Simulation-based model checking approach to cell fate specification

during C. elegans vulval development by HFPNe

Chen LI 　 Masao NagasakiKazuko 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

1.

2.

3.

Vulval induction in C. elegans

What is model checking?

Specification(Desired system properties)

Model checkerModel(System requirements)

AnswerYes: 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

VulvaHypodermis 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):679-693.

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, 2004.

• https://cionline.hgc.jp

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 sequenceTCAGGAAGTGCGCCA

transcriptionSubstance

Transcription stateAUGAAAGCAAUUUUCGUACG

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

https://cionline.hgc.jp

Modeling method

Simulating HFPNe model with model checking method on Cell IllustratorTwo 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

Anchor Cell formed, ablated

lin-12 wt, ko, gf

lin-15, vul, lst wt, ko

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 shortEarlier

First over-threshold state

Two rules of determining VPC fates

[ ]

3○ 3○ 2○ 1○ 2○ 3○

Cell fate pattern

Rule I or II

Simulation targets for evaluation

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]

In vivo dataIn vivo data*[3 3 2 1 2 3][2 1 2 1 2 2]

…[2 2 2 2 2 2]

? → 1 ◦, 2 ◦, 3 ◦

Hybrid lineages*[3 3 3 ? 3 3]

[3 3 3 1 3 3][3 3 3 2 3 3][3 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: 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).

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