http://www.cds.caltech.edu/~doyle/shortcourse.htm
Systems Biology Shortcourse
May 21-24
Winnett Lounge,
Caltech
Speakers: Adam Arkin (UC Berkeley), Frank Doyle (UCSB),
Drew Endy (MIT), Dan Gillespie (Caltech), Michael
Savageau (UC Davis)
Organized by John Doyle (Caltech). There is no registration or fees. Note: Friday
4pm talk by Adam Arkin in Beckman Institute Auditorium.
Collaborators and contributors
(partial list)
Theory: Parrilo, Carlson, Paganini, Papachristodoulo, Prajna,
Goncalves, Fazel, Lall, D’Andrea, Jadbabaie, many current
and former students, …
Web/Internet: Low, Willinger, Vinnicombe, Kelly, Zhu,Yu, Wang,
Chandy, Effros, …
Biology: Csete,Yi, Tanaka, Arkin, Savageau, Simon, AfCS,
Kurata, Khammash, El-Samad, Gross, Bolouri, Kitano,
Hucka, Sauro, Finney, …
Turbulence: Bamieh, Dahleh, Bobba, Gharib, Marsden, …
Physics: Mabuchi, Doherty, Barahona, Reynolds,
Asimakapoulos,…
Engineering CAD: Ortiz, Murray, Schroder, Burdick, …
Disturbance ecology: Moritz, Carlson, Robert, …
Caltech faculty
Finance: Martinez, Primbs, Yamada, Giannelli,…
Other Caltech
Other
Whole cell metabolism
Core
metabolism
Polymerization
and
assembly
Transport
Autocatalytic and regulatory feedback
Metabolite Enzyme
Autocatalysis
+Regulation
Metabolite Enzyme
Autocatalysis
+Regulation
 xk
+ + xk
x dt

k
Vk ( xk )
Vk 1 ( xk 1 )
Enzyme
Vk 1 ( xk 1 )
xk 1
xk
xk  Vk ( xk )  Vk 1 ( xk 1 )  xk
V  x(t )  
Vmax
Km
1
x(t )
x(t )
Vk ( xk )
Metabolite
Vmax
V  x(t )  
Km
1
x(t )
 xk
Stoichiometry or mass and energy balance
 nutrient flux 
 internal flux  


 product flux 
 n   Sn 
m   S  v
   m
 p   S p 
 Mass & 
 Reaction 


  Energy  

flux

 Balance  
reactions


metabolites 


Interna
l
Nutrients
Products
 Sn 
 
 Sm 
Sp 
 
Core
metabolism
Whole cell metabolism
Core
metabolism
Polymerization
and
assembly
Transport
Autocatalytic and regulatory feedback
Nested “bowties”
Core
metabolism
Polymerization
and
assembly
transport
Autocatalytic and regulatory feedback
Nested “bowties”
Core
metabolism
transport
Our first universal
architecture
Polymerization
and
assembly
The core metabolism “bowtie”
Nutrients
Products
Nucleotides
Catabolism
Carriers
and
Sugars
Precursor
Metabolites
Amino
Acids
Fatty acids
Energy and
reducing
Cartoon metabolism
Biosynthesis
Catabolism
Carriers
and
Precursor
Metabolites
Nucleotides
Sugars
Amino
Acids
Fatty acids
Energy and
reducing
The metabolism
“bowtie” protocol
Catabolism
Nutrients
Synthesis
Products
Core: special purpose enzymes controlled
by competitive inhibition and allostery
Edges: general purpose polymerases and
machines controlled by regulated recruitment
Core: Highly efficient
Edges: Robustness and flexibility
Almost everything complex is made this way:
Cars, planes, buildings, power, fuel, laptops,…
This “cartoon” is pure protocol.
Collect
Collect
and
and
import
import
raw
raw
materials
materials
Common
Common
currencies
currencies
and
and
building
building
blocks
blocks
Complex
Complex
assembly
assembly
Manufacturing and metabolism
Polymerization
and assembly
Taxis
and
transport
Core
metabolism
Autocatalytic and regulatory feedback
Electric
power
Variety of
producers
Electric
power
Variety of
consumers
Energy
carriers
Variety of
producers
•
•
•
•
•
110 V, 60 Hz AC
(230V, 50 Hz AC)
Gasoline
ATP, glucose, etc
Proton motive force
Variety of
consumers
Complex
assembly
Raw
materials
Raw
materials
Building
blocks
Complex
assembly
Collect
and
import
raw
materials
Common
currencies
and
building
blocks
Complex
assembly
Steel manufacturing
transport
metabolism
assembly
Core: special purpose machines
controlled by allostery
Variety of
producers
Energy
carriers
Variety of
consumers
transport
metabolism
assembly
Edges: general purpose machines
controlled by regulated recruitment
Variety of
producers
Energy
carriers
Variety of
consumers
transport
metabolism
assembly
Robust and evolvable
Variety of
producers
Energy
carriers
Variety of
consumers
transport
metabolism
assembly
Fragile and hard to change
Variety of
producers
Energy
carriers
Variety of
consumers
transport
metabolism
assembly
Preserved by selection on three levels:
1. Fragile to change (short term)
2. Facilitates robustness elsewhere (short term)
3. Facilitates evolution (long term)
Variety of
producers
Energy
carriers
Variety of
consumers
Modules and protocols
• Much confusion surrounds these terms
• Biologists already understand the important
distinction
• Most of basic sciences doesn’t
Modules and protocols in experiments
• Modules: components of experiments
• Protocols: rules or recipes by which the
modules interact
• This generalizes to most important
situations
• Important distinction in experiments
• Even more important in understanding the
complexity of biological networks
Modules and protocols example
• Suppose some specific experimental
protocol has a step that requires the use of a
PCR machine module.
• The PCR machine in turn implements a
complex protocol with its own modules.
• Thus protocols and modules are
hierarchically nested.
• A nested collection of protocols/modules is
called an architecture or protocol suite.
Modules and protocols example
• Consider this laptop/projector combination.
• The modules include software, hardware,
and connectors.
• The protocols are the rules by which these
modules must interact.
• Hardware modules change between talks
• Within talks slides change, not hardware
• Robust and “evolvable” yet fragile
Modules and protocols example
• Consider this laptop/projector combination.
• The modules include software, hardware,
and connectors.
• The protocols are the rules by which these
modules must interact.
• Hardware modules change between talks
• Within talks slides change, not hardware
• Robust and “evolvable” yet fragile
Varied
systems
Robust
Mesoscale
Varied
components
The
LEGO
connector
protocol
Early computing
Various
functionality
Software
Digital
Hardware
Analog
substrate
Applications
Software
Modern
Computing
Operating
System
Hardware
Hardware
Applications
Software
Modern
Computing
Operating
System
Hardware
Hardware
Modules and protocols
• Protocols and modules are complementary
(dual) notions
• Primitive technologies = modules are more
important than protocols
• Advanced technologies = protocols are at
least as important
• Even bacteria are “advanced technology”
Reductionism and protocols
• Reductionism = modules are more
important than protocols
• Usually: “Huh? What’s a protocol?”
• Systems approach: Protocols are as
important as modules
Necessity or “frozen accident”?
• Laws are absolute necessity.
• Conjecture: Protocols in biology are largely
necessary. (More so than in engineering!)
• Modules??? Appear to be more of a mix of
necessity and accident.
Necessity or “frozen accident”?
• Conservation laws are necessary.
• Bowtie protocols are essentially necessary
if robustness and efficiency are required.
• Conjecture: It is necessary that there is an
energy carrier, it may not be necessary that
it be ATP.
Conjectures on laws and protocols
• The important laws governing biological
complexity have yet to be fully articulated
• Biology has highly organized dynamics
using protocol suites
• Both are true for advanced technologies
Nested bowtie and hourglass
Core
metabolism
Conservation of energy
and moiety is a law.
Polymerization
and
assembly
Taxis
Enzymes are
and
modules.
transport
“Bowtie architectures”
is a protocol.
Autocatalytic and regulatory feedback
essential:
nonessential:
unknown:
total:
230
2373
1804
4407
http://www.shigen.nig.ac.jp/ecoli/pec
transport
metabolism
Autocatalytic feedback
Regulatory
feedback
assembly
transport
metabolism
assembly
Autocatalytic feedback
Knockouts often lose robustness,
not minimal functionality
Regulatory
feedback
Steering
Brakes
Anti-skid
Cruise control
Traction control
Shifting
Electronic ignition
Wipers Mirrors
GPS
Temperature control
Electronic fuel injection
Seatbelts
Bumpers Fenders
Suspension (control) Airbags
Radio
Headlights
Seats
Steering
Brakes
Anti-skid
Wipers Mirrors
Cruise control
GPS
Radio
Knockouts often lose robustness,
Traction control
Shifting not minimal functionality
Headlights
Electronic ignition
Temperature control
Seats
Electronic fuel injection
Seatbelts
Bumpers Fenders
Suspension (control) Airbags
metabolism
transport
assembly
Supplies
Materials &
Energy
Autocatalytic feedback
Robustness
 Complexity
Supplies
Robustness
Regulatory
feedback
transport
metabolism
assembly
Autocatalytic feedback
If feedback regulation is the dominant
protocol, what are the laws
constraining what’s possible?
Regulatory
feedback
transport
metabolism
assembly
A historical aside:
• These systems are not at the edge-of-chaos,
self-organized critical, scale-free, at an orderdisorder transition, etc
Autocatalytic feedback
•
•
•
Not only are they as opposite from this as can
possibly be (an observational fact)…
But also, it is provably impossible for robust
systems to have it otherwise (a theoretical
assertion)
Regulatory
The facts are easily
checked, what is the
feedback
theoretical foundation?
metabolism
transport
assembly
Supplies
Materials &
Energy
Autocatalytic feedback
What are the laws of robustness?
Supplies
Robustness
Regulatory
feedback
Whole cell metabolism
Transport
Core
metabolism
Polymerization
and
assembly
Autocatalytic and regulatory feedback
Metabolite Enzyme
Autocatalysis
+Regulation
Metabolite Enzyme
Autocatalysis
+Regulation
 xk
+ + xk
x dt

k
Vk ( xk )
Vk 1 ( xk 1 )
Enzyme
Vk 1 ( xk 1 )
xk 1
xk
xk  Vk ( xk )  Vk 1 ( xk 1 )  xk
V  x(t )  
Vmax
Km
1
x(t )
x(t )
Vk ( xk )
Metabolite
Vmax
V  x(t )  
Km
1
x(t )
 xk
Yi, Ingalls, Goncalves, Sauro
Product inhibition
x1  V1 ( x1 )  V0 ( xn )
V0  x(t )  
Vmax
 x(t  td ) 
1 
 K fb 


h
Vk 1 ( xk 1 )
xk  Vk ( xk )  Vk 1 ( xk 1 )
V  x(t )  
Vmax
K
1 m
x(t )
xk
Vk ( xk )
xn
perturbation xn
Step
increase
in
demand
for
“ATP.”
[ATP]
1.05
1
h=3
0.95
h=2
h=1
0.9
0.85
h=0
0.8
0
5
10
15
Time (minutes)
x1  V1 ( x1 )  V0 ( xn )
V0  x (t )  
Vmax
 x(t  td ) 
1 
 K fb 


h
h = [0 1 2 3]
20
h=3
h=2
h=1
Transients,
Oscillations
Tighter
steady-state
regulation
h=0
0
5
10
15
Higher feedback “gain”
Time
20
[ATP]
1.05
1
h=3
0.95
Time response
0.9
0.85
Yet
fragile
h=0
0.8
0
5
10
15
20
Time (minutes)
0.8
h=3
Robust
Log(Sn/S0)
0.6
Spectrum
0.4
0.2
h=0
0
-0.2
-0.4
-0.6
-0.8
0
2
4
Frequency
6
8
10
Yet
fragile
0.8
h=3
Robust
Log(Sn/S0)
0.6
0.4
0.2
h=0
0
-0.2
-0.4
-0.6
-0.8
0
2
4
Frequency
6
8
10
 log F(x ) d
n
 constant ?
Yet
fragile
0.8
Robust
Log(Sn/S0)
0.6
0.4
0.2
h=0
0
-0.2
-0.4
-0.6
-0.8
0
2
4
Frequency
6
8
10
Theorem
 log F(x ) d
 constant
n
Transients,
Oscillations
0.8
h=3
Tighter
steady-state
regulation
Log(Sn/S0)
0.6
0.4
h=2
0.2
h=0
0
h=1
-0.2
-0.4
log F(xn )
-0.6
-0.8
0
2
4
Frequency
6
8
10
This tradeoff is a law.
log|S |
Transients,
Oscillations

x ) d  constant
 log F(Biological
complexity is
n
Tighter
regulation
dominated by the evolution of
mechanisms to more finely tune
this robustness/fragility tradeoff.
This tradeoff is a law.
log|S |

Vk 1 ( xk 1 )
xk
Product inhibition
is a protocol.
Vk ( xk )
This tradeoff is a law.
log|S |
PFK and ATP are
modules.

Vk 1 ( xk 1 )
Product inhibition
is a protocol.
xk
Vk ( xk )
Define log S  "fragility"
S  F( xn )
log|S |

 log F(x ) d
n
 constant
Conservation of “fragility”
Diseases of complexity
Fragile
Complex development
Regeneration/renewal
Complex societies
Immune response
Parasites
Cancer
Epidemics
Auto-immune disease
Uncertainty
Robust
log|S |

We have a proof of this.
X0
X1
…
Xi
…
Xn
Error
X
This is a cartoon.
We have no proof of this.
Yet.
Complex development
Regeneration/renewal
Complex societies
Immune response
Fragile
Parasites
Cancer
Epidemics
Auto-immune disease
Uncertainty
Robust
Immune response
Parasites
Development
Cancer
Regeneration
Epidemics
renewal
Auto-immune
Societies
disease
Robust
Uncertainty
Fragile
Why should any biologists care
about this?
How does it effect what can be
done to understand complex
biological networks?
h=3
h=2
h=1
Transients,
Oscillations
h=0
0
5
10
Time
15
20
0.8
h=3
Tighter
steady-state
regulation
Log(Sn/S0)
0.6
0.4
h=2
0.2
h=0
0
h=1
-0.2
 log F(x ) d  constant
-0.4
n
-0.6
-0.8
0
2
4
Frequency
6
8
10
Autocatalysis
Enzyme

 log S ( ) d 
 log    log 
0
k
k
Metabolite
Energy
and
materials
+Regulation
transport
metabolism
assembly
Autocatalytic feedback
Even though autocatalytic feedback
contributes relatively modestly to
complexity, it has a huge indirect
Regulatory
impact on
regulatory complexity.
feedback
transport
metabolism
assembly
Autocatalytic feedback
•
•
•
Autocatalysis is everywhere in human and
natural systems as well as biology
Make energy, materials, and machines to make
energy, materials, and machines to make …
Consumers are investors are labor…
Regulatory
feedback
Regulatory
feedback
only
h=3
Transients,
Oscillations
h=0
h=2
h=1
0
5
10
Time
15
20
0.8
h=3
Tighter
steady-state
regulation
Log(Sn/S0)
0.6
0.4
h=2
0.2
h=0
0
h=1
-0.2
-0.4
-0.6
-0.8
0
2
4
Frequency
6
8
10
Add more
autocatalytic
feedback
Add
autocatalytic
feedback
Transients,
Oscillations
 log F(x ) d
n
Increases
Add more
regulator
feedback
 log F(x ) d
n
 constant  0
More
“instability”
aggravates


0
log S () d  log 
Increase log 
Control demo


0
log S ( ) d  log 1/ L
L
transport
Conservation
of energy,
moiety, and
fragility are
laws.
metabolism
Autocatalytic feedback
“Bowtie architectures”
with product inhibition
is a protocol suite.
Regulatory
feedback
assembly
Enzymes
are
modules.
Nested bowtie and hourglass
Core
metabolism
Conservation of energy
and moiety is a law.
Polymerization
and
assembly
Taxis
Enzymes are
and
modules.
transport
“Bowtie architectures”
is a protocol.
Autocatalytic and regulatory feedback
Key themes
1. Multiscale and large-scale stochastic simulation is
an essential technology for systems biology.
2. Simulation alone is not scalable to larger network
problems because complex, uncertain systems
need an exponentially large number of simulations
to answer biologically meaningful questions.
3. There are fundamental laws governing the
organization of biological networks.
Hypotheses
1. Multiscale and large-scale stochastic simulation.
Gillespie + Petzold for stiff stochastic
systems.
2. Simulation alone is not scalable. Automated
scalable inference using SOSTOOLS.
3. There are fundamental laws governing the
organization of biological networks. Without
exploiting these, the complexity is
overwhelming.
Recently, there has been a
remarkable convergences.
A coherent foundation
for a general understanding
of highly evolved complexity
Biology
Molecular biology has catalogued
cellular components, and network
structure is becoming more apparent.
Biology
Advanced
Technology
Advanced technologies are
producing networks approaching
biological levels of complexity
(which is hidden to the user).
Biology
Math
Advanced
Technology
New mathematics provides for the
first time a coherent theoretical
framework for complex networks
(but not yet an accessible one).
Biology
Math
Advanced
Technology
A coherent foundation
for a general understanding
of highly evolved complexity
After many false starts.
Biology
Math
Advanced
Technology
Complementary ways to tell this story:
1. Give lots of examples from biology and
technology
2. Prove relevant theorems
3. Deliver useful software tools
Biology
Math
Advanced
Technology
• Today: an attempt to distill an accessible
message from enormous amount of detail
• Focus on universal laws that transcend details
• Minimize math, maximize examples
• Provide broader context for the rest of the
shortcourse
Biology
Math
Advanced
Technology
This week:
• Case studies in microbial signaling and
regulation networks
• Will attempt to put details into broader context
• Saturday will consider computational
challenges
Hard
Problems
coNP
NP
P
“easy”
coNP
Hard
Problems
Economics
Algorithms
Controls
NP
Communications
Dynamical Systems
Physics
P
• Domain-specific assumptions
• Enormously successful
• Handcrafted theories
• Incompatible assumptions
• Tower of Babel where even
experts cannot communicate
• “Unified theories” failed
• New challenges unmet
Economics
Algorithms
Controls
Communications
Dynamical Systems
Physics
P
Hard
Problems
Internet
coNP
Economics
Algorithms
Controls
NP
Communications
Dynamical Systems
Physics
P
Hard
Problems
Biology
coNP
Economics
Algorithms
Controls
NP
Internet
Communications
Dynamical Systems
Physics
P
Biology and advanced technology
• Biology
– Integrates control, communications, computing
– Into distributed control systems
– Built at the molecular level
• Advanced technologies will increasingly do the same
• We need new theory and math, plus unprecedented
connection between systems and devices
• Two challenges for greater integration:
– Unified theory of systems
– Multiscale: from devices to systems
Hard
Unified
Problems
coNP
Goal
Theory
Economics
Algorithms
Biology
NP
Controls
Internet
Communications
Dynamical Systems
Physics
P
Hard
Problems
Biology
coNP
Economics
Algorithms
Controls
NP
Internet
Communications
Dynamical Systems
Physics
P