1. Simulation-based model checking approach to cell fate specification during C. elegans vulval development by HFPNe • Chen LI Masao Nagasaki • Kazuko Ueno Satoru Miyano

2. overview Overview of the work The topic of this presentation Establish a quantitative methodology to model and analyze in silico models incorporating model checking approach.

3. Overview of the work (Background) 1. Qualitative Model Checking • Discrete model • Computational Tree Logic (CTL), Linear Temporal Logic (LTL) Application: Vulval Precursor Cell (VPC) Fate Determination Model 2. Biological consideration (Rule I) Biological consideration (Rule1) Biological consideration (Rule II) Vulval induction in C. elegans Quantitative Model + Model Checking 3. Our work: HFPNe Model CheckingHFPNe: Hybrid Functional Petri Net with extension

4. Method : model checking What is model checking? • A high speed technique for automatic verification of systems. • Formal validation method applied to ensure consistency and correctness • Model checking: ⇒ Essential idea:conducts an exhaustive exploration of allpossible behaviors. Model(System requirements) Specification(Desired system properties) Answer Yes: if model satisfies specification Model checker No:if model does not satisfies specification Counterexample

5. Fate deterination mechanism Biological background of VPC fate determination Vulva Induced signal Lateral signal Hypodermis Vulva Hypodermis The fates of 1◦, 2 ◦ and 3 ◦ are the production of the coordination regulated by three signaling pathways. * Sternberg PW: Vulval development. WormBook 2005, 25:1-28.* Sternberg PW, Horvitz HR: The combined action of two intercellular signaling pathways specifies three cell fates during vulval induction in C. elegans. Cell 1989,58(4):679-693.

6. Modeling method Hybrid Functional Petri Net with extension (HFPNe) Continuous Connectors Processes Entities Process connector Continuous process Continuous entity Discrete Association connector speed delay Discrete process Inhibitation connector Discrete entity Various types Generic Transcription stateAUGAAAGCAAUUUUCGUACG DNA sequenceTCAGGAAGTGCGCCA Various operations Generic entity Generic process transcription Substance • Nagasaki, M., Doi, A., Matsuno, H., and Miyano, S., A versatile Petri net based architecture for modeling and simulation of complex biological processees, Genome Informatics, 15(1):180–197, 2004. • https://cionline.hgc.jp mRNA

7. Modeling method HFPNe model of VPC fate determination mechanism Signaling crosstalks underlying VPC fate determination HFPNe model on Cell Illustrator Online 4.0 Number of Entities: 427 Number of Processes: 554 Number of Connectors: 780 https://cionline.hgc.jp

8. Simulation Simulating HFPNe model with model checking method on Cell Illustrator • Two rules of determining VPCs for 48 genotypes • Temporal interval (Rule I) and temporal order (Rule II) • Combination of AC and four genes • Simulation targets for evaluation • Fate patterns from In silico and in vivo experiments

9. Two rules of determining VPC fates [Rule I]:Fate can sustain the behaviors at a certain over-thresholdstate within a given length of time. [Rule II]: Fate will be priorly adopted according to the temporal sequence of first time epoch inducing over-threshold state. ⇒ 2○ fate ⇒ 1○ fate Earlier Too short First over-threshold state

10. Two rules of determining VPC fates Rule I or II [ ] 3○ 3○ 2○ 1○ 2○ 3○ Cell fate pattern

11. Simulation targets for evaluation In vivo data In vivo data*[3 3 2 1 2 3][2 1 2 1 2 2]…[2 2 2 2 2 2] In silico data- model checking [3 3 2 2 2 3][3 1 1 1 1 3]…[1 1 1 1 1 1][3 1 1 1 1 1] Hybrid lineages* [3 3 3 ? 3 3] ? → 1 ◦, 2 ◦, 3 ◦ [3 3 3 1 3 3] [3 3 3 2 3 3] Cell fate patterns [3 3 3 3 3 3] • Investigate the variations of each fate pattern • Evaluate two rules by comparing simulation targets *Sternberg, P.W. and Horvitz, H.R., The combined action of two intercellular signaling pathways specifies three cell fates during vulval induction in C. elegans, Cell, 58(4):679–693,1989.

12. Simulation Simulation procedures • Purpose: • Investigate the variations of each fate pattern • Evaluate two rules by comparing simulation targets • Simulation targets for evaluation • Noise parameters: • Log-normal distribution: LSMass(arg1, arg2) • Emulation of temporal stimulations • Function of rand() • HFPNe models: 10,000 simulations for 48 sets of different genetic conditions (in total 480,000 runs). • Simulator: Cell Illustrator • “High-Speed Simulation Module” • 10,000 simulations conducted on a day on average⇒ 48 sets processed within 6 days with eight processors (Intel Xeon 3.0GHz processor with 16GB of memory).

13. Simulation results

14. Conclusion • Modeling and simulating biological systemsusing the model checking approach based on HFPNe. • Two rules for the quantitative model of the VPC fate specification are considered from two viewpoints. i.e., temporal interval and temporal order • The simulation targets including in silico and in vivo data are considered. Sp., observation of hybrid lineage data. • 480,000 simulations are performed to • Examine the consistency and the correctness of the model • Evaluate the two rules of VPC fate specification. Computational experiment and biological evaluation: could not be easily put into practice without the HFPNe modeling method and the functions of Cell Illustrator (“High-Speed Simulation Module”)