John Doyle 道陽 Jean-Lou Chameau Professor Control and Dynamical Systems, EE, & BioE

John Doyle 道陽Jean-Lou Chameau Professor

Control and Dynamical Systems, EE, & BioE

tech1#Ca

Universal laws and architectures:Theory and lessons from

brains, bugs, nets, grids, planes, docs, fire, bodies, fashion,

earthquakes, turbulence, music, buildings, cities, art, running, throwing, Synesthesia, spacecraft, statistical mechanics

accessibleaccountableaccurateadaptableadministrableaffordableauditableautonomyavailablecredibleprocess

capablecompatiblecomposable configurablecorrectnesscustomizabledebugabledegradabledeterminabledemonstrable

dependabledeployablediscoverable distributabledurableeffectiveefficientevolvableextensiblefail transparentfastfault-tolerantfidelityflexibleinspectableinstallableIntegrityinterchangeableinteroperable learnablemaintainable

manageablemobilemodifiablemodularnomadicoperableorthogonalityportableprecisionpredictableproducibleprovablerecoverablerelevantreliablerepeatablereproducibleresilientresponsivereusable robust

safety scalableseamlessself-sustainableserviceablesupportablesecurablesimplicitystablestandards

compliantsurvivablesustainabletailorabletestabletimelytraceableubiquitousunderstandableupgradableusable

Requirements on systems and architectures

accessibleaccountableaccurateadaptableadministrableaffordableauditableautonomyavailablecredibleprocess

capablecompatiblecomposable configurablecorrectnesscustomizabledebugabledegradabledeterminabledemonstrable

dependabledeployablediscoverable distributabledurableeffectiveefficientevolvableextensiblefail transparentfastfault-tolerantfidelityflexibleinspectableinstallableIntegrityinterchangeableinteroperable learnablemaintainable

manageablemobilemodifiablemodularnomadicoperableorthogonalityportableprecisionpredictableproducibleprovablerecoverablerelevantreliablerepeatablereproducibleresilientresponsivereusable robust

safety scalableseamlessself-sustainableserviceablesupportablesecurablesimplicitystablestandards

compliantsurvivablesustainabletailorabletestabletimelytraceableubiquitousunderstandableupgradableusable

Requirements on systems and architectures

When concepts fail, words arise. Mephistopheles, Faust, Goethe

Mephistopheles. …Enter the templed hall of Certainty.Student. Yet in each word some concept there must be.Mephistopheles. Quite true!

But don't torment yourself too anxiously;For at the point where concepts fail,At the right time a word is thrust in there…

When concepts fail, words arise. Mephistopheles, Faust, Goethe

• Concrete case studies• Theorems

Sorry, still too many words and slides.

Hopefully read later?

When concepts fail, words arise. Mephistopheles, Faust, Goethe

• Concrete case studies• Theorems

“Laws and Architecture” • Few words more misused• Few concepts more confused

What’s the best/simplest fix?

Reality is a crutch for people who can’t do math. Anon, Berkeley, 70’s

• Concrete case studies• Theorems

and words

• Brains• Nets/Grids (cyberphys)• Bugs (microbes, ants)• Medical physiology

• Lots of aerospace• Wildfire ecology• Earthquakes• Physics:

– turbulence, – stat mech (QM?)

• “Toy”: – Lego– clothing, fashion

• Buildings, cities• Synesthesia

Fundamentals!

Case Study

Focus today:• Neuroscience

+ People care+ Live demos

• Cell biology (esp. bacteria)+ Perfection Some people care

• Internet (of everything) (& Cyber-Phys)+ Understand the details- Flawed designs- Everything you’ve read is wrong (in science)*

• Medical physiology (esp. HRV)+ People care, somewhat familiar- Demos more difficult

* Mostly high impact “journals”

Focus today:• Neuroscience

+ People care+ Live demos

• Cell biology (esp. bacteria)+ Perfection Some people care

• Internet (of everything) (& Cyber-Phys)+ Understand the details- Flawed designs- Everything you’ve read is wrong (in science)*

• Medical physiology+ People care, somewhat familiar- Demos more difficult

* Mostly high impact “journals”

Glass 3.0

FaceWorld

Siri 3.0

What we want to build but can’t, yet.

The zombie apocalypse is already here…

accessibleaccountableaccurateadaptableadministrableaffordableauditableautonomyavailablecompatiblecomposable configurablecorrectnesscustomizabledebugabledegradabledeterminabledemonstrable

dependabledeployablediscoverable distributabledurableeffective

evolvableextensiblefail transparentfastfault-tolerantfidelityflexibleinspectableinstallableIntegrityinterchangeableinteroperable learnablemaintainable

manageablemobilemodifiablemodularnomadicoperableorthogonalityportableprecisionpredictableproducibleprovablerecoverablerelevantreliablerepeatablereproducibleresilientresponsivereusable

safety scalableseamlessself-sustainableserviceablesupportablesecurablesimplestablestandardssurvivable

tailorabletestabletimelytraceableubiquitousunderstandableupgradableusable

efficient

robust

sustainable

Sustainable robust + efficient

Priorities

• Functionality (behavior, semantics)• Robustness

– Uncertain environment and components– Fast (sense, decide, act)– Flexible (adaptable, evolvable)

• Efficiency– Energy– Other resources (make and maintain)

Simple, apparent, obvious

• Functionality • Robustness

– Uncertain environment and components– Fast (sense, decide, act)– Flexible (adaptable, evolvable)

• Efficiency

Hidden

Complexity Robustness

• Functionality (behavior, semantics)• Robustness

– Uncertain environment and components– Fast (sense, decide, act)– Flexible (adaptable, evolvable)

• Efficiency– Energy– Other resources (make and maintain)

accessibleaccountableaccurateadaptableadministrableaffordableauditableautonomyavailablecompatiblecomposable configurablecorrectnesscustomizabledebugabledegradabledeterminabledemonstrable

dependabledeployablediscoverable distributabledurableeffective

evolvableextensiblefail transparentfastfault-tolerantfidelityflexibleinspectableinstallableIntegrityinterchangeableinteroperable learnablemaintainable

manageablemobilemodifiablemodularnomadicoperableorthogonalityportableprecisionpredictableproducibleprovablerecoverablerelevantreliablerepeatablereproducibleresilientresponsivereusable

safety scalableseamlessself-sustainableserviceablesupportablesecurablesimplestablestandardssurvivable

tailorabletestabletimelytraceableubiquitousunderstandableupgradableusable

efficient

robust

sustainable

Sustainable robust + efficient

accessibleaccountableaccurateadaptableadministrableaffordableauditableautonomyavailablecompatiblecomposable configurablecorrectnesscustomizabledebugabledegradabledeterminabledemonstrable

dependabledeployablediscoverable distributabledurableeffective

evolvableextensiblefail

transparentfastfault-tolerantfidelityflexibleinspectableinstallableIntegrityinterchangeabl

einteroperable learnablemaintainable

manageablemobilemodifiablemodularnomadicoperableorthogonalit

yportableprecisionpredictableproducibleprovablerecoverablerelevantreliablerepeatablereproducibleresilientresponsivereusable

safety scalableseamlessself-sustainableserviceablesupportablesecurablesimplestablestandardssurvivable

tailorabletestabletimelytraceableubiquitousunderstandableupgradableusable

efficient

robust

sustainable

Simple dichotomous

tradeoff pairs

PCA Principal Concept Analysis

wasteful

fragile

efficient

robust

With function given

wasteful

fragile

efficient

robust

Actual

Ideal

The main tradeoff

Efficiency/instability/layers/feedback

• Sustainable infrastructure? (e.g. smartgrids)• Money/finance/lobbyists/etc• Industrialization• Society/agriculture/weapons/etc• Bipedalism• Maternal care• Warm blood• Flight• Mitochondria• Oxygen• Translation (ribosomes)• Glycolysis (2011 Science)

• New efficiencies but also instability/fragility• New distributed/layered/complex/active control

Live demo?

costly

fragile

efficient

robust

Tradeoffs(swim/crawl to run/bike)

Function=Locomotion

costly

fragile

efficient

robust

Tradeoffs

4x

>2x

wasteful

fragile

efficient

robust Ideal

Impossible (law)

Actual

Universal laws

wasteful

fragile

efficient

robust Ideal

Impossible (law)

Actual

The risk

wasteful

fragile

efficient

robust Ideal

Impossible (law)

Architecture

Universal laws and architectures

Flexibly achieves what’s possible

wasteful

fragile

efficient

robust Ideal

Impossible (law)

Architecture

Universal laws and architectures

Our heroes

Evolution Complexity

Efficiency/instability/layers/feedback

• Sustainable infrastructure? (e.g. smartgrids)• Money/finance/lobbyists/etc• Industrialization• Society/agriculture/weapons/etc• Bipedalism• Maternal care• Warm blood• Flight• Mitochondria• Oxygen• Translation (ribosomes)• Glycolysis (2011 Science)

• All create new efficiencies but also instabilities• Needs new distributed/layered/complex/active control

Major transitions

“Nothing in biology makes sense except in the light of evolution.”

T Dobzhansky

“Nothing in evolution makes sense except in the light of biology.”

Tony Dean (U Minn) paraphrasingT Dobzhansky

costly

fragile

efficient

robust

Tradeoffs

4x

>2x

wastefulefficient

Materials and energy have many “universal conservation laws” that limit achievable efficiency.

Perfect efficiency would have zero waste.

Impossible (law)

fragile

robust

Robustness also has “universal conservation laws” that are less familiar…

…though their consequence are surprisingly ubiquitous.

Impossible (law)

• Brains• Nets/Grids (cyberphys)• Bugs (microbes, ants)• Medical physiology• Lots of aerospace• Wildfire ecology• Earthquakes• Physics:

– turbulence, – stat mech (QM?)

• “Toy”: – Lego– clothing, fashion

• Buildings, cities• Synesthesia

fragile

robust

• Neuroscience+ People care

+Live demos!

1. experiments2. data3. theory4. universals

costly

fragile

efficient

robust

Tradeoffs

4x

>2x

Simpler demo?

costly

fragile

efficient

robust

hard

harder

A convenient cartoon

easy

Function=Movement

“costly”

fragile

“efficient?”

robust easy

hard

harder

A convenient cartoon demo

Function=Movement

“costly”

fragile

“efficient”

robust easy

hard

harder

up&short

cartoon demo

down or long

longshort

Impossible

Length is positive(not “waste,” but a cartoon)

cartoon demo

fragile

robust easy

hard

up&short down or long

Gravity is stabilizing

Gravity is destabilizing

Law #1 : MechanicsLaw #2 : Gravity

Universal laws?

Efficiency/instability/layers/feedback

• Sustainable infrastructure? (e.g. smartgrids)• Money/finance/lobbyists/etc• Industrialization• Society/agriculture/weapons/etc• Bipedalism• Maternal care• Warm blood• Flight• Mitochondria• Oxygen• Translation (ribosomes)• Glycolysis (2011 Science)

• New efficiencies but also instabilities• New distributed/layered/complex/active control

stabilizing

destabilizing

cartoon demo

Gravity is stabilizing

Gravity is destabilizing

Law #1 : MechanicsLaw #2 : Gravity

We think of mechanics and gravity as “obeying universal laws.”

But both “universal” and “law” are confused and overloaded, so unfortunate terminology.

Universal laws?

Gravity is stabilizing

Gravity is destabilizing

Law #1 : MechanicsLaw #2 : Gravity

We think of mechanics and gravity as “obeying universal laws.”

(Generally: constraints)

But the consequences (even of gravity) depend on other constraints.

Universal laws?

fragile

robust

harder

up&short down or long

More unstable

Law #1 : MechanicsLaw #2 : GravityLaw #3 : ??Law #4 : ??

fragile

robust

harder

up&short down or long

hardest!

hard harder hardest!

Easy to prove using simple models.

What is sensed matters.

Why?

Why?!?

fragile

robust

harder

up&short down or long

hardest!

Why?

Accident or necessity?Universal laws?

(4) Universal laws +

vision

Act

delay

+ Neuroscience

Balancing an inverted pendulum

Mechanics+Gravity +Light +

expz p

T pz p

Some minimal math details

easy

hard

Law #1 : MechanicsLaw #2 : Gravity

1d motion

Use “conservation laws”

2cos sin

cos sin 0

sinO

M m x ml u

x l g

y x l

M

m

l

l lengthm massM massg gravityu control force

y

x

u

Standard inverted pendulum

2cos sin

cos sin 0

sinO

M m x ml u

x l g

y x l

easy

hard

Law #1 : MechanicsLaw #2 : Gravity

0

O

M m x ml u

x l g

y x l

linearize

1d motion

2cos sin

cos sin 0

sinO

M m x ml u

x l g

y x l

eye

l

n noisee error

Law #3 : Light (vision)

0

O

M m x ml u

x l g

y x l n

hard harder

Easy to prove using simple models.

Why?vision

Act

delay

Law #3 : Light 0

O

M m x ml u

x l g

y x l n

eye

l

N noiseE error

ET j

N

Frequency domain

?T

eye vision

slow

Act

delay

Control

l

N noiseE error

ET j

N

expT p

Universal laws,art, music, Lego

vision

Act

delay

Balancing an inverted pendulum

Mechanics+Gravity +Light +

1p

l

.3s

22 2

2

2

1

( )

1

OO

O

x ls gu D s s Mls M m g

D s s

l l s gy x l u

D s

g m gp r r z

l M l l

0

O

M m x ml u

x l g

y x l n

Laplace transform

(One complex variable)

2 20

1exp ln exp ln

sup

exp lnexp

pT T j d

p

T T j

Tp

T

Fragility two ways (~ Bode* and Zames):

* With key help from Freudenberg and Seron et al

2 20

1exp ln exp ln

sup

pT T j d

p

T T j

exp ln

expT

pT

Amplification (noise to error)

Entropy rate

Energy (L2)

exp ln

expT

pT

Entropy rate

Energy (L2)

exp pt

delay

Before you can

react

time

state

intuition

10

100

Length, m.1 1.5.2

2

exp p1

pl

.3s

Shorter

Fragile

expT p

10

100

Length, m.1 1.5.2

2

exp p

.3s

.2sSlo

wer

1p

l

expT p

10

Length, m.1 1.5.2

2 loglog

0.2 0.4 0.6 0.8 12

4

6

8

10

linearF

ragile exp p

Fragile

Also exponential

in delay!

exp p

M m gp

Ml

10

Length, m.1 1.5.2

2

0.2 0.4 0.6 0.8 12

4

6

8

10

linearF

ragile

exp p

M

m

l

l lengthm massM massg gravity

Idealized model

exp p

M m gp

Ml

10

Length, m.1 1.5.2

2

0.2 0.4 0.6 0.8 12

4

6

8

10

linearF

ragile

exp p

M

m

l

l lengthm massM massg gravity

exp ln

expT

pT

Essential constraint (“law”):

eye vision

Act

delay

Control

l noise

error

P

+

noise

error

C

ET j

N

P

+

noise

error

C

ET j

N

sup sup Re( ) 0|T T j T s s

Max modulus

Proof?

1

exp

( ) ( ) exp

exp

Ms P s s

T M M p p p

T p

P

1

1

( ) ( )

P p T p

M p p

( ) ( ) ( ) ( ) 1

exp

T s M s s j

s s

P

+

noise

error

C

ET j

N

sup sup Re( ) 0|T T j T s s

( ) ( ) ( ) ( ) 1

exp

T s M s s j

s s

Max modulus

Proof?

M “minimum phase” (stably invertible) “all pass”

P

+

noise

error

C

ET j

N

sup sup Re( ) 0|T T j T s s

Max modulus

1

1

( ) ( )

P p T p

M p p

Proof?

( ) ( ) ( ) ( ) 1

exp

T s M s s j

s s

1

so 1

PCT

PCP p T p

P

+

noise

error

C

ET j

N

sup sup Re( ) 0|T T j T s s

Max modulus

Proof?

1

exp

( ) ( ) exp

exp

Ms P s s

T M M p p p

T p

P

1

1

( ) ( )

P p T p

M p p

( ) ( ) ( ) ( ) 1

exp

T s M s s j

s s

hard harder hardest!

Easy to prove using simple models.

What is sensed matters.

Why?

hard harder hardest!

What is sensed matters.

Unstable poles Unstable zeros

0l l0l l

exp ln

expT z p

pz pT

Fragility two ways (Bode* and Zames):

Unstable zeros

P

+

noise

error

C

sup sup Re( ) 0|T T j T s s

Proof?

( ) ( ) ( ) ( ) 1

exp

T s M s s j

s zs s

s z

1

exp

( ) ( ) exp

exp

M

s zs P s s

s z

z pT M M p p p

z p

z pT p

z p

P

P

+

noise

error

C

sup sup Re( ) 0|T T j T s s

Proof?

( ) ( ) ( ) ( ) 1

exp

T s M s s j

s zs s

s z

1so 1

& 0 0

PCT

PCP p T p

P z T z

P

+

noise

error

C

sup sup Re( ) 0|T T j T s s

Proof?

1

exp

( ) ( ) exp

exp

M

s zs P s s

s z

z pT M M p p p

z p

z pT p

z p

P

( ) ( ) ( ) ( ) 1

exp

T s M s s j

s zs s

s z

expexp

exl

pn z p

pz p

Tp

T

hardest!

0l l

0l l

exp p

expz p

pz p

10

100

Length, m

.1 1.5.22

1p

l

.3s

hardest!hard

expexp

exl

pn z p

pz p

Tp

T

10

100

Speed 1/

.1 1.5.22

.3s

exp p

Slower

vision

Act

delay

Vary delay?

easyharder

“costly”

fragile

“efficient”

robust

Hard tradeoff

“costly”

fragile

“efficient”

robust

Bad design

Gratuitous fragility

“costly”

fragile

“efficient”

robust

exp ln

expz pT

Tp

z p

Same constraints:Mechanics+Gravity+

Different consequences

Constrained sensing

unconstrained

The nature of “laws”

“costly”

fragile

“efficient”

robust easy

hard

harder hardest!

up&short down or long

Different consequences

wasteful

fragile

efficient

robust Ideal

Impossible (law)

Architecture

Universal laws and architectures

Flexibly achieves what’s possible

Cortex

eye vision

Actslow

delay

VOR

fast

Object motion

Head motion

Cerebellum

+

ErrorTune gain

gain

AOS

AOS = Accessory Optical system

noise

Act

Highly evolved (hidden)

architecture

Cortex

eye vision

Actslow

delay

VOR

fast

Object motion

Head motion

Cerebellum

+

ErrorTune gain

gain

AOS

AOS = Accessory Optical system

noise

Act

slowest

Cortex

eye vision

Actslow

delay

VOR

fast

Object motion

Head motion

Cerebellum

+

ErrorTune gain

gain

AOS

AOS = Accessory Optical system

noise

Act

Delays everywhere

Distributed control

slowest

Cortex

eye vision

Actslow

delay

VOR

fast

Object motion

Head motion

Cerebellum

+

ErrorTune gain

gain

AOS

noise

Act

slowestHeterogeneous

delays everywhere

Efficiency/instability/layers/feedback

• Sustainable infrastructure? (e.g. smartgrids)• Money/finance/lobbyists/etc• Industrialization• Society/agriculture/weapons/etc• Bipedalism• Maternal care• Warm blood• Flight• Mitochondria• Oxygen• Translation (ribosomes)• Glycolysis (2011 Science)

Major transitions

How universal? Very.

Chandra, Buzi, and Doyle

UG biochem, math, control theory

InsightAccessibleVerifiable

Glycolytic oscillations

• Exhaustively studied– Extensive experiments and data– Detailed models and simulations– Great! But all just deepen the mystery

• Perfectly illustrates “conservation law”• Without which? Bewilderment.

exp ln T z p

z pT

Law #1 : Chemistry (vs mechanics)Law #2 : Autocatalysis (vs gravity)

( RHP p and z)

exp ln T z p

z pT

Law #3:

k

z p

z p

10-1

100

10110

0

101

too fragile

complex

No tradeoff

expensive

fragile

Law #1 : ChemistryLaw #2 : Autocatalysis

( RHP p and z)

Law #3:

exp ln T z p

z pT

Metabolic overhead to make enzymes

fragile

Robust Efficiency in Energy Supply

Robust to in supply and demand

k

z p

z p

10-1

100

10110

0

101

too fragile

complex

No tradeoff

Metabolic overhead to make enzymes

fragile

Robust Efficiency in Energy Supply

Robust to in supply and demand

exp ln T z p

z pT

Core metabolism

Inside every cell (1030)

Metabolic pathways

No architecture

Catabolism

Pre

curs

ors

Carriers

Co-factors

Fatty acids

Sugars

NucleotidesAmino Acids

Metabolic pathways

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

Co-factors

Fatty acids

Sugars

NucleotidesAmino Acids

Catabolism

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

Extremely conserved

core

Pre

curs

ors

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

EfficientRobust

Evolvable

Constrained

DeconstrainedDeconstrained

DiverseDiverse

Inside every cell

Layered architecture

Catabolism

Precursors

Carriers

Biosynthesis

Cat

abol

ism

Pre

curs

ors

Carriers

Inside every cell

Layered architecture

Bio

synt

hesi

sCo-factors

Fatty acids

Sugars

NucleotidesAmino Acids

BiosyntheticPathways

Catabolism

Pre

curs

ors

Carriers

Co-factors

Fatty acids

Sugars

NucleotidesAmino Acids

Inside every cell

Core metabolic bowtieLayered architecture

food

Glucose

Oxygen

OrgansTissuesCellsMolecules

Universal metabolic system

Blood

EfficientRobust

Evolvable

food

Glucose

Oxygen

OrgansTissuesCellsMolecules

Blood

EfficientRobust

Evolvable

Constrained

DeconstrainedDeconstrained

EfficientRobust

Evolvable

Constrained

DeconstrainedDeconstrained

DiverseDiverse

Catabolism

Pre

curs

ors

Carriers

Co-factors

Fatty acids

Sugars

NucleotidesAmino Acids

Inside every cell

Core metabolic bowtieLayered architecture

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

metabolites

Enzymatically catalyzed reactions

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

Oxa

Cit

ACA

Enzymes (implement) catalyze

(virtual) 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

produced

consumedRest of cell

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

Autocatalysis

Control

Feedbacks

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

Unreadable

Why so complex?

source receiver

signalinggene expression

metabolismlineage

Biological pathways

source receiver

control

energy

materials

signalinggene expression

metabolismlineage

More complex

feedback

Chandra, Buzi, and Doyle

UG biochem, math, control theory

Most important paper so far.

Universal laws?

10

100

Length, m

.1 1.5.22

k10-1

100

10110

0

101

expensive

fragile

exp ln

expT z p

pz pT

wasteful

fragile

efficient

robust Ideal

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

Autocatalysis

Control

Feedbacks

Robust=maintain energy charge w/fluctuating cell demand

Efficient=minimize metabolic waste and overhead

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

Autocatalysis

Control

PEP2PG Pyr

Minimal model?

F6P

F1-6BP

Gly3p

13BPG

3PG

ATP

F6P

F1-6BP

Gly3p

13BPG

3PG

ATP

ControlPlus Autocatalytic Feedback

PEP Pyr

Rest of cell

Minimal model ~1 equilibrium 2 metabolites 3 “reactions”

F6P

F1-6BPATP

F6P

F1-6BPGly3p

13BPG

3PG

ATP

produced

consumed

Cell

PEPPyr

lump

Minimal model ~1 equilibrium 2 metabolites 3 “reactions”

Fragile

Robust

ATP Rest of cell

energy

ATP

disturbance

Robust = Maintain energy

(ATP concentration) despite demand fluctuation

Hard tradeoff in glycolysis

Fragile

Robust

disturbance

Robust Disturbance rejection

Accurate

What makes this hard?1. Instability (autocatalysis)2. Delay (enzyme amount)

Accurate vs sloppy

Fragile

Robust

What makes this hard?

1. Instability2. Delay

The CNS must cope with both!

ATP

Reaction 2 (“PK”)

Reaction 1 (“PFK”) energy

enzymes catalyze reactions

Rest of cell

ATP

Rest of cell

Reaction 2 (“PK”)

Reaction 1 (“PFK”)

Protein biosyn

energy

enzymes

enzymes

enzy

mes

Efficient = low metabolic overhead low enzyme amount

enzymes catalyze reactions, another

source of autocatalysis

ATP

Rest of cell

Protein biosyn

energy

enzymes

enzymes

enzy

mes

Efficient = low metabolic overhead» low enzyme amount( slow reactions)

enzymes catalyze reactions, another

source of autocatalysis

Can’t make too many enzymes here, need to supply rest of the cell.

reaction rates

enzyme amount

TCA

Gly

G1P

G6P

F6P

F1-6BP

PEP Pyr

Gly3p

13BPG

3PG

2PG

ATP

NADH

Oxa

Cit

ACA

Autocatalysis

Control

ATP

Rest of cell

Reaction 2 (“PK”)

Reaction 1 (“PFK”)

Protein biosyn

Autocatalysis

Autocatalysis

• Sustainable infrastructure? (e.g. smartgrids)• Money/finance/lobbyists/etc• Industrialization• Society/agriculture/weapons/etc• Bipedalism• Maternal care• Warm blood• Flight• Mitochondria• Oxygen• Translation (ribosomes)• Glycolysis (2011 Science)

• New forms important in most transitions• Major and poorly studies source of instability

Major transitions

k

z p

z p

10-1

100

10110

0

101

too fragile

complex

No tradeoff

Metabolic overhead to make enzymes

fragile

Robust Efficiency in Energy Supply

Robust to in supply and demand

exp ln T z p

z pT

k

z p

z p

10-1

100

10110

0

101

too fragile

complex

No tradeoff

Metabolic overhead

fragile

Robust to in supply and demand

Uncertain k

What (some) reviewers say• “…to establish universality … is simply wrong. It

cannot be done…• … a mathematical scheme without any real

connections to biological or medical… • …universality is well justified in physics… for

biological and physiological systems …a dream …never be realized, due to the vast diversity in such systems.

• …does not seem to understand or appreciate the vast diversity of biological and physiological systems…

• …a high degree of abstraction, which …make[s] the model useless …

What (some) reviewers say• “…to establish universality … is simply wrong. It

cannot be done…• … a mathematical scheme without any real

connections to biological or medical… • …universality is well justified in physics… for

biological and physiological systems …a dream …never be realized, due to the vast diversity in such systems.

• …does not seem to understand or appreciate the vast diversity of biological and physiological systems…

• …a high degree of abstraction, which …make[s] the model useless …

If you agree• You’re in good company • Stay off commercial aircraft

k

z p

z p

10-1

100

10110

0

101

too fragile

complex

No tradeoff

Metabolic overhead

fragile

Robust to in supply and demand

Uncertain k

M

m

l

l lengthm massM massg gravityu control force

y

x

u

Standard inverted pendulum

2

sin

cos sin 0

cos sin

Oy x l n

x l g

M m x ml u

Uncertainty?

eye vision

Act

delay

Control

l noise

error

In our model?In our brain?In our brain’s model?

• Parameters• Noise• Unmodeled dynamics

2

sin

cos sin 0

cos sin

Oy x l n

x l g

M m x ml u

Uncertainty?

In our model?In our brain?In our brain’s model?

• Parameters (real)• Noise (additive)• Unmodeled dynamics (complex)• Nonlinear dynamics

2

sin

cos sin 0

cos sin

Oy x l n

x l g

M m x ml u

Uncertainty?

AnalysisLimits/lawsSynthesis

controls

external disturbances

heart rateventilation

errors

O2BP

energy

Homeostasis and HRV

0 100 200 300 4000 100 200 300 400

40

60

80

100

120

140

160

180

HR

High mean, low variability

Low mean, high variability

The persistent mysteryYoung, fit, healthy more extreme

Seeking mechanistic explanations

sec

0 100 200 300 4000 100 200 300 400

40

60

80

100

120

140

160

180

HRHigh mean, low variability

Low mean, high variability

sec

controls

external disturbances

heart rateventilation

errors

O2BP

energy

Finally!

Homeostasis and HRV

sensor

controls

external disturbances

heart rateventilationvasodilationcoagulationinflammationdigestionstorage…

errors

O2BPpHGlucoseEnergy storeBlood volume…

infection

traumaenergy

Homeostasis and robust efficiency

internal noise

heart beatbreath

Mechanistic physiology

The main tradeoff: Robust efficiency

Mechanistic physiology + rigorous math and stats

sensor

controls

external disturbances

heart rateventilationvasodilationcoagulationinflammationdigestionstorage…

errors

O2BPpHGlucoseEnergy storeBlood volume…

infection

traumaenergy

Homeostasis

internal noise

heart beatbreath

costly

fragile

efficient

robust

Tradeoffs:• physiology • evolution • ecologically

relevant

Mechanistic physiology + rigorous math and stats

controls

external disturbances

heart rateventilation

errors

O2BP

energy

Homeostasis

Muscle

Lung

W

H

EV

CBF

H

sR

pump

pump

dilate

dilate

high variability

Disturbance: W

SaO2

Pas

O2

CBF

Health low variability

Why?

flow

pressure

O2

O2

Minimal cartoon

pump

pump

dilate

dilate

high variability

Disturbance:run

Healthy homeostasis

low variability

flow

pressure

O2

O2

Minimal cartoon

actuators

regulated variables

pump

pump

dilate

dilate

high variability Healthy homeostasis

low variability

flow

pressure

O2

O2

Minimal cartoon

+

actuators

regulated variablesDisturbance

0 100 200 300 4000 100 200 300 400

40

60

80

100

120

140

160

180

HR

High mean, low variability

Low mean, high variability

The persistent mysteryYoung, fit, healthy more extreme

Seeking mechanistic explanations

sec

actuators(controls)

+

(outputs)regulated variables

Disturbance

low variability errors+ large disturbances high variability controls

Universals

low variability errors+ large noise/delay high variability controls

Universals

Is loss of actuator

variability a precursor

of a crash?

eye vision

Act

delay

Control

l noise

error

Control actuators

Universal laws

10

100

Length, m

.1 1.5.22

k10-1

100

10110

0

101

expensive

fragile

wasteful

fragile

efficient

robust

sensor

controlsheart rateventilationvasodilationcoagulationinflammationdigestionstorage…

errors

O2BPpHGlucoseEnergyBlood vol

infection

traumaenergy

heart beatbreath

Homeostasis

Universal laws

10

100

Length, m

.1 1.5.22

k10-1

100

10110

0

101

expensive

fragile

wasteful

fragile

efficient

robust

sensor

controlsheart rateventilationvasodilationcoagulationinflammationdigestionstorage…

errors

O2BPpHGlucoseEnergyBlood vol

infection

traumaenergy

heart beatbreath

Homeostasis

Do these oscillations have a function/purpose?

Is loss of actuator variability a precursor?

eye vision

Act

delay

Control

l noise

error ET j

N

P

+

noise

error

C

Understand this more deeply?

+ Neuroscience

Mechanics+Gravity +

Light +Control theory

exp ln

expT z p

pz pT