Model checking the evolution of gene regulatory networks

Abstract

The behaviour of gene regulatory networks (GRNs) is typically analysed using simulation-based statistical testing-like methods. In this paper, we demonstrate that we can replace this approach by a formal verification-like method that gives higher assurance and scalability. We focus on Wagner's weighted GRN model with varying weights, which is used in evolutionary biology. In the model, weight parameters represent the gene interaction strength that may change due to genetic mutations. For a property of interest, we synthesise the constraints over the parameter space that represent the set of GRNs satisfying the property. We experimentally show that our parameter synthesis procedure computes the mutational robustness of GRNs-an important problem of interest in evolutionary biology-more efficiently than the classical simulation method. We specify the property in linear temporal logic. We employ symbolic bounded model checking and SMT solving to compute the space of GRNs that satisfy the property, which amounts to synthesizing a set of linear constraints on the weights.

ProPPA

“…Furthermore, the use of logic-based observations could enable additional analyses. We could explore, for example, how robust the behaviour of the system is with respect to high-level properties, in a similar spirit to recent work [21]. This would involve testing the satisfaction of given properties for di erent permissible values of the model's uncertain parameters.…”

Symbolic Coloured SCC Decomposition

“…represented as colours. Our interest in processing huge edge-coloured graphs is primarily motivated by applications taken from systems biology [5,29] and genetics [25] where we have to deal not only with giant graphs as measured by the number of vertices and edges but also with large sets of colours. The colours in such graphs represent various parameters that influence the dynamics of a biological system [5,9,46].…”

AEON: Attractor Bifurcation Analysis of Parametrised Boolean Networks

“…The development of formal methods for analysis and synthesis of Boolean networks has recently attracted a lot of attention [ 11 , 18 , 20 , 28 , 36 ]. In this paper, we are primarily interested in BN models for computational systems biology [ 29 ].…”

“…Another group of existing tools targets the parameter synthesis problem for parametrised BNs. The most prominent tools here are GRNMC [ 20 ], GINsim [ 10 ] (indirectly through NuSMV [ 14 ]), and TREMPPI [ 35 ]. In general, parameter synthesis tools can be used to identify parameters producing a specified long-term behaviour (depending on the logics employed), however, they do not provide a sufficient solution for identification and classification of all attractors in the system.…”