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2016 | Buch

A Look-Ahead Simulation Algorithm for DBN Models of Biochemical Pathways Kapitel lesen Erstes Kapitel lesen

Hybrid Systems Biology

5th International Workshop, HSB 2016, Grenoble, France, October 20-21, 2016, Proceedings

herausgegeben von: Eugenio Cinquemani, Alexandre Donzé

Verlag: Springer International Publishing

Buchreihe : Lecture Notes in Computer Science

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book constitutes the refereed proceedings of the 5th International Workshop on Hybrid Systems Biology, HSB 2016, held in Grenoble, France, in October 2016.

The 11 full papers presented in this book were carefully reviewed and selected from 26 submissions. They were organized and presented in 4 thematic sessions also reflected in this book: model simulation; model analysis; discrete and network modelling; stochastic modelling for biological systems.

Inhaltsverzeichnis

Frontmatter

Model Simulation

Frontmatter
A Look-Ahead Simulation Algorithm for DBN Models of Biochemical Pathways
Abstract
Dynamic Bayesian Networks (DBNs) have been proposed [16] as an efficient abstraction formalism of biochemical models. They have been shown to approximate well the dynamics of biochemical models, while offering improved efficiency for their analysis [17, 18]. In this paper, we compare different representations and simulation schemes on these DBNs, testing their efficiency and accuracy as abstractions of biological pathways. When generating these DBNs, many configurations are never explored by the underlying dynamics of the biological systems. This can be used to obtain sparse representations to store and analyze DBNs in a compact way. On the other hand, when simulating these DBNs, singular configurations may be encountered, that is configurations from where no transition probability is defined. This makes simulation more complex. We initially evaluate two simple strategies for dealing with singularities: First, re-sampling simulations visiting singular configurations; second filling up uniformly these singular transition probabilities. We show that both these approaches are error prone. Next, we propose a new algorithm which samples only those configurations that avoid singularities by using a look-ahead strategy. Experiments show that this approach is the most accurate while having a reasonable run time.
Sucheendra K. Palaniappan, Matthieu Pichené, Grégory Batt, Eric Fabre, Blaise Genest
Accelerated Simulation of Hybrid Biological Models with Quasi-Disjoint Deterministic and Stochastic Subnets
Abstract
Computational biological models are indispensable tools for in silico hypothesis testing. But with the increasing complexity of biological systems, traditional simulators become inefficient to tackle emerging computational challenges. Hybrid simulation, which combines deterministic and stochastic parts, is a promising direction to deal with such challenges. However, currently existing algorithms of hybrid simulation are impractical for implementing real and complex biological systems. One reason for such limitation is that the performance of hybrid simulation not only relies on the number of stochastic events, but also on the type as well as the efficiency of the deterministic solver. In this paper, a new method is proposed for improving the performance of hybrid simulators by reducing the frequent reinitialisation of the deterministic solver. The proposed approach works well with models that contain a substantial number of stochastic events and higher numbers of continuous variables with limited connections between the deterministic and stochastic regimes. We tested these improvements on a number of case studies and it turns out that, for certain examples, the amended algorithm is ten times faster than the exact method.
Mostafa Herajy, Monika Heiner
Hybrid Stochastic Simulation of Rule-Based Polymerization Models
Abstract
Modeling and simulation of polymer formation is an important field of research not only in the material sciences but also in the life sciences due to the prominent role of processes such as actin filament formation and multivalent ligand-receptor interactions. While the advantages of a rule-based description of polymerizations has been successfully demonstrated, no efficient simulation of these mostly stiff processes is currently available, in particular for large system sizes.
We present a hybrid stochastic simulation approach, in which the average changes of highly abundant species due to fast reactions are deterministically simulated while for the remaining species with small counts a rule-based simulation is performed. We propose a nesting of rejection steps to arrive at an approach that is efficient and accurate. We test our method on two case studies of polymerization.
Thilo Krüger, Verena Wolf

Model Analysis

Frontmatter
Toward Modelling and Analysis of Transient and Sustained Behaviour of Signalling Pathways
Abstract
Signalling pathways provide a complex cellular information processing machinery that evaluates particular input stimuli and transfers them into the genome by means of regulation of specific genes expression. In this short paper, we provide a preliminary study targeting minimal models representing the topology of main signalling mechanisms. A special emphasis is given to distinguishing between monotonous (sustained) and non-monotonous (transient) time-course behaviour. A set of minimal parametrised ODE models is formulated and analysed in a workflow based on formal methods.
Matej Hajnal, David Šafránek, Martin Demko, Samuel Pastva, Pavel Krejčí, Luboš Brim
Application of the Reachability Analysis for the Iron Homeostasis Study
Abstract
Our work is motivated by a model of the mammalian cellular Iron Homeostasis, which was analysed using simulations in [9]. The result of this analysis is a characterization of the parameters space such that the model satisfies a set of constraints, proposed by biologists or coming from experimental results. We now propose an approach to hypothesis validation which can be seen as a complement to the approach based on simulation. It uses reachability analysis (that is set-based simulation) to formally validate a hypothesis. For polynomials systems, reachability analysis using the Bernstein expansion is an appropriate technique. Moreover, the Bernstein technique allows us to tackle uncertain parameters at a small cost. In this work, we extend the reachability analysis method presented in [7] to handle polynomial fractions. Furthermore, to tackle the complexity of the Iron Homeostasis model, we use a piecewise approximation of the dynamics and propose a reachability method to deal with the resulting hybrid dynamics. These approximations and adaptations allowed us to validate a hypothesis stated in [9], with an exhaustive analysis over uncertain parameters and initial conditions.
Alexandre Rocca, Thao Dang, Eric Fanchon, Jean-Marc Moulis
Synchronous Balanced Analysis
Abstract
When modeling Chemical Reaction Networks, a commonly used mathematical formalism is that of Petri Nets, with the usual interleaving execution semantics. We aim to substitute to a Chemical Reaction Network, especially a “growth” one (i.e., for which an exponential stationary phase exists), a piecewise synchronous approximation of the dynamics: a resource-allocation-centered Petri Net with maximal-step execution semantics. In the case of unimolecular chemical reactions, we prove the correctness of our method and show that it can be used either as an approximation of the dynamics, or as a method of constraining the reaction rate constants (an alternative to flux balance analysis, using an emergent formally defined notion of “growth rate” as the objective function), or a technique of refuting models.
Andreea Beica, Vincent Danos

Discrete and Network Modelling

Frontmatter
Verification of Temporal Properties of Neuronal Archetypes Modeled as Synchronous Reactive Systems
Abstract
There exists many ways to connect two, three or more neurons together to form different graphs. We call archetypes only the graphs whose properties can be associated with specific classes of biologically relevant structures and behaviors. These archetypes are supposed to be the basis of typical instances of neuronal information processing. To model different representative archetypes and express their temporal properties, we use a synchronous programming language dedicated to reactive systems (Lustre). The properties are then automatically validated thanks to several model checkers supporting data types. The respective results are compared and depend on their underlying abstraction methods.
Elisabetta De Maria, Alexandre Muzy, Daniel Gaffé, Annie Ressouche, Franck Grammont
Relationship Between the Reprogramming Determinants of Boolean Networks and Their Interaction Graph
Abstract
In this paper, we address the formal characterization of targets triggering cellular trans-differentiation in the scope of Boolean networks with asynchronous dynamics. Given two fixed points of a Boolean network, we are interested in all the combinations of mutations which allow to switch from one fixed point to the other, either possibly, or inevitably. In the case of existential reachability, we prove that the set of nodes to (permanently) flip are only and necessarily in certain connected components of the interaction graph. In the case of inevitable reachability, we provide an algorithm to identify a subset of possible solutions.
Hugues Mandon, Stefan Haar, Loïc Paulevé
Discrete Abstraction of Multiaffine Systems
Abstract
Many biological systems can be modeled as multiaffine hybrid systems. Due to the nonlinearity of multiaffine systems, it is difficult to verify their properties of interest directly. A common strategy to tackle this problem is to construct and analyze a discrete overapproximation of the original system. However, the conservativeness of a discrete abstraction significantly determines the level of confidence we can have in the properties of the original system. In this paper, in order to reduce the conservativeness of a discrete abstraction, we propose a new method based on a sufficient and necessary decision condition for computing discrete transitions between states in the abstract system. We assume the state space partition of a multiaffine system to be based on a set of multivariate polynomials. Hence, a rectangular partition defined in terms of polynomials of the form \((x_i-c)\) is just a simple case of multivariate polynomial partition, and the new decision condition applies naturally. We analyze and demonstrate the improvement of our method over the existing methods using some examples.
Hui Kong, Ezio Bartocci, Sergiy Bogomolov, Radu Grosu, Thomas A. Henzinger, Yu Jiang, Christian Schilling

Stochastic Modelling

Frontmatter
On Observability and Reconstruction of Promoter Activity Statistics from Reporter Protein Mean and Variance Profiles
Abstract
Reporter protein systems are widely used in biology for the indirect quantitative monitoring of gene expression activity over time. At the level of population averages, the relationship between the observed reporter concentration profile and gene promoter activity is established, and effective methods have been introduced to reconstruct this information from the data. At single-cell level, the relationship between population distribution time profiles and the statistics of promoter activation is still not fully investigated, and adequate reconstruction methods are lacking.
This paper develops new results for the reconstruction of promoter activity statistics from mean and variance profiles of a reporter protein. Based on stochastic modelling of gene expression dynamics, it discusses the observability of mean and autocovariance function of an arbitrary random binary promoter activity process. Mathematical relationships developed are explicit and nonparametric, i.e. free of a priori assumptions on the laws governing the promoter process, thus allowing for the decoupled analysis of the switching dynamics in a subsequent step. The results of this work constitute the essential tools for the development of promoter statistics and regulatory mechanism inference algorithms.
Eugenio Cinquemani
Logic-Based Multi-objective Design of Chemical Reaction Networks
Abstract
The design of genetic or protein networks that satisfy a given set of behavioural specifications is one of the main challenges of synthetic biology. Model-based design is a natural choice in this respect. Here we consider the problem of tuning parameters of a stochastic model to force one or more behavioural goals to hold. In particular, we consider several objectives specified by signal temporal logic formulae, and we look for a parameter set making their satisfaction probability as large as possible. This formalisation results in a multi-objective optimisation problem, which we solve by considering an optimisation scheme combining satisfaction probability and average robustness of STL properties, leveraging state of the art multi-objective optimisation routines.
Luca Bortolussi, Alberto Policriti, Simone Silvetti
Backmatter
Metadaten
Titel
Hybrid Systems Biology
herausgegeben von
Eugenio Cinquemani
Alexandre Donzé
Copyright-Jahr
2016
Electronic ISBN
978-3-319-47151-8
Print ISBN
978-3-319-47150-1
DOI
https://doi.org/10.1007/978-3-319-47151-8

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