Formal Method for Biological Systems Modelling

A special issue of Computation (ISSN 2079-3197). This special issue belongs to the section "Computational Biology".

Deadline for manuscript submissions: closed (31 July 2021) | Viewed by 7599

Special Issue Editors


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Guest Editor
Inria & ENS, 75 230 Paris, France
Interests: systems biology; static analysis; programming languages; formal methods

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Guest Editor
1. IUT 'A' - University of Lille, Lille, France
2. CRISTAL, CNRS, UMR, 9189 Lille, France
Interests: systems biology; static analysis; programming languages; formal methods

Special Issue Information

Dear Colleagues,

The field of system biology poses many challenges to computer scientists. Regulatory networks, intra- and extra-cellular signalling pathways, metabolic networks and whole cells models suffer both from high conceptual difficulties and from a huge combinatorial complexity.  From the description of these models, by organising and collecting facts based on knowledge representation databases, to the execution of these models, through the abstraction of their main properties, formal methods offer promising potential approaches. While existing formal frameworks can be adapted to cope with the specific kinds of problems, new formal methods emerge from the confrontation with this new field of application. 

Besides the intrinsic combinatorial complexity, biological systems are characterised by the fact that they have not been humanly designed. Their dynamics are driven by competition for shared resources, time- and concentration-scale separation, and non-linear feedback loops. Many components have antagonistic effects according to the context. It is impossible to understand from which mechanisms the collective behaviour of these models come from.

Mainstream quantitative approaches (based on ODEs) suffer from various limitations. To cope with the combinatorial complexity, series of simplifications are usually required. This results in several drawbacks: not only does it usually restrict the context of the application of the models, but also, it is likely to skew the model in the direction of what is intended by the modeller. Moreover, their results are specific for particular sets of parameters and they are difficult to generalize. As a consequence, they usually offer an unsatisfying level of confidence.

Formal methods provide various means to increase confidence in models and to compute their properties. Formal languages provide hierarchical constructions to collect information about mechanistic interactions, in a more goal agnostic manner. Formal methods also assist the modeller to gradually refine/abstract information about a given process by including more/fewer details from the literature. Symbolic static analyses not only enhance confidence in models, but also provide new perspectives on models by efficiently computing informative invariants. Causal analyses provide explanations for the potential scenarios for events of interest to occur. The behaviour of models can be captured while avoiding the exploration of the different interleaving of these massively distributed agent-centric models. Lastly, model reduction provides new systems while identifying the elements that mainly drive the dynamics of these models.

This Special Issue is dedicated to formal methods developed for the analysis of biological systems and their application to current open questions in biology. Its scope covers the design of specific language and modelling tools, the design of static analyses, causal analyses, model reduction techniques. We are also interested in feedback on the usage of formal approaches in the design and the analysis of models to address biological issues. 

Dr. Jérôme Feret
Prof. Cédric Lhoussaine
Guest Editors

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Keywords

  • Systems biology
  • Formal methods
  • Static analysis
  • Logic

Published Papers (3 papers)

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32 pages, 750 KiB  
Article
Exact Boolean Abstraction of Linear Equation Systems
by Emilie Allart, Joachim Niehren and Cristian Versari
Computation 2021, 9(11), 113; https://doi.org/10.3390/computation9110113 - 21 Oct 2021
Cited by 1 | Viewed by 2123
Abstract
We study the problem of how to compute the boolean abstraction of the solution set of a linear equation system over the positive reals. We call a linear equation system ϕ exact for the boolean abstraction if the abstract interpretation of ϕ over [...] Read more.
We study the problem of how to compute the boolean abstraction of the solution set of a linear equation system over the positive reals. We call a linear equation system ϕ exact for the boolean abstraction if the abstract interpretation of ϕ over the structure of booleans is equal to the boolean abstraction of the solution set of ϕ over the positive reals. Abstract interpretation over the booleans is thus complete for the boolean abstraction when restricted to exact linear equation systems, while it is not complete more generally. We present a new rewriting algorithm that makes linear equation systems exact for the boolean abstraction while preserving the solutions over the positive reals. The rewriting algorithm is based on the elementary modes of the linear equation system. The computation of the elementary modes may require exponential time in the worst case, but is often feasible in practice with freely available tools. For exact linear equation systems, we can compute the boolean abstraction by finite domain constraint programming. This yields a solution of the initial problem that is often feasible in practice. Our exact rewriting algorithm has two further applications. Firstly, it can be used to compute the sign abstraction of linear equation systems over the reals, as needed for analyzing function programs with linear arithmetics. Secondly, it can be applied to compute the difference abstraction of a linear equation system as used in change prediction algorithms for flux networks in systems biology. Full article
(This article belongs to the Special Issue Formal Method for Biological Systems Modelling)
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56 pages, 1985 KiB  
Article
Metabolic Pathway Analysis in the Presence of Biological Constraints
by Philippe Dague
Computation 2021, 9(10), 111; https://doi.org/10.3390/computation9100111 - 19 Oct 2021
Viewed by 1814
Abstract
Metabolic pathway analysis is a key method to study a metabolism in its steady state, and the concept of elementary fluxes (EFs) plays a major role in the analysis of a network in terms of non-decomposable pathways. The supports of the EFs contain [...] Read more.
Metabolic pathway analysis is a key method to study a metabolism in its steady state, and the concept of elementary fluxes (EFs) plays a major role in the analysis of a network in terms of non-decomposable pathways. The supports of the EFs contain in particular those of the elementary flux modes (EFMs), which are the support-minimal pathways, and EFs coincide with EFMs when the only flux constraints are given by the irreversibility of certain reactions. Practical use of both EFMs and EFs has been hampered by the combinatorial explosion of their number in large, genome-scale systems. The EFs give the possible pathways in a steady state but the real pathways are limited by biological constraints, such as thermodynamic or, more generally, kinetic constraints and regulatory constraints from the genetic network. We provide results on the mathematical structure and geometrical characterization of the solution space in the presence of such biological constraints (which is no longer a convex polyhedral cone or a convex polyhedron) and revisit the concept of EFMs and EFs in this framework. We show that most of the results depend only on very general properties of compatibility of constraints with vector signs: either sign-invariance, satisfied by regulatory constraints, or sign-monotonicity (a stronger property), satisfied by thermodynamic and kinetic constraints. We show in particular that the solution space for sign-monotone constraints is a union of particular faces of the original polyhedral cone or polyhedron and that EFs still coincide with EFMs and are just those of the original EFs that satisfy the constraint, and we show how to integrate their computation efficiently in the double description method, the most widely used method in the tools dedicated to EFs computation. We show that, for sign-invariant constraints, the situation is more complex: the solution space is a disjoint union of particular semi-open faces (i.e., without some of their own faces of lesser dimension) of the original polyhedral cone or polyhedron and, if EFs are still those of the original EFs that satisfy the constraint, their computation cannot be incrementally integrated into the double description method, and the result is not true for EFMs, that are in general strictly more numerous than those of the original EFMs that satisfy the constraint. Full article
(This article belongs to the Special Issue Formal Method for Biological Systems Modelling)
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19 pages, 1224 KiB  
Article
A Language for Modeling and Optimizing Experimental Biological Protocols
by Luca Cardelli, Marta Kwiatkowska and Luca Laurenti
Computation 2021, 9(10), 107; https://doi.org/10.3390/computation9100107 - 16 Oct 2021
Viewed by 2819
Abstract
Automation is becoming ubiquitous in all laboratory activities, moving towards precisely defined and codified laboratory protocols. However, the integration between laboratory protocols and mathematical models is still lacking. Models describe physical processes, while protocols define the steps carried out during an experiment: neither [...] Read more.
Automation is becoming ubiquitous in all laboratory activities, moving towards precisely defined and codified laboratory protocols. However, the integration between laboratory protocols and mathematical models is still lacking. Models describe physical processes, while protocols define the steps carried out during an experiment: neither cover the domain of the other, although they both attempt to characterize the same phenomena. We should ideally start from an integrated description of both the model and the steps carried out to test it, to concurrently analyze uncertainties in model parameters, equipment tolerances, and data collection. To this end, we present a language to model and optimize experimental biochemical protocols that facilitates such an integrated description, and that can be combined with experimental data. We provide probabilistic semantics for our language in terms of Gaussian processes (GPs) based on the linear noise approximation (LNA) that formally characterizes the uncertainties in the data collection, the underlying model, and the protocol operations. In a set of case studies, we illustrate how the resulting framework allows for automated analysis and optimization of experimental protocols, including Gibson assembly protocols. Full article
(This article belongs to the Special Issue Formal Method for Biological Systems Modelling)
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