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Local
Error/flow control
Relay/MUX
Global
E/F control
Relay/MUX
Physical
Application
E/F control
Relay/MUX
Paths ahead?
Networks below
Local
Error/flow control
Relay/MUX
Global
E/F control
Relay/MUX
Physical
Application
E/F control
Relay/MUX
Networks below
Legitimate academic pursuits?
Local
Error/flow control
Relay/MUX
Global
E/F control
Relay/MUX
Physical
Application
E/F control
Relay/MUX
Complex
Network
Architecture:
A cartoon guide
Flow
Reactions
Protein level
Flow
Reactions
RNA level
Flow
Reactions
DNA level
John Doyle
John G Braun Professor
Control and Dynamical Systems
BioEngineering, Electrical Engineering
Caltech
• Is there hope of a theory?
• Are there even informative case studies?
• Is there anything but “hack and ship”?
• Hiding ignorance behind obfuscation?
Complex
Network
Architecture
Other Influences Not Here Today
• Biology/Medicine (Savageau, G&K, Mattick, Csete, Arkin, Alon, Caporale, de Duve, Exerc Physio, Acute Care, etc etc…)
• Internet (Kelly/Low, Willinger, Clark, Wroclawski, Day, Chang, etc etc)
• Architecture (Alexander, Salingeros,…)
• Aerospace (many, Maier is a good book)
• Philosophy/History (Fox Keller, Jablonka&Lamb)
• Physics/ecology (Carlson)
• Management (Baldwin,…)
• Resilience/Safety/Security Engineering/Economics(Wood, Anderson, Leveson, …)
Robust
yet
fragile
Constraints
that
deconstrain
Essential ideas: Architecture
Question Answer
Robust Yet Fragile
Question: Human complexity
Efficient, flexible metabolism
Regeneration & renewal
Rich microbial symbionts and
Immune systems
Complex societies
Advanced technologies
Obesity and diabetes
Cancer
Parasites, infection
Inflammation, Auto-Im.
Epidemics, war, …
Catastrophic failures
Robust Yet Fragile
Mechanism?
Efficient, flexible metabolism
Regeneration & renewal
Fat accumulation
Insulin resistance
Inflammation
Obesity and diabetes
Cancer
Fat accumulation
Insulin resistance
Inflammation
Fluctuating
energy
Static
energy
Robust Yet Fragile
Implications/
Generalizations Efficient, flexible metabolism Rich microbial symbionts and Immune systems Regeneration & renewal Complex societies Advanced technologies
Obesity and diabetes Parasites, infection Inflammation, Auto-Im. Cancer Epidemics, war, … Catastrophic failures
• Fragility = Hijacking, side effects, unintended… of mechanisms evolved for robustness • Complexity is driven by control, robust/fragile tradeoffs• Math: New robust/fragile conservation laws
• Resilience/safety/security Engineering/Economics: “Human error” and “human nature” is often a symptom of bad system architecture
Infrastructure networks?
• Power
• Transportation
• Water
• Waste
• Food
• Healthcare
• Finance
All examples of
“bad” architectures:
• Unsustainable
• Hard to fix
Where do we look for “good” examples?
“Architecture” in practice
• Internet, biology, energy, manufacturing,
transportation, water, food, waste, law, etc
• Many architectures are unsustainable/hard to fix
What does “architecture” mean here?
• Persistent, ubiquitous, global features
• Constrains the possible (for good or bad)
• Enables/prevents innovation, sustainability, etc,
• Theory is fragmented, incoherent, incomplete
• Needs rigor and relevance
• “Constraints that deconstrain” and “facilitated
variation” (Gerhart and Kirschner)
Math ControlEngineering
Bio/Med/Eco
Soc/Econ
Computing
Comms
Astrom bridge
Math ControlEngineering
Bio/Med/Eco
Soc/Econ
Computing
Comms
Cybernetics
Math
Engineering
Bio/Med/Eco
Soc/Econ
Physics
Comms
Computing
Robust
yet
fragile
Constraints
that
deconstrain
Essential ideas: Architecture
Question Answer
Simplest case studies
Internet Bacteria
Simplest case studies
• Successful architectures
• Robust, evolvable
• Universal, foundational
• Accessible, familiar
• Unresolved challenges
• New theoretical frameworks
• Boringly retro?
Internet Bacteria
• Universal, foundational
Techno-
sphere
Internet Bacteria
Bio-
sphere
• Universal, foundational
Techno-
sphere
Internet
Bio-
sphere
Bacteria
Spam
Viruses
Two lines of research:
1. Patch the existing Internet architecture so it handles its new roles
Techno-
sphere
Internet
• Real time
• Control over (not just of) networks
• Action in the physical world
• Human collaborators and adversaries
• Net-centric everything
Cyber-Physical Theories
• Thermodynamics
• Communications
• Control
• Computation
Physical
• Thermodynamics
• Communications
• Control
• Computation
Cyber
• Thermodynamics
• Communications
• Control
• Computation
Internet Bacteria
Case studies
Physical
• Thermodynamics
• Communications
• Control
• Computation
Cyber
• Thermodynamics
• Communications
• Control
• Computation
Promising unifications
Modern theory and the Internet
Verbal/cartoon
Data and
statistics
Modeling and
simulation
Analysis
Synthesis
Levels of
understanding
Traffic
Topology
Control and
dynamics
Layering
Architecture
Topics
Recent progress (1995-)
Traffic Topology C&D Layering Architect.
Cartoon
Data/stat
Mod/sim
Analysis
Synthesis
Recent progress (1995-)
Traffic Topology C&D Layering Architect.
Cartoon
Data/stat
Mod/sim
Analysis
Synthesis
Techno-
sphere
Internet
Two lines of research:
1. Patch the existing Internet architecture
2. Fundamentally rethink network architecture
?
Focus
Traffic Topology C&D Layering Architect.
Cartoon
Data/stat ?
Mod/sim ?
Analysis ?
Synthesis ?
1.
2. Fundamentally rethink network architecture
Techno-
sphere
Internet Bacteria
Bio-
sphere
Case studies
Biology versus the Internet
Similarities
• Evolvable architecture
• Robust yet fragile
• Constraints/deconstrain
• Layering, modularity
• Hourglass with bowties
• Feedback
• Dynamic, stochastic
• Distributed/decentralized• Not scale-free, edge-of-chaos, self-
organized criticality, etc
Differences
• Metabolism
• Materials and energy
• Autocatalytic feedback
• Feedback complexity
• Development and regeneration
• >4B years of evolution
• How the parts work?
Biology versus the Internet
Similarities
• Evolvable architecture
• Robust yet fragile
• Constraints/deconstrain
• Layering, modularity
• Hourglass with bowties
• Feedback
• Dynamics
• Distributed/decentralized• Not scale-free, edge-of-chaos, self-
organized criticality, etc
Differences
• Metabolism
• Materials and energy
• Autocatalytic feedback
• Feedback complexity
• Development and regeneration
• >4B years of evolution
Focus on
bacterial biosphere
In the real (vs virtual) world
What matters:
• Action
What doesn’t:
• Data
• Information
• Computation
• Learning
• Decision
• …
Biology versus the Internet
Similarities
• Evolvable architecture
• Robust yet fragile
• Constraints/deconstrain
• Layering, modularity
• Hourglass with bowties
• Feedback
• Dynamics
• Distributed/decentralized• Not scale-free, edge-of-chaos, self-
organized criticality, etc
Differences
• Metabolism
• Materials and energy
• Autocatalytic feedback
• Feedback complexity
• Development and regeneration
• >4B years of evolution
Focus on
bacterial biosphere
HTTP
TCPIP
my
computer Wireless
router
Optical
router
Physical
web
server
MAC
Switch
MAC MAC
Pt to Pt Pt to Pt
Diverse hardware
Operating
systems
Diverse applications
Layers (Net)
Computer
Ancient network
architecture:
“Bell-heads
versus
Net-heads”
Pathways (Bell)
Communications
Phone
systems
TCPIP
Physical
MAC
Switch
MAC MAC
Pt to Pt Pt to Pt
telephony
Diverse applications
telephony
Non-networked Systems
Local
control
Diverse Functions
Diverse Resources Local
LocalLocal
control
my
computer Wireless
router
Physical
MAC
Switch
TCPIP
my
computer Wireless
router
Physical
MAC
Switch
TCPIP
Error/flow control
Relaying/Multiplexing
Error/flow control
Relaying/MultiplexingLocal
Global
Differ in
• Details
• Scope
Local
Error/flow control
Relay/MUX
Global
E/F
control
Relay/MUX
Physical
Application
E/F
control
Relay/MUX
Recursive control structure
Local
Geographically local
Local
Semantic (functionally) local
Network requirements
Resources
Diverse, Distributed Functions
Local Local Resources Local
Global, universal control
Diverse, Distributed Functions
Layered solution
Universal controlConstraints
Global, universal control
Diverse Resources
Diverse Functions
Universal controlConstraints
That deconstrain
That deconstrain
Resources
Deconstrained
Applications
Deconstrained
Constraints
that
deconstrain
Control
constrained
And layers have sublayers
Physical
CircuitCircuitCircuit
LogicalInstructions
Physical
CircuitCircuitCircuit
LogicalInstructions
Local
Global
Physical
LocalLocal
Diverse, Distributed Functions
Local
Diverse, Distributed Functions
Physical
CircuitCircuitCircuit
LogicalInstructions
Huge range of dynamics
• Spatial
• Temporal
Bewildering w/out
clear grasp of
layered architecture
HTTP
TCPIP
my
computer Wireless
router
Optical
router
Physical
web
server
MAC
Switch
MAC MAC
Pt to Pt Pt to Pt
Resources
Deconstrained
Applications
Deconstrained
Theoretical framework: Constraints that deconstrain
• Optimization
• Optimal control
• Robust control
• Game theory
• Network coding
2 2min
arg max , ,
arg max ,s sv
R R dt
L R
x L v
x
v
x c x c
x v p p x c
p
Cyber-Physical Theories
• Thermodynamics
• Communications
• Control
• Computation
Homework: Reinterpret
your favorite separation
theorem as “layering”
Physical
IP
TCP
ApplicationArchitecture
is not graph
topology.
Architecture
facilitates
arbitrary
graphs.
Apps
Tools/
tech
Apps
Tools/
tech
Apps
Tools/
tech
Apps
Tools/
tech
Apps
Tools/
tech
EE, CS, ME, MS, APh, ChE, Bio, Geo, Eco, …
Academic stovepipes
Apps
Tools/
tech
Apps
Tools/
tech
Apps
Tools/
tech
Apps
Tools/
tech
Apps
Tools/
tech
“Multidisciplinary
cross-sterilization”
Funding
twine
New applications
New applications
Apps
Tools/
tech
Apps
Tools/
tech
Apps
Tools/
tech
Apps
Tools/
tech
Apps
Tools/
tech
?????Layering
academia?
Biology versus the Internet
Similarities
• Evolvable architecture
• Robust yet fragile
• Constraints/deconstrain
• Layering, modularity
• Hourglass with bowties
• Feedback
• Dynamics
• Distributed/decentralized• Not scale-free, edge-of-chaos, self-
organized criticality, etc
RNADNA Protein
From Pathways
Metabolic
pathways
“Central dogma” Network
architecture?
To Layers?
Local
Error/flow control
Relay/MUX
Global
E/F control
Relay/MUX
Physical
Application
E/F control
Relay/MUX
Recursive
control
structureFlow
Reactions
Protein level
Flow
Reactions
RNA level
Flow
Reactions
DNA level
Flow/erro
r
Reactions
Protein level
Flow/erro
r
Translation
RNA level
Flow/erro
r
Transcription
DNA level
Top to bottom
• Metabolically costly but
fast to cheap but slow
• Special enzymes to
general polymerases
• Allostery to regulated
recruitment
• Analog to digital
• High molecule count to
low (noise)
Rich Tradeoffs
Computational Resources
Global, universal control
Diverse Physiological Functions
Layered Brain (Hawkins)?
Computational Resources
Global, universal control
Diverse Physiological Functions
Diverse Physiological Functions
Prediction
Goals
Actions
erro
rs
Actions
Why this is all wrong
• Network science and emergulent chaocritiplexity
• Peta-phylia, the singularity is near
• Earth is <10K yrs old, evolution a hoax
• The rapture is near
• Global warming and “unsustainability” a hoax
• It’s so stupid it isn’t even wrong
Catabolism
Pre
curs
ors
Carriers
Nucleotides
Inside every cell
Core metabolic bowtie
Catabolism
Pre
curs
ors
Carriers
Nucleotides
Core
metabolism
Inside every
cell ( 1030)
Catabolism
Pre
curs
ors
Carriers
Catabolism
TCAPyr
Oxa
Cit
ACA
Gly
G1P
G6P
F6P
F1-6BP
PEP
Gly3p
13BPG
3PG
2PG
ATP
NADH
TCAPyr
Oxa
Cit
ACA
Gly
G1P
G6P
F6P
F1-6BP
PEP
Gly3p
13BPG
3PG
2PG
TCAPyr
Oxa
Cit
ACA
Gly
G1P
G6P
F6P
F1-6BP
PEP
Gly3p
13BPG
3PG
2PG
Pre
curs
ors
metabolites
Enzymatically
catalyzed reactions
TCA
Gly
G1P
G6P
F6P
F1-6BP
PEP Pyr
Gly3p
13BPG
3PG
2PG
Oxa
Cit
ACA
TCAPyr
Oxa
Cit
ACA
Gly
G1P
G6P
F6P
F1-6BP
PEP
Gly3p
13BPG
3PG
2PG
ATP
Autocatalytic
NADH
Pre
curs
ors
Carriers
TCAPyr
Oxa
Cit
ACA
Gly
G1P
G6P
F6P
F1-6BP
PEP
Gly3p
13BPG
3PG
2PG
ATP
Autocatalytic
NADH
produced
consumed
Rest of cell
Carriers
TCAPyr
Oxa
Cit
ACA
Gly
G1P
G6P
F6P
F1-6BP
PEP
Gly3p
13BPG
3PG
2PG
ATP
NADH
Reactions
Proteins
Control?
TCA
Gly
G1P
G6P
F6P
F1-6BP
PEP Pyr
Gly3p
13BPG
3PG
2PG
ATP
NADH
Oxa
Cit
ACA
Control
TCAPyr
Oxa
Cit
ACA
Gly
G1P
G6P
F6P
F1-6BP
PEP
Gly3p
13BPG
3PG
2PG
TCA
Gly
G1P
G6P
F6P
F1-6BP
PEP Pyr
Gly3p
13BPG
3PG
2PG
ATP
NADH
Oxa
Cit
ACA
If we drew the feedback loops the
diagram would be unreadable.
TCA
Gly
G1P
G6P
F6P
F1-6BP
PEP Pyr
Gly3p
13BPG
3PG
2PG
ATP
NADH
Oxa
Cit
ACA
( )
Mass &Reaction
Energyflux
Balance
dxSv x
dt
Stoichiometry
matrix
S
Regulation of enzyme levels by
transcription/translation/degradation
TCA
Gly
G1P
G6P
F6P
F1-6BP
PEP Pyr
Gly3p
13BPG
3PG
2PG
Oxa
Cit
ACA
( )
Mass &Reaction
Energyflux
Balance
dxSv x
dt
level
TCA
Gly
G1P
G6P
F6P
F1-6BP
PEP Pyr
Gly3p
13BPG
3PG
2PG
ATP
NADH
Oxa
Cit
ACA
( )
Mass &Reaction
Energyflux
Balance
dxSv x
dt
Allosteric regulation
of enzymes
Error/flow
TCA
Gly
G1P
G6P
F6P
F1-6BP
PEP Pyr
Gly3p
13BPG
3PG
2PG
ATP
NADH
Oxa
Cit
ACA
Mass &Reaction
( ) Energyflux
Balance
dxSv x
dt
Level
Error/flow
Reaction
TCA
Gly
G1P
G6P
F6P
F1-6BP
PEP Pyr
Gly3p
13BPG
3PG
2PG
ATP
NADH
Oxa
Cit
ACA
Flow/error
Reactions
Protein level
TCA
Gly
G1P
G6P
F6P
F1-6BP
PEP Pyr
Gly3p
13BPG
3PG
2PG
ATP
NADH
Oxa
Cit
ACA
Flow/error
Reactions
Protein level
Layered
architecture
Global, universal control
Diverse Resources
Diverse Functions
Universal controlConstraints
That deconstrain
Flow/error
Reactions
Macromolecules
Mature red blood
cells live 120 days
Running only the top layers
productsS reactions P
Enz1 reaction3 Enzyme form/activity
Reaction rate
Enz2
“metabolism first”
origins of life?
Flow/error
Reactions
Protein level
Flow/error
Reactions
RNA level
Flow/error
Reactions
DNA level
Flow/error
Reactions
Protein level
Flow/error
Reactions
RNA level
Flow/error
Reactions
DNA level
Protein
RNA
DNA
Flow/error
Reactions
Protein level
Flow/error
Translation
RNA level
Flow/error
Transcription
DNA level
Diverse Reactions
DNADNADNA
Diverse Genomes
Flow/error
Protein level
Flow/error
Reactions
RNA level
Flow/error
Reactions
Conserved
core
control
Flow/erro
r
Reactions
Protein level
Flow/erro
r
Reactions
RNA level
Flow/erro
r
Reactions
DNA level
Top to bottom
• Metabolically costly but
fast to cheap but slow
• Special enzymes to
general polymerases
• Allostery to regulated
recruitment
• Analog to digital
• High molecule count to
low (noise)
Rich Tradeoffs
Flow
Reactions
Protein level
Flow
Reactions
RNA level
Flow
Reactions
DNA level
Fragility example: Viruses
Viruses exploit the universal
bowtie/hourglass structure to
hijack the cell machinery.
Viral
genes
Viral
proteins
Biology versus the Internet
Similarities
• Evolvable architecture
• Robust yet fragile
• Constraints/deconstrain
• Layering, modularity
• Hourglass with bowties
• Feedback
• Dynamics
• Distributed/decentralized• Not scale-free, edge-of-chaos, self-
organized criticality, etc
Differences
• Metabolism
• Materials and energy
• Autocatalytic feedback
• Feedback complexity
• Development and regeneration
• >4B years of evolution
Control of the Internet
source receiver
Packets
control
packets
source receiver
signaling
gene expression
metabolism
lineage
Biological
pathways
source receiver
control
energy
materials
signaling
gene expression
metabolism
lineage
More
complex
feedback
source receiver
control
energy
materials
Autocatalytic feedback
source receiver
control
energy
materials
signaling
gene expression
metabolism
lineage
More
complex
feedback
What theory is relevant to
these more complex
feedback systems?
source receiver
control
energymaterials
More
complex
feedback
What theory is relevant to
these more complex
feedback systems?
signalinggene expression
metabolismlineage
2 2
0
1ln ln
z z pS j d
z z p
Flow/error
Protein level
Catabolism
Pre
curs
ors
Carriers
Nucleotides
RNA
DNA
Pre
curs
ors
Nucleotides
RNA
DNA
Biosynthesis
RNA level/
Transcription rate
DNA level
Biosynthesis
RNA
Gene
Transc. xRNA
RNAp
Pre
curs
ors
Co-factors
Cat
abo
lism
AA
RNA
RNAp
Pre
curs
ors
Gene
Transc. xRNA
Cat
abo
lism
AA
tRNA Ribosome
RNA
RNAp
transl. Enzymes
Pre
curs
ors
Gene
Transc. xRNA
mRNAncRNA
AA
Ribosome
RNA
RNAp
transl. Protein
Gene
Transc. mRNA
“Central dogma”
RNA
Flow
Transc.
DNA
Protein
Flow
Transl.
RNA
Cat
abo
lism
AA
tRNA Ribosome
RNA
RNAp
Autocatalysis
everywhere
transl. Proteins
xRNAtransc.
Pre
curs
ors
All the enzymes
are made from
(mostly) proteins
and (some) RNA.
Pyr
G6P
F6P
F1-6BP
PEP
Gly3p
13BPG
3PG
2PG
ATP
charging
consumption
= dischargingRest of cell
This is just charging and discharging
Flow/error
Protein level
RNA
DNA
AMP level
Pyr
F1-6BP
PEP
Gly3p
3PG
2PG
ATP
G6PF6P
13BPG
Rest of cell
A*P
ATP supplies
energy to all
layers
Flow/error
Protein level
RNA
DNA
AMP level
ATP
cellA*P
RNA
DNA
Lots of
ways to
draw this.
AA
tRNA
RNALayered
transl. Enzymes
xRNAtransc.
Cat
abo
lism
Pre
curs
ors
trans. EnzymesAA
mRNAncRNA
tRNA
Ribosome
RNA level/
Transcription rate
RNA form/activity
RNA
Gene
Transc. xRNA
RNAp
S reactions P
Enz1 reaction3
Enzyme level/
Translation rate
Enzyme form/activity
Reaction rate
Enz2
trans.
ncRNATransc.
productsreactions
reaction3
All products
feedback everywhere
ProteinsControl?
Local
Error/flow control
Relay/MUX
Global
E/F control
Relay/MUX
Physical
Application
E/F control
Relay/MUX
Recursive
control
structureFlow
Reactions
Protein level
Flow
Reactions
RNA level
Flow
Reactions
DNA level
Local
Error/flow control
Relay/MUX
Global
E/F control
Relay/MUX
Physical
Application
E/F control
Relay/MUX
Recursive
control
structureFlow
Reactions
Protein level
Flow
Reactions
RNA level
Flow
Reactions
DNA level
Huge range of dynamics
• Spatial
• Temporal
Bewildering w/out
clear grasp of
layered architecture
Archaea
Eukaryotes
Animals Fungi Plants
Bacteria Algae
What is locus
of early
evolution?HGT and
Shared
Protocols
Horizontal gene transfer
Architecture!?!
Archaea
Eukaryotes
Animals Fungi Plants
Bacteria Algae
HGT and
Shared
Protocols
trans. EnzymesAA
mRNA
ncRNAtRNARibosome
RNA level/
Transcription rate
RNA
form/activity
RNA
Gene
Transc. xRNA
RNAp
productsS reactions P
Enz1 reaction3
Enzyme level/
Translation rate
Enzyme
form/activity
Reaction
rate
Enz2
Archaea
Eukaryotes
Animals Fungi Plants
Bacteria Algae
DNA levelGene
Controlled,
dynamic
HGT and
Shared
Protocols
Horizontal gene transfer• Not a static database
• Not only point mutations
Diverse
function
Diverse
components
Universal
Control
fan-in
of diverse
inputs
fan-out
of diverse
outputs
universal
carriers
Bowties: flows
within layers
Robust
yet
fragile
Constraints
that
deconstrain
Essential ideas
Diverse
function
Diverse
components
fan-in
of diverse
inputs
fan-out
of diverse
outputs
Robust
yet fragile
Constraints that
deconstrain
Highly robust
• Diverse
• Evolvable
• Deconstrained
Highly fragile
• Universal
• Frozen
• Constrained
• Hijacking
Universal
Control
universal
carriers
Diverse
function
Diverse
components
Universal
Control
fan-in
of diverse
inputs
fan-out
of diverse
outputs
universal
carriers
Bowties: flows
within layers
Robust
yet
fragile
Constraints
that
deconstrain
Essential ideas
source receiver
control
energymaterials
More
complex
feedback
What theory is relevant to
these more complex
feedback systems?
signalinggene expression
metabolismlineage
2 2
0
1ln ln
z z pS j d
z z p
TCA
Gly
G1P
G6P
F6P
F1-6BP
PEP Pyr
Gly3p
13BPG
3PG
2PG
ATP
NADH
Oxa
Cit
ACA
TCA
Gly
G1P
G6P
F6P
F1-6BP
PEP Pyr
Gly3p
13BPG
3PG
2PG
ATP
NADH
Oxa
Cit
ACA
F6P
F1-6BP
Gly3p
13BPG
3PG
ATP
F6P
F1-6BP
Gly3p
13BPG
3PG
ATP
1 1
q
h
q Vx
x
1
1y
qk y
1
0xk x
y
x
Control
Autocatalytic
F6P
F1-6BP
Gly3p13BPG
3PG
ATP
1 1
q
h
q Vx
x
1
1y
qk y
1
0xk x
y
x
Control
Autocatalytic
1 1(1 )
1 1 01
q
h
x q qVxky
y x
1(1 )
0
1 1
q
h
q Vx
x
1
1y
qk yy
x
Control
Autocatalytic
Autocatalytic
Control
11
0
1 1
q
h
q Vx
x
1
1y
qk yy
x
input
output=x
Control theory cartoon
Caution: mixed cartoon
Controller
+
u
xS j
u
output=x
+
u
X jS j
U j
ln ln
ln ln
X jS j d d
U j
X j d U j d
Entropy rates
CP
lant
0
1ln 0S j d
Hard limits
0 5 10 15 200.8
0.85
0.9
0.95
1
1.05
Time (minutes)
[AT
P]
h >>1
h = 1
Time response)
Fourier
Transform
of error
h hS x = F(
0 2 4 6 8 10-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Frequency
Lo
g(|
Sn
/S0|)
h >>1
h = 1
Spectrum
1log loghS S
Ideal
0 5 10 15 200.8
0.85
0.9
0.95
1
1.05
Time (minutes)
[AT
P]
h >> 1
h = 1
0 2 4 6 8 10-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Frequency
Lo
g(S
n/S
0)
h >>1
h = 1
Spectrum
Time response
Robust
Yet
fragile
0ln lnhS j S j
0 2 4 6 8 10-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Frequency
Lo
g(S
n/S
0)
h = 3
h = 0 Robust
Yet
fragile
0
ln 0S j d
[a system] can have
[a property] robust for
[a set of perturbations]
Yet be fragile for
Or [a different perturbation]
[a different property] Robust
Fragile
Robust yet fragile = fragile robustness
output=x
+
u
X jS j
U j
ln ln
ln ln
X jS j d d
U j
X j d U j d
Entropy rates
CP
lant
0
1ln 0S j d
Hard limits
0 5 10 15 200.8
0.85
0.9
0.95
1
1.05
Time (minutes)
[AT
P]
h >> 1
h = 1
0 2 4 6 8 10-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Frequency
Lo
g(S
n/S
0)
h >>1
h = 1
Spectrum
Time response
Robust
Yet
fragile
0ln lnhS j S j
Pla
nt
output=x
+
u
X jS j
U j
C
2 2
0
1ln ln
z z pS j d
z z p
0
1ln 0S j d
The plant can make
this tradeoff worse.
Pla
nt
output=x
+
u
X jS j
U j
C
2 2
0
1ln ln
z z pS j d
z z p
0
1ln 0S j d
2kz p RHPzero s q k s k
q
All controllers:
Biological cells: =
Pla
nt
output=x
+
u
X jS j
U j
C
2 2
0
1ln ln
z z pS j d
z z p
0
1ln 0S j d
2kz p RHPzero s q k s k
q
Small z is bad.
kz
q
Small z is bad
(oscillations and crashes)
Small z =
• small k and/or
• large qEfficiency =
• small k and/or
• large q
Correctly predicts conditions
with “glycolytic oscillations”
2 2
0
1ln ln
z z pS j d
z z p
output=x
+
u
X jS j
U j
ln ln
ln ln
X jS j d d
U j
X j d U j d
Entropy rates
CP
lant
0
1ln 0S j d
Hard limits
Plant
output=x
+
uController
0
1ln 0S j d
Plant
output=x
+
uController
0
1ln 0S j d
Channel
Sensor+
Channel
Plant
output=x
+
u
Controller
0
1ln FBS j d C
Channel
Sensor+
Channel
0
1ln sensorS j d C Helps
Hurts
Flow/error
Reactions
Protein level
Flow/error
Trans*
*NA level
1(1 )
0
1 1
q
h
q Vx
x
1
1y
qk y zyw
xAutocatalytic
Control
Glycogen/
glucose
AA Biosyna
p1Prot1
x
Anaerobically on w
*NA1
Control
feedback
everywhere
Nuc Biosyn n
Polym
Protx
*NAx
Polym
p
x
DnaK
rpoH
Lon
Other
operons
motif
See El-Samad, Kurata, et al…
PNAS, PLOS CompBio
DnaK
rpoH
Lon
Other
operons
motif
Flow/error
Reactions
Protein level
Flow/error
Reactions
RNA level
Flow/error
Reactions
DNA level
Protein
RNA
DNA
Where are these layers?
DnaK
rpoH
Lon
DnaK
Lon
Heat
degradation
folded unfolded
Other
operons
motif
RNAP
DnaKRNAP
DnaK
rpoH
FtsH Lon
HeatmRNA
Other
operons
Lon
RNAP
DnaKRNAP
DnaK
rpoH
FtsH Lon
HeatmRNA
Other
operons
DnaK
DnaK
ftsH
Lon
Flow/error
Reactions
Protein level
Flow/error
Reactions
RNA level
Flow/error
Reactions
DNA level
Protein
RNA
DNA
Where are these layers?
Protein
DNA
RNA
RNA
DNA
RNAP
DnaK
RNAP
DnaK
rpoH
FtsH Lon
Heat
mRNA
Other
operons DnaK
DnaK
ftsH
Lon
RNA
RNA
RNAPRNAP
rpoH Heat
mRNA
Translation
was not
shown.
mRNA activity is
actively controlled.
RNAP
DnaK
RNAP
DnaK
rpoH
FtsH Lon
HeatmRNA
Other
operons
DnaK
DnaK
ftsH
Lon
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
levels
rates
Layered control architectures
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
levels
ratesThe greatest
complexity
here is
primarily in
the control
of rates
That is not always the case.
RNAP
DnaK
RNAP
DnaK
rpoH
FtsH Lon
HeatmRNA
Other
operons
DnaK
DnaK
ftsH
Lon
DnaK
rpoH
Lon
Other
operons
motif
All at the DNA layer
1(1 )
0
1 1
q
h
q Vx
x
1
1y
qk y zyw
xAutocatalytic
ControlAero-
bic
Reaction?
Glycogen/
glucose
AA Biosyna
p1
p2
Prot1
Prot2
x
Reaction?
*NA1*NA2
p? p?
*NA?*NA?
1(1 )
0
1 1
q
h
q Vx
x
1
1y
qk y zyw
xAutocatalytic
Control
Glycogen/
glucose
p1
p2
Prot1
Prot2
Anaerobically on w
Protein
level
1(1 )
0
1 1
q
h
q Vx
x
1
1y
qk y zyw
xAutocatalytic
Control
Glycogen/
glucose
AA Biosyn
a
p1
p2
Prot1
Prot2
degrade
x
Anaerobically on w
Control?
Cat
abo
lism
AA
tRNA Ribosome
RNA
RNAp
transl. Enzymes
Pre
curs
ors
Gene
Transc. xRNA
mRNAncRNA
Cat
abo
lism
AA
tRNA Ribosome
RNA
RNAp
Autocatalysis
everywhere
transl. Proteins
xRNAtransc.
Pre
curs
ors
All the enzymes
are made from
(mostly) proteins
and (some) RNA.
1(1 )
0
zyw
xAutocatalytic
Aero-
bic
Reaction?
Glycogen/
glucose
AA Biosyn
a
Reaction?
Aerobically on z
supply
p?p?
p? p?
Control?
1(1 )
0
1 1
q
h
q Vx
x
1
1y
qk y zyw
xAutocatalytic
ControlAero-
bic
Reaction?
Glycogen/
glucose
AA Biosyn
a
p1
p2
Prot1
Prot2
degrade
x
Reaction?
trans.
ncRNATransc.
productsreactions
reaction3
All products
feedback everywhere
ProteinsControl?
1(1 )
0
1 1
q
h
q Vx
x
1
1y
qk y zyw
xAutocatalytic
Control
Glycogen/
glucose
AA Biosyna
p1
p2
Prot1
Prot2
degradex
Anaerobically on w
*NA1*NA2
Control
feedback
everywhere
1(1 )
0
1 1
q
h
q Vx
x
1
1y
qk y zyw
xAutocatalytic
ControlAero-
bic
Reaction?
Glycogen/
glucose
AA Biosyna
p1
p2
Prot1
Prot2
x
Reaction?
*NA1*NA2
p? p?
*NA?*NA?
1(1 )
0
1 1
q
h
q Vx
x
1
1y
qk y zyw
xAutocatalytic
Control
Glycogen/
glucose
AA Biosyna
p1Prot1
x
Anaerobically on w
*NA1
Control
feedback
everywhere
Nuc Biosyn n
Polym
Protx
*NAx
Polym
p
x
