Robustness in immune system modeling and sepsis therapy Rüdiger W. Brause

1. Robustness in immune system modeling and sepsis therapy Rüdiger W. Brause

2. Introduction • Robustness, NOTevolvability or stability for • disturbances in ecosystems • cell response to environmental or genetic change • computer performance at input errors, disk failures, network overload • resilience of a political institution during societal flux • viability of a technological product in wildly changing markets Robustness= aspect of structural stability NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. State dynamic modeling: example 1)P'(t) ~ P P athogen cells will be increased by cell splitting 2)P'(t) ~ (Pmax–P)A limit of resources existwith concentration Pmax =1. 3)P'(t) ~ –M×P P will also decrease by macrophages and pathogens at the same place 4)M'(t) ~ M×P The number of macrophages will grow when a “combat indicator” is produced when they destroy the pathogen. Therefore, they grow with the probability of macrophages and pathogens at the same place 5)M'(t) ~ –M Macrophages die at constant rate 6)M'(t) ~ M×D There is a cell damage D which is caused by inflammation. Like the pathogens, the macrophages grow with the probability of being at the same place: 7)M'(t) ~ (1-M) A limit of resources exist for macrophages 8)D'(t) ~ –D The cell damage is repaired with a certain rate 9) D'(t) ~ h(M-q)Additional damage is indicated by a sigmoid function h() of the number of macrophages where q is a threshold NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

13. Modeling by ODE • Setting up ordinary differential equations P'(t) = 1P(1–P) – 2MP 1) +2) +3) i>0 M'(t) = –1M +M(1–M)(2P+ 3D) 4) +5)+6)+7) i>0 D'(t) = –1D + 2h((M–q)/c3) 8) + 9) i>0 • Fitting parameter values to measurements damage macrophages pathogen cells NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

14. Range of parameters • Problem: determination of parameters by observations • Experience: long adaptation, 3 may also be negative System becomes instable, but instabilities also fulfil the requirements ! NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

15. Problems • Static approach: • Which genes (proteins) should be in one cluster? • How should the cluster number be chosen? • How should the score be designed? • Alternatives with small score difference: which one to choose? • Dynamic approach: • How many variables (clusters should be chosen? • What values for coupling coefficients should be chosen? NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness

16. Proposition: robustness constraint • 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

17. Nature inspired robustness • Nature inspired heuristics • Parallel redundancy : different pathways with same effect • adaptive negative feedback • Nature inspired mathematical progress • stability (qualitative aspect) • sensitivity (quantitative aspect) • redundancy (structural aspect) • of differential equations needed. • Complexity research: degrees of freedom, number of parameters ! NiSIS Workshop, Mallorca 2006 R.Brause: Nature-inspired Robustness