In systems biology, reaction-based models are often small (compared to the complexity of the system), because they drastically summarize a mechanism as a consequence of a previous understanding or hypothesis. More explicit models based on mechanistic rules are closer to a formal representation of empirical facts considered as bricks that can be assembled to build larger systems without prejudging a particular behavior (in fact without a prior understanding). Nevertheless, this also makes them more difficult to understand, creating the need for concepts and computational tools to better analyze them. Among the concepts that seem particularly useful for understanding rule-based models is causality, understood as the retrospective analysis of how an event of interest occurred. The unit 6 introduces computational approaches to aspects of causality in the rule-based context :
(i) the static influence of one rule on another, defined in terms of overlapping patterns ;
(ii) the dynamic influence between rules, defined in terms of the extent to which the application of one rule modifies the propensity to apply another. A visualization of the changing network of dynamic influences between rules is discussed in the context of a molecular clock model (KaiABC) in cyanobacteria ;
(iii) trace causality, defined as a partially ordered precedence relation representing the extent to which events, triggered by the application of rules, could have been permuted in alternative histories. To be useful, trace-based causality requires a notion of causal compression. Roughly speaking, compression eliminates causal loops in which a series of events leads to a system state that is equivalent to a previously visited state, with regard to the realization of the event of interest ;
(iv) counterfactual causality, in which the event X causes the event Y if the absence of X should have resulted in the absence of Y. Whereas trace causality is " positive " in that it records events that bring a system closer to a target event, counterfactual causality provides insight into " negative " or inhibitory relationships between events. For example, in a particular fact, an event X could be the cause of an event Y, because X prevented event Z from occurring, which, had it occurred, would have prevented Y.
