Formal Methods in System Design - Special issue on The First Federated Logic Conference (FLOC'96), part II
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Modeling and querying biomolecular interaction networks
Theoretical Computer Science - Special issue: Computational systems biology
Queueing Networks and Markov Chains
Queueing Networks and Markov Chains
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
CMSB '08 Proceedings of the 6th International Conference on Computational Methods in Systems Biology
Some Investigations Concerning the CTMC and the ODE Model Derived From Bio-PEPA
Electronic Notes in Theoretical Computer Science (ENTCS)
Analysing Biochemical Oscillation through Probabilistic Model Checking
Electronic Notes in Theoretical Computer Science (ENTCS)
Integrated Simulation and Model-Checking for the Analysis of Biochemical Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
PRISM: probabilistic model checking for performance and reliability analysis
ACM SIGMETRICS Performance Evaluation Review
Formalisms for Specifying Markovian Population Models
RP '09 Proceedings of the 3rd International Workshop on Reachability Problems
Process Algebra Modelling Styles for Biomolecular Processes
Transactions on Computational Systems Biology XI
Query-based verification of qualitative trends and oscillations in biochemical systems
Theoretical Computer Science
SFM'07 Proceedings of the 7th international conference on Formal methods for performance evaluation
A Model and Analysis of the AKAP Scaffold
Electronic Notes in Theoretical Computer Science (ENTCS)
Temporal logic constraints in the biochemical abstract machine BIOCHAM
LOPSTR'05 Proceedings of the 15th international conference on Logic Based Program Synthesis and Transformation
Analysis of signalling pathways using continuous time markov chains
Transactions on Computational Systems Biology VI
Transactions on Computational Systems Biology VII
Characterizing oscillatory and noisy periodic behavior in markov population models
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
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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.