Biomedical event extraction from natural text is a challenging task as it searches for complex and often nested structures describing specific relationships between multiple molecular entities, such as genes, proteins, or cellular components. It usually is implemented by a complex pipeline of individual tools to solve the different relation extraction subtasks. We present an alternative approach where the detection of relationships between entities is described uniformly as questions, which are iteratively answered by a question answering (QA) system based on the domain-specific language model SciBERT. This model outperforms two strong baselines in two biomedical event extraction corpora in a Knowledge Base Population setting, and also achieves competitive performance in BioNLP challenge evaluation settings.