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A Monte Carlo model checker for probabilistic LTL with numerical constraints
We define the syntax and semantics of a new temporal logic called probabilistic LTL with numerical constraints (PLTLc).
We introduce an efficient model checker for PLTLc properties. The efficiency of the model checker is through approximation
using Monte Carlo sampling of finite paths through the model’s state space (simulation outputs) and parallel model checking
of the paths. Our model checking method can be applied to any model producing quantitative output – continuous or
stochastic, including those with complex dynamics and those with an infinite state space. Furthermore, our offline approach
allows the analysis of observed (real-life) behaviour traces. We find in this paper that PLTLc properties with constraints
over free variables can replace full model checking experiments, resulting in a significant gain in efficiency. This overcomes
one disadvantage of model checking experiments which is that the complexity depends on system granularity and number of
variables, and quickly becomes infeasible. We focus on models of biochemical networks, and specifically in this paper on
intracellular signalling pathways; however our method can be applied to a wide range of biological as well as technical
systems and their models. Our work contributes to the emerging field of synthetic biology by proposing a rigourous approach
for the structured formal engineering of biological systems
Petri nets for systems and synthetic biology
We give a description of a Petri net-based framework for
modelling and analysing biochemical pathways, which uni¯es the qualita-
tive, stochastic and continuous paradigms. Each perspective adds its con-
tribution to the understanding of the system, thus the three approaches
do not compete, but complement each other. We illustrate our approach
by applying it to an extended model of the three stage cascade, which
forms the core of the ERK signal transduction pathway. Consequently
our focus is on transient behaviour analysis. We demonstrate how quali-
tative descriptions are abstractions over stochastic or continuous descrip-
tions, and show that the stochastic and continuous models approximate
each other. Although our framework is based on Petri nets, it can be
applied more widely to other formalisms which are used to model and
analyse biochemical networks
On Estimating Derivatives of Input Signals in Biochemistry
The online estimation of the derivative of an input signal is widespread in
control theory and engineering. In the realm of chemical reaction networks
(CRN), this raises however a number of specific issues on the different ways to
achieve it. A CRN pattern for implementing a derivative block has already been
proposed for the PID control of biochemical processes, and proved correct using
Tikhonov's limit theorem. In this paper, we give a detailed mathematical
analysis of that CRN, thus clarifying the computed quantity and quantifying the
error done as a function of the reaction kinetic parameters. In a synthetic
biology perspective, we show how this can be used to design error correcting
terms to compute online functions involving derivatives with CRNs. In the
systems biology perspective, we give the list of models in BioModels containing
(in the sense of subgraph epimorphisms) the core derivative CRN, most of which
being models of oscillators and control systems in the cell, and discuss in
detail two such examples: one model of the circadian clock and one model of a
bistable switch
A Taxonomy of Causality-Based Biological Properties
We formally characterize a set of causality-based properties of metabolic
networks. This set of properties aims at making precise several notions on the
production of metabolites, which are familiar in the biologists' terminology.
From a theoretical point of view, biochemical reactions are abstractly
represented as causal implications and the produced metabolites as causal
consequences of the implication representing the corresponding reaction. The
fact that a reactant is produced is represented by means of the chain of
reactions that have made it exist. Such representation abstracts away from
quantities, stoichiometric and thermodynamic parameters and constitutes the
basis for the characterization of our properties. Moreover, we propose an
effective method for verifying our properties based on an abstract model of
system dynamics. This consists of a new abstract semantics for the system seen
as a concurrent network and expressed using the Chemical Ground Form calculus.
We illustrate an application of this framework to a portion of a real
metabolic pathway
Modelling Cell Cycle using Different Levels of Representation
Understanding the behaviour of biological systems requires a complex setting
of in vitro and in vivo experiments, which attracts high costs in terms of time
and resources. The use of mathematical models allows researchers to perform
computerised simulations of biological systems, which are called in silico
experiments, to attain important insights and predictions about the system
behaviour with a considerably lower cost. Computer visualisation is an
important part of this approach, since it provides a realistic representation
of the system behaviour. We define a formal methodology to model biological
systems using different levels of representation: a purely formal
representation, which we call molecular level, models the biochemical dynamics
of the system; visualisation-oriented representations, which we call visual
levels, provide views of the biological system at a higher level of
organisation and are equipped with the necessary spatial information to
generate the appropriate visualisation. We choose Spatial CLS, a formal
language belonging to the class of Calculi of Looping Sequences, as the
formalism for modelling all representation levels. We illustrate our approach
using the budding yeast cell cycle as a case study
Types for BioAmbients
The BioAmbients calculus is a process algebra suitable for representing
compartmentalization, molecular localization and movements between
compartments. In this paper we enrich this calculus with a static type system
classifying each ambient with group types specifying the kind of compartments
in which the ambient can stay. The type system ensures that, in a well-typed
process, ambients cannot be nested in a way that violates the type hierarchy.
Exploiting the information given by the group types, we also extend the
operational semantics of BioAmbients with rules signalling errors that may
derive from undesired ambients' moves (i.e. merging incompatible tissues).
Thus, the signal of errors can help the modeller to detect and locate unwanted
situations that may arise in a biological system, and give practical hints on
how to avoid the undesired behaviour
An overview of existing modeling tools making use of model checking in the analysis of biochemical networks
Model checking is a well-established technique for automaticallyverifying complex systems. Recently, model checkers have appearedin computer tools for the analysis of biochemical (and generegulatory) networks. We survey several such tools to assess thepotential of model checking in computational biology. Next, our overviewfocuses on direct applications of existing model checkers, as well ason algorithms for biochemical network analysis influenced by modelchecking, such as those using binary decision diagrams or Booleansatisfiability solvers. We conclude with advantages and drawbacks ofmodel checking for the analysis of biochemical networks
Modelling molecular networks: relationships between different formalisms and levels of details
This document is the deliverable 1.3 of French ANR CALAMAR. It presents a study of different formalisms used for modelling and analyzing large molecular regulation networks, their formal links, in terms of mutual encodings and of abstractions, and the corresponding levels of detail captured
Trend-based analysis of a population model of the AKAP scaffold protein
We formalise a continuous-time Markov chain with multi-dimensional discrete state space model of the AKAP scaffold protein as a crosstalk mediator between two biochemical signalling pathways. The analysis by temporal properties of the AKAP model requires reasoning about whether the counts of individuals of the same type (species) are increasing or decreasing. For this purpose we propose the concept of stochastic trends based on formulating the probabilities of transitions that increase (resp. decrease) the counts of individuals of the same type, and express these probabilities as formulae such that the state space of the model is not altered. We define a number of stochastic trend formulae (e.g. weakly increasing, strictly increasing, weakly decreasing, etc.) and use them to extend the set of state formulae of Continuous Stochastic Logic. We show how stochastic trends can be implemented in a guarded-command style specification language for transition systems. We illustrate the application of stochastic trends with numerous small examples and then we analyse the AKAP model in order to characterise and show causality and pulsating behaviours in this biochemical system
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