Microtubules and their post-translational modifications are involved in major cellular processes. In severe diseases such as neurodegenerative disorders, tyrosinated tubulin and tyrosinated microtubules are in lower concentration. We present here a mechanistic mathematical model of the microtubule tyrosination cycle combining computational modeling and high-content image analyses to understand the key kinetic parameters governing the tyrosination status in different cellular models. That mathematical model is parameterized, firstly, for neuronal cells using kinetic values taken from the literature, and, secondly, for proliferative cells, by a change of two parameter values obtained, and shown minimal, by a continuous optimization procedure based on temporal logic constraints to formalize experimental high-content imaging data. In both cases, the mathematical models explain the inability to increase the tyrosination status by activating the Tubulin Tyrosine Ligase enzyme. The tyrosinated tubulin is indeed the product of a chain of two reactions in the cycle: the detyrosinated microtubule depolymerization followed by its tyrosination. The tyrosination status at equilibrium is thus limited by both reaction rates and activating the tyrosination reaction alone is not effective. Our computational model also predicts the effect of inhibiting the Tubulin Carboxy Peptidase enzyme which we have experimentally validated in MEF cellular model. Furthermore, the model predicts that the activation of two particular kinetic parameters, the tyrosination and detyrosinated microtubule depolymerization rate constants, in synergy, should suffice to enable an increase of the tyrosination status in living cells.

MOTIVATION: Personalized medicine aims at providing patient-tailored therapeutics based on multi-type data toward improved treatment outcomes. Chronotherapy that consists in adapting drug administration to the patient's circadian rhythms may be improved by such approach. Recent clinical studies demonstrated large variability in patients' circadian coordination and optimal drug timing. Consequently, new eHealth platforms allow the monitoring of circadian biomarkers in individual patients through wearable technologies (rest-activity, body temperature), blood or salivary samples (melatonin, cortisol) and daily questionnaires (food intake, symptoms). A current clinical challenge involves designing a methodology predicting from circadian biomarkers the patient peripheral circadian clocks and associated optimal drug timing. The mammalian circadian timing system being largely conserved between mouse and humans yet with phase opposition, the study was developed using available mouse datasets. RESULTS: We investigated at the molecular scale the influence of systemic regulators (e.g. temperature, hormones) on peripheral clocks, through a model learning approach involving systems biology models based on ordinary differential equations. Using as prior knowledge our existing circadian clock model, we derived an approximation for the action of systemic regulators on the expression of three core-clock genes: Bmal1, Per2 and Rev-Erbα. These time profiles were then fitted with a population of models, based on linear regression. Best models involved a modulation of either Bmal1 or Per2 transcription most likely by temperature or nutrient exposure cycles. This agreed with biological knowledge on temperature-dependent control of Per2 transcription. The strengths of systemic regulations were found to be significantly different according to mouse sex and genetic background. AVAILABILITY AND IMPLEMENTATION: https://gitlab.inria.fr/julmarti/model-learning-mb21eccb. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Biochemical reaction networks are one of the most widely used formalisms in systems biology to describe the molecular mechanisms of high-level cell processes. However, modellers also reason with influence diagrams to represent the positive and negative influences between molecular species and may find an influence network useful in the process of building a reaction network. In this paper, we introduce a formalism of influence networks with forces, and equip it with a hierarchy of Boolean, Petri net, stochastic and differential semantics, similarly to reaction networks with rates. We show that the expressive power of influence networks is the same as that of reaction networks under the differential semantics, but weaker under the discrete semantics. Furthermore, the hierarchy of semantics leads us to consider a (positive) Boolean semantics that cannot test the absence of a species, that we compare with the (negative) Boolean semantics with test for absence of a species in gene regulatory networks à la Thomas. We study the monotonicity properties of the positive semantics and derive from them an algorithm to compute attractors in both the positive and negative Boolean semantics. We illustrate our results on models of the literature about the p53/Mdm2 DNA damage repair system, the circadian clock, and the influence of MAPK signaling on cell-fate decision in urinary bladder cancer.

MOTIVATION: Understanding the temporal behaviour of biological regulatory networks requires the integration of molecular information into a formal model. However, the analysis of model dynamics faces a combinatorial explosion as the number of regulatory components and interactions increases. RESULTS: We use model-checking techniques to verify sophisticated dynamical properties resulting from the model regulatory structure in the absence of kinetic assumption. We demonstrate the power of this approach by analysing a logical model of the molecular network controlling mammalian cell cycle. This approach enables a systematic analysis of model properties, the delineation of model limitations, and the assessment of various refinements and extensions based on recent experimental observations. The resulting logical model accounts for the main irreversible transitions between cell cycle phases, the sequential activation of cyclins, and the inhibitory role of Skp2, and further emphasizes the multifunctional role for the cell cycle inhibitor Rb. AVAILABILITY AND IMPLEMENTATION: The original and revised mammalian cell cycle models are available in the model repository associated with the public modelling software GINsim (http://ginsim.org/node/189). CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Constraint programming is traditionally presented as the combination of two components: a constraint model and a search procedure. In this paper we show that tree search procedures can be fully internalized in the constraint model with a fixed enumeration strategy. This approach has several advantages: 1) it makes search strategies declarative, and modeled as constraint satisfaction problems; 2) it makes it possible to express search strategies in existing front-end modeling languages supporting reified constraints without any extension; 3) it opens up constraint propagation algorithms to search constraints and to the implementation of novel search procedures based on constraint propagation. We illustrate this approach with a Horn clause extension of the MiniZinc modeling language and the modeling in this language of a variety of search procedures, including dynamic symmetry breaking procedures and limited discrepancy search, as constraint satisfaction problems. We show that this generality does not come with a significant overhead, and can in fact exhibit exponential speedups over procedural implementations, thanks to the propagation of the search constraints.

This special section contains the second series of journal articles made from a selection of papers presented at the Ninth International Conference on Computational Methods in Systems Biology, CMSB 2011. CMSB is an annual series of conferences, initiated in 2003, on the design of computational methods for modeling and analyzing biological systems, networks, data, and on their applications to study cases. This issue contains the second part which is composed of three papers.“The Propagation Approach for Computing Biochemical Reaction Networks” by Thomas A. Henzinger and Maria Mateescu revisits the chemical master equation, the rate equation and a combination of both, with the concepts of propagation models and propagation data type for abstracting from the further implementation choices made in simulators.“Curvature Analysis of Cardiac Excitation Wavefronts” by Abhishek Murthy, Ezio Bartocci, Flavio H. Fenton, James Glimm, Richard A. Gray, Elizabeth M. Cherry, Scott A. Smolka, and Radu Grosu, which describes a parallel curvature analysis algorithm of cardiac excitation wavefronts.The last paper, “Multiscale Modeling and Analysis of Planar Cell Polarity in the Drosophila Wing,” by Qian Gao, David Gilbert, Monika Heiner, Fei Liu, Daniele Maccagnola, and David Tree proposes the use of Hierarchically Colored Petri Nets to develop models of tissues at different spatial scales.

The articles in the special section focus on computational methods in systems biology.

MOTIVATION: In Systems Biology, an increasing collection of models of various biological processes is currently developed and made available in publicly accessible repositories, such as biomodels.net for instance, through common exchange formats such as SBML. To date, however, there is no general method to relate different models to each other by abstraction or reduction relationships, and this task is left to the modeler for re-using and coupling models. In mathematical biology, model reduction techniques have been studied for a long time, mainly in the case where a model exhibits different time scales, or different spatial phases, which can be analyzed separately. These techniques are however far too restrictive to be applied on a large scale in systems biology, and do not take into account abstractions other than time or phase decompositions. Our purpose here is to propose a general computational method for relating models together, by considering primarily the structure of the interactions and abstracting from their dynamics in a first step. RESULTS: We present a graph-theoretic formalism with node merge and delete operations, in which model reductions can be studied as graph matching problems. From this setting, we derive an algorithm for deciding whether there exists a reduction from one model to another, and evaluate it on the computation of the reduction relations between all SBML models of the biomodels.net repository. In particular, in the case of the numerous models of MAPK signalling, and of the circadian clock, biologically meaningful mappings between models of each class are automatically inferred from the structure of the interactions. We conclude on the generality of our graphical method, on its limits with respect to the representation of the structure of the interactions in SBML, and on some perspectives for dealing with the dynamics. AVAILABILITY: The algorithms described in this article are implemented in the open-source software modeling platform BIOCHAM available at http://contraintes.inria.fr/biocham The models used in the experiments are available from http://www.biomodels.net/.

MOTIVATION: Robustness is the capacity of a system to maintain a function in the face of perturbations. It is essential for the correct functioning of natural and engineered biological systems. Robustness is generally defined in an ad hoc, problem-dependent manner, thus hampering the fruitful development of a theory of biological robustness, recently advocated by Kitano. RESULTS: In this article, we propose a general definition of robustness that applies to any biological function expressible in temporal logic LTL (linear temporal logic), and to broad model classes and perturbation types. Moreover, we propose a computational approach and an implementation in BIOCHAM 2.8 for the automated estimation of the robustness of a given behavior with respect to a given set of perturbations. The applicability and biological relevance of our approach is demonstrated by testing and improving the robustness of the timed behavior of a synthetic transcriptional cascade that could be used as a biological timer for synthetic biology applications. AVAILABILITY: Version 2.8 of BIOCHAM and the transcriptional cascade model are available at http://contraintes.inria.fr/BIOCHAM/.

UNLABELLED: BIOCHAM (the BIOCHemical Abstract Machine) is a software environment for modeling biochemical systems. It is based on two aspects: (1) the analysis and simulation of boolean, kinetic and stochastic models and (2) the formalization of biological properties in temporal logic. BIOCHAM provides tools and languages for describing protein networks with a simple and straightforward syntax, and for integrating biological properties into the model. It then becomes possible to analyze, query, verify and maintain the model with respect to those properties. For kinetic models, BIOCHAM can search for appropriate parameter values in order to reproduce a specific behavior observed in experiments and formalized in temporal logic. Coupled with other methods such as bifurcation diagrams, this search assists the modeler/biologist in the modeling process. AVAILABILITY: BIOCHAM (v. 2.5) is a free software available for download, with example models, at http://contraintes.inria.fr/BIOCHAM/.

We present a prescriptive type system with parametric polymorphism and subtyping for constraint logic programs. The aim of this type system is to detect programming errors statically. It introduces a type discipline for constraint logic programs and modules, while maintaining the capabilities of performing the usual coercions between constraint domains, and of typing meta-programming predicates, thanks to the exibility of subtyping. The property of subject reduction expresses the consistency of a prescriptive type system w.r.t. the execution model: if a program is ‘well-typed’, then all derivations starting from a ‘well-typed’ goal are again ‘well-typed’. That property is proved w.r.t. the abstract execution model of constraint programming which proceeds by accumulation of constraints only, and w.r.t. an enriched execution model with type constraints for substitutions. We describe our implementation of the system for type checking and type inference. We report our experimental results on type checking ISO-Prolog, the (constraint) libraries of Sicstus Prolog and other Prolog programs.

No abstract available.

The class CC of concurrent constraint programming languages and its non-monotonic extension LCC based on linear constraint systems can be given a logical semantics in Girard's intuitionistic linear logic for a variety of observables. In this paper we settle basic completeness results and we show how the phase semantics of linear logic can be used to provide simple and very concise "semantical" proofs of safety properties for GC or LCC programs.