Storyline research links together events in stories and specifies shared participants in those stories. In these analyses, an atomic event is assumed to be a single clause headed by a single verb. However, many analyses of verbal semantics assume a decompositional analysis of events expressed in single clauses. We present a formalization of a decompositional analysis of events in which each participant in a clausal event has their own temporally extended subevent, and the subevents are related through causal and other interactions. This decomposition allows us to represent storylines as an evolving set of interactions between participants over time.