Control and Dynamical Systems,

Control and Dynamical Systems,
Polymerization and complex assembly G GDP GTP In Out P Ligand Receptor  RGS Autocatalytic feedback Taxis and transport Complexity and Proteins Core metabolism Sugars Catabolism Amino Acids Nutrients Precursors Nucleotides Trans* Fatty acids Genes Co-factors Carriers Architecture DNA replication John Doyle John G Braun Professor Control and Dynamical Systems, BioEng, and ElecEng Caltech

Core theory challenges
My interests Multiscale Physics Core theory challenges Network Centric, Pervasive, Embedded, Ubiquitous Systems Biology

Emphasis on motivation
Today: Emphasis on motivation Core math challenges Technology Biology

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 Caltech Former Caltech Longterm Visitor Other

Thanks to NSF ARO/ICB AFOSR NIH/NIGMS Boeing DARPA
Lee Center for Advanced Networking (Caltech) Hiroaki Kitano (ERATO) Braun family

Background progress Spectacular progress, both depth and breadth
Biological networks Technological networks Mathematical foundations Remarkably consistent, convergent, coherent Role of protocols, architecture, feedback, and dynamics Yet seemingly persistent errors and confusion both within science between science and public & policy

Terminology is “standard, conventional”
Math: dynamic, (non)random, (non)linear, conjecture, theorem, proof, evidence, etc. Biology: DNA, RNA, protein, allostery, covalent, precursor, carrier, kinase, evolution, etc. Technology: router, transistor, TCP/IP, protocol, hardware, software, verification, robustness, scalability, etc

Terminology is “standard, conventional”
Math Biology Technology Other communities are important but I don’t easily “speak their language” Speak the “native” language

Some ambiguities Some words are widely used but with substantial inconsistencies “Complex, emergent, irreducible,” etc “Design, architecture, evolvability, aesthetic,” etc. I will tend to math and/or tech usage

Background progress: Biological networks
(With molecular biology  details of components) + systems biology Organizational principles are increasingly apparent Beginning to see principles of architecture (as well as components and circuits)

Background progress: Technological networks
Complexity of advanced technology  biology Components extremely different Yet, striking convergence at network level: Architecture as constraints Layering and protocols Feedback control

Background progress: Mathematics
New mathematical frameworks suggests apparent network-level evolutionary convergence within/between biology/technology is not accidental But follows necessarily from universal requirements: efficient, adaptive, evolvable, robust (to both environment and component )

New mathematical frameworks suggests apparent network-level evolutionary convergence within/between biology/technology is not accidental But follows necessarily from universal requirements: efficient, adaptive, evolvable, robust For example (which we won’t talk about much today): New theories of Internet and related networking technologies confirm engineering intuition (Kelly, Low, many others… See IPAM 2002 program) Also lead to test and deployment of new protocols for high performance networking (e.g. FAST TCP)

Blends (from engineering) theories from optimization, control, information, and computational complexity with diverse elements in areas of mathematics (e.g. operator theory and algebraic geometry) not traditionally thought of as applied

Background progress Spectacular progress, both depth and breadth
Biological networks Technological networks Theoretical foundations Remarkably consistent, convergent, coherent Role of protocols, architecture, feedback, and dynamics Yet seemingly persistent errors and confusion both within science between science and public & policy

Persistent errors Errors and confusion both within science and between science and public & policy Evolution, stem cells, global warming,… Creationism, irreducible complexity and “intelligent design” “New sciences of…”, edge-of-chaos, self-organized criticality, scale-free networks, etc etc… Consensus among experts conflicts with “mainstream” (e.g. faith-based) views Mixed progress in “converting” the mainstream

Random Graphs and Dynamic Networks ?

Two interesting subjects with little overlap
Random Graphs Dynamic Networks Math Social networks? Math Biology Technology Ecology Social networks

Today Random Graphs Dynamic Networks Math Social networks? Math
Biology Technology Ecology Social networks

Networked dynamical systems
Single Agent Nonlinear/uncertain hybrid/stochastic etc. Complex networked systems Complexity of dynamics Multi-agent systems Flocking/synchronization consensus Complexity of interconnection

Single Agent Nonlinear/uncertain hybrid/stochastic etc. Complex networked systems Complexity of dynamics Flocking/synchronization consensus Multi-agent systems Complexity of interconnection

Incompatible assumptions (for 50+ years).
Bode Shannon d d e=d-u e=d-u Disturbance - - u Plant u Capacity C Channel Control Decode Encode Incompatible assumptions (for 50+ years). Hard bounds Achievable (assumptions) Solution decomposable (assumptions)

“Emergent” complexity
Simple question Undecidable Simulations and conjectures but no “proofs’ Chaos Fractals Mandelbrot

Networked dynamical systems
Single Agent Nonlinear/uncertain hybrid/stochastic etc. Complex networked systems Complexity of dynamics Multi-agent systems Flocking/synchronization consensus Complexity of interconnection

Nonlinear/uncertain hybrid/stochastic etc. Complex networked systems Complexity of dynamics Single Agent Multi-agent systems Flocking/synchronization consensus Complexity of interconnection

Working systems but no “proofs’

Simulations and conjectures but no “proofs’
Statistical Physics and emergence of collective behavior Simulations and conjectures but no “proofs’

“FAST” TCP/AQM theory Routers Hosts Papachristodoulou, Li
Arbitrarily complex network Topology Number of routers and hosts Nonlinear Delays Routers Short proof Global stability Equilibrium optimizes aggregate user utility Hosts packets Papachristodoulou, Li

Layering as optimization decomposition
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 Application: utility IP: routing Link: scheduling Phy: power application transport network link physical

Examples detailed survey in Proc. of IEEE, 2007
Optimal web layer: Zhu, Yu, Doyle ’01 HTTP/TCP: Chang, Liu ’04 application transport network link physical TCP: Kelly, Maulloo, Tan ’98, …… TCP/IP: Wang et al ’05, …… TCP/MAC: Chen et al ’05, …… TCP/power control: Xiao et al ’01, Chiang ’04, …… Rate control/routing/scheduling: Eryilmax et al ’05, Lin et al ’05, Neely, et al ’05, Stolyar ’05, this paper detailed survey in Proc. of IEEE, 2007

I2LSR, SC2004 Bandwidth Challenge
“FAST” TCP/AQM implementation Harvey Newman’s group, Caltech OC48 OC192 November 8, 2004 Caltech and CERN transferred 2,881 GBytes in one hour (6.86Gbps) between Geneva - US - Geneva (25,280 km) through LHCnet/DataTag, Abilene and CENIC backbones using 18 FAST TCP streams

Spectacular progress Nonlinear/uncertain hybrid/stochastic etc.
Single Agent Nonlinear/uncertain hybrid/stochastic etc. Complexity of dynamics Multi-agent systems Flocking/synchronization consensus Complexity of interconnection

Open questions ? ? Nonlinear/uncertain Complex networked systems
hybrid/stochastic etc. Complex networked systems ? Complexity of dynamics Single Agent ? Flocking/synchronization consensus Multi-agent systems Complexity of interconnection

Unifying concepts Robustness Constraints Ruthless oversimplification

Human complexity Robust Yet Fragile 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)

“Constraints” as unifying concept
“Robust yet fragile” is a hard constraint Architecture: “Constraints that deconstrain” Complexity of systems: due to constraints on robustness/evolvability rather than minimal functionality

Constraints in biology
Accessible Biology Authors Savageau Kirschner and Gerhart Caporale da Silva and Williams Woese Wachtershauser de Duve Networks and systems Physico- Chemical Components Biology as technology

Evolving evolvability?
“Random” Variation Structured Selection ?

Random variation is harmful, yet…
Structured Selection Random, Small, Harmful

Architecture E. coli genome Nutrients Polymerization and complex
assembly Autocatalytic feedback Taxis and transport Proteins Core metabolism Sugars Catabolism Amino Acids Nutrients Precursors Nucleotides Trans* Fatty acids Genes Co-factors Carriers DNA replication Architecture E. coli genome

Structured variation can be good
Selection Variation Structured, Large, Beneficial Architecture

Not random Structured Selection Variation Structured, Large, Beneficial Architecture

Robust architectures facilitate change: Small genotype   large, functional phenotype  (Wolves  Dogs)  regulatory regions Large (but functional) genotype  are facilitated (Antibiotic resistance) Horizontal gene transfer Structured Selection Variation Structured, Large, Beneficial Architecture

Structured Selection Structured Variation “facilitated” “structured” “organized” Architecture

Universal architectures
universal carriers fan-out of diverse outputs fan-in of diverse inputs Universal architectures Diverse function Bowties for flows Hourglasses for control Robust and evolvable Architecture = protocols = constraints Universal Control Diverse components

Universal architectures
Lego hourglass Diverse function Universal architectures Universal Control Diverse components Bowties for flows Hourglasses for control Robust and evolvable Architecture = protocols = constraints

Lego hourglass Diverse function Diverse components Universal Control
assembly

Standardized mechanisms
Lego hourglass Huge variety Standardized mechanisms Highly conserved control assembly Huge variety

Limited environmental
Lego Huge variety Limited environmental uncertainty needs minimal control Standard assembly Huge variety

Snap Diverse function Diverse components Standard assembly Variety of
systems Variety of bricks Snap

Variety of systems Variety of bricks Snap

Random Not random Variety of systems Variety of bricks Snap

Require additional layers
Lego hourglass Uncertain environments Require additional layers control assembly Huge variety

Real- time control NXT controller Variety of Variety of actuators
sensors Real- time control

Bowties and Hourglasses
universal carriers fan-out of diverse outputs fan-in of diverse inputs Diverse function Bowties and Hourglasses Universal Control Diverse components

Control Lego Bowties Snap Variety of Variety of actuators sensors
systems Variety of bricks Snap

Random Qualitatively unchanged by random rewiring SOC Lego?

Not random Almost certainly destroyed by random rewiring, yet…
Large structured rewirings are functional. The essence of architecture.

Not random Most of the complexity is in digital hardware and software.

Variety control Lego hourglass assembly Variety

Bacterial bowties Carriers Precursors Trans* 2CST Precursors
Transmitter Receiver Variety of Ligands & Receptors responses Carriers Precursors Trans* 2CST Bacterial bowties Sugars Fatty acids Precursors Catabolism Co-factors Amino Acids Nucleotides Genes Carriers Proteins Trans* DNA replication

Carriers Precursors Trans* 2CST
Transmitter Receiver “Modules” are less important than protocols: the “rules” by which modules interact. Precursors Carriers Trans*

Transmitter Receiver Constraints Precursors Carriers Trans*

Constraints That Deconstrain Precursors Catabolism Carriers Genes
Variety of Ligands & Receptors Variety of responses Transmitter Receiver Constraints That Deconstrain (Gerhart and Kirschner) Sugars Fatty acids Precursors Catabolism Co-factors Amino Acids Nucleotides Genes Carriers Proteins Trans* DNA replication

No variety Huge Variety Huge variety Virtually unlimited variability and heterogeneity (within and between organisms) E.g: Time constants, rates, molecular counts and sizes, fluxes, variety of molecules, … Very limited but critical points of homogeneity (within and between organisms)

Nested bowties & advanced technologies:
Everything is made this way: cars, planes, buildings, laptops,…

Electric power Variety of producers Variety of consumers

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

Why? No variety Huge Huge Variety variety
Provides “plug and play modularity” between huge variety of input and output components Facilitates robust regulation and evolvability on every timescale (“constraints that deconstrain”) But has extreme fragilities to parasitism and predation (knots are easily hijacked or consumed)

Bacterial hourglass Regulation of protein action Regulation of
Transmitter Receiver Variety of Ligands & Receptors responses Regulation of protein action Regulation of protein levels Core metabolism Sugars Fatty acids Catabolism Precursors Co-factors Amino Acids Nucleotides Genes Carriers Proteins Trans* DNA replication

Huge variety of environments, metabolisms, functions
Regulation of protein action Regulatory hourglass Regulation of protein levels Huge variety of components

Environments, metabolisms, functions
Huge variety Environments, metabolisms, functions Standardized mechanisms Highly conserved Regulation of protein action Regulation of protein levels Huge variety Components (genes) Variety is within a specie (across time and space) and of course between species.

The Internet hourglass
Applications Web FTP Mail News Video Audio ping napster Ethernet 802.11 Power lines ATM Optical Satellite Bluetooth Link technologies

Applications Web FTP Mail News Video Audio ping napster TCP IP Ethernet 802.11 Power lines ATM Optical Satellite Bluetooth Link technologies

Applications IP under everything Web FTP Mail News Video Audio ping napster TCP IP IP on everything Ethernet 802.11 Power lines ATM Optical Satellite Bluetooth Link technologies

IP Applications TCP/ AQM Link Top of “waist” provides
robustness to variety and uncertainty above TCP/ AQM Bottom of “waist” provides robustness to variety and uncertainty below IP Link

Main bowtie in Internet S
Variety of files Variety of files packets All sender files transported as packets All files are reconstructed from packets by receiver All advanced technologies have protocols specifying “knot” of carriers, building blocks, interfaces, etc This architecture facilitates control, enabling robustness and evolvability It also creates fragilities to hijacking and cascading failure

Many bowties in Internet
Variety of files Variety of files packets Applications TCP IP Link

Random Not random

Not random Random “Sets of measure zero.” But there many such sets…
What characterizes these sets? Constraints and robustness Not random Random

What is “complexity” and why?
Constraints and robustness Questions?

Constraints Systems requirements: functional, efficient,
robust, evolvable Constraints Hard constraints: Thermo (Carnot) Info (Shannon) Control (Bode) Compute (Turing) Architecture: Constraints That deconstrain Components and materials: Energy, moieties

System-level Robustness
Robustness by other names (smells as sweet?): Basic robustness = to variations in environment (and components) Evolvability = robustness of lineages on long time scales to (possibly large) variations Efficiency = robustness to resource scarcity Scalability = robustness to changes in system size and complexity Etc etc

Gene networks? essential: 230 nonessential: 2373 unknown: 1804
total:

Regulation & control E. coli genome Nutrients Polymerization
and complex assembly Autocatalytic feedback Taxis and transport Proteins Core metabolism Sugars Catabolism Amino Acids Nutrients Precursors Nucleotides Trans* Fatty acids Genes Co-factors Carriers DNA replication Regulation & control E. coli genome

Steering Brakes Anti-skid Wipers Mirrors Cruise control GPS Radio Traction control Shifting Headlights Electronic ignition Temperature control Seats Electronic fuel injection Seatbelts Fenders Bumpers Airbags Suspension (control)

Knockouts often lethal
Steering Brakes Anti-skid Wipers Mirrors Knockouts often lose robustness, not minimal functionality Cruise control GPS Radio Traction control Shifting Headlights Electronic ignition Temperature control Seats Electronic fuel injection Seatbelts Fenders Bumpers Airbags Suspension (control)

Regulation & control Knockouts often lethal
Polymerization and complex assembly Autocatalytic feedback Taxis and transport Proteins Core metabolism Sugars Catabolism Amino Acids Nutrients Precursors Nucleotides Knockouts often lethal Trans* Fatty acids Genes Co-factors Carriers DNA replication Knockouts often lose robustness, not minimal functionality Regulation & control

System-level Robustness
90% Complexity  Robustness 10% Complexity  Function Don’t take exact % too seriously.

Constraints Constraints (environment) = Robustness of system
Hard limits on systems Architecture: Constraints= Protocols Constraints (components) = Physico-chemical

Constraints Constraints = Robustness of system Constraints=
Hard limits on systems These are all constraints with no choices (and that do not deconstrain) Constraints= Physico-chemical

Robust power generation
Environment: Robust power generation Architecture: Carnot cycle (Combined cycle) System Hard limits: Entropy Components: Energy conserved

Environment: Robust power generation Architecture: Carnot cycle (Combined cycle) System Hard limits: Entropy Chance/choice Or Necessity? Components: Energy conserved

Environment: Robust power generation Chance/choice Or Necessity? Similar architectures System Hard limits: Entropy Similar Efficiencies: Overall (~30%-60%) Mechanical  Electrical (~100%) Components: Energy conserved

Necessity (Environment):
Robustness of system Chance/ choice Or Necessity? Necessity (Theory): Hard limits on Robustness Choice? Robust Architecture Complexity? Robustness Necessity: Physico-chemical

Hard limits: Thermo (Carnot) Info (Shannon) Control (Bode) Compute (Turing) Assume architectures a priori Fragmented and incompatible Initial unifications encouraging

How do these two sources of constraints relate? Constraints =
Robustness of system These constraints come from the environment and are on the system as a whole Functionality Robustness Evolvability Hard limits: Thermo (Carnot) Info (Shannon) Control (Bode) Comp (Turing) These are “universal” theoretical constraints that apply to all systems and components no matter the environment or component constraints, however: Assume architectures a priori that are Fragmented and incompatible

De Duve, Wachtershauser
PMF DNA Proteins Lipids RNA ATP NTP and (pyro-)phospho-transfer Choice of ions? (Ca2+, Na+, K+, Mg2+) Choice of metals? (Fe, etc.) Thioesters Group transfer Electron transfer Catalysis Carbon, Nitrogen, Hydrogen, … Energy, matter, “small moieties” Chance/ Choice? Necessity Necessity: Physico-chemical

De Duve Selective Necessity (Bottlenecks) Sufficiently Ergodic
Environment De Duve Deterministic Necessity Sufficiently Exploratory Systems

Necessity Sufficiently Ergodic Environment Sufficiently Exploratory
PMF DNA Proteins Lipids RNA ATP NTP and (pyro-)phospho-transfer Choice of ions? (Ca2+, Na+, K+, Mg2+) Choice of metals? (Fe, etc.) Thioesters Group transfer Electron transfer Catalysis Carbon, Nitrogen, Hydrogen, … Energy, matter, “small moieties” Necessity Sufficiently Exploratory Systems

Selective Bottlenecks (Necessity) Choice? Architecture: Constraints that Deconstrain Most crucial “choices” are here Growing list of examples Limited coherent theory Constraints = protocols Deterministic Necessity

Necessity (Environment): Robustness/evolvability
Chance/ choice Or Necessity? Catabolism Genes Co-factors Fatty acids Sugars Nucleotides Amino Acids Proteins Precursors DNA replication Trans* Carriers Necessity (Theory): Hard limits on Robustness Choice? Robust Architecture Diverse function components Universal Control Necessity: Physico-chemical

Constraints Constraints = Robustness of system Architecture:
Hard limits on systems Architecture: Constraints= Protocols Constraints= Physico-chemical

Fragile Yet Robust Robustness = Invariance of [a system] and
[a property] to [a set of perturbations] Robust Yet Fragile

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

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

Diseases of complexity
Fragile different perturbations Robust

Fragile Parasites Complex development different perturbations Robust

Fragile Parasites Complex development Immune response different perturbations Robust

Fragile Autoimmune disease Parasites Complex development Immune response different perturbations Robust

Fragile Autoimmune disease Parasites Complex development Immune response Regeneration/renewal different perturbations Robust

Fragile Cancer Autoimmune disease Parasites Complex development Immune response Regeneration/renewal different perturbations Robust

Fragile Cancer Autoimmune disease Parasites Complex development Immune response Regeneration/renewal Complex society different perturbations Robust

Fragile Epidemics Cancer Autoimmune disease Parasites Complex development Immune response Regeneration/renewal Complex society different perturbations Robust

Fragile Epidemics Robust Cancer Autoimmune disease Parasites Complex development Yet fragile Immune response Regeneration/renewal Complex society different perturbations Robust

Complexity? Fragile Robust Yet fragile different perturbations Robust
But there are unavoidable tradeoffs. Greater complexity can provide improved robustness. Yet fragile different perturbations Robust

Fragile Fragile Complex Fragile Complex Robust Complex
Universal challenge: Understand/ manage/ overcome this spiral Complex Fragile Robust Complex Fragile Robust Complex

Hard limits? Fragile Robust Yet fragile Robust
 new conservation laws of robustness/fragility. Fragile Robust If not, disasters loom. If exploited, net benefits are possible. Yet fragile Uncertainty Robust

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

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 Information theory Control theory CS cmplxt th. SOS/SDP

- http://www.glue.umd.edu/~nmartins/ e=d-u d Disturbance Remote Plant
Control Sensor Channel Encode Plant Remote d 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)

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

Fragile - Robust costs Good designs transform/manipulate robustness
Disturbance - e=d-u d Control Channel Remote Sensor Plant Sensor Channel Control Encode remote control benefits stabilize remote sensing feedback costs 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

Bode e=d-u d - u Plant  Control

Bode e=d-u d - u Plant  Control benefits costs

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

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

Bode’s integral formula
Yet fragile  Robust benefits costs

- Cost of stabilization Cost of control benefits costs Plant  e=d-u d
Disturbance - u Plant Cost of stabilization Control Cost of control  benefits costs

- Cost of remote control benefits costs e=d-u Plant Control Channel

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

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

- benefits costs e=d-u d Benefit of remote sensing Disturbance Remote
Sensor Plant Control Channel Sensor Channel Control Encode Benefit of remote sensing benefits costs

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

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

Good designs transform/manipulate energy Subject to hard limits

Fragile - Robust costs Good designs transform/manipulate robustness
Disturbance - e=d-u d Control Channel Remote Sensor Plant Sensor Channel Control Encode remote control benefits stabilize remote sensing feedback costs 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

[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]

[a property] robust for [a set of perturbations]
[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?

Emergent Emergent Fragile Robust Small Large Robust Simple Fragile
Organized Fragile 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.

Good designs transform/manipulate energy Subject (and close) to hard limits

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

Example: Hurricane Katrina?
Robust? Predictable? Rhetoric Coast Guard response Fragile? Unpredictable? Everything else

Robust/ fragile is unifying concept 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

“Architecture” is a central challenge
“The bacterial cell and the Internet have architectures that are robust and evolvable (yet fragile?)” What does “architecture” mean here? What does it mean for an “architecture” to be robust and evolvable? Robust yet fragile?

“Architecture” in organized complexity
Architecture involves or facilitates System-level function (beyond components) Organization and structure Protocols and modules Design or evolution Robustness, evolvability, scalability Various -ilities (many of them) Perhaps aesthetics but is more than the sum of these

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 Assume different architectures a priori.

“Architecture” in organized complexity
Design of architectures is replacing design of systems Architecture is central in biology and technology, but has been largely overlooked in other areas of “complexity” “Emergent” complexity can have “order,” “structure” and (ill-defined notions like) “self-organization” … … but “architecture” plays little role… Architecture also has little to do with aspects of networks that can be modeled using graph theory (or power laws)

“Architecture” examples
There are universal architectures that are ubiquitous in complex technological and biological networks Examples include Bowties for flows of materials, energy, redox, information, etc (stoichiometry) Hourglasses for layering and distribution of regulation and control (fluxes, kinetics, dynamics) Nascent theory confirms (reverse engineers) success stories but has (so far) limited forward engineering applications (e.g. FAST TCP/AQM)

Bowties with thin knot of large fan-out large fan-in of diverse
outputs large fan-in of diverse inputs universal carriers Bowties

Examples of universal carriers Packets in the Internet 60 Hz AC in the power grid Lego snap Money in markets and economics Lots of biology examples (coming up)

Applications IP under everything Web FTP Mail News Video Audio ping napster TCP IP IP on everything Ethernet 802.11 Power lines ATM Optical Satellite Bluetooth Link technologies

IP Applications TCP/ AQM Link Top of “waist” provides
robustness to variety and uncertainty above TCP/ AQM Bottom of “waist” provides robustness to variety and uncertainty below IP Link

Hourglasses Diverse function Diverse components
Hourglasses organize layered control architectures Examples include: Internet: TCP/IP Cell: Transcription/translation/degradation plus allosteric regulation Lego: Physical assembly plus Mindstorm NXT controller Diverse function Universal Control Diverse components

Bowties and Hourglasses
universal carriers fan-out of diverse outputs fan-in of diverse inputs Bowties and Hourglasses Diverse function Universal Control More and clearer examples of bowties than hourglasses Other hourglasses exist but are harder to explain Diverse components

Four big bowties in bacterial S
Metabolism, biosynthesis, assembly Carriers: Charging carriers in central metabolism Precursors: Biosynthesis of precursors and building blocks Trans*: DNA replication, transcription, and translation Signal transduction 2CST: Two-component signal transduction (Named after their central “knot”)

Carriers Precursors Trans* 2CST Precursors Catabolism Carriers Genes
Transmitter Receiver Variety of Ligands & Receptors responses Carriers Precursors Trans* 2CST Sugars Fatty acids Precursors Catabolism Co-factors Amino Acids Nucleotides Genes Carriers Proteins Trans* DNA replication

Carriers Precursors Trans* 2CST
Transmitter Receiver “Modules” are less important than protocols: the “rules” by which modules interact. Precursors Carriers Trans*

These bowties involve the flow of material and energy.
Carriers Precursors Trans* These bowties involve the flow of material and energy. Sugars Fatty acids Precursors Catabolism Co-factors Amino Acids Nucleotides Genes Carriers Proteins Trans* DNA replication

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 (?!?)

One big bowtie in Internet S
Variety of files Variety of files packets All sender files transported as packets All files are reconstructed from packets by receiver All advanced technologies have protocols specifying “knot” of carriers, building blocks, interfaces, etc This architecture facilitates control, enabling robustness and evolvability It also creates fragilities to hijacking and cascading failure

Why bowties? Metabolism, biosynthesis, assembly Signal transduction
Carriers: Charging carriers in central metabolism Precursors: Biosynthesis of precursors and building blocks Trans*: DNA replication, transcription, and translation Signal transduction 2CST: Two-component signal transduction

Metabolism, biosynthesis, assembly
Taxis and transport Autocatalytic feedback Polymerization and complex assembly Core metabolism Sugars Fatty acids Precursors Nutrients Catabolism Co-factors Amino Acids Genes Proteins Nucleotides Carriers Trans* DNA replication Regulation & control

Metabolism, biosynthesis, assembly
Taxis and transport Autocatalytic feedback Polymerization and complex assembly Core metabolism Sugars Fatty acids Precursors Nutrients Catabolism Co-factors Amino Acids Genes Proteins Nucleotides Carriers Trans* DNA replication The architecture of stoichiometry.

Nutrients Autocatalytic feedback Core metabolism Precursors Catabolism
Sugars Fatty acids Precursors Nutrients Catabolism Co-factors Amino Acids Genes Proteins Nucleotides Carriers Trans* DNA replication

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

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

The architecture of the cell.
Polymerization and complex assembly Autocatalytic feedback Taxis and transport Proteins Core metabolism Sugars Catabolism Amino Acids Nutrients Precursors Nucleotides Regulation & control Trans* Fatty acids Genes Co-factors Carriers DNA replication Regulation & control The architecture of the cell.

Nested bowties Core metabolism Catabolism Precursors Carriers Sugars
Amino Acids Precursors Nucleotides Fatty acids Co-factors Carriers Nested bowties

Catabolism Precursors Carriers Sugars Amino Acids Nucleotides
Fatty acids Co-factors

Catabolism Precursors Carriers

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

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

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

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

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

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

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

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

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

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

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

Nutrients Taxis and transport 12 Polymerization and complex assembly 8
Autocatalytic feedback Polymerization and complex assembly Core metabolism Sugars Fatty acids Precursors Nutrients Catabolism Co-factors Amino Acids Genes Proteins Nucleotides Carriers 8 Trans* 100 Huge Variety DNA replication 104 to  ∞ in one organisms

in one organisms Huge Variety
Autocatalytic feedback Few polymerases Highly conserved Polymerization and complex assembly Genes Proteins Trans* DNA replication 104 to  ∞ in one organisms Huge Variety

Why bowties? Metabolism, biosynthesis, assembly Signal transduction
Carriers: Charging carriers in central metabolism Precursors: Biosynthesis of precursors and building blocks Trans*: DNA replication, transcription, and translation Signal transduction 2CST: Two-component signal transduction

Signal transduction 50 such “two component” systems in E. Coli
All use the same protocol - Histidine autokinase transmitter - Aspartyl phospho-acceptor receiver Huge variety of receptors and responses Also multistage (phosphorelay) versions Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Signal transduction

Huge variety Huge variety
Two components Highly conserved Huge variety Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Huge variety Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses

Signal transduction Variety of Ligands & Receptors Variety of
responses Transmitter Receiver Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Transmitter Receiver Variety of Ligands & Receptors responses Signal transduction

Shared protocols Flow of “signal” Recognition, specificity Transmitter
Ligands & Receptors Transmitter Receiver Responses Recognition, specificity Transmitter Receiver Ligands & Receptors Responses Transmitter Receiver Ligands & Receptors Responses

Shared protocols Flow of “signal” Recognition, specificity
Ligands & Receptors Transmitter Receiver Responses Recognition, specificity Flow of packets Note: The wireless system in this room and the Internet to which it is connected work the same way. Internet sites Users Laptop Router Recognition, specificity

No variety Huge Variety Huge variety Virtually unlimited variability and heterogeneity (within and between organisms) E.g: Time constants, rates, molecular counts and sizes, fluxes, variety of molecules, … Very limited but critical points of homogeneity (within and between organisms)

Electric power Variety of producers Variety of consumers

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

Why? No variety Huge Huge Variety variety
Provides “plug and play modularity” between huge variety of input and output components Facilitates robust regulation and evolvability on every timescale (“constraints that deconstrain”) But has extreme fragilities to parasitism and predation (knots are easily hijacked or consumed)

“Random” Variation Structured Selection ?

Architecture E. coli genome Nutrients Polymerization and complex
assembly Autocatalytic feedback Taxis and transport Proteins Core metabolism Sugars Catabolism Amino Acids Nutrients Precursors Nucleotides Trans* Fatty acids Genes Co-factors Carriers DNA replication Architecture E. coli genome

Structured variation Architecture Variation Structured and large
Selection Variation Structured and large Architecture

Fragility example: Viruses
Autocatalytic feedback Core metabolism Viruses exploit the universal bowtie/hourglass structure to hijack the cell machinery. Sugars Fatty acids Precursors Nutrients Catabolism Co-factors Amino Acids Genes Proteins Nucleotides Carriers Trans* DNA replication Regulation & control

Viruses exploit the universal bowtie/hourglass structure to hijack the cell machinery. Precursors Carriers Trans*

Autocatalytic feedback Core metabolism Sugars Fatty acids Precursors Precursors Nutrients Catabolism Co-factors Amino Acids Viral genes Viral proteins Genes Proteins Nucleotides Carriers Carriers Trans* Trans* DNA replication Regulation & control

Energy & materials Regulation & control? E. coli genome Nutrients
Polymerization and complex assembly Energy & materials Autocatalytic feedback Taxis and transport Proteins Core metabolism Sugars Catabolism Amino Acids Nutrients Precursors Nucleotides Trans* Fatty acids Genes Co-factors Carriers DNA replication Regulation & control? E. coli genome

Not to scale Nutrients Polymerization and complex assembly Taxis and
Autocatalytic feedback Taxis and transport Proteins Core metabolism Sugars Catabolism Amino Acids Not to scale Nucleotides Nutrients Precursors Regulation & control Trans* Fatty acids Genes Co-factors Carriers DNA replication Regulation & control

Gene networks? essential: 230 nonessential: 2373 unknown: 1804
total:

Polymerization and complex assembly Autocatalytic feedback Proteins
Regulation & control Trans* Genes DNA replication

motif rpoH Other operons See El-Samad, Kurata, et al…
PNAS, PLOS CompBio DnaK Lon

motif Heat rpoH folded unfolded Other operons degradation DnaK Lon

Heat rpoH  mRNA  Other operons DnaK RNAP Lon  RNAP DnaK FtsH Lon

Heat  mRNA     rpoH DnaK Other operons DnaK DnaK RNAP ftsH Lon

Heat  mRNA     rpoH DnaK Other operons DnaK DnaK ftsH RNAP Lon

Heat Regulation of protein action Regulation of protein levels
rpoH  mRNA Regulation of protein action Regulation of protein levels   DnaK  DnaK DnaK ftsH RNAP Lon  RNAP DnaK FtsH Lon

Layered control architectures
RNAP DnaK  rpoH FtsH Lon Heat  mRNA ftsH Regulation of protein levels Regulation of protein action Regulation of protein levels protein action TCA Gly G1P G6P F6P F1-6BP PEP Pyr Gly3p 13BPG 3PG 2PG ATP NADH Oxa Cit ACA Layered control architectures Allosteric Trans*

Heat  mRNA     rpoH DnaK Other operons DnaK DnaK ftsH RNAP Lon

motif rpoH Other operons DnaK Lon

Control and Dynamical Systems,

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