Demand Theory of Gene Regulation and Design of TwoComponent Systems

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Demand Theory of Gene Regulation and Design of
Two-Component Systems

• Michael A. Savageau
• The University of California, Davis
• May 2003

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The problems faced by pre- and post-genomic
genetics are ... much the same -- they all
involve bridging the chasm between genotype and
phenotype. -- Sydney
Brenner, Science 2872173 (2000)
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Function of Gene Circuitry

• Superficial answer
• Genotype determined by the information encoded in
  the DNA sequence
• Phenotype by the context-dependent expression of
  the genome
• Circuitry interprets context and orchestrates
  expression
• Deeper answer
• Hierarchy of mechanisms
• Diversity of design issues
• Accident and rule

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Research Program

• Development of mathematical tools and approaches
  appropriate for biological systems
• Nonlinear mathematical formalisms and analysis
• Computational algorithms
• Applications to generic classes of biological
  systems at the molecular and cellular level
• Metabolic pathways
• Gene circuits
• Immune networks
• Long-term goal of understanding biological design
  principles
• Re-design for therapeutic purposes
• Optimization for technological purposes

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The Organism Escherichia coli

• Robust
• Versatile
• Efficient
• Responsive

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The Environments In Here and Out There
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Outline

• Demand theory of Gene Regulation
• Methodology
• Duality, realizability and evolvability
• Multiple demands, logic and timing
• Two-Component Systems for Signal Transduction
• Design
• Function
• Structure
• Design and construction of gene circuits
• Switches
• Oscillators

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Approach

• Emphasize large classes of circuits with a
  specific function
• Inducible catabolic circuits in bacteria
• 100 members
• Many tests of any general prediction
• Goals
• Understand the basis for nearly universal designs
• Discover rules for distinguishing alternative
  designs

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Requirements for the Elucidation of System Design
Principles

• Canonical nonlinear representation
• Constraints that reduce the space of meaningful
  comparison
• Methods for extracting implications implicit in
  the system equations
• Quantitative criteria for judging functional
  effectiveness

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Systemic Manifestations of the Power-Law Formalism
M. Savageau, J.T.B. 25370 (1969)
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Mathematically Controlled (Ideal) Comparisons

• Two designs are represented in a canonical
  nonlinear formalism
• Differences are restricted to a single specific
  process
• One design is chosen as the reference
• Internal equivalence is maintained
• External equivalence is imposed
• The systems are characterized by rigorous
  mathematical and computer analysis
• Comparisons are made on the basis of quantitative
  criteria for functional effectiveness

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Outline

• Demand theory of Gene Regulation
• Methodology
• Duality, realizability and evolvability
• Multiple demands, logic and timing
• Two-Component Systems for Signal Transduction
• Design
• Function
• Structure

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Dual Modes of Gene Control
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Mutations Rates
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Demand Theory of Gene Control

• A positive mode of control is predicted when
  there is a high demand for expression of a gene
• A negative mode of control is predicted when
  there is a low demand for expression of a gene

M. Savageau, PNAS 712453 (1974)
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Molecular Mode of Gene Control

• Experimental evidence
• Single demand functions gt100
• Logical coupling of functions 20
• Differentiated cell-specific functions 6

M. Savageau, PNAS 745647 (1977)
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Lac operon of E. coli

• Lac circuitry
• Life cycle and demand for expression
• Mutation
• Population dynamics
• Mathematical analysis
• Quantify rules of demand theory
• Predictions relating genotype and phenotype

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Lac Circuitry
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Life Cycle of Escherichia coli
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Mutations Rates
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Population Dynamics
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Graphical Solution
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Steady State
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Region of Realizability
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Rate and Extent of Selection
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Predictions

• Cycling without colonization ? 26 hours
• Colonization without cycling ? 66 years
• Rate of re-colonization ? 4 months
• Evolutionary response time ? 3 years

M. Savageau, Genetics 1491677 (1998)
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Outline

• Demand theory of Gene Regulation
• Methodology
• Duality, realizability and evolvability
• Multiple demands, logic and timing
• Two-Component Systems for Signal Transduction
• Design
• Function
• Structure

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Logic of Lac Control
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Six Possible Life Cycles
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Region of Realizability
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Rate Extent of Selection
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Six Possible Life Cycles
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Expression in Time and Space
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There is one important piece of information that
is almost totally missing the sequence
information that specifies when and where and for
how long a gene is turned on or off.
-- Sydney Brenner, Science 2872173 (2000)
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Outline

• Demand theory of Gene Regulation
• Methodology
• Duality, realizability and evolvability
• Multiple demands, logic and timing
• Two-Component Systems for Signal Transduction
• Design
• Function
• Structure

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Alternative Designs for Sensors of Two-Component
Systems
Bifunctional sensor
Monofunctional sensor
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Outline

• Demand theory of Gene Regulation
• Methodology
• Duality, realizability and evolvability
• Multiple demands, logic and timing
• Two-Component Systems for Signal Transduction
• Design
• Function
• Structure

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Equations
Bifunctional sensor
Monofunctional sensor
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Constraints for External Equivalence
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Functional Predictions

• Bifunctional sensors
• Attenuate secondary signals
• Suppress noisy cross-talk
• Monofunctional sensors
• Amplify secondary signals
• Integrate functional cross-talk

Alves Savageau, Mol. Microbiol. 4825 (2003)
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Alternative Designs for Sensors of Two-Component
Systems
Noise Suppression
Signal Integration
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Outline

• Demand theory of Gene Regulation
• Methodology
• Duality, realizability and evolvability
• Multiple demands, logic and timing
• Two-Component Systems for Signal Transduction
• Design
• Function
• Structure

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Alternative Designs for Sensors of Two-Component
Systems
Bifunctional sensor
Monofunctional sensor
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Predictions

• Sensor 3-D structures for templates
• EnvZ (Bifunctional)
• CheA (Monofunctional)
• Sensor DNA sequences for threading
• 2000 cases
• Many organisms
• Functional predictions
• Bifunctional
• Monofunctional

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What is Common to These Successful Explanations
of Design?

• A limited number of possible variations on a
  theme
• Simple equations whose structure was amenable to
  qualitative analysis (and to exhaustive numerical
  analysis when necessary)

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Summary

• Comparison Methodology
• Mathematically controlled comparisons
• Ideal control experiments
• Comparative optimization
• Examples of Design Principles
• Molecular mode of gene control
• Demand for expression
• Realizability and evolvability
• Logic and phasing
• Cross-talk between two-component modules
• Insulators
• Integrators

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(No Transcript)
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Outline

• Demand theory of Gene Regulation
• Methodology
• Duality, realizability and evolvability
• Multiple demands, logic and timing
• Two-Component Systems for Signal Transduction
• Design
• Function
• Structure
• Design and construction of gene circuits
• Switches
• Oscillators

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Genetic Construct and Kinetic Model for a Novel
Circuit in E. coli
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Design Space
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Toggle Switch Behavior
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Outline

• Demand theory of Gene Regulation
• Methodology
• Duality, realizability and evolvability
• Multiple demands, logic and timing
• Two-Component Systems for Signal Transduction
• Design
• Function
• Structure
• Design and construction of gene circuits
• Switches
• Oscillators

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Design Space
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Experimental Tests of Theory
M. Atkinson, et al., Cell in press (2003)
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Minimum Distance from Boundary of Oscillatory
Instability
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Parameter Sensitivity of Minimum Distance from
Boundary of Oscillatory Instability