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Indeed, update classes can be defined, grounded on the nature of the processes involved, e.g., different time scales associated with transcriptional and post-translational processes (Chaves et al., 2005). At each time step (or iteration), the selection of updated variables is directed by their associated priority classes (Faur�� et al., 2006), absolute ranks or probabilities (e.g., Albert and Thakar, 2014 and references therein). Generalizing the logical framework with a probabilistic interpretation, a finite Markov chain can be derived from the dynamics of a logical model. Considering the asynchronous update, Stoll et al. (2012) defined continuous or discrete time Markov processes by associating stochastic rates with the Megestrol Acetate updates of the model components, and relied on a Gillespie algorithm to simulate the time evolution of component levels. This allows to get a more quantitative view of the model behavior (cf. Section 5.2). In Cell Collective, synchronous simulations also result in a Markov chain when the input components are associated with a probability (see Section 3.2 and Todd and Helikar, 2012). When following a unique trajectory (defined by a synchronous update or selecting specific transitions among multiple asynchronous, concurrent trajectories), a natural alternative to the STG consists in displaying the evolution of the individual variables over time (see Figure ?Figure2C).2C). To provide a different view of the model behavior, it has been also proposed to consider the mean values g~i of a model variable gi over a sliding window of (user-defined) length w (Helikar and Rogers, 2009): ?gi��G,?t��0,g~i(t)=��0��kBirinapant order (3) It is worth recalling that different updating schemes lead to different dynamics, thus impacting related properties (e.g., see Albert and Thakar, 2014). Briefly, compared to the synchronous scheme, asynchronous dynamics are more realistic in accounting Gemcitabine price for delays between updating orders and their executions. While stable states are the same for both the synchronous and asynchronous schemes, a striking example of how the resulting dynamics can differ is that of isolated regulatory circuits, for which the synchronous scheme leads to the appearance of additional cyclic attractors (Remy et al., 2003). Not only cyclical attractors may be different, but reachability properties are also modified. The asynchronous scheme generates concurrent trajectories, some of which are potentially unfeasible in regard to well-grounded choices between concurrent events. Hence, refined asynchronous schemes have been considered, such as priorities, fixed ranks or probabilities, which may also affect attractors and their reachability properties. Indeed, as some trajectories are preempted, transient oscillatory behaviors may be turned into cyclic attractors. By way of conclusion, beyond the model definition as presented in Section 2.

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