Syntactic Markovian Bisimulation for Chemical Reaction Networks

In chemical reaction networks (CRNs) with stochastic semantics based on continuous-time Markov chains (CTMCs), the typically large populations of species cause combinatorially large state spaces. This makes the analysis very difficult in practice and represents the major bottleneck for the applicability of minimization techniques based, for instance, on lumpability. In this paper we present syntactic Markovian bisimulation (SMB), a notion of bisimulation developed in the Larsen-Skou style of probabilistic bisimulation, defined over the structure of a CRN rather than over its underlying CTMC. SMB identifies a lumpable partition of the CTMC state space a priori, in the sense that it is an equivalence relation over species implying that two CTMC states are lumpable when they are invariant with respect to the total population of species within the same equivalence class. We develop an efficient partition-refinement algorithm which computes the largest SMB of a CRN in polynomial time in the number of species and reactions. We also provide an algorithm for obtaining a quotient network from an SMB that induces the lumped CTMC directly, thus avoiding the generation of the state space of the original CRN altogether. In practice, we show that SMB allows significant reductions in a number of models from the literature. Finally, we study SMB with respect to the deterministic semantics of CRNs based on ordinary differential equations (ODEs), where each equation gives the time-course evolution of the concentration of a species. SMB implies forward CRN bisimulation, a recently developed behavioral notion of equivalence for the ODE semantics, in an analogous sense: it yields a smaller ODE system that keeps track of the sums of the solutions for equivalent species.Comment: Extended version (with proofs), of the corresponding paper published at KimFest 2017 (http://kimfest.cs.aau.dk/

Biochemical Programs and Analog-Digital Mixed Algorithms in the Cell

International audienceIn this chapter, we take an IT perspective in seeking to understand how computation is carried out in the cell to maintain itself in its environment, process signals and make the decisions that determine its fate. The continuous nature of many protein interactions leads us to consider mixed analog-digital computation models, for which recent results in the theory of analog computability and complexity establish fundamental links with classical programming. We derive from these results a compiler of behavioral specifications into biochemical reactions, which can be compared to natural circuits acquired through evolution. We illustrate this approach through the example of the mitogen-activated protein kinase (MAPK) signaling module, which has a function of analog-digital converter in the cell, and through the cell cycle control

Programmes biochimiques et algorithmes mixtes analogiques-digitaux dans la cellule

National audienceIn this chapter we take an IT perspective in seeking to understand how computation is carried out in the cell to maintain itself in its environment, process signals and make the decisions that determine its fate. The continuous nature of many protein interactions leads us to consider mixed analog-digital computation models, for which recent results in the theory of analog computability and complexity establish fundamental links with classical programming. We derive from these results a compiler of behavioural specifications into biochemical reactions which can be compared to natural circuits acquired through evolution. We illustrate this approach through the example of the MAPK signaling module which has a function of analog-digital converter in the cell, and through the cell cycle control.Dans ce chapitre nous adoptons un point de vue d'informaticien pour chercher à comprendre les calculs qu'effectue la cellule pour se maintenir dans son environnement, traiter les signaux qu'elle capte, et prendre les décisions qui déterminent son destin. L'aspect continu de beaucoup d'interactions protéiques nous conduit à considérer des modes de calcul mixtes analogiques-digitaux, pour lesquels des résultats récents en théorie de la calculabilité et de la complexité analogique établissent des liens fondamentaux avec la programmation classique. Nous dérivons de ces résultats un compilateur de spécifications comportementales en systèmes de réactions biochimiques que l'on peut comparer aux circuits naturels résultats de l'évolution. Nous illustrons cette démarche par l'exemple du module de signalisation MAPK qui a une fonction de convertisseur analogique-digital dans la cellule, et par le contrôle du cycle cellulaire

Turing Universality of the Biochemical Ground Form

We explore the expressive power of languages that naturally model biochemical interactions with relative to languages that naturally model only basic chemical reactions, identifying molecular association as the basic mechanism that distinguishes the former from the latter. We use a process algebra, the Biochemical Ground Form (BGF), which extends with primitives for molecular association CGF, a process algebra proved to be equivalent to the traditional notations for describing basic chemical reactions. We first observe that, differently from CGF, BGF is Turing universal as it supports a finite precise encoding of Random Access Machines, a well-known Turing powerful formalism. Then we prove that the Turing universality of BGF derives from the interplay between the molecular primitives of association and dissociation. In fact, the elimination from BGF of the primitives already present in CGF does not reduce the computational strength of the process algebra, while if either association or dissociation is removed then BGF is no longer Turing complete