Influence Systems vs Reaction Systems

Abstract

In Systems Biology, modelers develop more and more reaction-based models to describe the mechanistic biochemical reactions underlying cell processes. They may also work, however, with a simpler formalism of influence graphs, to merely describe the positive and negative influences between molecular species. The first approach is promoted by reaction model exchange formats such as SBML, and tools like CellDesigner, while the second is supported by other tools that have been historically developed to reason about boolean gene regulatory networks. In practice, modelers often reason with both kinds of formalisms, and may find an influence model useful in the process of building a reaction model. In this paper, we introduce a formalism of influence systems with forces, and put it in parallel with reaction systems with kinetics, in order to develop a similar hierarchy of boolean, discrete, stochastic and differential semantics. We show that the expressive power of influence systems is the same as that of reaction systems under the differential semantics, but weaker under the other interpretations, in the sense that some discrete behaviours of reaction systems cannot be expressed by influence systems. This approach leads us to consider a positive boolean semantics which we compare to the asynchronous semantics of gene regulatory networks à la Thomas. We study the monotonicity properties of the positive boolean semantics and derive from them an efficient algorithm to compute attractors.

Pint: A Static Analyzer for Transient Dynamics of Qualitative Networks with IPython Interface

“…The main difference with these latter frameworks is the explicit specification of local transitions for each automaton (node) of the network, compared to a function-centred specification for Boolean and multi-valued networks [7,19].…”

Reduction of Qualitative Models of Biological Networks for Transient Dynamics Analysis

“…In general, automata networks can encode non-deterministic functions, which is not directly possible with usual Boolean and multi-valued networks. See [37] for a thorough comparison of functioncentered and transition-centered systems.…”

Probably Approximately Correct Learning of Regulatory Networks from Time-Series Data

“…Note that the positive Boolean semantics simply ignores the negative sources of an influence. This is motivated by the abstraction and approximation relationships that link the Boolean semantics to the stochastic semantics and to the differential semantics, for which the presence of an inhibitor decreases the force of an influence but does not prevent it to apply [9].…”

“…The difference with the previous general influence systems is that the activation and deactivation functions are exclusive and defined by one single function. As shown in [9], non-terminal self-loops cannot be represented in Thomas functional influence systems. Given a general influence system with activation functions x i + and x i − , one can associate a Thomas network with attractor function 7…”

“…k-CNF formulae), and can be learned from Boolean traces with a number of Boolean transition samples per species quasi-linear in the precision of the learned model, using Valiant's PAC learning algorithm for k-CNF formulae. We also show that Boolean influence systems with their positive Boolean semantics discussed in [9] can be naturally represented by monotone DNF formulae, and learned actively from a set of positive samples with calls to an oracle.…”