Complexity and Robustness

Complexity and Robustness
Polymerization and complex assembly G GDP GTP In Out P Ligand Receptor  RGS Autocatalytic feedback Taxis and transport Proteins Core metabolism Sugars Catabolism Amino Acids Nutrients Precursors Nucleotides Trans* Fatty acids Genes Co-factors Carriers Complexity and Robustness DNA replication John Doyle John G Braun Professor Control and Dynamical Systems, BioEng, and ElecEng Caltech

Collaborators and contributors (partial list)
Biology: Csete,Yi, Tanaka, Arkin, Savageau, Simon, AfCS, Kurata, Khammash, El-Samad, Gross, Kitano, Hucka, Sauro, Finney, Bolouri, Gillespie, Petzold, F Doyle, Stelling, … Theory: Parrilo, Carlson, Paganini, 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, Vinnicombe, Kelly, Zhu,Yu, Wang, Chandy, … Turbulence: Bamieh, Bobba, Gharib, Marsden, … Physics: Mabuchi, Doherty, Barahona, Reynolds, Disturbance ecology: Moritz, Carlson,… Finance: Martinez, Primbs, Yamada, Giannelli,… Engineering CAD: Ortiz, Murray, Schroder, Burdick, … Current Caltech Former Caltech Longterm Visitor Other

Core theory challenges
Multiscale Physics Core theory challenges Network Centric, Pervasive, Embedded, Ubiquitous Systems Biology

Today’s focus Core theory challenges Network Centric, Pervasive, Embedded, Ubiquitous Systems Biology

Status Systems Biology
Yet also striking increase in unnecessary confusion??? Consistent, coherent, convergent understanding. Remarkably common core theoretical challenges. Core theory challenges Core theory challenges Dramatic recent progress in laying the foundation. Core theory challenges Pervasive, Networked, Embedded Systems Biology

The danger of biomemetics
Feathers and flapping? Or lift, drag, propulsion, and control? The danger of biomemetics

Wilbur Wright on Control, 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.”

Hard constraints Simple models Short proofs Architecture

A look back and forward The Internet architecture was designed without a theory. Many academic theorists told the engineers it would never work. We now have a nascent theory that confirms that the engineers were right. For systems biology, future networks, and other new technologies, let’s hope we can avoid a repeat of this history.

Architecture? “The bacterial cell and the Internet have
architectures that are robust and evolvable” What does “architecture” mean? What does it mean for an “architecture” to be robust and evolvable? Robust yet fragile? Rigorous and coherent theory?

Hard constraints On systems and their components
Thermodynamics (Carnot) Communications (Shannon) Control (Bode) Computation (Turing/Gödel) Fragmented and incompatible We need a more integrated view and have the beginnings Assume different architectures a priori.

Hard constraints (progress)
Thermodynamics (Carnot) Communications (Shannon) Control (Bode) Computation (Turing/Gödel) We need a more integrated view and have the beginnings

Work in progress Thermodynamics (Carnot) Communications (Shannon)
Control (Bode) Computation (Turing/Gödel) We need a more integrated view and have the beginnings

Short proofs (progress)
Robust yet fragile systems Proof complexity implies problem fragility (!?!) Designing for robustness and verifiability are compatible objectives Hope for a unifying framework? SOS, Psatz (Prajna, P*) Temporal specifications (Pnueli) SAT (Selman) Integrating simple models and short proofs?

Simple models (challenges)
Rigorous connections between Multiple scales Experiment, data, and models Essential starting point for short proofs Microscopic state: discrete, finite, enormous Packet level Software, digital hardware Molecular-level interactions Macroscopic behavior: robust yet fragile

The architecture of the cell.
Polymerization and complex assembly Autocatalytic feedback Taxis and transport Proteins Core metabolism Sugars Catabolism Amino Acids Nutrients Precursors Nucleotides Regulation & control Trans* Fatty acids Genes Co-factors Carriers DNA replication Regulation & control The architecture of the cell.

Universal organizational structures/architectures
Bowtie: Flow of energy and materials Universal organizational structures/architectures Organization of control Hourglass

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

Autocatalytic and regulatory feedback
Robustness: Efficient and flexible metabolism Fragility: Obesity and diabetes Cell Glucose and Oxygen Cell Transport Cell Autocatalytic and regulatory feedback

Robust Yet Fragile Human robustness and fragility
Efficient, flexible metabolism Complex development and Immune systems Regeneration & renewal Complex societies Obesity and diabetes and Rich parasite ecosystem Auto-immune disease Cancer Epidemics, war, genocide, … Human robustness and fragility

Nightmare? Biology: We might accumulate more complete parts lists but never “understand” how it all works. Technology: We might build increasingly complex and incomprehensible systems which will eventually fail completely yet cryptically. Nothing in the orthodox views of complexity says this won’t happen (apparently).

HOPE? Interesting systems are robust yet fragile.
Identify the fragility, evaluate and protect it. The rest (robust) is “easy”. Nothing in the orthodox views of complexity says this can’t happen (apparently).

Architecture? “The bacterial cell and the Internet have
architectures that are robust and evolvable” What does “architecture” mean? What does it mean for an “architecture” to be robust and evolvable? Robust yet fragile? Rigorous and coherent theory?

Cartoons and stories No math Taxis and transport Regulation & control
RNAP DnaK  rpoH FtsH Lon Heat  mRNA ftsH Regulation of protein levels Regulation of protein action Cartoons and stories No math Autocatalytic feedback Taxis and transport PMF + Proteins Core metabolism Sugars Catabolism TCA Gly G1P G6P F6P F1-6BP PEP Pyr Gly3p 13BPG 3PG 2PG ATP NADH Oxa Cit ACA Amino Acids Precursors Nucleotides Trans* Fatty acids Genes Co-factors Carriers Regulation & control From Taylor, Zhulin, Johnson

motif rpoH Other operons DnaK Lon

motif Heat rpoH folded unfolded Other operons degradation DnaK Lon

Heat rpoH  mRNA  Other operons DnaK RNAP Lon  RNAP DnaK FtsH Lon

Heat  mRNA     rpoH DnaK Other operons DnaK DnaK RNAP ftsH Lon

Heat  mRNA     rpoH DnaK Other operons DnaK DnaK ftsH RNAP Lon

Heat Regulation of protein action Regulation of protein levels
rpoH  mRNA Regulation of protein action Regulation of protein levels   DnaK  DnaK DnaK ftsH RNAP Lon  RNAP DnaK FtsH Lon

Signal transduction Ubiquitous protocol “Hourglass”
Variety of Ligands & Receptors Ubiquitous protocol “Hourglass” “Robust yet fragile” Robust & evolvable Fragile to “hijacking” Manages extreme heterogeneity with selected homogeneity Accident or necessity? Variety of responses Ligands & Receptors G- proteins Primary targets Transmitter Receiver Variety of responses Signal transduction

Universal control architecture Regulation of enzyme levels
Bio: Huge variety of environments, metabolisms Allosteric regulation Universal control architecture Regulation of enzyme levels Huge variety of genomes Huge variety of components

The Internet hourglass
Applications Web FTP Mail News Video Audio ping napster Ethernet 802.11 Power lines ATM Optical Satellite Bluetooth Link technologies

Applications Web FTP Mail News Video Audio ping napster TCP IP Ethernet 802.11 Power lines ATM Optical Satellite Bluetooth Link technologies

Applications IP under everything Web FTP Mail News Video Audio ping napster TCP IP IP on everything Ethernet 802.11 Power lines ATM Optical Satellite Bluetooth Link technologies

Bio: Huge variety of environments, metabolisms
Internet: Huge variety of applications Huge variety of components

Internet: Huge variety of applications Both components and applications are highly uncertain. Huge variety of components

Internet: Huge variety of applications Huge variety of genomes Huge variety of physical networks Huge variety of components

Identical control architecture
Hourglass architectures Bio: Huge variety of environments, metabolisms Internet: Huge variety of applications Identical control architecture Feedback control Huge variety of genomes Huge variety of physical networks Huge variety of components

Allosteric Trans* Regulation of protein levels Regulation of
RNAP DnaK  rpoH FtsH Lon Heat  mRNA ftsH Regulation of protein levels Regulation of protein action Gly G1P G6P F6P F1-6BP Gly3p ATP 13BPG Allosteric 3PG TCA Oxa 2PG PEP Pyr ACA Trans* NADH Cit

Feedback Control TCP/IP Metabolism/biochem
5:Application/function: variable supply/demand Feedback Control 4:TCP 4:Allosteric 3:Transcriptional 3:IP 2:Potential physical network 1:Hardware components

TCP/IP robustness/evolvability on many timescales
Shortest: File transfers from different users Application-specific navigation (application) Congestion control to share the net (TCP) Ack-based retransmission (TCP) Short: Fail-off of routers and servers Rerouting around failures (IP) Hot-swaps and rebooting of hardware Long: Rearrangements of existing components Applications/clients/servers can come and go Hardware of all types can come and go Longer: New applications and hardware Plug and play if they obey the protocols

TCP/IP fragility on many timescales
Shortest: File transfers from different users End systems w/o congestion control won’t fairly share Short: Fail-on of components Distributed denial of service Black-holing and other fail-on cascading failures Long: Spam, viruses, worms Longer: No economic model for ISPs?

Robustness/evolvability on many timescales
Shortest to short: Fluctuations in supply/demand Allosteric regulation of enzymes (4) Expression of enzyme level (3) Short: Failure/loss of individual enzyme molecules (3) Chaperones attempt repair, proteases degrade Transcription makes more Long: Incorporating new components Acquire new enzymes by lateral gene transfer Longer: Creating new applications and hardware Duplication and divergent evolution of new enzymes that still obey basic protocols

Biochem fragility on many timescales
Shortest: Fluctuations in demand/supply that exceeds regulatory capability (e.g. glycolytic oscillations) Short: Fail-on of components Indiscriminate kinases, loss of repression, … Loss of tumor suppressors Long: Infectious hijacking Longer: Diabetes, obesity

Robust yet fragile (RYF)
The same mechanisms responsible for robustness to most perturbations Allows possible extreme fragilities to others Usually involving hijacking the robustness mechanism in some way High variability (and thus power laws)

Experimental (and network) biology
Laws: Conservation of energy and matter Modules: Pipettes, Petri dishes, PCR machines, microscopes,… Protocols: Rules and recipes by which modules interact to create function All 3 must be understood. Laws are immutable Protocols are more important than modules

Nutrients Polymerization and complex assembly Taxis and transport
Autocatalytic feedback Taxis and transport Proteins Core metabolism Sugars Laws: Conservation of energy, matter, and robustness/fragility Modules: Enzymes and metabolites Protocols: Control, bowties and hourglasses Principles??? Catabolism Amino Acids Nucleotides Nutrients Precursors Regulation & control Trans* Fatty acids Genes Co-factors Carriers DNA replication Regulation & control

Bacterial cell Environment Environment Huge Variety Huge Variety

Nutrients 20 same in all Taxis and cells transport 100 same Huge
Core metabolism Sugars Catabolism Amino Acids Nutrients Precursors Nucleotides Fatty acids Co-factors Carriers 100 same in all organisms Huge Variety

Nested bowties Core metabolism Catabolism Precursors Carriers Sugars
Amino Acids Precursors Nucleotides Fatty acids Co-factors Carriers Nested bowties

Catabolism Precursors Carriers Sugars Amino Acids Nucleotides
Fatty acids Co-factors

Catabolism Precursors Carriers

Catabolism TCA Gly G1P G6P F6P 3PG 2PG Gly3p ATP 13BPG NADH Pyr Oxa
Cit ACA Gly G1P G6P F6P F1-6BP PEP Gly3p 13BPG 3PG 2PG ATP NADH

Precursors TCA Gly G1P G6P F6P 3PG 2PG Gly3p 13BPG Pyr Oxa Cit ACA
F1-6BP PEP Gly3p 13BPG 3PG 2PG Precursors

Autocatalytic Precursors Carriers TCA Gly G1P G6P F6P 3PG 2PG Gly3p
F1-6BP Gly3p Carriers ATP 13BPG 3PG TCA Oxa 2PG PEP Pyr ACA NADH Cit

20 same in all cells Precursors Carriers TCA Gly G1P G6P F6P 3PG 2PG
F1-6BP Gly3p Carriers ATP 13BPG 3PG TCA Oxa 2PG PEP Pyr ACA NADH Cit

Regulatory TCA Gly G1P G6P F6P 3PG 2PG Gly3p ATP 13BPG NADH F1-6BP Oxa
PEP Pyr ACA NADH Cit

This is still a cartoon. (Cartoons are useful.)
Gly This is still a cartoon. (Cartoons are useful.) G1P G6P F6P F1-6BP Gly3p ATP 13BPG 3PG TCA Oxa 2PG PEP Pyr ACA NADH Cit

Gly G1P G6P F6P F1-6BP Gly3p 13BPG 3PG TCA Oxa 2PG PEP Pyr ACA Cit

TCA If we drew the feedback loops the diagram would be unreadable. Gly
G1P G6P F6P F1-6BP Gly3p ATP 13BPG 3PG TCA Oxa 2PG PEP Pyr ACA NADH Cit

This can be modeled to some extent as a graph.
Gly Gly G1P G1P This cannot. G6P G6P F6P F6P F1-6BP F1-6BP This can be modeled to some extent as a graph. Gly3p Gly3p ATP 13BPG 13BPG 3PG 3PG 2PG PEP Pyr ACA 2PG PEP Pyr ACA NADH Unfortunate and unnecessary confusion results from not “getting” this.

Stoichiometry plus regulation
Biology is not a graph. Stoichiometry plus regulation

Stoichiometry matrix S TCA Gly G1P G6P F6P 3PG 2PG Gly3p ATP 13BPG
F1-6BP PEP Pyr Gly3p 13BPG 3PG 2PG ATP NADH Oxa Cit ACA S Stoichiometry matrix

Regulation of enzyme levels by transcription/translation/degradation
Gly G1P G6P F6P F1-6BP Gly3p Regulation of enzyme levels by transcription/translation/degradation 13BPG 3PG TCA Oxa 2PG PEP Pyr ACA Cit

Allosteric regulation of enzymes
Gly G1P G6P F6P F1-6BP Gly3p Allosteric regulation of enzymes ATP 13BPG 3PG TCA Oxa 2PG PEP Pyr ACA NADH Cit

Allosteric regulation of enzymes Regulation of enzyme levels
Gly G1P G6P Allosteric regulation of enzymes F6P F1-6BP Regulation of enzyme levels Gly3p ATP 13BPG 3PG TCA Oxa 2PG PEP Pyr ACA NADH Cit

Allosteric regulation of enzymes Regulation of enzyme levels
protein action Allosteric regulation of enzymes Regulation of protein levels Regulation of enzyme levels

Not to scale Nutrients Polymerization and complex assembly Taxis and
Autocatalytic feedback Taxis and transport Proteins Core metabolism Sugars Catabolism Amino Acids Not to scale Nucleotides Nutrients Precursors Regulation & control Trans* Fatty acids Genes Co-factors Carriers DNA replication Regulation & control

Gene networks? essential: 230 nonessential: 2373 unknown: 1804
total:

Regulation & control E. coli genome Nutrients Polymerization
and complex assembly Autocatalytic feedback Taxis and transport Proteins Core metabolism Sugars Catabolism Amino Acids Nutrients Precursors Nucleotides Trans* Fatty acids Genes Co-factors Carriers DNA replication Regulation & control E. coli genome

Fragility example: Viruses
Precursors Trans* Carriers Viruses exploit the universal bowtie/hourglass structure to hijack the cell machinery.

Fragility example: Viruses
Viral proteins Proteins Core metabolism Sugars Catabolism Amino Acids Precursors Nucleotides Nutrients Trans* Fatty acids Genes Co-factors Viral genes Carriers DNA replication Viruses exploit the universal bowtie/hourglass structure to hijack the cell machinery.

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