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Robustness in system modeling Rüdiger W. Brause

Robustness in system modeling Rüdiger W. Brause. Traditional Modelling. Modelling, e.g. modelling of biochemical pathways Traditional time dynamic modeling fuzzy clustering stage

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Robustness in system modeling Rüdiger W. Brause

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  1. Robustness in system modeling Rüdiger W. Brause

  2. Traditional Modelling Modelling, e.g. modelling of biochemical pathways • Traditional time dynamic modeling • fuzzy clustering stage • dynamical interaction of the clusters by linear differential equations based on the expression data of selected genes • selection criterion: most simple network But: after long evolutionary development, small genetic mutations will not cause fatal changes any more. NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

  3. Example plasmid replication • Escherichia coli Col E1 • plasmids = short DNA loops • give resistance against toxics and antibiotics • replicated separately • segregated on cell division High plasmid replication: longer bacteria replication time, smaller fraction of population No plasmid replication: smaller fitness in the long run, not in the short. Modest plasmid replication regulation – how? NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

  4. Example: replication control pathways • Col E1 plasmid replication regulation loop Brendel, Perelson 1993 RNA I & RNA II & ROM complex RNA I & RNA II & ROM complex • Mean 38 copies for binomial segregation • Prob plasmid free cell = 7.3·10-12 • Observed: much higher !?? RNA I-modulator ROM stable with RNA I &RNA II Plasmid DNA in unstable complex Negative feedback loop Plasmid DNA in complex with short RNA II Plasmid DNA Plasmid DNA in complex with long RNA II for replication NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

  5. Stochastic Petri net model • Col E1 plasmid replication Goss, Peccoud 1999 Molecular interpretation of SPN terminology SPN term Molecular interpretation Place Molecular species Token Molecule Marking Number of molecules Transition Reaction Input place Reactant Output place Product Weight function Rate of reaction To be enabled For a reaction to be possible To fire For a reaction to occur • Simulates the molecular motion stochastically • models timing of molecular reactions NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

  6. simulation results COLE1 plasmid replication regulation loop • Adapts to mean value 19 per segregation • Variance enhancement: 2.3·10-8,factor 10,000! • bacterium: 3811 in 95% interval NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

  7. Simulation results • No ROM protein  double plasmids/bacterium • Kinetic parameters adapted for same plasmid mean like wild type  bigger variance of mutant  2-6 fold plasmid loss ! • No segregation variance assumed  variance is due to timing NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

  8. Sepsis and immune system • Infection and trauma: sepsis symptomes(fever, tachycardia, ..) pro-inflammatory time anti-inflammatory • Problem SIRS, sept. shock correction of overshooting reaction of immune system Many factors involved (~80): • tumor necrose factor TNF-, interleucin IL-1, IL-6, IL-8 • IL-4, IL-10, IL-11, IL-13, TGF-, IL-1 receptor antagonists,… • ……. NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

  9. Immune system pathways • Suppression of single mediators, e.g. TNF, do not influence SIRS  Existence of multiple redundant mediator pathways Example: cluster state modelling of cellular immune response Guthke, Thies, Möller 2003 MHC-II STAT1 IL-1 NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

  10. Differential equation modeling n clusters, n time series xj(t) of representative genes Setupndifferential equations by • Select variable xj whichdetermines a set of measurements • Select next variable xi which is only determined by xj • By induction, continue the modeling by with u(t>0) = 1, u(t<0) = 0 and xi(0) = 0. • Coupling coefficients wi,j are determined approximately • Time delay r is included. NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

  11. Differential equation modeling Critics: • The number of clusters, i.e. the number of variables is chosen according to some criteria which do not take possible interactions and redundancy into account. • The dependency evaluation of the xi is taken by measuring correlations • Also, the values of the coupling coefficients are due to some side conditions which do not include possible deviations of the computed parameter values. • The criteria for modelling performance is the mean squared error, but probability distributions instead of the MSE of the results may better represent the resulting networks and give better probability estimations for redundant branches. NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

  12. Proposition 1: black box modeling • Model causalities H(X) = entropy (average information) of variable X I(X;Y) = mutual information between X and Y if I(X;Y) = H(Y) and H(Y) < H(X) then„Y depends on X“ • Black box modeling Dyi (t) = fi(x1(t-1), x2(t-1), ..., xn(t-1) ) e.g. neural network approximation Select only those xi with I(Y;X1,X2,..,Xn) > 90% (ranked list) NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

  13. Simple sepsis model Preferred modeling strategy: make it simple! • make clusters • choose clusters representatives • model state dynamics between representatives as simple as possible Example protein interaction map of pheromone cell response B Steffe, Petti, Aach, D‘haeseleer, Church 2002 start signal protein target 70 proteins, 354 pathways score > median top 15 graph, node size =S path scores NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

  14. Proposition 2: robustness constraints • Select robust pathway modeling • predict new signalling pathways compared to literature • identify previously unknown members of documented pathways • identify relevant groups of interacting proteins • Robustness Criteria • fault tolerance:random faults should not propagate and impede essential system functions • inherent stability: no system deviation by noise or random input, even by internal component change NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

  15. Proposition 2: Model Robustness Differential equations ? NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness • Observed simple interactions are modelled by • Additional branches within the network • complex modules (fault masking, neg. loops) with the same behavior • All providing additional robustness • Explaining the variance observed NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

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