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Model Reduction for Parameter Estimation

Model Reduction for Parameter Estimation. Eric Mjolsness Scientific Inference Systems Laboratory (SISL) University of California, Irvine www.ics.uci/edu/~emj and Caltech Biological Network Modeling Center (BNMC)

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Model Reduction for Parameter Estimation

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  1. Model Reduction for Parameter Estimation Eric Mjolsness Scientific Inference Systems Laboratory (SISL) University of California, Irvine www.ics.uci/edu/~emj and Caltech Biological Network Modeling Center (BNMC) in collaboration with Rebecca Castaño, Dasha Chudova, Michael Duff, Victoria Gor, Henrik Jönsson, Tobias Mann, George Marnellos, Elliot Meyerowitz, John Reinitz, Bruce Shapiro, David Sharp, Padhraic Smyth, Yuanfeng Wang, Barbara Wold, Guy Yosiphon, Li Zhang Parameter Estimation In Systems Biology (PESB) Pascal Workshop, Manchester, UK March 28, 2007 Manchester PESB Workshop 28/3/07

  2. Topics • A long-running thread in parameter estimation • Biological applications: • transcriptional regulation • development • Perspectives: • a near-universal bio. modeling language and semantics and its implications for … • parameter estimation and model reduction Manchester PESB Workshop 28/3/07

  3. Transcriptional Gene Regulation Networks • Gene Regulation Network [MSR’91] model E.g. Drosophila A-P axis: Drosophila gap gene expression patterns. Reinitz, Mjolsness, Sharp, Journal Experimental Zoology 271(47-56) 1995. Fitting method demonstrated in Mittenthal and Baskin, The Principles of Organization of Organisms, Addison Wesley 1992. [Mjolsness et al. J. Theor. Biol. 152: 429-453, 1991] Manchester PESB Workshop 28/3/07

  4. GRN Parameter Optimization • Simulated Annealing [1990, ’92] • Lam/Delosme SA for real-valued params • Gap genes [JEZ 271(47-56) 1995]: • 33 real-valued parameters • Genetic Algorithm • Distributed over islands with migration, for diversity • SA, GA compared in G. Marnellos thesis [1997] • GA won on evolution (life history) problems • SA won on development problems • Other apps to GRN’s and signaling [Gor, Zhang] • Then many others. Recently: • Kozlov BGRS 2006: differential evolution • Tomlin 2006: Adjoint method ~BP/cont. time Manchester PESB Workshop 28/3/07

  5. GRN ANN Equations ’91 Model statement and its derivation from stat mech: [Mjolsness Sharp and Reinitz, J. Theor. Biol. 152: 429-453, 1991] Key properties: (1) additivity, (2) saturation above and below, (3) monotonicity. Manchester PESB Workshop 28/3/07

  6. Model Reduction Example:Gene Regulation NetworkDerived from Stat Mech • [MSR91] equations are no longer just “phenomenological”. [J. Theor. Biol. 152: 429-453, 1991] Manchester PESB Workshop 28/3/07 [J.Bioinformatics & Comp. Biology, in press 2007]

  7. v M T Cluster Dynamical Model Reduction via Clustering • Core/Halo Models: • “From Coexpression to Coregulation …” [NIPS 1999 p.928-34] • Identifiability by Gibbs sampling [Duff et al., ICSB 2005] • Functional Mixture Models [Chudova et al. NIPS 2003] Manchester PESB Workshop 28/3/07

  8. Core/Leaf Model Inference • 3-node oscillator + leaves • Modeled by SDE • topologies • Identifiability: • x25 time points: identifiable • x10 points: not identifiable • x10 points x2 genotypes: ~identifiable (ranked #3) • [Duff et al. ICSB2005] Manchester PESB Workshop 28/3/07

  9. SDE Advantages • Intermediate cost for stochastic simulation • Relationship to stochastic optimization • Derivation from Fokker-Planck equation • Eg. for GRN, HCA: [JBCB in press 2007]: Manchester PESB Workshop 28/3/07

  10. Hierarchical Cooperative Activation:Alternative diagram notations • Bio-like: • Machine learning: Manchester PESB Workshop 28/3/07

  11. Hierarchical Cooperative Activation Model (HCA) In: Computational Methods in Molecular Biology, eds. J. M. Bower and H. Bolouri, MIT Press 2001 Manchester PESB Workshop 28/3/07

  12. How to model transcriptional regulation? E.g. Drosophila D-V axis: [Robert P. Zinzen, Kate Senger, Mike Levine, and Dmitri Papatsenko. Current Biology 16, 1–8, July 11, 2006] Manchester PESB Workshop 28/3/07

  13. Hard vs. Soft Logic Hierarchical Cooperative Activation (HCA) Zinzen et al. modification Experiment: Yuanfeng Wang, UCI Physics Manchester PESB Workshop 28/3/07

  14. A model reduction: HCA- Z and ANN-like Equations • Assume many binding sites per module • Assume extreme (usually low) occupancy per site where Manchester PESB Workshop 28/3/07

  15. GRSN: Gene Regulation + Signal Transduction Network + … [Marnellos, Mjolsness, Shapiro] L Drosophila neurogenesis [Marnellos, Mjolsness PSB ’98] Xenopus ciliated cells [PSB ’00] cell ligands nucleus Arabidopsis SAM [Gor, Mjolsness,Meyerowitz, NASA Evolvable Hardware ’99] receptors T transcriptional regulation targets Manchester PESB Workshop 28/3/07

  16. ArabidopsisShoot Apical Meristem (SAM) Manchester PESB Workshop 28/3/07

  17. WUS Fletcher et al., Science v. 283, 1999 Brand et. al., Science 289, 617-619, (2000) Manchester PESB Workshop 28/3/07

  18. SAM growth imageryH2B cell nuclei V. Reddy, Caltech Manchester PESB Workshop 28/3/07

  19. clv1 wus X diffusive clv3 Z L1 Y diffusive CLV3/WUS networks V. Agrawal, B. Shapiro, Caltech Manchester PESB Workshop 28/3/07

  20. CLV/WUS model behavior Activation domains in Cellerator model: WUS (yellow), CLV3I1 (green), CLV3 (blue and purple), CLV1 (red and purple). B. Shapiro, JPL/Caltech Manchester PESB Workshop 28/3/07

  21. CLV/WUS Parameter Optimization by SA 14 parameters Courtesy H. Jönsson 2007; cf. ICSB 2006 Manchester PESB Workshop 28/3/07

  22. Objects(L+2) Processes(L+1) … Objects(L+1) Processes(L) … Objects(L) Processes(L-1) Objects(L-1) Processes(L-1) Perspective … Biological scale hierarchies mutant Noun and verb hierarchies: Biology, networks, & models: Manchester PESB Workshop 28/3/07 wild type

  23. Dynamical Grammar Aims • Biology: Model complex systems • developmental biology (fly embryo, plant shoot/root) • molecular complexes • multiple-scale, heterogeneous,variable-structure systems • Mathematics: Capture, unify, extend techniques • Generalized reactions cover all processes • Operator algebra, perturbation theory, … [Annals of Math. and A. I., 47(3-4), January 2007] Manchester PESB Workshop 28/3/07

  24. Elementary Reactions • A B+ C with rate kf • B+ C A with rate kr • Effective conservation laws E.g. NA+ NB, NA+ NC Manchester PESB Workshop 28/3/07

  25. Elementary Processes • A(x)  B(y) + C(z)withrf (x, y, z) • B(y) + C(z)  A(x) withrr (y, z, x) • Examples • Chemical reaction networks w/o params • . • XXX from paper • Effective conservation laws • E.g. ∫ NA(x) dx + ∫ NB(y) dy , ∫ NA(x) dx + ∫ NC(z) dz Manchester PESB Workshop 28/3/07

  26. Elementary process models • Composition is by independent parallelism • Create elementary processes from yet more elementary “Basis operators” • Term creation/annihilation operators: for each parm value, • Obeying Heisenberg algebra • Yet classical, not quantum, probabilities Manchester PESB Workshop 28/3/07

  27. SPG Modeling Language: SemanticsSemantic map Y: GH from Grammar to Stochastic Process • Commutative diagrams for composition operations • Translation of a Rule G’ G    S H’, dp’/dt H, dp/dt Manchester PESB Workshop 28/3/07

  28. Time Ordered Product Expansion (TOPE) • Time Ordered Product Expansion (TOPE) formula: • H0 = the easy part (if only recursively) • Feynman diagrams result (QFT: Perturbation theory, Wick’s theorem) • Gillespie stochastic simulation algorithm • H0 = diag( 1· H´) ; H1 = H´ • Mixed (heterogeneous) ODE/SSA algorithm (novel) • Implemented in “Plenum” (Yosiphon) [Annals of Math. and A. I., 47(3-4), January 2007] Manchester PESB Workshop 28/3/07

  29. Model Reduction for Dynamical Systems • Diagram: • Objectives: Thus, parameter estimation can aid model reduction • Uses of diagram: [UCI ICS TR #05-09] Manchester PESB Workshop 28/3/07

  30. ISA INA ISA INA Composition vs. Specializationin a Lattice of Models • Orthogonal kinds of model reduction/expansion (PartOf~InA, IsA) • Commutative diagram for model lattice: • Specialization: eg. discretized (DBN) vs. continuous (ODE) vs. quantized (stochastic) vbls, time, space - heterogeneous dynamics • Initialize param search in specialized model • high-level vision app [NIPS 1990]: • Thus, model reduction can aid parameter estimation Manchester PESB Workshop 28/3/07

  31. A Parameter Estimation Future • Parameter estimation  model reduction • Multiscale, heterogeneous, variable-structure, … models all incorporated in a lattice • Common (operator algebra) semantics • Perpetual data assimilation • Continual influx of data • Perpetual fitting to an expanding lattice of models • Specialize to the limit of identifiability • Model analyses to explain the “hits” Manchester PESB Workshop 28/3/07

  32. Conclusions • Model reductions for transcriptional regulation: • GRN’91, HCA • Model reduction for large-scale data: • Core/Halo, Functional Mixture, … models • Common framework: generalized reactions • Dynamical grammars  operator algebra • Parameter estimation  model reduction • Mutually enhancing interaction Manchester PESB Workshop 28/3/07

  33. For further information: • www.ics.uci.edu/~emj • www.computableplant.org • Funding: US National Science Foundation FIBR program, • NIH BISTI program • Invitation… Manchester PESB Workshop 28/3/07

  34. Manchester PESB Workshop 28/3/07

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