl. Protein Gene Transc. mRNA “Central dogma” RNA Flow Transc. DNA Protein

128. Catabolism AA tRNA Ribosome RNA RNAp Autocatalysis everywhere transl. Proteins xRNA transc. Precursors Nucl. AA All the enzymes are made from (mostly) proteins and (some) RNA.

129. Pyr G6P F6P F1-6BP PEP Gly3p 13BPG 3PG 2PG ATP charging consumption = discharging Rest of cell This is just charging and discharging

130. Catabolism Precursors Carriers Co-factors Fatty acids Sugars Nucleotides Amino Acids The carrier (AMP) must be synthesized

131. Precursors Carriers Nucleotides The carrier (AMP) must be synthesized And then “charged” with energy (P added) Before it can be used as an energy source in the cell Think of AMP as a battery, and ATP as the charged battery. There are two autocatalytic processes requiring the feedback of resources: manufacturing the “battery,” and then repeatedly charging/using the “battery”

132. trans. Protein AA Precursors Nucl. AA Protein level/ Translation rate AMP level Protein level The carrier (AMP) must be synthesized The amino acids must be synthesized The protein must be made

133. Protein Protein level/ Translation rate AMP level Protein level The carrier must be “charged” with energy (P added) in a controlled manner Flow/error We know what’s going on here, but it’s hard to draw the layers neatly. The carrier (AMP) must be both synthesized, and then charged in a controlled way. The protein must be both synthesized and then its form and activity controlled.

134. Flow/error Protein level RNA DNA AMP level Pyr F1-6BP PEP Gly3p 3PG 2PG ATP G6P F6P 13BPG Rest of cell A*P ATP supplies energy to all layers

135. Flow/error Protein level RNA DNA AMP level ATP cell A*P RNA DNA Lots of ways to draw this.

136. AA tRNA RNA Layered transl. Enzymes xRNA transc. Catabolism Precursors Nucl. AA

137. trans. Enzymes AA mRNA ncRNA tRNA Ribosome RNA level/ Transcription rate RNA form/activity RNA Gene Transc. xRNA RNAp S reactions P Enz1 reaction3 Enzyme level/ Translation rate Enzyme form/activity Reaction rate Enz2

138. trans. ncRNA Transc. products reactions reaction3 All products feedback everywhere Proteins Control?

139. Local Error/flow control Relay/MUX Global E/F control Relay/MUX Physical Application E/F control Relay/MUX Recursive control structure Flow Reactions Protein level Flow Reactions RNA level Flow Reactions DNA level

140. Flow Reactions Protein level Flow Reactions RNA level Flow Reactions DNA level Fragility example: Viruses Viruses exploit the universal bowtie/hourglass structure to hijack the cell machinery. Viral genes Viral proteins

141. Flow/err or Reactions Protein level TCA Pyr Oxa Cit ACA Gly G1P G6P F6P F1-6BP PEP Gly3p 13BPG 3PG 2PG ATP NADH Layering revisited Flow/err or Reactions ProteinsCarriers More complete picture ?

142. Flow/err or Reactions ProteinsCarriers Flow/error Reactions RNA level Flow/error Reactions DNA level Translation Transcription “Power supply” This is a “database” of instructions

143. application TCP IP my computer router Physical server MAC Switch MAC Pt to Pt Applications Hardware Operating System Physical Circuit Logical Instructions ? ? ? Flow/erro r Reactions Proteins Flow/erro r Reactions RNA level Flow/erro r Reactions DNA level Translation Transcription Where is the power supply? Where are the designs and processes that produce the chips, PCs, routers, etc? What are the additional layers? Carriers

144. Diverse function Diverse components Universal Control fan-in of diverse inputs fan-out of diverse outputs universal carriers Bowties: flows within layers Robust yet fragile Constraints that deconstrain Essential ideas

145. Diverse function Diverse components fan-in of diverse inputs fan-out of diverse outputs Robust yet fragile Constraints that deconstrain Highly robust Diverse Evolvable Deconstrained

146. Robust yet fragile Constraints that deconstrain Highly fragile Universal Frozen Constrained Universal Control universal carriers

147. Diverse function Diverse components Universal Control fan-in of diverse inputs fan-out of diverse outputs universal carriers Bowties: flows within layers Robust yet fragile Constraints that deconstrain Essential ideas

148. sourcereceiver control energy materials More complex feedback What theory is relevant to these more complex feedback systems? signaling gene expression metabolism lineage

149. [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 Robust yet fragile = fragile robustness

150. [a system] can have [a property] robust for [a set of perturbations] Robust yet fragile = fragile robustness [ property] = robust for [one set of perturbations] fragile for [another property] or [another set of perturbations] [ a property ] [ a perturbation ] Apply recursively

151. [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.

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

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

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

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

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

157. y x Control Autocatalytic Control

158. y x input output= x Control theory cartoon Caution: mixed cartoon Controller +

159. output= x + Entropy rates C Plant Hard limits

160. 05101520 0.8 0.85 0.9 0.95 1 1.05 Time (minutes) [ATP] h >>1 h = 1 Time response 0246810 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Frequency Log(|Sn/S0|) h >>1 h = 1 Spectrum Ideal

161. 05101520 0.8 0.85 0.9 0.95 1 1.05 Time (minutes) [ATP] h >> 1 h = 1 0246810 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Frequency Log(Sn/S0) h >>1 h = 1 Spectrum Time response Robust Yet fragile

162. 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

163. [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 Robust yet fragile = fragile robustness

164. output= x + Entropy rates C Plant Hard limits Note: Nature doesn’t care much about entropy rates.

165. 05101520 0.8 0.85 0.9 0.95 1 1.05 Time (minutes) [ATP] h >> 1 h = 1 0246810 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Frequency Log(Sn/S0) h >>1 h = 1 Spectrum Time response Robust Yet fragile Note: Nature cares more about this tradeoff.

166. Plant output= x + C The plant can make this tradeoff worse.

167. Plant output= x + C

168. Plant output= x + C Small z is bad.

169. Small z is bad (oscillations and crashes) Small z = small k and/or large q Efficiency = small k and/or large q Correctly predicts conditions with “glycolytic oscillations”

170. output= x + Entropy rates C Plant Hard limits

171. Plant output= x + Controller

172. Plant output= x + Controller Channel Sensor+ Channel

173. Plant output= x + Controller Channel Sensor+ Channel Helps Hurts

174. Taxonomy covers standard usages Unified picture Can make the definitions more precise Have “hand crafted” theorems in every major complexity class (but lack a unified theory) SmallLarge Robust Simple Organized Fragile Chaocritical Irreducible

175. Apps Tools/ tech Apps Tools/ tech Apps Tools/ tech Apps Tools/ tech Apps Tools/ tech EE, CS, ME, MS, APh, ChE, Bio, Geo, Eco, … Academic stovepipes

176. Apps Tools/ tech Apps Tools/ tech Apps Tools/ tech Apps Tools/ tech Apps Tools/ tech “Multidisciplinary cross-sterilization” Funding twine Diverse applications

177. Apps Tools/ tech Apps Tools/ tech Apps Tools/ tech Apps Tools/ tech Apps Tools/ tech ????? Layering academia? Diverse resources

178. End What follows are additional details on the glycolysis fragility example.

179. y x Control Autocatalytic Control

180. produced consumed y x

181. y x rate

182. y x More enzyme level rate

183. y x Autocatalytic Control consumed produced

184. y x Autocatalytic Control form/activity rate

185. y x Autocatalytic Control level form/activity rate Layered control

186. y x Autocatalytic Control level form/activity rate Layered control Fast response Slow

187. consumed x

188. y w x stable

189. y x Autocatalytic

190. y x Control

191. y x Autocatalytic Control