Repairing Boolean logical models from time-series data using Answer Set Programming

Abstract

Background: Boolean models of biological signalling-regulatory networks are increasingly used to formally describe and understand complex biological processes. These models may become inconsistent as new data become available and need to be repaired. In the past, the focus has been shed on the inference of (classes of) models given an interaction network and time-series data sets. However, repair of existing models against new data is still in its infancy, where the process is still manually performed and therefore slow and prone to errors.

Results: In this work, we propose a method with an associated tool to suggest repairs over inconsistent Boolean models, based on a set of atomic repair operations. Answer Set Programming is used to encode the minimal repair problem as a combinatorial optimization problem. In particular, given an inconsistent model, the tool provides the minimal repairs that render the model capable of generating dynamics coherent with a (set of) time-series data set(s), considering either a synchronous or an asynchronous updating scheme.

Conclusions: The method was validated using known biological models from different species, as well as synthetic models obtained from randomly generated networks. We discuss the method's limitations regarding each of the updating schemes and the considered minimization algorithm.

Keywords: (A)synchronous dynamics; Answer Set Programming; Biological regulatory networks; Boolean functions; Model repair.

Fig. 1

An example of a logical regulatory graphs. A logical regulatory graph with four nodes and four edges with positive sign associated

Fig. 2

Overview of the tool. The different components of the proposed tool

Fig. 3

Cardinality minimal solutions for steady state. Model of a signalling-regulatory network at steady state before and after repair operations. The repair operations shown are some of the cardinality minimal solutions. Green (red) nodes represent the assignment of a node to the value true (false)

Fig. 4

The average execution time to find the first optimal solution. Average execution time to find the first optimal solution to the networks with 10 nodes and with the number of arguments following the poison distribution with lambda 1 (and 3 time steps)