Not random

1
Random
Not random
2
Sets of measure zero. But there many such
sets What characterizes these sets?
Constraints and robustness
Not random
Random
3
What is complexity and why?
Constraints and robustness
4
Systems requirements functional,
efficient, robust, evolvable
Constraints
Hard constraints Thermo (Carnot) Info
(Shannon) Control (Bode) Compute (Turing)
Architecture Constraints That deconstrain
Components and materials Energy, moieties
5
System-level Robustness

• Robustness by other names (smells as sweet?)
• Basic robustness to variations in environment
  (and components)
• Evolvability robustness of lineages on long
  time scales to (possibly large) variations
• Efficiency robustness to resource scarcity
• Scalability robustness to changes in system
  size and complexity
• Etc etc

6
Gene networks?
essential 230   nonessential 2373  
unknown 1804   total 4407
http//www.shigen.nig.ac.jp/ecoli/pec
7
Polymerization and complex assembly
Autocatalytic feedback
Taxis and transport
Proteins
Core metabolism
Sugars
Catabolism
Amino Acids
Nucleotides
Precursors
Nutrients
Trans
Fatty acids
Genes
Co-factors
Carriers
DNA replication
Regulation control
E. coli genome
8
Steering
Brakes
Mirrors
Wipers
Anti-skid
Cruise control
GPS
Radio
Traction control
Headlights
Shifting
Electronic ignition
Temperature control
Seats
Electronic fuel injection
Seatbelts
Fenders
Bumpers
Airbags
Suspension (control)
9
Knockouts often lethal
Steering
Brakes
Mirrors
Wipers
Anti-skid
Knockouts often lose robustness, not minimal
functionality
Cruise control
GPS
Radio
Traction control
Headlights
Shifting
Electronic ignition
Temperature control
Seats
Electronic fuel injection
Seatbelts
Fenders
Bumpers
Airbags
Suspension (control)
10
Polymerization and complex assembly
Autocatalytic feedback
Taxis and transport
Proteins
Core metabolism
Sugars
Catabolism
Amino Acids
Nucleotides
Precursors
Nutrients
Trans
Knockouts often lethal
Fatty acids
Genes
Co-factors
Carriers
DNA replication
Knockouts often lose robustness, not minimal
functionality
Regulation control
11
System-level Robustness
90 Complexity ? Robustness 10 Complexity
? Function
Dont take exact too seriously.
12
Constraints (environment) Robustness of system
Constraints
Constraints Hard limits on systems
Architecture Constraints Protocols
Constraints (components) Physico-chemical
13
Constraints Robustness of system
Constraints
Constraints Hard limits on systems
These are all constraints with no choices (and
that do not deconstrain)
Constraints Physico-chemical
14
Necessity (Environment) Robustness of system
Chance/ choice Or Necessity?
Necessity (Theory) Hard limits on Robustness
Choice? Robust Architecture
Complexity?
Robustness
Necessity Physico-chemical
15
Hard limits Thermo (Carnot) Info
(Shannon) Control (Bode) Compute (Turing)

• Assume architectures a priori
• Fragmented and incompatible
• Initial unifications encouraging

16
How do these two sources of constraints relate?
Constraints Robustness of system

• These constraints come from the environment and
  are on the system as a whole
• Functionality
• Robustness
• Evolvability

Hard limits Thermo (Carnot) Info
(Shannon) Control (Bode) Comp (Turing)

• These are universal theoretical constraints
  that apply to all systems and components no
  matter the environment or component constraints,
  however
• Assume architectures a priori that are
• Fragmented and incompatible

17
De Duve, Wachtershauser

• PMF
• DNA
• Proteins
• Lipids
• RNA
• ATP
• NTP and (pyro-)phospho-transfer
• Choice of ions? (Ca2, Na, K, Mg2)
• Choice of metals? (Fe, etc.)
• Thioesters
• Group transfer
• Electron transfer
• Catalysis
• Carbon, Nitrogen, Hydrogen,
• Energy, matter, small moieties

Chance/ Choice? Necessity
Necessity Physico-chemical
18
Selective Necessity (Bottlenecks)
Sufficiently Ergodic Environment
De Duve
Deterministic Necessity
Sufficiently Exploratory Systems
19
Sufficiently Ergodic Environment

• PMF
• DNA
• Proteins
• Lipids
• RNA
• ATP
• NTP and (pyro-)phospho-transfer
• Choice of ions? (Ca2, Na, K, Mg2)
• Choice of metals? (Fe, etc.)
• Thioesters
• Group transfer
• Electron transfer
• Catalysis
• Carbon, Nitrogen, Hydrogen,
• Energy, matter, small moieties

Necessity
Sufficiently Exploratory Systems
20
Selective Bottlenecks (Necessity)
Choice? ArchitectureConstraints
that Deconstrain

• Most crucial choices are here
• Growing list of examples
• Limited coherent theory
• Constraints protocols

Deterministic Necessity
21
Necessity (Environment) Robustness/evolvability
Chance/ choice Or Necessity?
Necessity (Theory) Hard limits on Robustness
Choice? Robust Architecture
Necessity Physico-chemical
22
Necessity (Environment) Robustness/evolvability
Chance/ choice Or Necessity?
Necessity (Theory) Hard limits on Robustness
Choice? Robust Architecture
Necessity Physico-chemical
23
Constraints Robustness of system
Constraints
Constraints Hard limits on systems
Architecture Constraints Protocols
Constraints Physico-chemical
24
Hard limits and tradeoffs
Robust/ fragile is unifying concept

• 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

25
Architecture is a central challenge

• The bacterial cell and the Internet have
• architectures
• that are robust and evolvable (yet fragile?)
• What does architecture mean here?
• What does it mean for an architecture to be
  robust and evolvable?
• Robust yet fragile?

26
Architecture in organized complexity

• Architecture involves or facilitates
• System-level function (beyond components)
• Organization and structure
• Protocols and modules
• Design or evolution
• Robustness, evolvability, scalability
• Various -ilities (many of them)
• Perhaps aesthetics
• but is more than the sum of these

27
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

Assume different architectures a priori.
28
Defining Architecture

• The elements of structure and organization that
  are most universal, high-level, persistent
• Must facilitate system level functionality
• And robustness/evolvability to uncertainty and
  change in components, function, and environment
• Architectures can be designed or evolve, but when
  possible should be planned
• Usually involves specification of
• protocols (rules of interaction)
• more than modules (which obey protocols)

29
Architecture in organized complexity

• Design of architectures is replacing design of
  systems
• Architecture is central in biology and
  technology, but has been largely overlooked in
  other areas of complexity
• Emergent complexity can have order,
  structure and (ill-defined notions like)
  self-organization
• but architecture plays little role
• Architecture also has little to do with aspects
  of networks that can be modeled using graph
  theory (or power laws)

30
A few asides

• Robust yet fragile, architecture-based, bio and
  techno networks have high variability everywhere
• High variability is fundamental and important.
• High variability yields power laws because of
  their strong invariance Central Limit Theorem,
  marginalization, maximization, mixtures
• Power laws are more normal than Normal
• This strong statistical invariance also yields
  power laws due to analysis errors, which are
  amazingly widespread
• Architecture also has little to do with aspects
  of networks that can be modeled using graph
  theory (or power laws)

31
Architecture examples

• There are universal architectures that are
  ubiquitous in complex technological and
  biological networks
• Examples include
• Bowties for flows of materials, energy, redox,
  information, etc (stoichiometry)
• Hourglasses for layering and distribution of
  regulation and control (fluxes, kinetics,
  dynamics)
• Nascent theory confirms (reverse engineers)
  success stories but has (so far) limited forward
  engineering applications (e.g. FAST TCP/AQM)

32
with thin knot of
large fan-out of diverse outputs
large fan-in of diverse inputs
universal carriers
Bowties
33
Examples of
universal carriers

• Packets in the Internet
• 60 Hz AC in the power grid
• Lego snap
• Money in markets and economics
• Lots of biology examples (coming up)

34
The Internet hourglass
Applications
IP under everything
Web
FTP
Mail
News
Video
Audio
ping
napster
TCP
IP
Ethernet
802.11
Satellite
Optical
Power lines
Bluetooth
ATM
Link technologies
35
Applications
Top of waist provides robustness to variety
and uncertainty above
TCP/ AQM
Bottom of waist provides robustness to
variety and uncertainty below
IP
36
Hourglasses

• Hourglasses organize layered control
  architectures
• Examples include

• Internet TCP/IP
• Cell Transcription/translation/degradation plus
  allosteric regulation
• Lego Physical assembly plus Mindstorm NXT
  controller

Diverse function
Universal Control
Diverse components
37
fan-out of diverse outputs
universal carriers
fan-in of diverse inputs
Bowties andHourglasses
Diverse function
Universal Control

• More and clearer examples of bowties than
  hourglasses
• Other hourglasses exist but are harder to explain

Diverse components
38
Four big bowties in bacterial S

• Metabolism, biosynthesis, assembly
• Carriers Charging carriers in central metabolism
  
• Precursors Biosynthesis of precursors and
  building blocks
• Trans DNA replication, transcription, and
  translation
• Signal transduction
• 2CST Two-component signal transduction
• (Named after their central knot)

39

• Carriers
• Precursors
• Trans
• 2CST

Sugars

Fatty acids
Precursors
Co-factors
Catabolism
Amino Acids
Nucleotides
Genes
Proteins
Carriers
Trans
DNA replication
40

• Carriers
• Precursors
• Trans
• 2CST

Modules are less important than protocols the
rules by which modules interact.
Precursors
Carriers
Trans
41

• Carriers
• Precursors
• Trans

These bowties involve the flow of material and
energy.
Sugars

Fatty acids
Precursors
Catabolism
Co-factors
Amino Acids
Nucleotides
Genes
Proteins
Carriers
Trans
DNA replication
42
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 (?!?)
43
One big bowtie in Internet S


Variety of files
Variety of files
packets

• All sender files transported as packets
• All files are reconstructed from packets by
  receiver
• All advanced technologies have protocols
  specifying knot of carriers, building blocks,
  interfaces, etc
• This architecture facilitates control, enabling
  robustness and evolvability
• It also creates fragilities to hijacking and
  cascading failure

44
Why bowties?

• Metabolism, biosynthesis, assembly
• Carriers Charging carriers in central metabolism
  
• Precursors Biosynthesis of precursors and
  building blocks
• Trans DNA replication, transcription, and
  translation
• Signal transduction
• 2CST Two-component signal transduction

45
Metabolism, biosynthesis, assembly
Taxis and transport
Autocatalytic feedback
Polymerization and complex assembly
Core metabolism
Sugars

Fatty acids
Precursors
Co-factors
Catabolism
Nutrients
Amino Acids
Genes
Proteins
Nucleotides
Carriers
Trans
DNA replication
Regulation control
46
Metabolism, biosynthesis, assembly
Taxis and transport
Autocatalytic feedback
Polymerization and complex assembly
Core metabolism
Sugars

Fatty acids
Precursors
Co-factors
Catabolism
Nutrients
Amino Acids
Genes
Proteins
Nucleotides
Carriers
Trans
DNA replication
The architecture of stoichiometry.
47
Autocatalytic feedback
Core metabolism
Sugars

Fatty acids
Precursors
Co-factors
Catabolism
Nutrients
Amino Acids
Genes
Proteins
Nucleotides
Carriers
Trans
DNA replication
48
Bacterial cell
Environment
Environment
Huge Variety
Huge Variety
49
Same 12 in all cells
Taxis and transport
Core metabolism
Sugars
Catabolism
Amino Acids
Nucleotides
Precursors
Nutrients
Fatty acids

• ?100
• same
• in all
• organisms

Co-factors
Carriers
Same 8 in all cells
Huge Variety
50
Polymerization and complex assembly
Autocatalytic feedback
Taxis and transport
Proteins
Core metabolism
Sugars
Catabolism
Amino Acids
Precursors
Nucleotides
Regulation control
Nutrients
Trans
Fatty acids
Genes
Co-factors
Carriers
DNA replication
Regulation control
The architecture of the cell.
51
Core metabolism
Sugars
Catabolism
Amino Acids
Nucleotides
Precursors
Fatty acids
Co-factors
Carriers
Nested bowties
52
Sugars
Amino Acids
Nucleotides
Fatty acids
Co-factors
53
(No Transcript)
54
Catabolism
55
Precursors
56
Gly
G1P
G6P
Precursors
F6P
Autocatalytic
F1-6BP
Gly3p
Carriers
ATP
13BPG
TCA
3PG
Oxa
ACA
Pyr
PEP
2PG
NADH
Cit
57
Gly
G1P
G6P
Regulatory
F6P
F1-6BP
Gly3p
ATP
13BPG
TCA
3PG
Oxa
ACA
PEP
Pyr
2PG
NADH
Cit
58
Gly
G1P
G6P
F6P
F1-6BP
Gly3p
13BPG
TCA
3PG
Oxa
ACA
Pyr
PEP
2PG
Cit
59
If we drew the feedback loops the diagram would
be unreadable.
Gly
G1P
G6P
F6P
F1-6BP
Gly3p
ATP
13BPG
TCA
3PG
Oxa
ACA
PEP
Pyr
2PG
NADH
Cit
60
S
Stoichiometry matrix
61
Gly
G1P
G6P
F6P
F1-6BP
Gly3p
Regulation of enzyme levels by transcription/trans
lation/degradation
13BPG
TCA
3PG
Oxa
ACA
PEP
Pyr
2PG
Cit
62
Gly
G1P
G6P
F6P
F1-6BP
Gly3p
Allosteric regulation of enzymes
ATP
13BPG
TCA
3PG
Oxa
ACA
PEP
Pyr
2PG
NADH
Cit
63
Gly
G1P
G6P
Allosteric regulation of enzymes
F6P
F1-6BP
Regulation of enzyme levels
Gly3p
ATP
13BPG
TCA
3PG
Oxa
ACA
PEP
Pyr
2PG
NADH
Cit
64
Gly
Fast
G1P
G6P
Allosteric regulation of enzymes
F6P
F1-6BP
Regulation of enzyme levels
Gly3p
ATP
13BPG
Slow
TCA
3PG
Oxa
ACA
PEP
Pyr
2PG
NADH
Cit
65
Taxis and transport
12
Autocatalytic feedback
Polymerization and complex assembly
Core metabolism
Sugars

Fatty acids
Precursors
Co-factors
Catabolism
Nutrients
Amino Acids
Genes
Proteins
Nucleotides
Carriers
Trans
8

• ?100

Huge Variety
DNA replication

• ?104 to ? 8
• in one
• organisms

66
Autocatalytic feedback
Few polymerases Highly conserved
Polymerization and complex assembly
Genes
Proteins
Trans
DNA replication

• ?104 to ? 8
• in one
• organisms

Huge Variety
67
Why bowties?

• Metabolism, biosynthesis, assembly
• Carriers Charging carriers in central metabolism
  
• Precursors Biosynthesis of precursors and
  building blocks
• Trans DNA replication, transcription, and
  translation
• Signal transduction
• 2CST Two-component signal transduction

68

• ?50 such two component systems in E. Coli
• All use the same protocol
• - Histidine autokinase transmitter
• - Aspartyl phospho-acceptor receiver
• Huge variety of receptors and responses
• Also multistage (phosphorelay) versions

Signal transduction
69
Two components Highly conserved
Huge variety
Huge variety
70


Variety of Ligands Receptors
Variety of responses
Transmitter
Receiver
Signal transduction
71
Flow of signal
Shared protocols


Ligands Receptors
Transmitter
Receiver
Responses
Recognition, specificity
72
Flow of signal
Shared protocols


Ligands Receptors
Transmitter
Receiver
Responses
Recognition, specificity
Flow of packets
Note The wireless system in this room and the
Internet to which it is connected work the same
way.
Laptop
Router
Recognition, specificity
73
No variety
Huge Variety
Huge variety

• Virtually unlimited variability and
  heterogeneity (within and between organisms)
• E.g Time constants, rates, molecular counts and
  sizes, fluxes, variety of molecules,
• Very limited but critical points of homogeneity
  (within and between organisms)

74
Nested bowties advanced technologies
Everything is made this way cars, planes,
buildings, laptops,
75
Electric power
Variety of producers
Variety of consumers
76
Standard
interface
Variety of consumers
Variety of producers
Energy carriers

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

77
Nested bowties advanced technologies
Everything is made this way cars, planes,
buildings, laptops,
78
No variety
Why?
Huge Variety
Huge variety

• Provides plug and play modularity between huge
  variety of input and output components
• Facilitates robust regulation and evolvability
  on every timescale (constraints that
  deconstrain)
• But has extreme fragilities to parasitism and
  predation (knots are easily hijacked or consumed)

79
Evolving evolvability?
Random Variation
Structured Selection
?
80
Polymerization and complex assembly
Autocatalytic feedback
Taxis and transport
Proteins
Core metabolism
Sugars
Catabolism
Amino Acids
Nucleotides
Precursors
Nutrients
Trans
Fatty acids
Genes
Co-factors
Carriers
DNA replication
Architecture
E. coli genome
81
Structured variation
Structured Selection
Variation
Structured and large
Architecture
82
Fragility example Viruses
Autocatalytic feedback
Core metabolism
Viruses exploit the universal bowtie/hourglass
structure to hijack the cell machinery.
Sugars

Fatty acids
Precursors
Co-factors
Catabolism
Nutrients
Amino Acids
Genes
Proteins
Nucleotides
Carriers
Trans
DNA replication
Regulation control
83
Fragility example Viruses
Viruses exploit the universal bowtie/hourglass
structure to hijack the cell machinery.
Precursors
Carriers
Trans
84
Fragility example Viruses
Autocatalytic feedback
Core metabolism
Sugars

Fatty acids
Precursors
Precursors
Co-factors
Catabolism
Nutrients
Viral genes
Amino Acids
Viral proteins
Genes
Proteins
Nucleotides
Carriers
Carriers
Trans
Trans
DNA replication
Regulation control
85
Polymerization and complex assembly
Energy materials
Autocatalytic feedback
Taxis and transport
Proteins
Core metabolism
Sugars
Catabolism
Amino Acids
Nucleotides
Precursors
Nutrients
Trans
Fatty acids
Genes
Co-factors
Carriers
DNA replication
Regulation control?
E. coli genome
86
Polymerization and complex assembly
Autocatalytic feedback
Taxis and transport
Proteins
Core metabolism
Sugars
Catabolism
Amino Acids
Nucleotides
Precursors
Nutrients
Trans
Fatty acids
Genes
Co-factors
Carriers
DNA replication
Regulation control
E. coli genome
87
Polymerization and complex assembly
Autocatalytic feedback
Taxis and transport
Proteins
Core metabolism
Sugars
Catabolism
Amino Acids
Not to scale
Nucleotides
Precursors
Regulation control
Nutrients
Trans
Fatty acids
Genes
Co-factors
Carriers
DNA replication
Regulation control
88
Gene networks?
essential 230   nonessential 2373  
unknown 1804   total 4407
http//www.shigen.nig.ac.jp/ecoli/pec
89
Polymerization and complex assembly
Autocatalytic feedback
Taxis and transport
Proteins
Core metabolism
Sugars
Catabolism
Amino Acids
Nucleotides
Precursors
Nutrients
Trans
Fatty acids
Genes
Co-factors
Carriers
DNA replication
Regulation control
E. coli genome
90
Polymerization and complex assembly
Autocatalytic feedback
Proteins
Regulation control
Trans
Genes
DNA replication
91
(No Transcript)
92
(No Transcript)
93
motif
rpoH
Other operons
See El-Samad, Kurata, et al PNAS, PLOS CompBio
DnaK
Lon
94
motif
Heat
rpoH
folded
unfolded
Other operons
DnaK
Lon
DnaK
Lon
95
Heat
rpoH
? mRNA
?
Other operons
DnaK
RNAP
Lon
RNAP
?
DnaK
FtsH
Lon
96
Heat
rpoH
? mRNA
?
?
DnaK
Other operons
?
DnaK
DnaK
RNAP
ftsH
Lon
RNAP
?
DnaK
FtsH
Lon
97
Heat
rpoH
? mRNA
?
?
DnaK
Other operons
?
DnaK
DnaK
ftsH
RNAP
Lon
?
RNAP
DnaK
FtsH
Lon
98
Heat
rpoH
? mRNA
Regulation of protein action
Regulation of protein levels
?
?
DnaK
?
DnaK
DnaK
ftsH
RNAP
Lon
?
RNAP
DnaK
FtsH
Lon
99
Layered control architectures
Allosteric
Trans
100
Heat
rpoH
? mRNA
?
?
DnaK
Other operons
?
DnaK
DnaK
ftsH
RNAP
Lon
?
RNAP
DnaK
FtsH
Lon
101
motif
rpoH
Other operons
DnaK
Lon
102
(No Transcript)