co-factors

Co-factors

Fatty acids

Sugars

Nucleotides

Amino Acids

Catabolism

Polymerization and complex

assembly

Proteins

Pre

curs

ors

Autocatalytic feedback Taxis and transport

Nut

rien

ts

Carriers

Core metabolism

Genes

DNA replication

Trans*

John DoyleJohn G Braun Professor

Control and Dynamical Systems,BioEng, and ElecEng

Caltech

GGGDP GTP

GDPGTP

In

In

Out

P

Ligand

Receptor

RGS

www.cds.caltech.edu/~doyle

Collaborators and contributors(partial list)

Biology: Csete,Yi, Tanaka, Arkin, Savageau, Simon, AfCS, Kurata, Khammash, El-Samad, Gross, Kitano, Hucka, Sauro, Finney, Bolouri, Gillespie, Petzold, F Doyle, Stelling, …

Theory: Parrilo, Carlson, Paganini, 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, Vinnicombe, Kelly, Zhu, Yu, Wang, Chandy, …

Turbulence: Bamieh, Bobba, Gharib, Marsden, …Physics: Mabuchi, Doherty, Barahona, Reynolds,Disturbance ecology: Moritz, Carlson,…Finance: Martinez, Primbs, Yamada, Giannelli,…Engineering CAD: Ortiz, Murray, Schroder, Burdick, …

Current Caltech Former Caltech OtherLongterm Visitor

MultiscalePhysics

SystemsBiology

Network Centric,Pervasive,Embedded,Ubiquitous

Core theory

challenges

SystemsBiology


Core theory

challenges

Today’s focus

Core theory challenges



SystemsBiology

Pervasive,Networked,Embedded

…is on stories you are unlikely

to hear from anyone else.

Today’s focus

Caution: maybe others are more sensible than I

am.




Consistent, coherent, convergent understanding.

Status

Dramatic recent

progress in laying the

foundation.

Yet also striking increase in

unnecessary confusion???

SystemsBiology

Pervasive,Networked,Embedded

Remarkably common core

theoretical challenges.

A look back and forward

• The Internet architecture was designed without a “theory.”

• Many academic theorists told the engineers it would never work.

• We now have a nascent theory that confirms that the engineers were right.

• Parallel stories exist in “theoretical biology.”• For future networks and other new technologies,

as well as systems biology of the cell, organism and brain, let’s hope we can avoid a repeat of this history.

Robust yet fragile (RYF)

• The same mechanisms responsible for robustness to most perturbations

• Allows possible extreme fragilities to others

Robust

1. Efficient, flexible

metabolism

2. Complex development

and

3. Immune systems

4. Regeneration & renewal

5. Complex societies

1. Obesity and diabetes

and

2. Rich parasite

ecosystem

3. Auto-immune disease

4. Cancer

5. Epidemics, war,

genocide, …

Yet Fragile

Human robustness and fragility

Robust1. Efficient, flexible metabolism2. Complex development and3. Immune systems4. Regeneration & renewal 5. Complex societies

6. Advanced technologies

1. Obesity and diabetes and 2. Rich parasite ecosystem 3. Auto-immune disease4. Cancer5. Epidemics, war, …

6. ?????

Yet Fragile

What about technology?

TCP/IP robustness/evolvability on many timescales

• Shortest: File transfers from different users– Application-specific navigation (application)

– Congestion control to share the net (TCP)

– Ack-based retransmission (TCP)

• Short: Fail-off of routers and servers– Rerouting around failures (IP)

– Hot-swaps and rebooting of hardware

• Long: Rearrangements of existing components– Applications/clients/servers can come and go

– Hardware of all types can come and go

• Longer: New applications and hardware– Plug and play if they obey the protocols

TCP/IP fragility on many timescales

• Shortest: File transfers from different users– End systems w/o congestion control won’t

fairly share

• Short: Fail-on of components– Distributed denial of service– Black-holing and other fail-on cascading

failures

• Long: Spam, viruses, worms

• Longer: No economic model for ISPs?




• Usually involving hijacking the robustness mechanism in some way

• Ubiquitous in biology and advanced technology

• High variability (and thus power laws)

Nightmare? Biology: We might accumulate more complete

parts lists but never “understand” how it all works.

Technology: We might build increasingly complex and incomprehensible systems which will eventually fail completely yet cryptically.

Nothing in the orthodox views of complexity says this won’t happen (apparently).

HOPE?

Interesting systems are robust yet fragile.

Identify the fragility, evaluate and protect it.

The rest (robust) is “easy”.

Nothing in the orthodox views of complexity says this can’t happen (apparently).

Working systems but no “proofs’

Spectacular progress….

Progress• Understanding mice and elephants• “Primal-dual” decompositions for layering• Global stability analysis with delays• New solutions to “classic” problems

Many challenges• Rigorous multiscale models• Latency-based utilities• Wireless, MANETs• Interdomain routing

Hosts

Routers

packets

“FAST” theoryArbitrarily complex network• Topology• Number of routers and hosts• Nonlinear• Delays

Short proof• Global stability• Equilibrium optimizes aggregate user utility

Papachristodoulou, Li

I2LSR, SC2004 Bandwidth Challenge

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

Harvey Newman’s group, Caltechhttp://dnae.home.cern.ch/dnae/lsr4-nov04

Yet growing confusion…

…sorry, but in the interest of scientific hygiene, we have to admit

that all is not well…

One ofthe most-read papers ever on

the Internet!

100

101

102

103

100

101

102

power-law degrees

High degree hub-like core

“Scale-free” networks and the “Achilles’ heel” of the Internet


Delete these “hubs” and the network disconnects!

Delete “non-hubs” with little effect!

Robust yet fragile!?!?!?

SOX

SFGP/AMPATH

U. Florida

U. So. Florida

Miss StateGigaPoP

WiscREN

SURFNet

Rutgers U.

MANLAN

NorthernCrossroads

Mid-AtlanticCrossroads

Drexel U.

U. Delaware

PSC

NCNI/MCNC

MAGPI

UMD NGIX

DARPABossNet

GEANT

Seattle

Sunnyvale

Los Angeles

Houston

Denver

KansasCity

Indian-apolis

Atlanta

Wash D.C.

Chicago

New York

OARNET

Northern LightsIndiana GigaPoP

MeritU. Louisville

NYSERNet

U. Memphis

Great Plains

OneNetArizona St.

U. Arizona

Qwest Labs

UNM

OregonGigaPoP

Front RangeGigaPoP

Texas Tech

Tulane U.

North TexasGigaPoP

TexasGigaPo

P

LaNet

UT Austin

CENIC

UniNet

WIDE

AMES NGIX

PacificNorthwestGigaPoP

U. Hawaii

PacificWave

ESnet

TransPAC/APAN

Iowa St.

Florida A&MUT-SWMed Ctr.

NCSA

MREN

SINet

WPI

StarLight

IntermountainGigaPoP

Abilene BackbonePhysical Connectivity

0.1-0.5 Gbps0.5-1.0 Gbps1.0-5.0 Gbps5.0-10.0 Gbps

Internet router-level topology

Internet router-level topology


100

101

102

103

100

101

102

power-law degrees

Low degree mesh-like core

Completely different networks can have the same node degrees.

High variability edge systems

rank

100

101

102

103

100

101

102

identical power-law degrees


Low degree mesh-like core

Completely different networks can have the same node degrees.

• Low degree core• High performance

and robustness

• High degree “hubs”• Poor performance

and robustness

See PNAS, Sigcomm, TransNet papers for details.

Nothing like the real Internet.


• Hard constraints

• Simple models

• Short proofs

• Architecture

Architecture?

• “The bacterial cell and the Internet have – architectures– that are robust and evolvable”

• What does “architecture” mean?

• What does it mean for an “architecture” to be robust and evolvable?

• Robust yet fragile?

• Rigorous and coherent theory?

Hard constraints

On systems and their components

• Thermodynamics (Carnot)

• Communications (Shannon)

• Control (Bode)

• Computation (Turing/Gödel)

• Fragmented and incompatible

• We need a more integrated view and have the beginnings

Assume different architectures a priori.

Hard constraints (progress)



• Control (Bode)


• We need a more integrated view and have

the beginnings

Work in progress



• Control (Bode)



the beginnings

• Robust yet fragile systems

• Proof complexity implies problem fragility (!?!)

• Designing for robustness and verifiability are compatible objectives

• Hope for a unifying framework?

• Integrating simple models and short proofs?

Short proofs (progress)

Simple models (challenges)

• Rigorous connections between– Multiple scales – Experiment, data, and models

• Essential starting point for short proofs• Microscopic state: discrete, finite, enormous

– Packet level – Software, digital hardware– Molecular-level interactions (biology)

• Macroscopic behavior: robust yet fragile

Architecture?

• “The bacterial cell and the Internet have – architectures– that are robust and evolvable”

• What does “architecture” mean?

• What does it mean for an “architecture” to be robust and evolvable?

• Robust yet fragile?

• Rigorous and coherent theory?

Co-factors

Fatty acids

Sugars

NucleotidesAmino Acids

Catabolism


assemblyProteins

Pre

curs

ors


Nut

rien

ts

Regulation & control

Carriers

Core metabolism

Genes

DNA replicationRegulation & control

Trans*

The architecture of the cell.

Feathers and

flapping?

Or lift, drag, propulsion, and control?

The danger of biomemetics

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

RNAP

DnaK

RNAP

DnaK

rpoH

FtsH Lon

Heat

mRNA

DnaK

DnaK

ftsH

Lon

Regulation of

protein levels

Regulation of protein action

PMF

++

++

From Taylor, Zhulin, Johnson

Co-factors

Fatty acids

Sugars


Catabolism

Proteins

Prec

urso

rs


Carriers

Core metabolism

Genes


Trans*

Lessons from the cell and Internet

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

Co-factors

Fatty acids

Sugars


Catabolism


assemblyProteins

Pre

curs

ors


Nut

rien

ts


Carriers

Core metabolism

Genes


Trans*


Bowtie: Flow of energy and materials

Hourglass

Organization of control

Universal organizational structures/architectures

The Internet hourglass

Web FTP Mail News Video Audio ping napster

Applications

Ethernet 802.11 SatelliteOpticalPower lines BluetoothATM

Link technologies


IP


Applications

TCP


Link technologies


IP


Applications

TCP


Link technologies

IP under everything

IP oneverything

Bio: Huge variety of environments, metabolismsInternet: Huge variety of applications

Huge variety of components



Both components and applications are

highly uncertain.



Huge variety of genomesHuge variety of physical networks



Huge variety of genomesHuge variety of physical networks

Feedback control

Identical control

architecture

Hourglass architectures

5:Application/function: variable supply/demand

4:TCP

3:IP

2:Potential physical network

1:Hardware components

4:Allosteric

3:Transcriptional

TCP/IP Metabolism/biochem

FeedbackControl


Hourglass



Co-factors

Fatty acids

Sugars


Catabolism


assemblyProteins

Pre

curs

ors


Nut

rien

ts


Carriers

Core metabolism

Genes


Trans*


EnvironmentEnvironment EnvironmentEnvironment

Huge Variety

Huge Variety

Bacterial cell

Co-factors

Fatty acids

Sugars


Catabolism

Pre

curs

ors

Taxis and transport

Nut

rien

ts

Carriers

Core metabolism

Huge Variety

100same

in allorganisms

20same in all cells

Co-factors

Fatty acids

Sugars


Catabolism

Pre

curs

ors

Carriers

Core metabolism

Nested bowties

Catabolism

Pre

curs

ors

Carriers

Co-factors

Fatty acids

Sugars


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

Pre

curs

ors

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

NADH

Pre

curs

ors

Carriers

20 same in all cells

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

Regulatory

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

This is still a cartoon. (Cartoons are useful.)

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.

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

ACA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG ACA

This can be modeled to some extent as a graph.

This cannot.

Unfortunate and unnecessary confusion results from not “getting” this.

( )

Mass &Reaction

Mass&Energy Energyflux

Balance

dxSv x

dt

d

dt

Stoichiometry plus regulation

Biology is not a graph.

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

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

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


Regulation of enzyme levels

Regulation of protein levels




Co-factors

Fatty acids

Sugars


Catabolism


assembly

Proteins

Pre

curs

ors


Nut

rien

ts


Carriers

Core metabolism

Genes


Trans*

Not to scale

essential: 230 nonessential: 2373 unknown: 1804 total: 4407

http://www.shigen.nig.ac.jp/ecoli/pec

Gene networks?

Co-factors

Fatty acids

Sugars

Nucleotides

Amino Acids

Catabolism


assembly

Proteins

Pre

curs

ors


Nut

rien

ts

Carriers

Core metabolism

Genes

DNA replication

Trans*

Regulation & control E. coli

genome

Trans*

Viruses exploit the universal bowtie/hourglass structure to hijack the cell machinery.

Fragility example: Viruses

Pre

curs

ors

Carriers

Co-factors

Fatty acids

Sugars


Catabolism

Proteins

Nut

rien

ts

Core metabolism

Genes

DNA replication

Trans*

Viruses exploit the universal bowtie/hourglass structure to hijack the cell machinery.

Fragility example: Viruses

Viralgenes

Viralproteins

Pre

curs

ors

Carriers

Co-factors

Fatty acids

Sugars


Catabolism


assembly

Proteins

Pre

curs

ors


Nut

rien

ts


Carriers

Core metabolism

Genes


Trans*

Co-factors

Fatty acids

Sugars

Nucleotides

Amino Acids

Catabolism


assembly

Proteins

Prec

urso

rs


Nut

rien

ts


Carriers

Core metabolism

Genes


Trans*

Co-factors

Fatty acids

Sugars

Nucleotides

Amino Acids

Catabolism


assembly

Proteins

Prec

urso

rs


Nut

rien

ts


Carriers

Core metabolism

Genes


Trans*

Co-factors

Fatty acids

Sugars

Nucleotides

Amino Acids

Catabolism


assembly

Proteins

Prec

urso

rs


Nut

rien

ts


Carriers

Core metabolism

Genes


Trans*

Co-factors

Fatty acids

Sugars

Nucleotides

Amino Acids

Catabolism


assembly

Proteins

Prec

urso

rs


Nut

rien

ts


Carriers

Core metabolism

Genes


Trans*

Co-factors

Fatty acids

Sugars

Nucleotides

Amino Acids

Catabolism


assembly

Proteins

Prec

urso

rs


Nut

rien

tsRegulation & control

Carriers

Core metabolism

Genes


Trans*

Co-factors

Fatty acids

Sugars

Nucleotides

Amino Acids

Catabolism


assembly

Proteins

Prec

urso

rs


Nut

rien

ts


Carriers

Core metabolism

Genes


Trans*


Multicellularity

Robustness:Efficient and flexible metabolism

Transport

Glucoseand

Oxygen

Autocatalytic and regulatory feedback

Cell

Cell

CellCell

CellCell

Cell

CellCell

Fragility: Obesity and diabetes

Robust

1. Efficient, flexible

metabolism

2. Complex development

and

3. Immune systems

4. Regeneration & renewal

5. Complex societies

1. Obesity and diabetes

and

2. Rich parasite

ecosystem

3. Auto-immune disease

4. Cancer

5. Epidemics, war,

genocide, …

Yet Fragile

Human robustness and fragility

Co-factors

Fatty acids

Sugars

Nucleotides

Amino Acids

Catabolism


assembly

Proteins

Pre

curs

ors


Nut

rien

ts

Carriers

Core metabolism

Genes

DNA replication

Trans*

Regulation & control E. coli

genome

Allosteric regulation


Bio: Huge variety of environments, metabolisms


Huge variety of genomes

Universal control

architecture

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

Allosteric

Trans*

RNAP

DnaK

RNAP

DnaK

rpoH

FtsH Lon

Heat

mRNA

DnaK

DnaK

ftsH

Lon

Regulation of

protein levels


5:Application/function: variable supply/demand

4:TCP

3:IP

2:Potential physical network

1:Hardware components

4:Allosteric

3:Transcriptional


FeedbackControl

Protocols and modules

• Protocols are the rules by which modules are interconnected

• Protocols are more fundamental to “modularity” than modules

IP IPIP IP IP

TCP

Application

TCP

Application

TCP

Application

RoutingProvisioning

Ver

tica

l dec

ompo

siti

onP

roto

col S

tack

Each layer can evolve independently provided:

1. Follow the rules2. Everyone else does

“good enough” with their layer

IP IPIP IP IP

TCP

Application

TCP

Application

TCP

Application

RoutingProvisioning

Horizontal decompositionEach level is decentralized and asynchronous


Hourglass



Facilitate regulation on multiple time scales:1. Fast: allostery2. Slower: transcriptional regulation (by regulated

recruitment) and degradation3. Even slower: transfer of genes4. Even slower: copying and evolution of genes

Co-factors

Fatty acids

Sugars



assembly

Proteins

Pre

curs

ors

Carriers

Genes

DNA replication

Trans*

Nutrient


Co-factors

Fatty acids

Sugars



assembly

Proteins

Pre

curs

ors

Autocatalytic feedback


Carriers

Genes


Trans*

Nutrient

5:Apps: Supply and demand of packet flux

4:TCP: robustness to changing supply/demand, and packet losses

3:IP: routes on physical network, rerouting for router losses

2:Physical: Raw physical network

1:Hardware catalog: routers, links, servers, hosts,…

5:Apps:supply and demand of nutrients and products

4:Allosteric regulation of enzymes: robust to changing supply/demand

3:Transcriptional regulation of enzyme levels

2:Genome: Raw potential stoichiometry network

1:Hardware catalog: DNA, genes, enzymes, carriers,…


Facilitate regulation on multiple time scales:1. Fast: allostery2. Slower: transcriptional regulation (by regulated

recruitment) and degradation3. Even slower: transfer of genes4. Even slower: copying and evolution of genes

TCP/IP robustness/evolvability on many timescales

• Shortest: File transfers from different users– Application-specific navigation (application)

– Congestion control to share the net (TCP)

– Ack-based retransmission (TCP)

• Short: Fail-off of routers and servers– Rerouting around failures (IP)

– Hot-swaps and rebooting of hardware

• Long: Rearrangements of existing components– Applications/clients/servers can come and go

– Hardware of all types can come and go

• Longer: New applications and hardware– Plug and play if they obey the protocols

TCP/IP fragility on many timescales

• Shortest: File transfers from different users– End systems w/o congestion control won’t

fairly share

• Short: Fail-on of components– Distributed denial of service– Black-holing and other fail-on cascading

failures

• Long: Spam, viruses, worms

• Longer: No economic model for ISPs?

Robustness/evolvability on many timescales• Shortest to short: Fluctuations in supply/demand

– Allosteric regulation of enzymes (4)

– Expression of enzyme level (3)

• Short: Failure/loss of individual enzyme molecules (3)– Chaperones attempt repair, proteases degrade

– Transcription makes more

• Long: Incorporating new components– Acquire new enzymes by lateral gene transfer

• Longer: Creating new applications and hardware– Duplication and divergent evolution of new enzymes

that still obey basic protocols

Co-factors

Fatty acids

Sugars



assembly

Proteins

Pre

curs

ors

Carriers

Genes

DNA replication

Trans*

Nutrient


Co-factors

Fatty acids

Sugars



assembly

Proteins

Pre

curs

ors



Carriers

Genes


Trans*

Nutrient


– Allosteric regulation of enzymes (4)– Expression of enzyme level (3)

• Short: Failure/loss of individual enzyme molecules (3)– Chaperones attempt repair, proteases degrade – Transcription makes more





assembly

Proteins



Genes

DNA replication

Trans*

DnaK

rpoH

Lon

Other operons

motif

DnaK

rpoH

Lon

DnaK

Lon

Heat

degradation

folded unfolded

Other operons

motif

RNAP

DnaKRNAP

DnaK

rpoH

FtsH Lon

Heat mRNA

Other operons

Lon

RNAP

DnaK

RNAP

DnaK

rpoH

FtsH Lon

Heat

mRNA

Other operons

DnaK

DnaK

ftsH

Lon

RNAP

DnaK

RNAP

DnaK

rpoH

FtsH Lon

Heat

mRNA

DnaK

DnaK

ftsH

Lon

Regulation of

protein levels


RNAP

DnaK

RNAP

DnaK

rpoH

FtsH Lon

Heat

mRNA

Other operons

DnaK

DnaK

ftsH

Lon

DnaK

rpoH

Lon

Other operons

motif

What if a pathway is needed?

But isn’t there?

Slower time scales ( hours-days), genes are transferred between organisms.

This is only possible with shared protocols.





• Longer: Creating new applications and hardware– Duplication and divergent evolution of new

enzymes that still obey basic protocols

Slowest time scales ( forever), genes are copied and mutate to create new enzymes.

Evolving evolvability?

VariationVariation Selection

?

Evolving evolvability?

VariationVariation Selection

“facilitated”“structured”“organized”

Variety ofconsumers

Variety of producers

Energy carriers

transport assemblymetabolism

Robust?: Fragile to fluctuations Evolvable?: Hard to change

Biochem fragility on many timescales

• Shortest: Fluctuations in demand/supply that exceeds regulatory capability (e.g. glycolytic oscillations)

• Short: Fail-on of components– Indiscriminate kinases, loss of repression, …– Loss of tumor suppressors

• Long: Infectious hijacking

• Longer: Diabetes, obesity




• Are there robustness/fragility “conservation laws”?

Hard constraints



• Control (Bode)


• Consider simplest case with distributed sensing and actuation and nontrivial communications and controls

-e=d-u

Control

ControlChannel

u

CC

Cost of remote control

Actuator

Minimal networking issues:• Real-time control of (possibly unstable) plant subject to disturbances• Actuation may be remote, necessitating control over a communication channel.• (For simplicity, won’t show actuator explicitly in sequel…)

Disturbance

d

Plant+local

sensor

Summary

Disturbance-e=d-u

Control SensorChannel Encode

Plant+local

sensorRemoteSensor

dd

r

ControlChannel SC

u

CC

More networking issues:• Remote real-time control of (possibly unstable) plant subject to disturbances• Network may provide an “early warning” via remote sensing of disturbance• Communication may be involved in both remote control and sensing

Benefit of remote sensing

Disturbance-e=d-u


Plant+local

sensorRemoteSensor

dd

r

ControlChannel

SC

u

CC

ES

D

Summary

Minimal networking “hard constraints”:• What are the benefits of remote sensing using a channel to signal to a controller?• What are the costs of remote control over a channel?• Express results in terms relevant to control of the plant, such as sensitivity:

or logS S

Disturbance-e=d-u


Plant RemoteSensor

dd

r

ControlChannel SC

u

CC

log S d

log S d

CClog( )a

0SC d u r

d u r

max

Benefit of control

Costs of:

Stabilization

Remote actuation

Feedback Benefit of remote sensing

Need high capacity

and low latency

/S E D Results

Attenuation of

disturbance

Cost of stabilization

log|S| “benefit” has an interpretation as entropy reduction from disturbance to error.

log S d

log S d

log( )a

-e=d-u

Control

Plant+local

sensor

u

• This benefit has various limits and costs, which in simple local control not involving remote sensing or actuation is just

Amplification of

disturbance

• Note that feedback control can thus give no net attenuation of disturbances, but simply moves log|S| around…

d /S E D

log S d

log S d

CClog( )a

0SC d u r

d u r

max

Benefit of control Costs of:

Stabilization

Remote actuation

Feedback Benefit of remote sensing

Need high capacity

and low latency

New results

The benefits of control are:• Aggravated by plant instability and remote actuation• Enhanced by remote sensing

Hard bounds explicitly depends on both capacity and latency of communication

Disturbance-e=d-u

Decode Channel

u

Encode

d delayd

delay

rCapacity C

As ,

( ) 0

d

h D C e

( ) ( )h E h D C

Features of the theory:1. Hard bounds2. Achievable (assumptions)3. Solution decomposable (assumptions)

ShannonRecall

r = total delay of encoding, decoding, and channeld =disturbance arrival delay from where it is remotely sensed

*

* The interpretation of depends on the details of the model.

Disturbance-e=d-u

Decode Channel

u

Encode

d delayd

delay

rCapacity C

As ,

( ) 0

d

h D C e

( ) ( )h E h D C

ShannonRecall

This is a nonstandard way of describing the results but will be convenient later.r = total delay of encoding, decoding, and channeld =disturbance arrival delay from where it is remotely sensed

Disturbance-e=d-u

Decode &Control

Channel

u

Encode

d delayd

delay

rCapacity C

( ) ( )h E h D C

Shannon

• We can think of this as a simple “network” control problem with a disturbance that can be remotely sensed.• A “controller” decodes a signal sent over a noisy channel and attempts to make the error small.• The entropy reduction in the error is bounded by the channel capacity.• We’ll return to this after motivating more complex control…

Biology motivation

• Illustrate hard constraints on feedback control

• Except in core metabolism, efficiency is not a dominant constraint

• In general, biological complexity is driven by robustness and control

• Start with illustration of results due to Bode circa 1940…

Metab

oliteE

nzym

e

kx

1 1

max

( ) ( )

( )1

( )

k k k k k k

m

x V x V x

VV x t

t

x

K

x

max( )1

( )m

VV x t

K

x t

( )x t

1 1( )k kV x

1kx

( )k kV xkx

Thermodynamics and metabolism

kx

1 1

max

( ) ( )

( )1

( )

k k k k k

m

x V x V x

VV x t

K

x t

1 1( )k kV x

( )k kV x

nx

1 0 1 1

max0

( ) ( )

( )

( )1

n

d

fb

x V x V x

VV x t

hx t t

K

perturbation

Product inhibition

Yi, Ingalls, Goncalves, Sauro

nx

0 ( )nV x

h = [0 1 2 3]

0 5 10 15 200.8

0.85

0.9

0.95

1

1.05

Time (minutes)

[AT

P]

h = 2

h = 1

h = 0

1 1 1 0

max0

( ) ( )

( )

( )1

n

d

fb

x V x V x

VV x t

x t t

K

h

Step increase in demand for product or “ATP.”

h = 3

Ideal product concentration

nxperturbation

nx

0 ( )nV x

0 5 10 15 20Time

h = 3

h = 2

h = 1

h = 0

Tighter steady-stateregulation

Transients, Oscillations

Higher feedback “gain”

It is well-known that many biological regulatory networks can oscillate, and presumably many more will be discovered.

0 5 10 15 20Time

h = 3

h = 2

h = 1

h = 0



• Are these tradeoffs an artifice of this model?• Does it matter if the model is nonlinear, stochastic, distributed, PDEs, etc? Does it depend on the model at all?• Are these tradeoffs due to a frozen accident of evolution and not an absolute necessity?

• The answer to all these questions is no.

0 5 10 15 200.8

0.85

0.9

0.95

1

1.05

Time (minutes)

[AT

P]

h = 3

h = 0

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(S

n/S

0)

h = 3

h = 0

Spectrum

0log loghS S

Ideal

0 5 10 15 200.8

0.85

0.9

0.95

1

1.05

Time (minutes)

[AT

P]

h = 3

h = 0

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

Spectrum

Time response

Robust

Yet fragile

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 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 = 0 Robust

Yet fragile

log ) ?nx d constant 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(S

n/S

0)

h = 3

h = 2

h = 1

h = 0

log )nxF(



log )nx d constant F(

Theorem

log )nx d constant F(

log|S |

Tighter regulation


Biological complexity is dominated by the evolution of

mechanisms to more finely tune this robustness/fragility tradeoff.

This tradeoff is a law.

log S d

log S d

benefits costs

log S d

log S d

• benefits = attenuation of disturbance• goal: make this as negative as possible

cost = amplificationgoal: make this small

Constraint:

-e=d-u

Control

uPlant

d

delay

u

log 0S d

Bode

ES

D

• What helps or hurts this tradeoff?• Helps: remote sensing• Hurts: instability, remote control

Control demo

0log ( ) /S d L

L

Note: assumes continuous time

• A classic illustration of instability and control, the simple inverted pendulum experiment, illustrates the essential point.

• Here the pendulum is the plant, and the human is the controller. The experiment can be done with sticks of different lengths or with an extendable pointer, holding the proximal tip between thumb and forefinger so that it is free to rotate but not otherwise slip.

• Unstable plants are intrinsically more difficult to control than stable ones, and are generally avoided unless the instability confers some great functional advantage, which it often does.

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

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

-e=d-u

Control

uPlant

d

delay

u

log S dL

/ L

ES

D

L

Freudenberg and Looze, 1984

a

-e=d-u

Control

uPlant

d

delay

u

log S d

Bode

a

ES

D

log S d

benefits costs stabilize

a

-e=d-u

Control

uPlant

d

delay

u

log S d

Bode

a

ES

D

log S d

benefits costs stabilize

Negative is good

-e=d-u

Control

uPlant

d

delay

u

Bode

a

ES

D

alog S d

log S d

1. Hard bounds2. Achievable (assumptions)3. Solution decomposable (assumptions)

With Martins and Dahleh

New theory, including comms..

0log ( ) /S d L

Switch to discrete time.

0

1log ( ) log( ) log 1 1/S d a L

L

Disturbance-e=d-u

Decode Channel

u

Encode

d delayd

delay

rCapacity C

As , ( ) 0d h D C e

( ) ( )h E h D C


ShannonRecall

-e=d-u

Control

uPlant

d

delay

u

Disturbance-e=d-u

Decode Channel

u

Encode

d delayd

delay

rCapacity C

log log( )S d a As , ( ) 0d h D C e

( ) ( )h E h D C


Incompatible assumptions (for 50+ years).

Bode Shannon

Disturbance-

Control Channel

u

Encode

RemoteSensor

d delayd

delay

u

delay

rCapacity C

-e=d-u

Control

uPlant

d

delay

u

0 d u r

C d u r

log log( )S d a

Disturbance-e=d-u

Control Channel

u

Encode

PlantRemoteSensor

d delayd

delay

u

delay

rCapacity C

What is the benefit to control of remote sensing?

Disturbance-e=d-u

Control Channel

u

Encode

PlantRemoteSensor

d delayd

delay

u

delay

rCapacity C

0log log( )

d u rS d a

C d u r

Cost of stabilization

Benefits of remote sensing

Need relatively low

latency

Disturbance-e=d-u

Control Channel

u

Encode

PlantRemoteSensor

d delayd

delay

u

delay

rCapacity C

0log log( )

d u rS d a

C d u r


New unified comms, controls, and stat mech.?

Disturbance-e=d-u

Control Channel

u

Encode

PlantRemoteSensor

d delayd

delay

u

delay

rCapacity C

0log log( )

d u rS d a

C d u r

Claim (or irresponsible speculation?):1. Biological complexity is dominated

by the tradeoffs which are captured (simplistically) in this theorem.

2. Ditto for techno-networks.

Disturbance-e=d-u

Control Channel

u

Encode

PlantRemoteSensor

d delayd

delay

u

delay

rCapacity C

0log log( )

d u rS d a

C d u r

What is likely (though not agreed upon) is Bode/Shannon is a much better point-to-point communication theory to serve as a foundation for networks than either Bode or Shannon alone.

log( )alog S d

log( )a

log S d

benefits costs

Disturbance-e=d-u

Control Channel

u

Encode

PlantRemoteSensor

d delayd

delay

u

delay

rCapacity C

C


-e=d-u

Control

Plant

ControlChannel

u

CC


What is the cost if the control action must be done remotely and communication to an actuator is over a channel with capacity CC ?

Actuator

-e=d-u

Control

Plant ControlChannel

u

CC


benefits costs

log( )alog S d

CC

(Note: needs directed information…)

Note: Actuator not shown.

-e=d-u

Control

Plant ControlChannel

u

CCCost of remote control


log( )alog S d

log S d

benefits costs

C

log( )alog S d

CC

Putting it all together

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

dd

r

ControlChannel

SC

u

CC

log S d

log S d

benefits

feedback

SC

CCstabilize

remotesensing

remote control

log( )a

costs

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

dd

r

ControlChannel SC

u

CC

Bode/Shannon is likely a better p-to-p comms theory to serve as a foundation for networks than either Bode or Shannon alone.

log S d

log S d

SC

CClog( )a

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

dd

r

ControlChannel SC

u

CC

log S d

log S d

SC

CClog( )a

http://www.glue.umd.edu/~nmartins/

Nuno C Martins and Munther A Dahleh, Feedback Control in the Presence of Noisy Channels: “Bode-Like” Fundamental Limitations of Performance.(Submitted to the IEEE Transactions on Automatic Control) Abridged version in ACC 2005Fundamental Limitations of Disturbance Attenuation in the Presence of Side InformationNuno C. Martins, Munther A. Dahleh and John C. Doyle(Submitted to the IEEE Transactions on Automatic Control) Abridged version in CDC 2005

http://www.glue.umd.edu/~nmartins/bode1.pdf

http://www.glue.umd.edu/~nmartins/bode1.pdf

Work in progress



• Control (Bode)



the beginnings

The search for simplicity

Question

AnswerSimple

Simple Simplicity

• Seek the hidden simplicity in our apparently complex world

The end of certainty

Question

AnswerSimple

Simple,

PredictableSimplicity

Complex,

Unpredictable

Emergence

1 0

1bounded 1 , =

2k k kc z cz z z

“Emergent” complexity

• Simple question• Undecidable

• No short proof• Chaos• Fractals

Mandelbrot

The complete picture

Question

AnswerSimple

Simple Simplicity

ComplexEmergence

Simple, predictable, reliable, robust versus

Complex, unpredictable, fragile


Question

AnswerSimple Complex

Simple Simplicity Organization

ComplexEmergence

Irreducibility




Question

AnswerSimple Complex

Simple Simplicity Organization

ComplexEmergence

Irreducibility



Nightmare

1 1k k kz cz z

But simulation is fundamentally limited• Gridding is not scalable• Finite simulation inconclusive

0

1

2z

The way forward?

Question

AnswerSimple

Simple,


Complex,

Unpredictable

Emergence

It’s easy to prove that this disk is in M.

Other points in M are fragile to the definition of the map.

1 1 k k kz c z z

Merely stating the obvious.

Main idea

Main idea

The longer the proof, the more fragile the remaining regions.

The proof of this region is a bit longer.

Main idea

And so on…

Proof even longer.

Easy to prove these points are in Mset.

Easy to prove these points are not in Mset.

Proofs get harder.(But all still “easy.”)

What’s left gets more fragile.

What’s left gets more fragile.

Breaking hard problems

• SOSTOOLS proof theory and software (Parrilo, Prajna, Papachristodoulou)

• Nested family of (dual) proof algorithms• Each family is polynomial time• Recovers many “gold standard” algorithms

as special cases, and immediately improves• No a priori polynomial bound on depth

(otherwise P=NP=coNP)• Conjecture: Complexity implies fragility

c “Robust yet

fragile” systems?

• Long proofs indicate fragility:• True fragility (which must be fixed) or• Artifact of the model (which must be rectified) or• Weakness in the proof techniques (ditto)

• Potentially fundamentally changes the apparent intractability of organized complexity• Brings back together two research areas :

• Numerical analysis and ill-conditioning• Computational complexity (P, NP/coNP, undecidable)

The way forward?

Question

AnswerSimple

Simple,


Complex,

FragileEmergence

Variety ofresponses

Variety of Ligands & Receptors

G-proteinsPrimary targets

Variety ofresponses


Transmitter

Receiver

• Ubiquitous protocol• “Hourglass”• “Robust yet fragile”• Robust & evolvable• Fragile to “hijacking”• Manages extreme

heterogeneity with selected homogeneity

• Accident or necessity?

Signal transduction

Random walk

Ligand Motion Motor

Bacterial chemotaxis

Ligand

SignalTransduction

gradient

Biased random walk

Motion Motor

CheY

PMF

++

++


Variety of receptors/

ligands Common cytoplasmic

domains

Common signal carrier

Common energy carrier

Mot

or

Var

iety

of

Lig

ands

& R

ecep

tors

Tra

nsm

itte

r R

ecei

ver

Motor

Variety of Ligands& Receptors

Transmitter Receiver

Variety ofresponses


Transmitter

Receiver

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

Signal transduction

IP

TCP

Applications

Link

Variety ofresponses


Transmitter

Receiver

Motor



Motor



OtherResponses

Other Receptors &

Ligands


OtherResponses

Other Receptors &

Ligands


OtherResponses

Other Receptors &

Ligands


OtherResponses

Other Receptors &

Ligands


OtherResponses

Other Receptors &

Ligands


OtherResponses

Other Receptors &

Ligands


OtherResponses

Other Receptors &

Ligands


OtherResponses

Other Receptors &

Ligands


OtherResponses

Other Receptors &

Ligands


OtherResponses

Other Receptors &

Ligands


OtherResponses

Other Receptors &

Ligands


OtherResponses

Other Receptors &

Ligands



• All use the same protocol- Histidine autokinase

transmitter- Aspartyl phospho-

acceptor receiver• Huge variety of receptors

and responses

Molecular phylogenies show evolvability of the bowtie architecture.

invariant active-site residues

conserved residues of interaction surface with phosphotransferase domains

highly variable amino acids of the interaction surface

that are responsible for specificity of the

interaction

conserved functional domains

highly variability for

specificity of the interaction

• Automobiles: Keys provide specificity but no other function. Other function conserved, driver/vehicle interface protocol is “universal.”• Ethernet cables: Specificity via MAC addresses, function via standardized protocols.

MAC

invariant active-site residues

http://www.gifart.com/cgi-bin/affiliate/clickthru.cgi/directory

Variety ofresponses



Variety ofresponses


Transmitter

Receiver


• Ubiquitous eukaryote protocol

• Huge variety of – receptors/ligands– downstream responses

• Large number of G-proteins grouped into similar classes

• Handful of primary targets

GGGDP GTP

GDPGTP

In

In

Out

P

RhoRhoGDP GTP

GDPGTP

In

In

Out

P

Ligand

Receptor

RGS

GDI

GDI

GEF

GAP

Responses

Receptors


GDP GTP

GDPGTP

In

In

Out

P

P

GDP GTP

GDPGTP

Out

In

InSignal integration: High “fan in” and “fan out”

RobustnessImpedance matching:Independent of G of inputs and outputs

Speed, adaptation, integration, evolvability

UncertainUncertain

UncertainUncertain

Variety ofresponses


IntermediatesFragile

and hard to change

Robust and highly

evolvable

RhoRhoGDP GTP

GDPGTPIn

In

Out

P

GDI

GDI

GEF

GAP

Fragility?

• A huge variety of pathogens attack and hijack GTPases.

• A huge variety of cancers are associated with altered (hijacked) GTPase pathways.

• The GTPases may be the least evolvable elements in signaling pathways, in part because they facilitate evolvability elsewhere

GGGDP GTP

GDPGTP

In

C-AMP

P

Ligand

Receptor

Cholera toxin

Hijacking

Cholera toxins hijack the signal transduction by blocking a GTPase activity.

Bacterial virulence factors targeting Rho GTPases: parasitism or symbiosis?

Patrice Boquet and Emmanuel Lemichez

TRENDS in Cell Biology May 2003

Variety ofresponses



Variety ofresponses


Transmitter

Receiver

• Ubiquitous protocol• “Hourglass”• Robust & evolvable• Fragile to “hijacking”• Manages extreme



But you already knew all this.

A look back and forward

• The Internet architecture was designed without a theory.

• Many academic theorists told the engineers it would never work.

• We now have a nascent theory that confirms that the engineers were right.

• For MANETs and other new technologies, let’s hope we can avoid a repeat of this history.

MultiscalePhysics

SystemsBiology


Core theory

challenges

RNAP

DnaK

RNAP

DnaK

rpoH

FtsH Lon

Heat

mRNA

DnaK

DnaK

ftsH

Lon

Regulation of

protein levels


PMF

++

++


Co-factors

Fatty acids

Sugars


Catabolism

Proteins

Prec

urso

rs


Carriers

Core metabolism

Genes


Trans*

Lessons from the cell and Internet

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

Variety ofresponses



Variety ofresponses


Transmitter

Receiver

• Ubiquitous protocol• “Hourglass”• “Robust yet fragile”• Robust & evolvable• Fragile to “hijacking”• Manages extreme



Signal transduction



Bio: Huge variety of environments, metabolisms


Huge variety of genomes

Universal control

architecture

co-factors

Documents

nascent theory

systems biology

theoretical biology

fragilehuman robustness

dynamical systems

parallel stories

convergent understanding

mechanisms responsible