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Statistical Mechanics of SloppyModels
Bacterial Cell-CellCommunication and More
Josh Waterfall, Jim Sethna,Steve Winans
Quorum Sensing
•Cell-cell signaling network formonitoring population density
Low populationdensity:pheromonemolecule lost toenvironment.
High density:pheromone ispicked up fromneighbors andsignaling pathwayis activated.
Agrobacterium tumefaciens
plant pathogen -transfersoncogenic DNAto plant, co-opting plantmachinery tomake nutrients.
Quorum triggers sharingof tumor inducingplasmid
pheromone =
•TraI synthesizes small molecule (OOHL) at low, basal rate•TraR needs OOHL to fold properly•Active TraR turns on transcription of other genes, including traI•Hierarchically regulated by separate systems (opine and phenoliccompound metabolism)
OOHL
TraI
TraR
Genes
TraR
TraI
26 reactions19 chemicals24 rate constants
How to live with 24free parameters andstill make falsifiablepredictions???
24 Parameter “Fit” to Data• Cost _ Energy
• Also fit to six other sets ofgenetic and biochemicalexperiments (38 datapoints)
• Still misses data
• Hand-tuning, then fancyoptimizations
• How much can the fitparameters vary, and stillfit the data? (Will giveerror bars)
∑=
−=
RN
i i
iyyC1
2
2))((
2
1)(
σθ
θ
rr
TraR protein is stable only withOOHL
Rad
ioac
tivity
minutes 450
Ensemble of ModelsWe want to consider not just minimum cost solutions, but all
solutions consistent with the available data. New level ofabstraction: statistical mechanics in model space.
Generate an ensemble ofstates with Boltzmannweights exp(-C/T) andcompute for an observable:
O is chemical concentration, orrate constant …
222
1
)()(
)(1
θθσ
θ
rr
r
OO
ON
O
O
N
ii
E
E
−=
= ∑=
bare
eigen
•Huge range of scales from stiffto sloppy : 1 inch = 103 miles•Eigendirections not aligned withbare parameters
Wide range of natural scales
Eigenvalues – not allparameters are createdequal. Range of e20!
Sloppiness – fluctuations ineigenparameters in ensemble upto tens of orders of magnitude!
50
-20
Log Eigenvalues
Eigenparameter
Stiffest eigenparameterpredominantly bacterialdoubling time
Second stiffest adds ratiobetween production of TraRand degradation of TraR andOOHL
Biological insight from eigenparameters
Bare Parameter
Stiffest Eigenparameter2nd Stiffest Eigenparameter
Bare Parameter
Predictions for experiments are constrained
Growth factor signaling model
Although rateconstant valuesare wildlyundetermined,predictions fornew experimentsare not (always).
Other Sloppy systems past, present, future
• Growth Factor Signaling
• Receptor Trafficking
• Translation Dynamics
• Transcription Dynamics
• E-Coli Whole Cell Model
• Nitrogen Cycle in Forests
• Radioactive decay
• Classical Potentials: Molybdenum
Acknowledgements
Biology:Stephen WinansCathy White
Modeling:Jim SethnaKevin Brown
Funding:NSF ITRDOE Computational Science GraduateFellowship