architecture, networks, and complexity john doyle john g braun professor control and dynamical...
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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
Cells
Molecules
Universal metabolic system
Blood
Peter Sterling and Allostasis
VTA
Prefrontalcortex
Accumbensdopamine
Universal reward systemssportsmusicdancecrafts arttoolmaking sexfood
Dopamine,
Ghrelin,
Leptin,…
VTA
Prefrontalcortex
Accumbensdopamine
Universal reward systemssportsmusicdancecrafts arttoolmaking sexfood
Glucose
Oxygen
Organs
Tissues
Cells
Molecules
Universal metabolic system
Bloodfood
VTA
Prefrontalcortex
Accumbensdopamine
workfamily communitynature
Universal reward systems
Robust and adaptive, yet …
food sextoolmakingsportsmusicdancecrafts art
sexfoodtoolmakingsportsmusicdancecrafts art
VTA
Prefrontalcortex
Accumbensdopamine
workfamily communitynature
workfamily communitynature
sexfoodtoolmakingsportsmusicdancecrafts art
VTA
Prefrontalcortex
Accumbensdopamine
Vicarious
money
saltsugar/fatnicotinealcohol
industrialagriculture
market/consumerculture
workfamily communitynature
sextoolmakingsportsmusicdancecrafts art
VTA
Prefrontalcortex
Accumbensdopamine
Vicarious
money
saltsugar/fatnicotinealcohol
cocaineamphetamine
Vicarious
money
saltsugar/fatnicotinealcohol
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
money
saltsugar/fatnicotinealcohol
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
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)
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
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
• 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
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?
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
1 1
q
h
q Vx
x
1
1 y
qk y
y
x
Control
1
0 xk x Autocatalytic
reaction reactionmetabolite
consumption
1 1
1 1 01
q
y xh
x q qVxk y k x
y x
Catabolism
Pre
curs
ors
Carriers
Co-factors
Fatty acids
Sugars
NucleotidesAmino Acids
Core metabolism
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
TCA
Gly
G1P
G6P
F6P
F1-6BP
PEP Pyr
Gly3p
13BPG
3PG
2PG
ATP
NADH
Oxa
Cit
ACA
Regulatory
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.
( )
Mass &Reaction
Energyflux
Balance
dxSv x
dt
Stoichiometry or mass and energy balance
Nutrients Products
Internal
Biology is not a graph.
( )
Mass &Reaction
Mass&Energy Energyflux
Balance
dxSv x
dt
d
dt
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 (?!?)
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
Allosteric regulation of enzymes
Regulation of enzyme levels
TCA
Gly
G1P
G6P
F6P
F1-6BP
PEP Pyr
Gly3p
13BPG
3PG
2PG
ATP
NADH
Oxa
Cit
ACA
Allosteric regulation of enzymes
Regulation of enzyme levels
Fast response
Slow
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
1 1
q
h
q Vx
x
1
1 y
qk y
1
0 xk x
y
x
Control
Autocatalytic
F6P
F1-6BP
Gly3p
13BPG
3PG
ATP
1 1
q
h
q Vx
x
1
1 y
qk y
1
0 xk x
y
x
Control
Autocatalytic
F6P
F1-6BPGly3p
13BPG
3PG
ATP
1 1
q
h
q Vx
x
1
1 y
qk y
1
0 xk x
y
x
Control
Autocatalytic
1
0 xk x
1 1
q
h
q Vx
x
1
1 y
qk y
y
x
Control
Autocatalytic
1 1
1 1 01 y x
q
h
x q qVxk y k x
y x
Autocatalytic
1
0 xk x
1 1
q
h
q Vx
x
1
1 y
qk y
y
x
Control
11 1
1 1 0
q
h
y
x
Vx
xx q q
k yy
k x
Autocatalytic
( )
Mass &Reaction
Energyflux
Balance
dxSv x
dt
1 1
1 1 01
q
y xh
x q qVxk y k x
y x
1
0 xk x
1 1
q
h
q Vx
x
1
1 y
qk y
y
x
1 1
1 1 01 1
q
h
x q qVxky x
y V x
WOLOG normalize concentration and time
1 1
1 1 01 y x
q
h
x q qVxk y k x
y x
1
0 xk x
1 1
q
h
q Vx
x
1
1 y
qk y
y
x
1 1
1 1 01 1
q
h
x q qVxky x
y V x
Linearization:
1 1
1 1 0
11
x q qx ky x
y
q hV
st
nd
NominalVariable Process
Value?
autocatalysis 1
inhibition 2.5
1 enzyme 3
2 enzyme .3
q
h
V
k
0 1
0 1
x
y
Steady state: 1x
time10 15 20
-1
-0.5
0
0.5
1x error
Linearization:
1 1
1 1 0
11
x q qx ky x
y
q hV
st
nd
NominalVariable Process
Value?
autocatalysis 1
inhibition 2.5
1 enzyme 3
2 enzyme .3
q
h
V
k
x error
time0 5 10 15 20
-1
-0.5
0
0.5
1
V=3
V=10
V=1.1
Linearization:
1 1
1 1 0
11
x q qx ky x
y
q hV
st
nd
NominalVariable Process
Value?
autocatalysis 1
inhibition 2.5
1 enzyme 3
2 enzyme .3
q
h
V
k
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:
1 1
1 1 0
11
x q qx ky x
y
q hV
st
nd
NominalVariable Process
Value?
autocatalysis 1
inhibition 2.5
1 enzyme 3
2 enzyme .3
q
h
V
k
Stable iff
11
1 11 1
k
q
kq h q
V 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:
1 1
1 1 0
11
x q qx ky x
y
q hV
st
nd
NominalVariable Process
Value?
autocatalysis 1
inhibition 2.5
1 enzyme 3
2 enzyme .3
q
h
V
k
Stable iff
11
1 11 1
k
q
kq h q
V q
.1 6k V 1 1
1k
h qV q
0 5 10 15 20-1
-0.5
0
0.5
1
oscillations
Stable iff
11
1 11 1
k
q
kq h q
V q
.1 6k V 1 1
1k
h qV q
0 5 10 15 20-1
-0.5
0
0.5
1
0 10 20 30 40 50 600
0.5
1
1.5Nonlinear
Linearization:
1 1
1 1 0
11
x q qx ky x
y
q hV
st
nd
NominalVariable Process
Value?
autocatalysis 1
inhibition 2.5
1 enzyme 3
2 enzyme .3
q
h
V
k
Stable iff
11
1 11 1
k
q
kq h q
V q
11 1q h
V 0 5 10 15 20
-1
-0.5
0
0.5
1
1.1V
.1h
Linearization:
1 1
1 1 0
11
x q qx ky x
y
q hV
st
nd
NominalVariable Process
Value?
autocatalysis 1
inhibition 2.5
1 enzyme 3
2 enzyme .3
q
h
V
k
0 5 10 15 20-1
-0.5
0
0.5
1
1h
3.3h
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
-0.5
0
0.5
1
1h
3.3h
x
time
)
Fourier
Transform
of error
h hS x = F(
ln lnh nomS S
Spectrum
freq
3.3h
1h 0 1 2 3 4 5
-2
-1
0
1
2
3
0 5 10 15 20-1
-0.5
0
0.5
1
1h
3.3h
x
time
ln
ln
h
nom
S
S
freq
3.3h
1h 0 1 2 3 4 5
-2
-1
0
1
2
3
0
1ln
10
S j d
Vh
V
Theorem:
x
time
ln
ln
h
nom
S
S
freq
0
1ln
10
S j d
Vh
V
Theorem:
5V 1k
0 5 10 15 20-1
-0.5
0
0.5
1
0 1 2 3 4 5-2
-1
0
1
2
3
.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.
1
0 xk x
1 1
q
h
q Vx
x
1
1 y
qk y
y
x
1 1
1 1 01 1
q
h
x q qVxky x
y V 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
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(
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
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: advanced warning, remote sensing• Hurts: instability, remote control
-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
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.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
Variety of producers
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
dd
r
ControlChannel
log S d
log S d
benefits
feedback
SC
CCstabilizeremotesensing
remote control
log( )a
costs
Robust
log( )a
Fragile
a
-e=d-u
Control
uPlant
d
delay
u
log S d
Bode
a
ES
D
log S d
benefits costs stabilize
log S d a
a
-e=d-u
Control
uPlant
d
delay
u
log S d
Bode
log S d
benefits costs stabilize
Negative is good
a
ES
D
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
u
Plant
d delayd
delay
u
Cost of control
Cost of stabilization
-e=d-u
Control
Plant ControlChannel
u
CC Cost of remote control
log( )alog S d
log S d
benefits costs
log( )alog S d
CC
Disturbance-e=d-u
Control
Plant
dd
ControlChannel
u
CC
log S d
log S d
benefits
feedback
CCstabilize remote control
log( )a
costs
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
Benefit of remote sensing
log( )alog S d
log S d
benefits costs
C
log( )alog S d
CC
Disturbance-e=d-u
ControlSensor
ChannelEncode
PlantRemoteSensor
dd
r
ControlChannel
SC
u
CC
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
Variety of producers
Electric powernetwork
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
dd
r
ControlChannel
log S d
log S d
benefits
feedback
SC
CCstabilizeremotesensing
remote control
log( )a
costs
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 of producers
Electric powernetwork
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
log S d
SC
CClog( )a
Robust
log( )a
FragileControl
ControlChannel
Cat
abol
ism
Genes
Co-factorsFatty acidsSugars
Nucleotides
Amino Acids Proteins
Pre
curs
ors
DNA replication
Trans*
Carriers
Components and materials:Energy, moieties
Systems requirements: functional, efficient,
robust, evolvable
Hard constraints:Thermo (Carnot)Info (Shannon)Control (Bode)Compute (Turing)
Protocols
Constraints
Diverse
Diverse
UniversalControl
Questions?
End of part 1
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