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 SystemsBioEngineering, Electrical Engineering

Caltech

Theory DataAnalysis

Numerical Experiments

LabExperiments

FieldExercises

Real-WorldOperations

• 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

DoyleArchitecture of complex networks

Robust yet fragile

Constraints that

deconstrain

Essential ideas: Architecture

Question Answer

The ConversationThe Conversation

““APPLICATIONAPPLICATIONLAYER”LAYER”

SPECIALIZED - Collaboration - Sit Awareness - Command/Control - Integration/Fusion

SPECIALIZED - Collaboration - Sit Awareness - Command/Control - Integration/Fusion

““NETWORKNETWORKLAYER”LAYER”

““PHYSICALPHYSICALLAYER”LAYER”

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 LAYERHUMAN / COGNITIVE LAYERSocial/CulturalSocial/Cultural OrganizationalOrganizational PoliticalPolitical EconomicEconomic

A Layered View of HFN Architecture

Layering?

Robust yet fragile?

Constraints that

deconstrain?

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?

Robust yet fragile

Constraints that

deconstrain

Essential ideas: Architecture

Question Answer

Simplest case studies

Internet Bacteria

Simplest case studies

• Successful architectures• Robust, evolvable• Universal, foundational• Accessible, familiar• Unresolved challenges• New theoretical frameworks• Boringly retro?

Internet Bacteria

• Universal, foundational

Techno-sphere

Internet Bacteria

Bio-sphere

• Universal, foundational

Techno-sphere

Internet

Bio-sphere

Bacteria

SpamViruses

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

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 architecture2. Fundamentally rethink network architecture

Two lines of research:1. Patch the existing Internet architecture2. Fundamentally rethink network architecture

Techno-sphere

Internet Bacteria

Bio-sphere

Case studies

Robust yet fragile*

Essential ideas: Architecture

Question

* Carlson

Cat

abol

ism

Genes

Co-factorsFatty acidsSugars

Nucleotides

Amino Acids Proteins

Pre

curs

ors

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

Diverse

UniversalControl

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)

Physical

• Thermodynamics • Communications • Control• Computation

Cyber

• Thermodynamics • Communications• Control• Computation

Internet Bacteria

Case studies

[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.

Robust

Fragile

Theorems : RYF tradeoffs are hard limits

PhysicalPhysical

• Thermodynamics • Communications • Control• Computation

Cyber

• Thermodynamics • Communications• Control• Computation

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.

Constraints that

deconstrain*

Essential ideas: Architecture

Answer

* Gerhart and Kirschner

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

Components and materials:Energy, moieties

Systems requirements: functional, efficient,

robust, evolvable

ProtocolsAre there universal

architectures?

Pathways (Bell)

Layers (Net)Ancient network

architecture: “Bell-heads versus

Net-heads”

Operating

systems

Phone systems

HTTP

TCPIP

mycomputer Wireless

routerOptical router

Physical

webserver

MACSwitch

MAC MACPt to Pt Pt to Pt

Layering?

HTTP

mycomputer

webserver

Applications

Browsing the web

Wirelessrouter

Optical router

Physical

mycomputer

webserver

The physical pathway

Wirelessrouter

Optical router

Physical

HTTP

mycomputer

webserver

Applications

Wirelessrouter

Optical router

Physical

HTTP

mycomputer

webserver

Applications

Diverse Resources

Diverse Applications

Share?

Resources

TCPIP

Error/flow control

Relaying/Multiplexing

(Routing)

Applications

TCPIP

Error/flow control

Relaying/Multiplexing

(Routing)

Error/flow

Relay/MUX

Resources

Applications

Control

Xx

pcRx

xUi

iix

)( tosubj

)( max0

Resources

Applications

diverseand

changing

Error/flow

Relay/MUX

Xx

pcRx

xUi

iix

)( tosubj

)( max0

Control

Fixed and universal

ResourcesDeconstrained

ApplicationsDeconstrained

Constraints that deconstrain

Gerhart and

Kirschner

Xx

pcRx

xUi

iix

)( tosubj

)( max0

mycomputer Wireless

router

Physical

TCPIP

mycomputer Wireless

router

Physical

MACSwitch

TCPIP

mycomputer Wireless

router

Physical

MAC Error/flow control

Relaying/MultiplexingSwitch

Resources

MAC Error/flow control

Relaying/MultiplexingSwitch

Applications

Wirelessrouter

Local

mycomputer Wireless

router

Physical

MACSwitch

TCPIP

Error/flow control

Relaying/Multiplexing

Error/flow control

Relaying/MultiplexingLocal

Global

Differ in • Details• Scope

Wirelessrouter

Optical router

Physical

webserver

TCPIP

Wirelessrouter

Optical router

Physical

webserver

MACPt to Pt

TCPIP

Wirelessrouter

Optical router

Physical

webserver

MACPt to Pt

Error/flow control

Relay/MUXLocal

TCPIP

Error/flow control

Relay/MUXGlobal

HTTP

TCPIP

mycomputer Wireless

routerOptical router

Physical

webserver

MACSwitch

MAC MACPt to Pt Pt to Pt

Local

Global

Physical

Application

Recursive control structure

LocalLocal

Scope

Error/flow control

Relay/MUX

Physical

Application

Recursive control structure

Local

Error/flow control

Relay/MUXGlobal

E/F control

Relay/MUX

Physical

Application

E/F control

Relay/MUX

Recursive control structure

Recu

rsion

Physical

IP

TCP

ApplicationArchitecture is not graph topology.

Architecture facilitates arbitrary graphs.

ResourcesDeconstrained

ApplicationsDeconstrained

Constraints that deconstrain

Generalizations• Optimization• Optimal control• Robust control• Game theory• Network coding

2 2min

arg max , ,

arg max ,s sv

R R dt

L R

x L v

x

v

x c x c

x v p p x c

p

• 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

Xx

pcRx

xUi

iix

)( tosubj

)( max0

Layering as optimization decomposition

application

transport

network

link

physical

Application: utility

IP: routing Link: scheduling

Phy: power

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

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

Protocol decomposition: TCP/AQM

TCP/AQM as distributed primal-dual algorithm over the network to maximize aggregate utility (Kelly ’98 , Low ’99, ’03)

router

TCP AQM

my PC

source algorithm (TCP)

iterates on rates

link algorithm (AQM) iterates on prices

cRx

xUs

ssx

s.t.

)( max0

ll

ls l

llssssxp

cppRxxUs

)( max min00

Primal: Dual

horizontal decomposition

Generalized utility maximization

Objective function: user application needs and network cost

Constraints: restrictions on resource allocation (could be physical or economic)

Variables: Under the control of this design Constants: Beyond the control of this design

)(

tosubj

)( max,,,

pXc

cRx

RxλxU T

iii

pcRx

Application utility

IP: routing Link: scheduling

Phy: power

Network cost

Layering as optimization decomposition

Network generalized NUM Layers sub-problems Interface functions of primal/dual

variables Layering decomposition methods

• Vertical decomposition: into functional modules of different layers

• Horizontal decomposition: into distributed computation and control

IP

TCP/AQM

Physical

Application

Link/MAC

Case study I: Cross-layer congestion/routing/scheduling design

)}(max))()(( max{min

),()( .. )( max

0

,

:Dual

:Primal

fApxHpxU

ffAxHtsxU

T

f

T

sss

xp

sss

fx

Rate control Scheduling Routing

Rate constraint Schedulability constraint

Cross-layer implementation

Rate control:

Routing: solved with rate control or scheduling Scheduling:

)()()(maxarg))(()( xHtpxUtpxtx T

sss

x

)()(maxarg))(()( fAtptpftf T

f

Network

Transport

Physical

Application

Link/MAC

A Wi-Fi implementation by Warrier, Le and Rhee shows significantly better performance than the current system.

0min{max ( ) ( )) max ( )} (Dual: T T

s sp x f

s

U x p H x p A f

Rate control Scheduling Routing

Case study II: Integrating network coding

jim

mji

mji

mdji

mi

Lijj

mdij

Ljij

mdji

m

mm

fgx

cffg

dixgg

xU

,,,,

),(:,

),(:,

,,

,

, s.t.

)( max

Optimization based model for rate control: back-pressure based scheme

(1,1,1)

S

d2d1

(1,1,1) (1,1,1)

(1,0,1)

(1,0,1) (1,1,0)

(1,1,0) (1,0,1)

(1,1,0)

),,( 21,,,dji

djiji ggf

coding subgraph

information flow

physical flow

Constraint from NC

Case study II: Integrating network coding

Optimization based model for rate control: back-pressure based scheme

)(1'

m

mDd

mdsm

m pUx

mDd

mdj

mdi

mji ppm ][maxarg,

)]([ ,,j

mdij

j

mdji

mdi

mdi

mdi ggxpp

otherwise

0& if

0,,

,

mdj

mdijijimd

ji

ppmmcg

Rate control

Session scheduling

Congestion price update

Backpressure in congestion

S1

2

d2

b1

b1+b2

S2

2

d1

b2

b1+b2

b1+b2

b1

b2

a new optimization approach to inter-session network coding

three sessions: (s1;d1), (s2;d2), (s1,s2;d1,d2)

1 2

A

B3

A

B

B

A+B

1 2

A3

forwarding

network coding

physical network coding

correlated data gathering in senor networks

LZ coder

input datacoded 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(p1

)'s(Usx

)(sp t

s(t)=arg max{ps(t)cs(t)}

BS MS

(t)fpf(t) T

Πf maxarg

Other case studies

Dual dynamics: TCP/AQM

router

TCP AQM

my PC

source algorithm (TCP)

iterates on rates

link algorithm (AQM) iterates on prices

cRx

xUs

ssx

s.t.

)( max0

ll

ls l

llssssxp

cppRxxUs

)( max min00

Primal: Dual

horizontal decomposition

Dual dynamics

( , ) ( )

( )

T

T T

L U R

U R

x p x p x c

x p x p cVector notation

arg max ,

l ls s ls

s sv

p R x c

x L v

p

• Controller is fully decentralized• Globally stable to optimal equilibrium• Generalizations to delays, other controllers

arg max ( , )

R

L

v

p x c

x v p

What else is this good for?

arg max ( , )

R

L

v

p x c

x v p

• 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

But are the dynamics optimal?

arg max ( , )

R

L

v

p x c

x v p

• 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?

2 2min

xkp x dt p x

x kp

State weigh

t

Control

weight

dynamics

p x

x kp

Inverse optimality toy example

What is this controller optimal for?

dynamicscontroller

Optimal control

2 2min

xkp x dt p x

x kp

State weigh

t

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

2 2min

xkp x dt p x

x kp

State weigh

t

Control

weight

dynamics

2 2min

xp c x c dt p x c

x p

Simple changep x

x kp

p x c

x p

Optimal control

2 2min

xp c x c dt p x c

x p

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

2 2min

xp c x c dt p x c

x p

p x c

x p Simple change

arg max ,v

p x c

x L v p

22

min arg max ,

arg max ,

x v

v

L v p c x c dt p x c

x L v p

Optimal

control

Optimal

control

22

min arg max ,

arg max ,

x v

v

L v p c x c dt p x c

x L v p

State weigh

t

Control

weight

dynamics

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

Optimal

control

22

min arg max ,

arg max ,

x v

v

L v p c x c dt p x c

x L v p

2 2

min

arg max , ,

arg max ,

ls s l ls s lx

l s s

s s l ls s lv

s

s sv

R x c R x c dt

x L v p R x c

x L v

p

p

Network

2 2min

arg max , ,

arg max ,s sv

R R dt

L R

x L v

x

v

x c x c

x v p p x c

p

Vector notation

2 2

min

arg max , ,

arg max ,

ls s l ls s lx

l s s

s s l ls s lv

s

s sv

R x c R x c dt

x L v p R x c

x L v

p

p

State weigh

t

Control

weight

dynamics

What is this controller optimal for?• IQ penalty on deviation from equilibrium• Balance state versus control penalty• Optimal controller is decentralized

2 2min

arg max , ,

arg max ,s sv

R R dt

L R

x L v

x

v

x c x c

x v p p x c

p

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

2 2min

arg max , ,

arg max ,s sv

R R dt

L R

x L v

x

v

x c x c

x v p p x c

p

• Finite horizon version• Terminal cost is lagrangian

2 2

0

min arg max ,

arg max , ,

arg max ,

T

s sv

R R dt L T

L R

x L v

x v

v

x c x c v p( )

x v p p x c

p

74

An additional constraint: energy aware design

Energy has become a key issue in systems design

Tradeoff between energy usage and traditional performance metrics such as throughput and delay

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

Our current focus is on wireless networks

75

Case study: wireless downlink scheduling

“natural” speed scaling)1ln( ii phc

EwTwi

iki 0 min

weighted sum of response time and energy

}/ ii min{w}max{w1

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

1n

Nn

1p

Np

B

76

Generalization to game theory

Developed to study strategic interactions Provides a series of equilibrium solution concepts Considers informational constraints explicitly

Equilibria arise as a result of adaptation and learning, subject to informational constraint

Provides a basis for designing systems to achieve the given desired goals (e.g., mechanism design)

ii

iii

Cx

xxP

subject to

);( maximize

Player i payoff function

Player i strategy

Player i strategy space

Game theory: Engineering perspective

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

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

Game theory based decomposition

system-wide performance objective

design agent utility and define game

look for distributed converging algorithm

protocol design: protocols as distributed updatealgorithms to achieve equilibira

must respect informational constraints

Eco vs. Eng 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

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 Tradeoff among computational, informational, and

incentive issues

79

80

Case study: Throughput optimal channel access scheme

to achieve maximum throughput under weighted fairness constraint

utility

distributed converging algorithm

.,1 , LmlT

T

m

l

m

l

)1ln()1

1()1()(*

*

ll

ll

ll pepe

pU

isiiiiii tpqtpUttptp )))](())(()(()([)1( '

can be seen as an axiomatic approach

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

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

Control of the Internet

source receiver

Packets

controlpackets

source receiver

signalinggene expression

metabolismlineage

Biological pathways

source receiver

control

energy

materials

signalinggene expression

metabolismlineage

More complex

feedback

source receiver

control

energymaterials

Autocatalytic feedback

source receiver

control

energy

materials

signalinggene expression

metabolismlineage

More complex

feedback

What theory is relevant to these more complex feedback systems?

RNADNA Protein

Pathways

Metabolic pathways

“Central dogma”

Network architecture?

Layers?

Catabolism

Pre

curs

ors

Carriers

Co-factors

Fatty acids

Sugars

NucleotidesAmino Acids

Metabolism

energymaterials

Catabolism

Pre

curs

ors

Carriers

Co-factors

Fatty acids

Sugars

NucleotidesAmino Acids

Core metabolism

Inside every cell (1030)

Genes

Co-factorsFatty acidsSugars

Nucleotides

Amino Acids

Proteins

Pre

curs

ors

Autocatalytic feedback

Nut

rien

ts

Core metabolism

DNA replication

Trans*

Cat

abol

ism

Carriers

EnvironmentEnvironment EnvironmentEnvironment

Huge Variety

Huge Variety

Bacterial cell

Co-factors

Fatty acids

Sugars

NucleotidesAmino Acids

Catabolism

Pre

curs

ors

Taxis and transport

Nut

rien

ts

Carriers

Core metabolism

Huge Variety

Same 12

in all cells

Same 8

in all cells

100

same

in all

organism

s

Genes

Co-factorsFatty acidsSugars

Nucleotides

Amino Acids

Polymerization and complex

assemblyP

roteinsP

recu

rsor

s

Autocatalytic feedback

Taxis and transport

Nut

rien

ts

Core metabolism

DNA replication

Trans*

Cat

abol

ism

Carriers

100 104 to ∞in one

organisms

Huge Variety

12

8

Polymerization and complex

assembly

Autocatalytic feedback

Genes

ProteinsDNA

replication

Trans*

104 to ∞in one

organismsHuge

VarietyFew polym

erases

Highly conserved

Co-factors

Fatty acids

Sugars

NucleotidesAmino Acids

Catabolism

Polymerization and complex

assemblyProteins

Pre

curs

ors

Autocatalytic feedback Taxis and transport

Nut

rien

ts

Regulation & control

Carriers

Core metabolism

Genes

DNA replicationRegulation & control

Trans*

The bowtie architecture of the cell.

Flow/error

Reactions

Proteins

Flow/error

Reactions

RNA level

Flow/error

Reactions

DNA level

Translation

Transcription

Carriers

The hourglass architecture of the cell.

Need a more coherent cartoon to visualize how these fit together.

Catabolism

Pre

curs

ors

Carriers

Catabolism

TCAPyr

Oxa

Cit

ACA

Gly

G1P

G6P

F6P

F1-6BP

PEP

Gly3p

13BPG

3PG

2PG

ATP

NADH

TCAPyr

Oxa

Cit

ACA

Gly

G1P

G6P

F6P

F1-6BP

PEP

Gly3p

13BPG

3PG

2PG

TCAPyr

Oxa

Cit

ACA

Gly

G1P

G6P

F6P

F1-6BP

PEP

Gly3p

13BPG

3PG

2PG

Pre

curs

ors

metabolites

Enzymatically catalyzed reactions

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

Oxa

Cit

ACA

TCAPyr

Oxa

Cit

ACA

Gly

G1P

G6P

F6P

F1-6BP

PEP

Gly3p

13BPG

3PG

2PG

ATP

Autocatalytic

NADH

Pre

curs

ors

Carriers

TCAPyr

Oxa

Cit

ACA

Gly

G1P

G6P

F6P

F1-6BP

PEP

Gly3p

13BPG

3PG

2PG

ATP

Autocatalytic

NADH

produced

consumedRest of cell

Carriers

TCAPyr

Oxa

Cit

ACA

Gly

G1P

G6P

F6P

F1-6BP

PEP

Gly3p

13BPG

3PG

2PG

ATP

NADH

Reactions

Proteins

Control?

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

Control

TCAPyr

Oxa

Cit

ACA

Gly

G1P

G6P

F6P

F1-6BP

PEP

Gly3p

13BPG

3PG

2PG

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

If we drew the feedback loops the diagram would be unreadable.

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

( )

Mass &Reaction

Energyflux

Balance

dxSv x

dt

Stoichiometry matrix

S

Regulation of enzyme levels by transcription/translation/degradation

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

Oxa

Cit

ACA

( )

Mass &Reaction

Energyflux

Balance

dxSv x

dt

level

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

( )

Mass &Reaction

Energyflux

Balance

dxSv x

dt

Allosteric regulation of enzymes

Error/flow

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

Mass &Reaction

( ) Energyflux

Balance

dxSv x

dt

Level

Error/flow

Reaction

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

Flow/error

Reactions

Protein level

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

Flow/error

Reactions

Protein level

Fast response

Slow

Layered architecture

Flow/error

Reactions

Protein level

Flow/error

Reactions

RNA level

Flow/error

Reactions

DNA level

Flow/error

Reactions

Protein level

Flow/error

Reactions

RNA level

Flow/error

Reactions

DNA level

Protein

RNA

DNA

Translation

Transcription

Flow/error

Reactions

Protein level

Flow/error

Translation

RNA level

Flow/error

Transcription

DNA level

Recursion

Flow/error

Reactions

Protein level

RNA

FlowReact

DNA

FlowReact

DNA

FlowReact

DNA

Scope

Diverse Reactions

DNADNADNA

Diverse Genomes

Diverse Reactions

DNADNADNA

Diverse Genomes

Flow/error

Protein level

Flow/error

Reactions

RNA level

Flow/error

Reactions

Translation

Transcription

Conserved core

control

Flow/error

Protein level

Flow/error

Reactions

RNA level

Flow/error

Reactions

Translation

Transcription

Flow/error

Reactions

Protein level

TCAPyr

Oxa

Cit

ACA

Gly

G1P

G6P

F6P

F1-6BP

PEP

Gly3p

13BPG

3PG

2PG

ATP

NADH

Flow/error

Reactions

Protein level

TCAPyr

Oxa

Cit

ACA

Gly

G1P

G6P

F6P

F1-6BP

PEP

Gly3p

13BPG

3PG

2PG

ATP

NADH

Layering revisited

Flow/error

Reactions

ProteinsCarriers

More complete picture

Flow/errorProtein level

Catabolism

Pre

curs

ors

Carriers

Co-factors

Fatty acids

Sugars

NucleotidesAmino Acids

RNADNA

Pre

curs

ors

Co-factors

Fatty acids

Sugars

NucleotidesAmino Acids

RNADNA

Biosynthesis

RNA level/ Transcription rate

DNA level

Biosynthesis

RNA

Gene

Transc.xRNA

RNAp

Pre

curs

ors

Co-factors

Fatty acidsSugars

Nucleotides

Amino Acids

Cat

abol

ism

AA

RNA

RNAp

Pre

curs

ors

Nucl.

AA

Gene

Transc.xRNA

Cat

abol

ism

AA

tRNA Ribosome

RNA

RNAp

transl. EnzymesPre

curs

ors

Nucl.

AA

Gene

Transc.xRNA

mRNAncRNA

AA

Ribosome

RNA

RNAp

transl. Protein

Gene

Transc.mRNA

“Central dogma”

RNA

FlowTransc.

DNA

Protein

Cat

abol

ism

AA

tRNA Ribosome

RNA

RNAp

Autocatalysis everywhere

transl. Proteins

xRNAtransc.

Pre

curs

ors

Nucl.

AA

All the enzymes are made from (mostly) proteins and (some) RNA.

Pyr

G6P

F6P

F1-6BP

PEP

Gly3p

13BPG

3PG

2PG

ATP

charging

consumption= discharging

Rest of cell

This is just charging and discharging

Flow/errorProtein level

RNADNA

AMP level

Pyr

F1-6BP

PEP

Gly3p

3PG2PG

ATP

G6PF6P

13BPG

Rest of cell

A*P

ATP supplies energy to all layers

Flow/error

Protein level

RNADNA

AMP level

ATP

cellA*P

RNA

DNA

Lots of ways to draw this.

AA

tRNA

RNALayered

transl. Enzymes

xRNAtransc.

Cat

abol

ism

Pre

curs

ors

Nucl.

AA

trans.EnzymesAA

mRNAncRNA

tRNA

Ribosome

RNA level/ Transcription rate

RNA form/activity

RNA

Gene

Transc.xRNA

RNAp

S reactionsP

Enz1 reaction3

Enzyme level/Translation rate

Enzyme form/activity

Reaction rate

Enz2

trans.

ncRNATransc.

productsreactions

reaction3

All products feedback everywhere

ProteinsControl?

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

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.

Viralgenes

Viralproteins

Flow/error

Reactions

Protein level

TCAPyr

Oxa

Cit

ACA

Gly

G1P

G6P

F6P

F1-6BP

PEP

Gly3p

13BPG

3PG

2PG

ATP

NADH

Layering revisited

Flow/error

Reactions

ProteinsCarriers

More complete picture ?

Flow/error

Reactions

ProteinsCarriers

Flow/error

Reactions

RNA level

Flow/error

Reactions

DNA level

Translation

Transcription

“Power supply”

This is a “database” of instructions

applicationTCPIP

mycomputer

router

Physical

server

MACSwitch

MACPt to Pt

Applications

Hardware

OperatingSystem

Physical

CircuitCircuitCircuit

LogicalInstructions

?

?

?

Flow/error

Reactions

Proteins

Flow/error

Reactions

RNA level

Flow/error

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

Diversefunction

Diversecomponents

UniversalControl

fan-in of diverse

inputs

fan-out of diverse

outputs

universal carriers

Bowties: flows within layers

Robust yet fragile

Constraints that

deconstrain

Essential ideas

Diversefunction

Diversecomponents

fan-in of diverse

inputs

fan-out of diverse

outputs

Robust yet fragile

Constraints that deconstrain

Highly robust • Diverse• Evolvable• Deconstrained

Robust yet fragile

Constraints that deconstrain

Highly fragile • Universal• Frozen• Constrained

UniversalControl

universal carriers

Diversefunction

Diversecomponents

UniversalControl

fan-in of diverse

inputs

fan-out of diverse

outputs

universal carriers

Bowties: flows within layers

Robust yet fragile

Constraints that

deconstrain

Essential ideas

source receiver

control

energymaterials

More complex

feedback

What theory is relevant to these more complex feedback systems?

signalinggene expression

metabolismlineage

2 20

1ln ln

z z pS j d

z z p

[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

[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

[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.

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?

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

F6P

F1-6BP

Gly3p

13BPG

3PG

ATP

F6P

F1-6BP

Gly3p

13BPG

3PG

ATP

1 1

q

h

q Vx

x

1

1 y

qk y

1

0 xk x

y

x

Control

Autocatalytic

F6P

F1-6BPGly3p

13BPG

3PG

ATP

1 1

q

h

q Vx

x

1

1 y

qk y

1

0 xk x

y

x

Control

Autocatalytic

1 1(1 )

1 1 01

q

h

x q qVxky

y x

1(1 )

0

1 1

q

h

q Vx

x

1

1 y

qk y

y

x

Control

Autocatalytic

Autocatalytic

Control

11

0

1 1

q

h

q Vx

x

1

1 y

qk y

y

x

input

output=x

Control theory cartoon

Caution: mixed cartoon

Controller

+

u

xS j

u

output=x

+

u

X jS j

U j

ln ln

ln ln

X jS j d d

U j

X j d U j d

Entropy rates

CP

lant

0

1ln 0S j d

Hard limits

0 5 10 15 200.8

0.85

0.9

0.95

1

1.05

Time (minutes)

[AT

P]

h >>1

h = 1

Time response)

Fourier

Transform

of error

h hS x = F(

0 2 4 6 8 10-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Frequency

Lo

g(|

Sn

/S0|

)

h >>1

h = 1

Spectrum

1log loghS S

Ideal

0 5 10 15 200.8

0.85

0.9

0.95

1

1.05

Time (minutes)

[AT

P]

h >> 1

h = 1

0 2 4 6 8 10-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Frequency

Lo

g(S

n/S

0)

h >>1

h = 1

Spectrum

Time response

Robust

Yet fragile

0ln lnhS j S j

0 2 4 6 8 10-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Frequency

Lo

g(S

n/S

0)

h = 3

h = 0 Robust

Yet fragile

0

ln 0S j d

[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

output=x

+

u

X jS j

U j

ln ln

ln ln

X jS j d d

U j

X j d U j d

Entropy rates

CP

lant

0

1ln 0S j d

Hard limits

Note: Nature doesn’t

care much about

entropy rates.

0 5 10 15 200.8

0.85

0.9

0.95

1

1.05

Time (minutes)

[AT

P]

h >> 1

h = 1

0 2 4 6 8 10-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Frequency

Lo

g(S

n/S

0)

h >>1

h = 1

Spectrum

Time response

Robust

Yet fragile

0ln lnhS j S j

Note: Nature cares more

about this tradeoff.

Plant

output=x

+

u

X jS j

U j

C

2 20

1ln ln

z z pS j d

z z p

0

1ln 0S j d

The plant can make this tradeoff worse.

Plant

output=x

+

u

X jS j

U j

C

2 20

1ln ln

z z pS j d

z z p

0

1ln 0S j d

2kz p RHPzero s q k s k

q

All controllers:

Biological cells: =

Plant

output=x

+

u

X jS j

U j

C

2 20

1ln ln

z z pS j d

z z p

0

1ln 0S j d

2kz p RHPzero s q k s k

q

Small z is bad.

kz

q

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”

2 20

1ln ln

z z pS j d

z z p

output=x

+

u

X jS j

U j

ln ln

ln ln

X jS j d d

U j

X j d U j d

Entropy rates

CP

lant

0

1ln 0S j d

Hard limits

Plant

output=x

+

uController

0

1ln 0S j d

Plant

output=x

+

uController

0

1ln 0S j d

Channel

Sensor+Channel

Plant

output=x

+

uController

0

1ln FBS j d C

Channel

Sensor+Channel

0

1ln sensorS j d C

Helps

Hurts

• 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)

Small Large

Robust Simple Organized

FragileChaocritical

Irreducible

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

Apps

Tools/tech

Apps

Tools/tech

Apps

Tools/tech

Apps

Tools/tech

Apps

Tools/tech

“Multidisciplinary cross-sterilization”

Funding twine

Diverse applications

Diverse applications

Apps

Tools/tech

Apps

Tools/tech

Apps

Tools/tech

Apps

Tools/tech

Apps

Tools/tech

?????Layering academia?

Diverse resources

End

What follows are additional details on the glycolysis fragility example.

1 1(1 )

1 1 01

q

h

x q qVxky

y x

1(1 )

0

1 1

q

h

q Vx

x

1

1 y

qk y

y

x

Control

Autocatalytic

Autocatalytic

Control

produced

consumed

yk yy

x

( )yk y

y

yk yy

x

( )yk y

y

yk y

rate

yk yy

x

( )yk y

y

yk yMore enzyme

level

rate

1( )k x y

xAutocatalytic

Control

consumed

produced

1( )k x

x

1( )k x y

xAutocatalytic

Control

1( )k x

x

form/activity

rate

1( )k x y

xAutocatalytic

Control

1( )k x

x

level

form/activity

rate

Layered control

1( )k x y

xAutocatalytic

Control

1( )k x

x

level

form/activity

rate

Layered control

Fast response

Slow

1 1(1 )

1 1 0x

x q qk x ky

y

consumed

1(1 )

0

x

1(1 )

0

wk w yk yyw

x

( )k

stable

1(1 )

0

1 1

q

h

q Vx

x

1

1 y

qk y

y

xAutocatalytic

( )k

1(1 )

0

1 1

q

h

q Vx

x

1

1 y

qk y

y

xAutocatalytic

1( )k x

( )yk y

Control

Enzyme complexity,Strong inhibition

Oscillations

Low autocatalysis Inefficiency,High reaction rates metabolic load

Robust Yet Fragile

1(1 )

0

1 1

q

h

q Vx

x

1

1 y

qk y

y

xAutocatalytic

Control