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Statistical Mechanics of Sloppy Models

Statistical Mechanics of Sloppy Models. Bacterial Cell-Cell Communication and More. Josh Waterfall, Jim Sethna, Steve Winans. Quorum Sensing. Agrobacterium tumefaciens. Cell-cell signaling network for monitoring population density.

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Statistical Mechanics of Sloppy Models

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  1. Statistical Mechanics of Sloppy Models Bacterial Cell-Cell Communication and More Josh Waterfall, Jim Sethna, Steve Winans

  2. Quorum Sensing Agrobacterium tumefaciens • Cell-cell signaling network for monitoring population density plant pathogen - transfers oncogenic DNA to plant, co-opting plant machinery to make nutrients. Low population density: pheromone molecule lost to environment. High density: pheromone is picked up from neighbors and signaling pathway is activated. pheromone = Quorum triggers sharing of tumor inducing plasmid

  3. 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 phenolic compound metabolism) TraR OOHL TraI TraR TraI Genes

  4. How to live with 24 free parameters and still make falsifiable predictions??? 26 reactions 19 chemicals 24 rate constants

  5. 24 Parameter “Fit” to Data • Cost ≡ Energy • Also fit to six other sets of genetic and biochemical experiments (38 data points) • Still misses data • Hand-tuning, then fancy optimizations • How much can the fit parameters vary, and still fit the data? (Will give error bars) Radioactivity 0 45 minutes TraR protein is stable only with OOHL

  6. Ensemble of Models eigen bare We want to consider not just minimum cost solutions, but all solutions consistent with the available data. New level of abstraction: statistical mechanics in model space. • Huge range of scales from stiff to sloppy : 1 inch = 103 miles • Eigendirections not aligned with bare parameters Generate an ensemble of states with Boltzmann weights exp(-C/T) and compute for an observable: O is chemical concentration, or rate constant …

  7. Wide range of natural scales Log Eigenvalues 5 0 Eigenvalues – not all parameters are created equal. Range of e20! -20 Sloppiness – fluctuations in eigenparameters in ensemble up to tens of orders of magnitude! Eigenparameter

  8. Biological insight from eigenparameters Stiffest Eigenparameter 2nd Stiffest Eigenparameter Bare Parameter Bare Parameter Stiffest eigenparameter predominantly bacterial doubling time Second stiffest adds ratio between production of TraR and degradation of TraR and OOHL

  9. Predictions for experiments are constrained Although rate constant values are wildly undetermined, predictions for new experiments are not (always). Growth factor signaling model

  10. 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

  11. Acknowledgements Biology: Stephen Winans Cathy White Modeling: Jim Sethna Kevin Brown Funding: NSF ITR DOE Computational Science Graduate Fellowship

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