A proposal for a project (3rd year, master)
Adding Time to Discrete Models of Genetic Regulatory Networks
In the book of Thomas and D'Ari, Biological Feedback, the author
introduce an asynchronous discrete models for describing the dynamics
of genetic regulatory network. In these models the dynamics is based
on the following principles:
The state space is discretized (gene is "on" or "off", and a protein
product is present or absent (the discretization can be refined to
include various ranges of product levels;
The interaction between genes and products are given qualitatively
by diagrams with arrows which mean something like gene X encourages
the production of product x, or more complex dependencies between
several variables;
The dynamics is based on delays: when a gene X is "on" than after
some time product x will become present
These models are asynchronous and qualitative: they do not suppose any
relations between the delays of different reactions and hence the
"global" automaton representing the system may have many behaviors,
each corresponding to a different choice of the delay values.
The project intends to extend the model with timing information on the
reactions and use timed automata to model the whole network. Timing
constraints will reduce the set of behaviors by eliminating behaviors
the violate these constraints. The modeling will be inspired by the
work of Maler and Pnueli (95) on quantitative modeling of delays in
digital circuits.
The work will include understanding of the kinetic logic model of
Thomas and D'Ari, learning the principles of timed automata and
circuit delays and then defining new models and studying their
dynamical properties, possibly using existing verification tools. Some
applications in synthetic biology will be considered.
References:
The book Biological Feedback which is available online
O. Maler and A. Pnueli paper on asynchronous circuits and timed automata
A recent attempt to add time to the models by Siebert and Bockmayr