Boa noite a todos,

Teremos na quinta-feira, 16 de Fevereiro, das 14:30 às 15:30, a sétima sessão
do THOR. Esta sessão será conduzida pelo Pedro Monteiro em que irá apresentar
e discutir o seguinte problema de contagem:

On the number and structure of Boolean functions compatible with a
regulatory network topology

Mathematical modelling allows to tackle the complex behaviours of
regulatory networks. In this context, the logical framework has proven
well-adapted since quantitative data is generally lacking and networks of
interest are large. Furthermore, despite coarse grain abstractions, logical
models lead to relevant outcomes. Here, we focus on Boolean gene networks:
each component is associated to a Boolean variable (e.g. denoting its
presence / absence); a Boolean function defines the values of this
variable, depending on the regulators of that component. The asynchronous
dynamics of such models are classically represented as a state transition
graphs.

For a component with n regulators, 2^2^n Boolean functions can be defined.
This combinatorial explosion leads to laborious choices, motivating the
selection of default functions; e.g. a component is activated if at least
one activator is present and all its inhibitors are absent.

Here, I will first characterize the set of Boolean functions that are
consistent with a regulatory topology (regulators and their signs); these
are non-degenerated monotone Boolean functions, which define non-dual
functional regulators (each regulator has an observable effect, always
according to its sign). We can show that these functions define a Partial
Ordered Set (PO-Set), and we have defined an algorithm to navigate in the
neighbourhood of any function. Overall, the properties of this PO-Set
provides insights on the number of states whose behaviours differ for two
distinct Boolean functions. I will show that these means to assess the
impact of the function selection on the dynamics could be useful for model
inference and revision.

Temos reservada a sala 020 no INESC-ID.

Saudações,

Alexandre Francisco