Quantitative Measurements and Computational Modeling of the Mating Response

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Quantitative Measurementsand Computational
Modeling of the Mating Response

• Kirsten Benjamin
• The Molecular Sciences Institute

June 2005 Alpha Symposium
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Why build mathematical models and predict their
consequences by simulation?

• To test current understanding of the pathway
• To reveal non-obvious and non-trivial
  relationships between outputs and inputs or
  parameters
• To explore the consequences of competing models
  or alternative mechanisms
• To make predictions about potential experimental
  outcomes under circumstances that have not been
  tested or are difficult to test

Modeling, simulation Larry Lok Joyce Macabea Ty
Thomson
Experimentation Alejandro Colman-Lerner Andrew
Gordon Richard Yu
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Modeling the Mating Signal Transduction Pathway
as a Chemical Reaction Network
Outline

• Introduction to challenges of model building
• Experimental quantitative measurements
• Mathematical and computational approaches
• Effects of pathway perturbations in vivo and in
  silico example a changes in protein abundance

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How to Make a Model of a Simple Reaction Network
Ordinary differential equations (ODEs)
List reactions
(1) (2) (3) (4) (5) (6)
Parameters Atot, Btot, Ctot k1, k-1, k2, k3, k-3,
k4
Conservation equations
(7) (8) (9)
Atot A AB
Btot B AB B CB
Ctot C CB
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How to Make a Model of a Simple Reaction Network
Ordinary differential equations (ODEs)
List reactions
(1) (2) (3) (4) (5) (6)
Parameters Atot, Btot, Ctot k1, k-1, k2, k3, k-3,
k4
Conservation equations
(7) (8) (9)
Atot A AB
ODE model 305 species, 120 free parameters
Btot B AB B CB
Ctot C CB
Ty Thomson
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Challenges of Ignorance

• Listing reactions
• What can we safely leave out?
• How to decide between alternative mechanisms?

Assigning values to parameters How to measure or
estimate quantitative features?

• Measure parameters directly
• Scour literature
• Attempt to infer values by fitting simulation
  results to observed pathway behavior (under
  standard conditions)
• Devise experimental regimes to help infer values
  (mutants, varying inputs, etc.)

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How to Measure One Class of Parameter Directly
Count Number of Protein Molecules per Cell
To use Western blotting assay, needed

• Improved, quantitative protocol
• Protein standards for calibration
• Antibodies that specifically recognize pathway
  components
• Secondary antibodies linked to fluorophore, not
  enzyme

Standard
Cell lysate
Slope units signal/molecule
Slope units signal/cell
molecules/cell lysate slope/standard slope
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Molecules of Pathway Proteins Per
Cell(population average)
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How Much is Guesswork?
Ty Thomson
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Timing and Extent of Pathway Events Can Inform
Choice of Parameter Values
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Ste5-Ste4 association
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Phosphorylation of Fus3
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Dig1-Ste12 dissociation or rearrangement
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Transcription of FUS1 or PRM1
Richard Yu Andrew Gordon Alejandro Colman-Lerner
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Timing of Pathway Events
Richard Yu Andrew Gordon Alejandro Colman-Lerner
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How to Change Parameter Values if Experiment and
Simulation Do Not Match?
Richard Yu Andrew Gordon Alejandro Colman-Lerner
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Split Pathway into Modules
Possible Module Boundaries
INPUT a factor free Ste4 active Ste12
OUTPUT free Ste4 Fus3-PP mRNA
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Mathematical Simplification of Small Sets of
Reactions
Before
Example One reversible reaction and three
irreversible reactions, 7 species, 12
parameters. Assume k110-5, k-110-3, X0106
After
(1) (2)
dy dt
-y2 - e/2 k2yI
dX2 dt
(e2-2/2e2) y2 - e/2X2(k3 P - k4 I)
Where yX/X0 , e0.1 , tet/2
(8) (9)
Itot I IX IX2
Ptot P X2P
Joyce Macabea
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Feedback Transgresses Modular Boundaries
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Simulations of Unreduced Sets of
Reactions/Equations
ODE Solvers (e.g., MatLab)

• Results correspond to average behavior over
  large population of cells
• Fast simulations, little computational burden

Gillespie Stochastic Simulation Programs (e.g.,
Moleculizer)

• Results correspond to single experiment in a
  single cell
• Recapitulates noise and stochastic responses
• Computationally more costly
• Allows very complex models with vast numbers of
  species

Larry Lok Roger Brent, Nature Biotech., Jan.2005
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Moleculizer Solves the Combinatorial Explosion
ProblemRule-based vs. Explicit enumeration
Moleculizer
ODE (5Ste5 3Fus3, etc.)
Ste5 has a binding site called to Fus3 Fus3
has a binding site called to Ste5 Any Ste5
molecule with an unoccupied to Fus3 binding
site can bind to any Fus3 with an unoccupied to
Ste5 binding site, with a probability
corresponding to an on-rate of k1 and an off-rate
of k-1
And on and on
Larry Lok Roger Brent, Nature Biotech., Jan.2005
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ODE
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Comparison of Pathway Perturbations in vivo and
in silico Can Assist Model Validation and
Refinement
How do changes in protein number affect pathway
output?
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Simulations Predict Strong Dependence of Fus3
Phosphorylation on Amounts of Fus3 and Ste7
Wild-type level
Wild-type level
Fus3-PP per cell
Fus3-PP per cell
Fus3 per cell
Ste7 per cell
ODE model 305 species, 120 free parameters
Ty Thomson
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Large Cell-to-Cell Variation in Protein Levels
FUS3-YFP
STE7-YFP
817 cells mean 1.00 SD 0.29
882 cells mean 1.00 SD 0.35
Number of cells
Number of cells
YFP concentration (normalized)
YFP concentration (normalized)
Population average 20,400 molecules/cell Lowest
10 average 12,000 Highest 10 average 31,000
Population average 920 molecules/cell Lowest
10 average 400 Highest 10 average 1500
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Make Cells with More or Less Protein
PSTE7
Wild-type
STE7
YFP
Inducible
PIND
100 10 1 0.1 0.01
STE7
YFP
Ste7-YFP
Wild-type level
inducer
Promoter set
P1
STE7
YFP
P2
100 10 1 0.1 0.01
STE7
YFP
P3
Ste7-YFP
Wild-type level
STE7
YFP
P4
STE7
YFP
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2
3
4
5
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P5
promoters
STE7
YFP
P6
STE7
YFP
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Acknowledgements
Larry Lok (MSI) Moleculizer stochastic
simulator Ty Thomson Drew Endy (MIT) ODE and
Moleculizer models Joyce Macabea (MSI)
mathematical analysis of dynamical
systems Richard Yu Alejandro Colman-Lerner
Andrew Gordon (MSI) timing of pathway events and
microscopy data analysis Roger Brent P.I. of
the Alpha Project, President and Research
Director of the Molecular Sciences Institute
Funding NIH NHGRI
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