Reconciling qualitative, abstract, and scalable modeling of biological networks

Abstract

Predicting biological systems’ behaviors requires taking into account many molecular and genetic elements for which limited information is available past a global knowledge of their pairwise interactions. Logical modeling, notably with Boolean Networks (BNs), is a well-established approach that enables reasoning on the qualitative dynamics of networks. Several dynamical interpretations of BNs have been proposed. The synchronous and (fully) asynchronous ones are the most prominent, where the value of either all or only one component can change at each step. Here we prove that, besides being costly to analyze, these usual interpretations can preclude the prediction of certain behaviors observed in quantitative systems. We introduce an execution paradigm, the Most Permissive Boolean Networks (MPBNs), which offers the formal guarantee not to miss any behavior achievable by a quantitative model following the same logic. Moreover, MPBNs significantly reduce the complexity of dynamical analysis, enabling to model genome-scale networks.

Mathematical modeling of the Candida albicans yeast to hyphal transition reveals novel control strategies

“…The emerging theoretical understanding of Boolean dynamical systems indicates that both perfect synchrony and complete lack of synchrony can limit possible state transitions in a way that leads to artificial oscillations [ 29 , 37 ]. These limitations are avoided in the recently proposed Most Permissive Boolean Networks [ 38 ]. We found very similar results for the two update methods: the phenotypes are the same and the probabilities to converge into each phenotype are similar (see Tables 2 and 4 ).…”

Modeling the C. elegans Germline Stem Cell Genetic Network using Automated Reasoning

“…We briefly summarize the main formal definitions and concepts underlying the reasoning framework [11,51,53]. At the core of the approach are Abstract Boolean Networks, an extension of Boolean Networks (BNs) [50,52].…”

Scalable Reaction Network Modeling with Automatic Validation of Consistency in Event-B

“…It is remarkably difficult to capture all the necessary details of such a system in a single all-encompassing modeling step 1 : details that are critical in some parts of the model are neutral in other parts of it; modules build upon each other in a structured way; there can be several levels of detail. An effective solution that has been proposed for this problem [2][3][4][5][6][7] is to use model refinement: gradually adding details to a model while preserving its consistency. This splits the modeling processes into two stages: build first a simplified, abstract version of the model (and verify/ensure its consistency) and then add details to it step-by-step in a way that ensures that the model remains consistent.…”

“…This approach allows to also separate the reasoning about the system under development into smaller steps. Model refinement has been introduced in biomodeling in several different frameworks, such as ODE-based modeling 8 , Boolean networks 7 , process algebras 3,9 , rule-based modeling 5,10 , and Petri nets [11][12][13] . The key challenge in deploying this method in practice is verifying the consistency of the initial/basic model and ensuring that the model remains consistent in each step of the refinement.…”

“…The molecular model for the eukaryotic heat shock response proposed in20 . (1) 2 hsf ⇄ hsf 2(7) hsp + hsf 3 → hsp: hsf +2 hsf (2) hsf + hsf 2 ⇄ hsf 3 (8) hsp + hsf 3 : hse → hsp: hsf +2 hsf + hse (3) hsf 3 + hse ⇄ hsf 3 : hse (9) hsp → / 0 (4) hsf 3 : hse → hsf 3 : hse + hsp (10) prot → mfp (5) hsp + hsf ⇄ hsp: hsf (11) hsp + mfp ⇄ hsp: mfp (6) hsp + hsf 2 → hsp: hsf + hsf (12) hsp: mfp → hsp + prot…”