Simulation-based model checking
approach to cell fate specification
during C. elegans vulval development
by HFPNe
Chen LI
Kazuko Ueno
Masao Nagasaki
Satoru Miyano
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.
Overview of the work (Background)
1.
Qualitative Model Checking
• Discrete model
• Computational Tree Logic (CTL), Linear Temporal Logic (LTL)
2.
Application: Vulval Precursor Cell (VPC)
Fate Determination Model
Biological consideration
Biological consideration
(Rule
I)
(Rule1)
(Rule II)
Vulval induction in C. elegans
Quantitative Model
+
Model Checking
3.
Our work: HFPNe  Model Checking
HFPNe: Hybrid Functional Petri Net with extension
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 all possible
behaviors.
Specification
(Desired system properties)
Answer
Yes: if model satisfies
specification
Model
(System requirements)
Model checker
No: if model does not
satisfies specification
Counterexample
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.
Modeling method
Hybrid Functional Petri Net with extension (HFPNe)
Continuous
Entities
Processes
Connectors
Process
connector
Continuous
entity
Continuous
process
Discrete
Association
connector
delay
Discrete
entity
speed
Discrete
process
Inhibitation
connector
Various types
Generic
Various operations
Generic
entity
DNA sequence
TCAGGAAGTGCGCCA
Generic
process
Transcription state
AUGAAAGCAAUUUUCGUACG
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
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
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
Anchor Cell
lin-12
lin-15, vul, lst

formed, ablated
wt, ko, gf
wt, ko
Simulation targets for evaluation

Fate patterns from In silico and in vivo experiments
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. ⇒ 2○ fate
[Rule II]: Fate will be priorly adopted according to the temporal sequence
of first time epoch inducing over-threshold state. ⇒ 1○ fate
Earlier
Too short
First over-threshold
state
Two rules of determining VPC fates
Rule I or II
[3
○
3
○
2
○
1
○
Cell fate pattern
2
○
3]
○
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
In vivodata*
data
[3 3 2 1 2 3]
[2 1 2 1 2 2]
…
[2 2 2 2 2 2]
Hybrid lineages*
[3 3 3 ? 3 3]
? → 1 ◦, 2 ◦, 3 ◦
Cell fate patterns
[3 3 3 1 3 3]
[3 3 3 2 3 3]
[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.
Simulation procedures

Simulation
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 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”)