Collaborators and contributors partial list

1
Collaborators and contributors(partial list)

• Theory Parrilo, Carlson, Paganini,
  Papachristodoulo, Prajna, Goncalves, Fazel, Lall,
  DAndrea, Jadbabaie, many current and former
  students,
• Biology Csete,Yi, Tanaka, Arkin, Simon, AfCS,
  Kurata, Khammash, El-Samad, Gross, Bolouri,
  Kitano, Hucka, Sauro, Finney,
• Web/Internet Low, Willinger, Vinnicombe, Kelly,
  Zhu,Yu, Wang, Chandy, Effros,
• Turbulence Bamieh, Dahleh, Bobba, Gharib,
  Marsden,
• Physics Mabuchi, Doherty, Barahona, Reynolds,
  Asimakapoulos,
• Engineering CAD Ortiz, Murray, Schroder,
  Burdick,
• Disturbance ecology Moritz, Carlson, Robert,
• Finance Martinez, Primbs, Yamada, Giannelli,

Caltech faculty
Other Caltech
Other
2
Complexity
Advanced Technology
Math
Biology
A coherent foundation is emerging.
After many false starts.
3
Complexity
Advanced Technology
Math
Biology

• Complementary ways to tell this story
• Give lots of examples
• Prove theorems and give you software tools

4
Advanced Technology
Math
Biology

• Minimal assumptions
• Biology and biochemistry you know lots (this is
  not a tutorial on biology)
• Math familiarity with modeling and simulating
  simple biochemical networks
• Advanced technology some familiarity with
  technology you use regularly laptops, phones,
  cars, planes, Internet

5
Advanced Technology
Math
Biology

• Ideally (but not assumed)
• Biology know lots about bacterial regulation and
  signal transduction networks
• Math comfortable with control, computational
  complexity, duality and optimization
• Advanced technology know essential details of
  how technology you use regularly (laptops,
  phones, cars, planes, Internet, ..) actually work

6
Advanced Technology
Math
Biology
It is important to get beyond needing to know
everything.

• Ideally (but not assumed)
• Biology know lots about bacterial regulation and
  signal transduction networks
• Math comfortable with control, computational
  complexity, duality and optimization
• Advanced technology know essential details of
  how technology you use regularly (laptops,
  phones, cars, planes, Internet, ..) actually work

7
Advanced Technology
Math
Biology

• Well cover
• Biology some examples to warm up
• Advanced technology superficially, for
  comparison of convergent evolution
• Math (hopefully) self-contained exposition of
  the essential elements, with software to take
  home and use (and break) on your problems

8
Software development (the real work)

• SBML Systems Biology Markup Language
• SBW Systems Biology Workbench
• Mike Hucka is technical lead on SB
• SOStools Sum-Of-Squares SemiDefinite Programming
  toolbox (Parrilo, Papachristodoulo, Prajna)
• Multiscale simulation (Gillespie Petzold)

9

• Broader manifesto
• March 1, 2002

10
Biochemical Network E. Coli Metabolism
Enzyme
Mass Transfer in Metabolism
Metabolite
From Adam Arkin
from EcoCYC by Peter Karp
11
Biochemical Network E. Coli Metabolism
Feedback Interactions
From Adam Arkin
from EcoCYC by Peter Karp
12
Autocatalysis
Regulation
Enzyme
Metabolite
from EcoCYC by Peter Karp
13
Autocatalysis
Regulation
Enzyme
Autocatalysis
Enzyme
Regulation
14
Enzyme
Metabolite
15
Stoichiometry or mass and energy balance
Internal
Products
Nutrients
16
Graphs are cartoons. So we must be careful.
Mass Transfer in Metabolism
17
E. Coli all metabolism
External
metabolites
Other inputs
98
105
111
Reduced carriers
Activated carriers
174
180
Precursor
192
metabolites
275
Amino acids
295
membrane lipid
Vitamin and cofactor
Nucleotides
351
359

• Highly structured
• Scale-rich (not scale-free)
• Self-dissimilar (not self-similar)

Lipid and LPS
397
408
Fatty acids and
CO2, Pi, H etc CC
506
514
Other outputs
537
140
282
440
553
608
739
Membrane
Amino acids
Nucleotides
Catabolism
transport
18
Biochemical Network E. Coli Metabolism
Feedback Interactions
Robustness ? Complexity
Supplies Materials Energy
Supplies Robustness
From Adam Arkin
from EcoCYC by Peter Karp
19

• Highly structured
• Scale-rich (not scale-free)
• Self-dissimilar (not self-similar)

20
Biochemical Network E. Coli Metabolism
Feedback Interactions
Complexity ? Fragility
Supplies Materials Energy
Supplies Robustness
From Adam Arkin
from EcoCYC by Peter Karp
21
Metabolism Constraints Mass and Energy balance
Nutrients, ions, gases,
Nucleotides
Carbohydrates
Lipids
Amino Acids
Energy
22
Nutrients, ions, gases,
Is this complexity needed? Is this network
optimal? If so, in what sense?
23
Core metabolism
24
Whole cell metabolism
Core metabolism
Autocatalytic and regulatory feedback
25
Polymerization and assembly
Nested bowties
Core metabolism
transport
Autocatalytic and regulatory feedback
26
Nested bowties
Necessity or frozen accident?
27
The core metabolism bowtie
Nutrients
Products
28
Catabolism
Carriers and Precursor Metabolites
Cartoon metabolism
29
Catabolism
Nucleotides
Carriers and Precursor Metabolites
Sugars
Amino Acids
Fatty acids
Energy and reducing
The metabolism bowtie protocol
30
Uncertain
Uncertain
31
Uncertain
Uncertain
32
The metabolism bowtie protocol.
Products
Nutrients
33
Aside Modules and protocols

• Much confusion surrounds these terms
• Biologists already understand the important
  distinction
• Most of basic sciences doesnt

34
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

35
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

36
Reductionism and protocols

• Reductionism modules are more important than
  protocols
• Usually Huh? Whats a protocol?
• Systems approach Protocols are as important as
  modules

37
Nested bowtie and hourglass
Polymerization and assembly
Core metabolism
Conservation of energy and moiety is a law.
Taxis and transport
Enzymes are modules.
Bowtie architectures is a protocol.
Autocatalytic and regulatory feedback
38
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.

39
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.

40
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

41
Almost everything complex is made this way Cars,
planes, buildings, power, fuel, laptops,
This cartoon is pure protocol.
42
Manufacturing and metabolism
Collect and import raw materials
Common currencies and building blocks
Complex assembly
Collect and import raw materials
Common currencies and building blocks
Complex assembly
Polymerization and assembly
Taxis and transport
Core metabolism
Autocatalytic and regulatory feedback
43
Collect and import raw materials
Common currencies and building blocks
Complex assembly
Steel manufacturing
44
Petroleum extraction and refining
45
Electric power
Variety of producers
46
Electric power
Variety of consumers
47
Variety of consumers
Variety of producers
Energy carriers

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

48
Reductionism and protocols

• Reductionism Modules only
• Systems Protocols are as important as modules

49
Minimal theoretical requirements for bowtie
metabolism

• Conservation (e.g. energy, redox, moiety, etc)
• Robustness
• varying nutrient sources
• varying product demand
• Efficiency
• Few genes, enzymes, reactions
• Simple reactions

50
Minimal theoretical requirements

• Conservation
• Robustness (low fragility)
• Efficiency (low waste)

• Even simple, abstract assumptions yield bowtie
  protocol/architecture
• Applies to any advanced manufacturing process
  that has these features

51
Emergent bowtie protocol features

• Hierarchical, modular, structured
• Scale-rich and self-dissimilar
• The complete opposite of scale-free and
  self-similar (popular science notwithstanding)
• Robust and evolvable
• With fragile and hard to change elements

52
Uncertain
Uncertain
53
Nested bowtie and hourglass
Polymerization and assembly
Core metabolism
Transport
Autocatalytic and regulatory feedback
54
Uncertain
Uncertain
55
Polymerization and assembly
Core metabolism
Transport
Autocatalytic and regulatory feedback
56
essential 230   nonessential 2373  
unknown 1804   total 4407
http//www.shigen.nig.ac.jp/ecoli/pec
57
assembly
metabolism
transport
Autocatalytic feedback
Regulatory feedback
58
assembly
metabolism
transport
Knockouts often lethal
Autocatalytic feedback
Knockouts often lose robustness, not minimal
functionality
Regulatory feedback
59
assembly
metabolism
transport
Autocatalytic feedback
If feedback regulation is the dominant protocol,
what are the laws constraining whats possible?
Regulatory feedback
60
Autocatalytic feedback
Regulatory feedback
Disturbance
Plant
FF sensor
FB sensor
A universal architecture
Computer
Actuator
61
Heat shock
An interesting gene regulation network
62
?70
rpoH
Heat
? mRNA
RNAP
unfolded
folded
This is the block diagram that molecular
biologists use to describe the E. Coli heat shock
control system. It is broken down into modules
which can be identified with molecular states.
Molecular Modules
?
?
DNAK
?
RNAP
DNAK
ftsH
aggregate
Lon
RNAP
?
degradation
DnaK
FtsH
Lon
63
?70
rpoH
Heat
? mRNA
RNAP
unfolded
folded
Molecular Modules
?
?
DNAK
?
RNAP
DNAK
ftsH
aggregate
Lon
RNAP
?
degradation
DnaK
FtsH
Lon
64
Functional modules
Disturbance
FF sensor
Plant
FB sensor
Computer
Actuator
A control theorists view. How do these two views
relate?
65
Control versus molecular modules
Heat
? mRNA
FF sensor
Plant
FB sensor
Computer
?
?
DNAK
Actuator
?
RNAP
DNAK
ftsH
Lon
RNAP
?
DnaK
FtsH
Lon
66
Autocatalytic feedback
Regulatory feedback
Disturbance
Plant
FF sensor
FB sensor
A universal architecture
Computer
Actuator
67
Disturbance
FF sensor
FB sensor
Plant
Computer
Actuator
Demo
68
Motivation

• The heat shock response is a highly conserved
  mechanism in many organisms
• It has been the center of a large research effort
  since 1978 when the E. coli heat responsive genes
  were first discovered in Neidhart and Yura labs.
• It is involved in a generalized cellular stress
  response (ethanol, viral infections, etc)
• There is a fairly coherent story about this
  mechanism, but also a lot of speculation
  (temperature downshift, role of chaperones in
  proteolyses of proteins, etc).
• So studying the heat shock response is an
  interesting exercise in its own right.
• In addition, it turns out that that it can be
  also used for pedagogical purposes It is fairly
  complex to form a case study for emergent
  techniques that address biological complexity,
  but sufficiently tractable to test the results.

69
Cell
Temp cell
Temp environ
70
Cell
How does the cell build barriers (in state
space) to stop this cascading failure event?
Temp cell
Temp environ
71
Temp cell
Folded Proteins
Temp environ
72
Temp cell
Folded Proteins
Temp environ
73
More robust ( Temp stable) proteins
Unfolded Proteins
Aggregates
Temp cell
Folded Proteins
Temp environ
74

• Key proteins can have multiple (allelic or
  paralogous) variants
• Allelic variants allow populations to adapt
• Regulated multiple gene loci allow individuals
  to adapt

Unfolded Proteins
Aggregates
Temp cell
Folded Proteins
Temp environ
75
37o
42o
Log of E. Coli Growth Rate
46o
21o
-1/T
76
Robustness/performance tradeoff?
37o
42o
Log of E. Coli Growth Rate
46o
21o
-1/T
77
Heat shock response involves complex feedback and
feedforward control.
Unfolded Proteins
Temp cell
Folded Proteins
Temp environ
78
Alternative strategies
Why does biology (and advanced technology)
overwhelmingly opt for the complex control
systems instead of just robust components?

• Robust proteins
• Temperature stability
• Allelic variants
• Paralogous isozymes
• Regulate temperature
• Thermotax
• Heat shock response
• Up regulate chaperones and proteases
• Refold or degraded denatured proteins

79
Control versus molecular modules
Heat
? mRNA
FF sensor
Plant
FB sensor
Computer
?
?
DNAK
Actuator
?
RNAP
DNAK
ftsH
Lon
RNAP
?
DnaK
FtsH
Lon
80
Molecular and functional modules
Plant
Plant the basic system to be controlled
81
Molecular and functional modules
Heat
Plant the basic system to be controlled
82
Building Blocks of the Heat Shock Response The
Heat Shock Proteins
DnaK/DnaJ/GrpE chaperone team, GroEL/GroEs
chaperone team, HtpG, IbpA/B
Lon, FtsH, Clp family of proteases, ClpY(HslU),
hflB
83
Molecular and functional modules
Heat
Plant
84
In order to have an efficient heat shock
response, heat shock proteins have to be produced
fast and reliably when they are needed
85
RNA Polymerase

s32 factor
86
Molecular and functional modules
Heat
Plant
?
Actuator
RNAP
DNAK
Lon
RNAP
?
DnaK
FtsH
Lon
87
The heat shock proteins are the product of the
s32 regulon.
The level of heat shock proteins can be regulated
by controlling the number and level of activity
of s32
88

• Synthesis of s32 Translational Regulation
  (feedforward)
• Heat-induced s32 translation by melting of mRNA
  secondary structure

Initiation codon
Translational Induction of heat shock
transcription factor s32 evidence of a
built-in thermosensor. Morita et. al, Genes
Dev. 1999
89
Molecular and functional modules
Heat
? mRNA
FF sensor
Plant
Computer
?
Actuator
RNAP
DNAK
Lon
RNAP
?
DnaK
FtsH
Lon
90
Regulation of s32 Activity Chaperones inhibit
s32 activity by sequestering s32 away from RNAP.
Unfolded proteins increase s32 activity.
91
Regulation of s32 Activity Chaperones inhibit
s32 activity by sequestering s32 away from RNAP.
Unfolded proteins increase s32 activity.
Transcription Translation
RNAP
hsp1
hsp2
92
Molecular and functional modules
Heat
? mRNA
FF sensor
Plant
FB sensor
Computer
?
?
DNAK
Actuator
RNAP
DNAK
Lon
RNAP
?
DnaK
FtsH
Lon
93
Heat
? mRNA
FF sensor
Plant
FB sensor
Computer
?
?
DNAK
Actuator
DNAK
Main FB and FF loops
RNAP
?
DnaK
FtsH
94
Regulation of s32 Degradation s32 is degraded by
proteases that it transcribes for
E. Coli FtsH is a membrane bound ATP-dependent
protease which degrades the heat shock
transcription factor s32, Tomoyasu et. Al, EMBO
J., 1995
95
Molecular and functional modules
Heat
? mRNA
FF sensor
Plant
Computer
?
?
DNAK
Actuator
RNAP
DNAK
Lon
RNAP
?
DnaK
FtsH
Lon
96
Regulation of Heat-Shock Response
97
Feedback and feedforward Architecture of the
Heat-Shock Response
Dnak translation transcription dynamics
degradation rate
98
Mathematical Model
Protein Synthesis
99
Binding Equations
Mass Balance Equations
100
Solution of the Resulting Large-Scale DAE System

• Different time scales.
• Singular perturbation, or quasi-steady-state
  approximations.
• The resulting set of equations is a
  Differential-Algebraic set of equations (DAE). It
  is of index I and is an implicit set of ODEs.
• Numerical solutions using DASSL and DASKP.

• The Numerical Solution of Initial Value Problems
  in Differential-Algebraic Equations, K.E. Brenan,
  S.L. Campbell, and L.R. Petzold 1996, SIAM
  Classics Series    

• Software and Algorithms for Sensitivity
  Analysis of Large-Scale Differential-Algebraic
  Systems,
• S. Li and L.R. Petzold, to appear, J. Comp. Appl.
  Math.

101
Full Model Simulations
102
Model Prediction Vs Data
Levels of are reproduced for wild type
and ftsh null mutants
DnaK rates are reproduced for wild type and ftsh
null mutants
Data taken from
Heat Shock Regulation in the FtsH null mutant Of
E. coli Dissection of Stability and activity
control mechanisms of sigma32 in vivo, Tatsuta
et. al, Molecular Microbiology, 1998. look at
paper
103
An Example of a Successful Prediction
rpoH gene
Transcription
Heat
Degradation
-
Translation
-
Activity
-
hsp1
hsp2
HslVU FtsH
Proteases
104
An Example of a Successful Prediction
rpoH gene
Transcription
Heat
Dynamic change in s32 stability explains the
apparent shutoff
Degradation
-
Translation
-
Activity
-
hsp1
hsp2
Translational Repression
HslVU FtsH
Proteases
105
Multiple loops are involved in the regulatory
strategy of the heat shock responseDo the
regulatory loops have redundant or rather
specialized functions?
106
A Simple Design that would conceivably work
Open Loop Design with Feedforward
107
However, sensitivity to parametric uncertainty is
extensive, for example
Noise
100
90
80
70
60
50
change in the level of chaperones
40
Open Loop
30
20
10
0
0
10
20
30
40
50
60
70
80
90
100
change in the transcription rate
108
Closing the loop Sequestration Feedback Loop
Translation
Transcription and
Protein
Synthesis
Translation of HSP
Folding
of Sigma32
-
109
With the sequestration loop in place, sensitivity
is reduced
110
Feedfoward Sequestration Loop Degradation
Loop
HEAT
HSP transcription/ translation protein folding
Binding to promoter
translation
Sequestration
degradation
111
Role of the degradation loop in attenuating
stochastic fluctuations. Simulations done using
the Stochastic Simulation Algorithm of Gillespie
112
Basic Architecture of HS Response
HEAT
HSP transcription/ translation protein folding
Binding to promoter
translation
Sequestration
degradation
Robustness to Parameteric Uncertainty Lowering
the metabolic burden
Sequestration
Regulation of Speed of response/ Noise
attenuation
Degradation
Speed Efficiency of Protein Folding
Feedforward
113
Those results were obtained by simulations and in
silico mutations

• In the rest of the workshop, some of these
  results will be revisited in the context of model
  validation/invalidation and proven
  algorithmically using SOSTOOLS

Model Validation and Robustness Analysis of the
Bacterial Heat Shock Response Using SOSTOOLS, H.
El Samad, S.Prajna A. Papachristodolou, M.
Khammash, J.C. Doyle, submitted to CDC03
114
Reduced order model
3-state model S s32 D Chaperone Uf
Unfolded Protein
115
ODE stiffness
Heat
Srna
P
D
DU
S
SD
U
FSD
F
SR
Sdegraded
Can write a 2-state ODE with everything else as
algebraic, because the rest is fast and quickly
reaches equilibrium. Thus the full 30 state DAE
description of this is extremely stiff.
R
SR
DnaK
FtsH
116
We were able to do this drastic model reduction

• Because of the different time scales
• and because of the wide difference in the
  numbers of the molecular species
• It was done by inspection, but
• We think it is an example of a more general
  principle systematic model reduction can be
  carried on for complex nonlinear systems with
  time scale separation. Work is still preliminary.
  
• Some intuition on that in later talks, but for
  now we will focus on the insight given by the
  smaller model.

117
Reduced Order Model

• More amenable to useful decomposition, for
  example extracting functionally modular
  structures, identifying the important pathways,
  fluxes, protocols, etc...
• A universal way for thinking about regulatory
  networks is in terms of a universal control
  architecture

118
A Typical Scheme in Man-Made Control Systems
119
Functional modules
Disturbance
FF sensor
Plant
FB sensor
Computer
Actuator
A control theorists view. How do these two views
relate?
120
Molecular and functional modules
Heat
? mRNA
FF sensor
Plant
FB sensor
Computer
?
?
DNAK
Actuator
RNAP
DNAK
RNAP
?
DnaK
FtsH
121
Heat
Computional/Logic unit Integration
of Information
Feedback Sensor
Df
St
Sf
Degradation
Folding Plant
Dt
Uf
Actuator The heat shock proteins
Sf Free Sigma, Dt total chaperone, Uf unfolded
proteins
122
The Stochastic Challenges

• SSA of Gillespie
• Could not simulate the whole system because of
  the large number of molecules of some species, in
  addition to fast reactions that made the step
  size in the simulation very small.
• The simulated part did not exhibit any noticeably
  different behavior from the deterministic
• But posed interesting questions.

123
Stochastic stiffness
High fluxes
Sfree very small
D
SD
This is the interesting and rare reaction.
FSD
SR

• The binding between S and D happens almost surely
  because of the large number of D. It happens
  often, making the SSA very slow.
• The binding of S to R happens only rarely, but it
  is the interesting reaction since it is the basis
  of the regulation of HSPs
• Wed like to capture the interesting reaction
  (Sfree ? SR), while leaping over the Sfree ? SD
  .

124
Stochastic stiffness
This is the interesting and rare reaction.
125
This kind of situations is abundant in biology

• It is a challenge for any stochastic approach to
  chemical kinetics relevant to biology. More
  details and thorough discussions on the latest in
  this area are going to be addressed in subsequent
  talks in the Friday PM sessions.

126
Disturbance
1 protocol 3 kinds of modularity
Feedforward
Disturbance
FF sensor
?32 Translation
FB sensor
Plant
Computer
Servo
ftsH
Feedback
dnaK
Actuator
Feedback




127
Developing the math model Start with the
modularity of concentrations of each chemical
component plus conservation constraints.
molecular module
128
This may seem trivial, but each macromolecular
concentration is a module, and viewing this
system as the dynamics of changing concentrations
is a big abstraction and assumption, one that
will have to be relaxed somewhat to more fully
examine stochastic effects. This modeling is
bottoms-up in defining relevant molecular
concentrations and their rates of change.
molecular module
129
Disturbance
Feedforward
?32 Translation
Flux modules
Fluxes implement functionality in biochemical
reactions.
dnaK
Feedback
130
Heat
? mRNA
FF sensor
Plant
FB sensor
Computer
?
?
DNAK
Actuator
DNAK
Main FB and FF loops
RNAP
?
DnaK
FtsH
131

• Actuator servo loop
• Amplification
• FB to reject uncertainty and noise
• Implemented via ftsH degradation

? mRNA
FF sensor
FB sensor
Computer
?
?
DNAK
Actuator
?
ftsH
RNAP
?
DnaK
FtsH
132
?32 transcription
Disturbance
Feedforward
?32 Translation
Flux modules
Servo
ftsH
?32 degradation
Feedback
dnaK
Feedback
Amplifier
133
Disturbance
Feedforward
?32 Translation
Flux modules
dnaK
Feedback
134
Flux modules
?32 transcription
Heat
? mRNA
?32 Translation
?
?
DNAK
?
RNAP
DNAK
ftsH
RNAP
?
DnaK
FtsH
degradation
135
Flux modules
?32 transcription
Heat
? mRNA
?32 Translation
?
?
DNAK
?
RNAP
DNAK
ftsH
RNAP
?
DnaK
FtsH
degradation
136
Feedforward
Disturbance
?32 Translation
Flux modules or pathways
Servo
ftsH
Decompose dynamics into functional fluxes which
sum to yield overall rates.
Feedback
dnaK
Feedback
Hopefully this will appear natural.
137
Disturbance
1 protocol 3 kinds of modularity
Feedforward
Disturbance
FF sensor
?32 Translation
FB sensor
Plant
Computer
Servo
ftsH
Feedback
dnaK
Actuator
Feedback




138
Variety of robust functions
FF
FB
Plant
Variety of physical implementations
139
Variety of Ligands Receptors
Hourglass

• Hourglasses organize
• regulatory and signaling systems
• horizontal and vertical decompositions

Intermediates
Variety of responses
140
Molecular and functional modules
Heat
? mRNA
FF sensor
Plant
FB sensor
Computer
?
?
DNAK
Actuator
RNAP
DNAK
Lon
RNAP
?
DnaK
FtsH
Lon
141
Molecular and functional modules
Heat
? mRNA
FF sensor
Plant
FB sensor
Computer
?
?
DNAK
Actuator
RNAP
DNAK
Lon
RNAP
?
DnaK
FtsH
Lon
142
Molecular and functional modules
Heat
? mRNA
FF sensor
Plant
FB sensor
Computer
?
?
DNAK
Actuator
RNAP
DNAK
Lon
RNAP
?
DnaK
FtsH
Lon
143
Molecular and functional modules
Heat
? mRNA
FF sensor
Plant
FB sensor
Computer
?
?
DNAK
Actuator
RNAP
DNAK
Lon
RNAP
?
DnaK
FtsH
Lon
144
Molecular and functional modules
Actuator
DNAK
Lon
RNAP
?70
DnaK
Lon