Continuous valuations of temporal logic specifications with applications to parameter optimization and robustness measures

Abstract

Finding mathematical models satisfying a specification built from the formalization of biological experiments, is a common task of the modeler that techniques like modelchecking help solving, in the qualitative but also in the quantitative case. In this article we go one step further by defining a continuous degree of satisfaction of temporal logic formulae with constraints. We show how such a satisfaction measure can be used as a fitness function with state-of-the-art evolutionary optimization methods in order to find biochemical kinetic parameter values satisfying a set of biological properties formalized in temporal logic. We also show how it can be used to define a measure of robustness of a biological model with respect to some temporal specification. These methods are evaluated on models of the cell cycle and of the MAPK signalling cascade.

Strong Turing Completeness of Continuous Chemical Reaction Networks and Compilation of Mixed Analog-Digital Programs

“…This reaction system, produced with initial concentration value f p = 1 at time 0 (and 0 for all other variables), is designed for the differential semantics. Its robustness to extrinsic noise can be measured with respect to perturbations of the parameter values [42]. Such a reaction system can also be interpreted in the stochastic semantics [22], and simulated using Gillespie's SSA algorithm [24] to analyze its robustness to intrinsic noise.…”

Cells as Machines: Towards Deciphering Biochemical Programs in the Cell

“…In [43,17], it is shown how the validity domain D (s0,...,sn),φ of the free variables of an FO-LTL(R lin ) formula φ on a finite trace (s 0 , ..., s n ), can be computed by finite unions and intersections of polyhedra, by a simple extension of the modelchecking algorithm, as follows:…”

Qualitative modelling via constraint programming

“…Other approaches include process calculi and temporal logics, which are successful at the molecular level [7] and the protein network level [8,42], but not as yet at inter-and intra-cellular levels. Despite this, the process calculus and temporal logic communities are engaging in active current research to improve techniques and widen access to other scientific areas.…”