We propose a novel mathematical model for the activity of microbloggers during an external, event-driven spike. The model leads to a testable prediction of who would become most active if a spike were to take place. This type of insight into human behaviour has many applications, as it identifies key players who can be targeted with information in real time when the network is most receptive. The model takes account of the fact that dynamic interactions evolve over an underlying, static network that records "who listens to whom". Our fundamental assumption is that, in the case where the entire community has become aware of an external news event, a key driver of activity is the motivation to participate by responding to incoming messages. We validate the resulting algorithm on a large scale Twitter conversation concerning the appointment of a UK Premier League football club manager. We also find that the half-life of a spike in activity can be quantified in terms of the network size and the typical response rate.