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Hybrid Gene Networks: a new Framework and a Software Environment

Emilien Cornillon, Jean-Paul Comet, Gilles Bernot, Gilles En´ee

University Nice Sophia Antipolis, I3S laboratory - UMR CNRS 7271, Sophia Antipolis, France

The modelling framework of Ren´e Thomas [Tho73] allows one to design abstract models of gene regulatory networks. In this formalism, time is only represented by the succession of discrete events. However, for numerous gene networks, the delay between two events is of primary interest like for the circadian cycle. This poster introduces a hybrid Thomas’ formalism, allowing to take into account chronometrical information, and presents a first version of a

user-friendly software platform named HyMBioNet. We illustrate our approach on an extremely simplified network of the circadian clock.

1 - The Molecular Circadian Clock

The circadian clock relies on a gene network that oscillates with a 24 h period and regulates many physiological processes. Light is a universal synchronizer (Zeitgeber) to the external LD cycle in all species.

Simplified model of the mammalian clock

3 - Dynamics of Hybrid Gene Regulatory Network

pc

g

Rg = {} Rg = {}

Rpc = {}

Rpc = {} Rpc = {mpc}

Rg = {mg} Rg = {mg} Rpc = {mpc}

Cg,,0 Cg,,1

Cg,{mg},0

g on

g off

AbsenceofpcPresenceofpc

Cg,{mg},1

Cpc,{mpc},0 Cpc,{mpc},1 Cpc,,1

Cpc,,0

4 - Application to the Circadian Clock

g pc

0 1

0 1

Constant dark

g pc

0 1

0 1

Constant light

g pc

0 1

0 1

Dark/light oscillations

Constant dark : sustained oscillations. The presence of a sliding on a boundary is the only one condition to obtain a limit cycle [CCBE16].

Constant light : Very long period.

Dark/light oscillations : The light change the trajectory and the oscillations get a period of 24h.

6 - The HyMBioNet Software

Simulation interface in NetLogo

2 - Hybrid Gene Regulatory Network of Circadian Clock

Simplified network of circadian clock [CBD+12] :

g : per and cry genes

pc : phosphorylated PER-CRY in the nucleus

L : Light (zeitgeber)

Circles : variables of the system

Rectangles : multiplexes (encode the conditions of interactions)

g pc

L

(g > 1) mpc

¬(pc > 1) mg

¬(L > 1) mL

A celerity Cv,ω,n represents the speed of a variable v inside a discrete state.

It is indexed by :

a variable of the system v.

a set of resources, ω: the set of multiplex predecessors of v whose formula is evaluated to true.

a discrete level of v, n.

5 - Simulations

In this frame, all figures represent the trajectory of the system in 24 hours.

g pc

0 1

0 1

16/8 Dark/Light (winter)

g pc

0 1

0 1

12/12 Dark/Light (equinox)

g pc

0 1

0 1

8/16 Dark/Light (summer)

Jet lag toward East

g pc

0 1

0 1

(Day 1)

g pc

0 1

0 1

(Day 5)

g pc

0 1

0 1

(Day 7) Sychronisation in 7 days

Jet lag toward West

g pc

0 1

0 1

(Day 1)

g pc

0 1

0 1

(Day 2)

g pc

0 1

0 1

(Day 4) Sychronisation in 4 days

References

Jean-Paul Comet, Gilles Bernot, Aparna Das, Francine Diener, Camille Massot, and Am´elie Cessieux.

Simplified models for the mammalian circadian clock. Procedia Computer Science, 11(0):127 – 138, 2012.

Proceedings of the 3rd International Conference on Computational Systems-Biology and Bioinformatics.

Emilien Cornillon, Jean-Paul Comet, Gilles Bernot, and Gilles En´ee. Proc. of the Thematic Research School on Advances in Systems and Synthetic Biology, Modelling Complex Biological Systems in the Context of Genomics, chapter Hybrid Gene Networks: a new Framework and a Software Environment. EDP Sciences, ISBN : 978-2-7598-1971-3, 2016.

Ren´e Thomas. Boolean formalization of genetic control circuits. Journal of Theoretical Biology, 42(3):563–585, 1973.

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