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

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

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

What is model checking? Specification (Desired system properties) Model checker Model (System requirements) Answer Yes: if model satisfies specification No: if model does not satisfies specification Counterexample 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 all possible behaviors. Method : model checking

Biological background of VPC fate determination Induced signal Lateral signal Vulva The fates of 1 ◦, 2 ◦ and 3 ◦ are the production of the coordination regulated by three signaling pathways. Fate deterination mechanism Vulva Hypodermis * 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):

Hybrid Functional Petri Net with extension (HFPNe) Continuous Discrete 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, speed Entities Processes Connectors delay Continuous entity Discrete entity Continuous process Discrete process Process connector Association connector Inhibitation connector Generic entity Various types Generic process Various operations Generic DNA sequence TCAGGAAGTGCGCCA transcription Substance Transcription state AUGAAAGCAAUUUUCGUACG mRNA Modeling method

HFPNe model of VPC fate determination mechanism Number of Entities:427 Number of Processes:554 Number of Connectors:780 HFPNe model on Cell Illustrator Online 4.0 Signaling crosstalks underlying VPC fate determination Modeling method

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 Simulation

Two rules of determining VPC fates [Rule I]: Fate can sustain the behaviors at a certain over-threshold state 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 Too short Earlier First over-threshold state

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

Simulation targets for evaluation In silico data - model checking [ ] [ ] … [ ] [ ] In vivo data In vivo data* [ ] [ ] … [ ] ? → 1 ◦, 2 ◦, 3 ◦ Hybrid lineages* [3 3 3 ? 3 3] [ ] [ ] [ ] Cell fate patterns *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. Investigate the variations of each fate pattern Evaluate two rules by comparing simulation targets

Simulation procedures Purpose: 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 “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). Simulation

Simulation results

Conclusion Modeling and simulating biological systems using 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: HFPNe modeling method High-Speed Simulation Module could not be easily put into practice without the HFPNe modeling method and the functions of Cell Illustrator (“High-Speed Simulation Module”)