What Can Formal Methods Bring to Systems Biology?

Abstract

Abstract. This position paper argues that the operational modelling approaches from the formal methods community can be applied fruitfully within the systems biology domain. The results can be complementary to the traditional mathematical descriptive modelling approaches used in systems biology. We discuss one example: a recent Petri net analysis of C. elegans vulval development. Systems BiologySystems biology studies complex interactions in biological systems, with the aim to understand better the entirety of processes that happen in such a system, as well as to grasp the emergent properties of such a system as a whole. This can for instance be at the level of metabolic or interaction networks, signal transduction, genetic regulatory networks, multi-cellular development, or social behaviour of insects.The last decade has seen a rapid and successful development in the collaboration between biologists and computer scientists in the area of systems biology and bioinformatics. It has turned out that formal modelling and analysis techniques that have been developed for distributed computer systems, are applicable to biological systems as well. Namely, both kinds of systems have a lot in common. Biological systems are built from separate components that communicate with each other and thus influence each other's behaviour. Notably, signal transduction within a cell consists of cascades of biochemical reactions, by which for instance genes are activated or down-regulated. The genes themselves produce the proteins that drive signal transduction, and cells can be connected in a multicellular organism, making this basically one large, complex distributed system. Another, very different, example at the organism level is how ants in one colony send stimuli to each other in the form of pheromones.Biological systems are reactive systems, as they continuously interact with their environment. In November 2002, David Harel [11] put forward a grand challenge to computer science, to build a fully animated model of a multi-cellular organism as a reactive system; specifically, he suggested to build such a model of the C. elegans nematode worm, which serves as a one of the model organisms in developmental biology.Open questions in biology that could be addressed in such a modelling framework include the following, listed in order from a detailed, molecular viewpoint to a more global view of whole organisms: -How complete is our knowledge of metabolic, signalling and regulatory processes at a molecular level?

Hard-wired heterogeneity in blood stem cells revealed using a dynamic regulatory network model

“…Simple negative feedback loops have previously been proposed to result in oscillatory expression of important cell fate regulators (Hirata et al , 2002; Lahav et al , 2004). To better understand the potential for oscillatory behaviour in increasingly complex networks, future developments might need to include building more fine-grained models, such as the use of Petri nets, which can be readily adapted to move from a Boolean range of values towards discrete multi-valued expression levels (Bonzanni et al , 2009a, b). …”

The ability of transcription factors to differentially regulate gene expression is a crucial component of the mechanism underlying inversion, a frequently observed genetic interaction pattern

“…To simulate the regulatory effects of two upstream genes (R1 and R2), 200 tokens were provided to represent the mRNA resources for each regulator, except when one of the regulators has an incoming edge from the other regulator as shown in (S5A Fig). Each step in the simulation process comprises of firing all enabled transitions (maximal parallel execution) [88,89]. A transition is enabled to fire when resources (tokens) in the input place(s) match or exceed the weight(s) on the respective incoming arc(s) to the transition (S5B Fig).…”

Petri Nets Are a Biologist’s Best Friend

“…Formal models can be an excellent way to store and share knowledge on biological systems, and to reason about such systems [15]. Petri nets in particular are among the most used formal frameworks; for a review see [16,17].…”