Architecture, networks, and complexity John Doyle John G Braun Professor Control and dynamical...

Architecture, networks, and complexity

John Doyle

John G Braun Professor

Control and dynamical systemsBioEngineering, Electrical Engineering

Caltech

NRC theory report: Bad news and good news

Bad: Attempts to connect with theory• Topology, modularity, information,…Good: Biology motivation• Diversity• Metabolism• Cell interior• Architecture (is not topology)• Robustness• Decision• Behavior

Alternative: Essential ideas• Listening to physicians, biologists, and

engineers

• Robust yet fragile (RYF)• “Constraints that deconstrain” (G&K)• Unity creating diversity

• Network architecture • Layering• Control and dynamics (C&D)• Hourglasses and Bowties

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 OtherLongterm Visitor

Thanks to you for inviting me, and

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

MultiscalePhysics

SystemsBiology & Medicine

Network Centric,Pervasive,Embedded,Ubiquitous

Core theory

challenges

My interests

Sustainability?

SystemsBiology & Medicine

Bacterial networks• Necessity in chemotaxis• Design principles in heat shock response• Architecture of metabolism• Origin of high variability and power laws• Architecture of the cell• Control of core metabolism and glycolytic oscillations

SBML/SBWSOSTOOLSWildfire ecologyPhysiology and medicine (new)

Publications: Science, Nature, Cell, PNAS, PLOS, Bioinfo., Trends, IEEE Proc., IET SysBio, FEBS, PRL,…

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.”

Feathers and

flapping? Or lift, drag, propulsion, and control?

Recommendations

• (Obviously…) More and better theory

• Need an “architecture” for research that is as networked as biology and our best technologies

• Create the right “waist” of the research hourglass

• E.g. find the constraints that deconstrain

Robust Yet Fragile

Human complexity

Efficient, flexible metabolism Complex development and Immune systems Regeneration & renewal Complex societies Advanced technologies

Obesity and diabetes Rich microbe ecosystem Inflammation, Auto-Im. Cancer Epidemics, war, … Catastrophic failures

• Evolved mechanisms for robustness allow for, even facilitate, novel, severe fragilities elsewhere

• often involving hijacking/exploiting the same mechanism• There are hard constraints (i.e. theorems with proofs)

food intake

Glucose

Oxygen

Amino acids

Fatty acids

Organs

Tissues

Molecules

Universal metabolic system

Peter Sterling and Allostasis

Prefrontalcortex

Accumbensdopamine

Universal reward systemssportsmusicdancecrafts arttoolmaking sexfood

Dopamine,

Ghrelin,

Leptin,…

Prefrontalcortex

Accumbensdopamine

Universal reward systemssportsmusicdancecrafts arttoolmaking sexfood

Glucose

Oxygen

Organs

Tissues

Molecules

Universal metabolic system

Bloodfood

Prefrontalcortex

Accumbensdopamine

workfamily communitynature

Universal reward systems

Robust and adaptive, yet …

food sextoolmakingsportsmusicdancecrafts art

sexfoodtoolmakingsportsmusicdancecrafts art

Prefrontalcortex

Accumbensdopamine

sexfoodtoolmakingsportsmusicdancecrafts art

Prefrontalcortex

Accumbensdopamine

Vicarious

saltsugar/fatnicotinealcohol

industrialagriculture

market/consumerculture

sextoolmakingsportsmusicdancecrafts art

Prefrontalcortex

Accumbensdopamine

Vicarious

cocaineamphetamine

Vicarious

high sodium

obesity

overwork

smoking

alcoholism

drug abuse

hyper-tension

athero-sclerosis

diabetes

inflammation

immunesuppression

coronary,cerebro-vascular,reno-vascular

cancer

cirrhosis

accidents/homicide/suicide

Vicarious

high sodium

obesity

overwork

smoking

alcoholism

drug abuse

hyper-tension

athero-sclerosis

diabetes

inflammation

immunesuppression

coronary,cerebro-vascular,reno-vascular

cancer

cirrhosis

accidents/homicide/suicide

VTA dopamine

Glucose

Oxygen

Robust Yet Fragile

Human complexity

• 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)

Robust yet fragileSystems can have robustness of

– Some properties to– Some perturbations in – Some components and/or environment

Yet fragile to other properties or perturbations.

Many issues are special cases, e.g.:• Efficiency: robustness to resource scarcity• Scalability: robustness to changes in scale• Evolvability: robustness of lineages on long times

to possibly large perturbations

Case studies

Today (primary):• Cell biology

Today (secondary):• Internet• Toy example: Lego• Wildfire ecology• Physiology• Power grid• Manufacturing• Transportation

Other possibilities:• Turbulence• Statistical mechanics• Physiology (e.g. HR

variability, exercise and fatigue, trauma and intensive care)

• RYF physio (e.g. diabetes, obesity, addiction, …)

• Disasters statistics (earthquakes)

Bio and hi-tech nets

Exhibit extremes of

• Robust Yet Fragile

• Simplicity and complexity

• Unity and diversity

• Evolvable and frozen

• Constrained and deconstrained

What makes this possible and/ or inevitable?

Architecture

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

Architecture

Robust Yet Fragile

Human complexity

• It is much easier to create the robust features than to prevent the fragilities.

• There are poorly understood “conservation laws” at work

Robust yet fragile

Most essential challenge in technology, society, politics, ecosystems, medicine, etc:

• Managing spiraling complexity/fragility

• Not predicting what is likely or typical

• But understanding what is catastrophic (though perhaps rare)

What community will step up and be central in this challenge?

Components and materials

Systems requirements: functional, efficient,robust, evolvable,

scalable

Robust yet fragile

System and architecture

Perturbations

Component

System-level

Emergent Protocols

Architecture= Constraints

Aim: a universal taxonomy of complex systems and theories

• Describe systems/components in terms of constraints on what is possible

• Decompose constraints into component, system-level, protocols, and emergent

• Not necessarily unique, but hopefully illuminating nonetheless

Contraints that deconstrain

fan-in of diverse

inputs

fan-out of diverse

outputs

universal carriers

Diversefunction

Diversecomponents

UniversalControl

Universal architectures

• Hourglasses for layering of control

• Bowties for flows within layers

Evolution of theory

• Verbal arguments (stories, cartoons, diagrams)• Data and statistics (plots, tables)• Modeling and simulation (dynamics, numerics)• Analysis (theorems, proofs)• Synthesis (hard limits on the achievable, reverse

engineering good designs, forward engineering new designs)

All levels interact and iterate

Example: Theory of planetary motion

• Verbal (Ptolemy, Copernicus)• Data & stats (Brahe, Galileo, Kepler)• Model & sim (Newton, Einstein)• Analysis (Lagrange, Hamilton,

Poincare)• Synthesis (NASA/JPL)

All levels interact and iterate

Drill down

• Describe theory• Show some math• Just to give a flavor• You can ignore details• Always return to verbal

descriptions and hand-waving summaries

Verbal

Data/stat

Mod/sim

Analysis

Synthesis

Synthesis theories: Limits and tradeoffs

On systems and their components

• Thermodynamics (Carnot)

• Communications (Shannon)

• Control (Bode)

• Computation (Turing/Gödel)

Assume different architectures a priori.

No networks

Hard limits and tradeoffs

On systems and their components• Thermodynamics (Carnot)• Communications (Shannon)• Control (Bode) • Computation (Turing/Gödel)

• Fragmented and incompatible• Cannot be used as a basis for

comparing architectures• New unifications are encouraging

No dynamics or feedback

Hard limits and tradeoffs

On systems and their components• Thermodynamics (Carnot)• Communications (Shannon)• Control (Bode) • Computation (Turing/Gödel)

• Include dynamics and feedback• Extend to networks• New unifications are encouraging

Robust/fragile

is unifyingconcept

Why glycolytic oscillations?

• Various answers depend on meaning of “why”• Will go deeper into “why” using stages…• Start with simplest possible models• Motivate generalizable and scalable methods• Extremely familiar and “done” problem in biology

and dynamics at the small circuit level• Convenient to introduce new theory and thinking

using the most familiar possible examples

Basics of glyc-oscillations

• Verbal arguments (stories, cartoons, diagrams)• Data and statistics (plots, tables)

Result: Cells and extracts show oscillatory behavior.

Why? Modeling and simulation

• Verbal arguments (stories, cartoons, diagrams)• Data and statistics (plots, tables)• Modeling and simulation (dynamics, numerics)

• Why = propose mechanism, model, simulate, compare with data

• Has been done extensively for this problem• What’s new? Simplicity and robustness

Control

0 xk x Autocatalytic

reaction reactionmetabolite

consumption

1 1 01

x q qVxk y k x

Catabolism

Carriers

Co-factors

Fatty acids

Sugars

NucleotidesAmino Acids

Core metabolism

Catabolism

Carriers

Catabolism

TCAPyr

F1-6BP

TCAPyr

F1-6BP

TCAPyr

F1-6BP

Autocatalytic

Carriers

F1-6BP

PEP Pyr

Regulatory

TCAPyr

F1-6BP

PEP Pyr

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

Mass &Reaction

Energyflux

Balance

dxSv x

Stoichiometry or mass and energy balance

Nutrients Products

Internal

Biology is not a graph.

Mass &Reaction

Mass&Energy Energyflux

Balance

dxSv x

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 (?!?)

F1-6BP

PEP Pyr

Mass &Reaction

Energyflux

Balance

dxSv x

Stoichiometry matrix

Regulation of enzyme levels by transcription/translation/degradation

F1-6BP

PEP Pyr

Mass &Reaction

Energyflux

Balance

dxSv x

F1-6BP

PEP Pyr

Mass &Reaction

Energyflux

Balance

dxSv x

Allosteric regulation of enzymes

F1-6BP

PEP Pyr

Mass &Reaction

( ) Energyflux

Balance

dxSv x

Regulation of enzyme levels

F1-6BP

PEP Pyr

Regulation of enzyme levels

Fast response

F1-6BP

PEP Pyr

F1-6BP

0 xk x

Control

Autocatalytic

F1-6BP

0 xk x

Control

Autocatalytic

F1-6BPGly3p

0 xk x

Control

Autocatalytic

0 xk x

Control

Autocatalytic

1 1 01 y x

x q qVxk y k x

Autocatalytic

0 xk x

Control

xx q q

Autocatalytic

Mass &Reaction

Energyflux

Balance

dxSv x

1 1 01

x q qVxk y k x

0 xk x

1 1 01 1

x q qVxky x

WOLOG normalize concentration and time

1 1 01 y x

x q qVxk y k x

0 xk x

1 1 01 1

x q qVxky x

Linearization:

x q qx ky x

NominalVariable Process

Value?

autocatalysis 1

inhibition 2.5

1 enzyme 3

2 enzyme .3

Steady state: 1x

time10 15 20

1x error

Linearization:

x q qx ky x

Value?

autocatalysis 1

inhibition 2.5

1 enzyme 3

2 enzyme .3

x error

time0 5 10 15 20

Linearization:

x q qx ky x

Value?

autocatalysis 1

inhibition 2.5

1 enzyme 3

2 enzyme .3

Why? Modeling and simulation

• Why = propose mechanism, model, simulate, compare with data

• Scalable to larger systems? Yes• Nonlinear? Yes• Explore parameter space? Awkward• Explore sets of uncertain models? Awkward

Why: Analysis

• Verbal arguments (stories, cartoons, diagrams)• Data and statistics (plots, tables)• Modeling and simulation (dynamics, numerics)• Analysis (theorems, proofs)

• Why = parameter regimes of instability, global results with nonlinearities

Linearization:

x q qx ky x

Value?

autocatalysis 1

inhibition 2.5

1 enzyme 3

2 enzyme .3

Stable iff

1 11 1

kq h q

• Explicit regions of (in)stability• Easy to compare with experiments• Oscillations caused by

• nonzero q (autocatalytic)• small k (low enzyme)• large V (high flux)• large h (strong inhibition)

• Slow response caused by• large q (autocatalytic)• small V (low flux)• small h (weak inhibition)

oscillationsslow

Linearization:

x q qx ky x

Value?

autocatalysis 1

inhibition 2.5

1 enzyme 3

2 enzyme .3

Stable iff

1 11 1

kq h q

.1 6k V 1 1

h qV q

0 5 10 15 20-1

oscillations

Stable iff

1 11 1

kq h q

.1 6k V 1 1

h qV q

0 5 10 15 20-1

0 10 20 30 40 50 600

1.5Nonlinear

Linearization:

x q qx ky x

Value?

autocatalysis 1

inhibition 2.5

1 enzyme 3

2 enzyme .3

Stable iff

1 11 1

kq h q

11 1q h

V 0 5 10 15 20

Linearization:

x q qx ky x

Value?

autocatalysis 1

inhibition 2.5

1 enzyme 3

2 enzyme .3

0 5 10 15 20-1

Conservation law?

Analysis issues

• Why = parameter regimes of instability, global results with nonlinearities

• Scalable to larger systems? Less than sim• Nonlinear? Yes• Explore parameter space? Better than sim• Explore sets of uncertain models? Better than sim• Prove what models can’t do? Yes

• Major research frontier

Why: Synthesis

• Are there intrinsic tradeoffs or is this a “frozen accident”? (The former.)

• What are the relevant engineering principles? • How to separate necessity from accident? • Are there hard limits or conservation laws that

apply? (Yes)• Is biology near these limits? (Apparently)• Why does autocatalysis and other efficiency issues

aggravate regulation? (Stay tuned)

0 5 10 15 20-1

Fourier

Transform

of error

h hS x = F(

ln lnh nomS S

Spectrum

1h 0 1 2 3 4 5

0 5 10 15 20-1

1h 0 1 2 3 4 5

Theorem:

0 5 10 15 20-1

0 1 2 3 4 5-2

.3k .1k

Why: Synthesis

• There are too many hard limits on achievable performance to show in one hour…

• Most are aggravated by – large q (more autocatalysis)

– small V and k (less enzyme)

• Thus tradeoffs between control response and efficiency

• Can summarize with hand-waving argument.• Why = it’s an inevitable consequence of

engineering tradoffs.

0 xk x

1 1 01 1

x q qVxky x

Why: Synthesis (to do)

• There are hard contraints and tradeoffs• Biology is hard up against these limits• Yet there remains “design freedom”• Why these particular “choices”?

• What has evolution optimized?

• Robustness (and evolvability)?

0 5 10 15 200.8

Time (minutes)

0 2 4 6 8 10-0.8

Frequency

Spectrum

Time response

Robust

Yet fragile

0 2 4 6 8 10-0.8

Frequency

h = 0 Robust

Yet fragile

0 2 4 6 8 10-0.8

Frequency

h = 0 Robust

Yet fragile

log ) ?nx d constant F(

0 2 4 6 8 10-0.8

Frequency

log )nxF(

Tighter steady-stateregulation

Transients, Oscillations

log )nx d constant F(

Theorem

log )nx d constant F(

log|S |

Tighter regulation

Transients, Oscillations

Biological complexity is dominated by the evolution of

mechanisms to more finely tune this robustness/fragility tradeoff.

This tradeoff is a law.

log S d

benefits costs

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

log 0S d

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

-e=d-u

Control

uPlant

log S dL

Freudenberg and Looze, 1984

-e=d-u

Control

uPlant

log S d

benefits costs stabilize

-e=d-u

Control

uPlant

log S d

Negative is good

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

ControlChannel SC

log S d

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.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)

Variety of producers

Electric powernetwork

Variety ofconsumers

• Good designs transform/manipulate energy• Subject to hard limits

Variety ofconsumers

Energy carriers

• 110 V, 60 Hz AC• (230V, 50 Hz AC)• Gasoline• ATP, glucose, etc• Proton motive force

Standard interface

Constraint that deconstrains

• Good designs transform/manipulate robustness• Subject to hard limits• Unifies theorems of Shannon and Bode (1940s)• Claim: This is the most crucial (known) limit

against which network complexity must cope

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

ControlChannel

log S d

benefits

feedback

CCstabilizeremotesensing

remote control

log( )a

Robust

log( )a

Fragile

-e=d-u

Control

uPlant

log S d

log S d a

-e=d-u

Control

uPlant

log S d

Negative is good

log S d a

log( )alog S d

log S d

benefits costs

Robust

log( )a Yet fragile

Bode’s integral formula

log( )alog S d

log( )a

log S d

benefits costs

Disturbance-e=d-u

Control

d delayd

Cost of control

Cost of stabilization

-e=d-u

Control

Plant ControlChannel

CC Cost of remote control

log( )alog S d

log S d

benefits costs

log( )alog S d

Disturbance-e=d-u

Control

ControlChannel

log S d

benefits

feedback

CCstabilize remote control

log( )a

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

ControlChannel

log S d

benefits

feedback

CCstabilize

remotesensing

remote control

log( )a

Benefit of remote sensing

log( )alog S d

log S d

benefits costs

log( )alog S d

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

ControlChannel

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

ControlChannel

log S d

benefits

feedback

CCstabilize

remotesensing

remote control

log( )a

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

ControlChannel SC

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

CClog( )a

Variety ofconsumers

• Good designs transform/manipulate energy• Subject to hard limits

• Good designs transform/manipulate robustness• Subject to hard limits• Unifies theorems of Shannon and Bode (1940s)• Claim: This is the most crucial (known) limit

against which network complexity must cope

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

ControlChannel

log S d

benefits

feedback

CCstabilizeremotesensing

remote control

log( )a

Robust

log( )a

Fragile

[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

[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.

• But if robustness/fragility are conserved, what does it mean for a system to be robust or fragile?

Robust

Fragile

• Robust systems systematically manage this tradeoff.• Fragile systems waste robustness.

• Some fragilities are inevitable in robust complex systems.

Emergent

Variety ofconsumers

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

• Robust designs transform/manipulate robustness• Subject (and close) to hard limits• Fragile designs are far away from hard limits and

waste robustness.

Disturbance-e=d-u

ControlSensor

ChannelEncode

PlantRemoteSensor

dControlChannel

log S d

CClog( )a

Robust

log( )a

FragileControl

ControlChannel

Co-factorsFatty acidsSugars

Nucleotides

Amino Acids Proteins

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

UniversalControl

Questions?

End of part 1

Architecture, networks, and complexity John Doyle John G Braun Professor Control and dynamical...

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