Exact model reduction of combinatorial reaction networks

Conzelmann, H.; Fey, Dirk; Gilles, Ernst Dieter

doi:10.1186/1752-0509-2-78

Cited by 61 publications

(57 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…4A) (32,33). Therefore, we built the model using rule-based modelling (34)(35)(36)(37), which develops the ODEs on the basis of a framework of rules describing the reactions and states of the system. Constructed in this fashion, the model implemented 23 rules, which resulted in 258 reactions and 36 parameters (table S1).…”

Section: Mathematical Modelling Of the Jnk Network Dynamicsmentioning

confidence: 99%

Signaling pathway models as biomarkers: Patient-specific simulations of JNK activity predict the survival of neuroblastoma patients

et al. 2015

Self Cite

View full text Add to dashboard Cite

Signaling pathways control cell-fate decisions that ultimately determine the behavior of cancer cells.Therefore, the dynamics of pathway activity may contain prognostically relevant information different from that contained in the static nature of other types of biomarkers. To investigate this hypothesis, we characterized the network that regulated stress signaling by the Jun N-terminal kinase (JNK) pathway in neuroblastoma cells. We generated an experimentally calibrated and validated computational model of this network and used the model to extract prognostic information from neuroblastoma patient-specific simulations of JNK activation. Switch-like JNK activation mediates cell death by apoptosis. An inability to initiate switch-like JNK activation in the simulations was significantly associated with poor overall survival for patients with neuroblastoma with or without MYCN amplification, indicating that patientspecific simulations of JNK activation could stratify patients. Furthermore, our analysis demonstrated that extracting information about a signaling pathway to develop a prognostically useful model requires understanding not only components and disease-associated changes in the abundance or activity of the components, but how those changes affect pathway dynamics.

show abstract

Section: Mathematical Modelling Of the Jnk Network Dynamicsmentioning

confidence: 99%

Signaling pathway models as biomarkers: Patient-specific simulations of JNK activity predict the survival of neuroblastoma patients

et al. 2015

Self Cite

View full text Add to dashboard Cite

show abstract

“…We are not aware of general automated approaches to ODE equivalences as done in this paper, though there is a large literature of techniques in domain-specific situations. The combinatorial explosion of CRN biochemical models has spurred considerable research in this area, e.g., [15,16,20,24,25,28,35,36]. The fragmentation approach for κ identifies a coarse-grained ODE system for models with mass-action semantics through sums of variables; this is weaker than an equivalence relation over species, because one variable may appear in more than one block (a fragment) [28,36].…”

Section: Introductionmentioning

confidence: 99%

Symbolic computation of differential equivalences

et al. 2016

View full text Add to dashboard Cite

Ordinary differential equations (ODEs) are widespread in many natural sciences including chemistry, ecology, and systems biology, and in disciplines such as control theory and electrical engineering. Building on the celebrated molecules-as-processes paradigm, they have become increasingly popular in computer science, with high-level languages and formal methods such as Petri nets, process algebra, and rule-based systems that are interpreted as ODEs. We consider the problem of comparing and minimizing ODEs automatically. Influenced by traditional approaches in the theory of programming, we propose differential equivalence relations. We study them for a basic intermediate language, for which we have decidability results, that can be targeted by a class of high-level specifications. An ODE implicitly represents an uncountable state space, hence reasoning techniques cannot be borrowed from established domains such as probabilistic programs with finite-state Markov chain semantics. We provide novel symbolic procedures to check an equivalence and compute the largest one via partition refinement algorithms that use satisfiability modulo theories. We illustrate the generality of our framework by showing that differential equivalences include (i) well-known notions for the minimization of continuous-time Markov chains (lumpability), (ii)~bisimulations for chemical reaction networks recently proposed by Cardelli et al., and (iii) behavioral relations for process algebra with ODE semantics. With a prototype implementation we are able to detect equivalences in biochemical models from the literature that cannot be reduced using competing automatic techniques.

show abstract

“…Unlike many model-reduction approaches for CRNs (e.g., [1,7,8,10]) or control systems (see [26] and references therein) BDE cannot be seen as an instance of that framework. Hence, its geometric interpretation is a new result in its own right.…”

Section: Introductionmentioning

confidence: 99%

Comparing chemical reaction networks: A categorical and algorithmic perspective

Cardelli

Tribastone

Tschaikowski

et al. 2019

Theoretical Computer Science

View full text Add to dashboard Cite

We study chemical reaction networks (CRNs) as a kernel language for concurrency models with semantics based on ordinary differential equations. We investigate the problem of comparing two CRNs, i.e., to decide whether the trajectories of a source CRN can be matched by a target CRN under an appropriate choice of initial conditions. Using a categorical framework, we extend and relate model-comparison approaches based on structural (syntactic) and on dynamical (semantic) properties of a CRN, proving their equivalence. Then, we provide an algorithm to compare CRNs, running linearly in time with respect to the cardinality of all possible comparisons. Finally, we apply our results to biological models from the literature.

show abstract

Exact model reduction of combinatorial reaction networks

Cited by 61 publications

References 53 publications

Signaling pathway models as biomarkers: Patient-specific simulations of JNK activity predict the survival of neuroblastoma patients

Signaling pathway models as biomarkers: Patient-specific simulations of JNK activity predict the survival of neuroblastoma patients

Symbolic computation of differential equivalences

Comparing chemical reaction networks: A categorical and algorithmic perspective

Contact Info

Product

Resources

About