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We present a framework to assist the diagrammatic modelling of complex biological systems using the unified modelling language (UML). The framework comprises three levels of modelling, ranging in scope from the dynamics of individual model entities to system-level emergent properties. By way of an immunological case study of the mouse disease experimental autoimmune encephalomyelitis, we show how the framework can be used to produce models that capture and communicate the biological system, detailing how biological entities, interactions and behaviours lead to higher-level emergent properties observed in the real world. We demonstrate how the UML can be successfully applied within our framework, and provide a critique of UML's ability to capture concepts fundamental to immunology and biology more generally. We show how specialized, well-explained diagrams with less formal semantics can be used where no suitable UML formalism exists. We highlight UML's lack of expressive ability concerning cyclic feedbacks in cellular networks, and the compounding concurrency arising from huge numbers of stochastic, interacting agents. To compensate for this, we propose several additional relationships for expressing these concepts in UML's activity diagram. We also demonstrate the ambiguous nature of class diagrams when applied to complex biology, and question their utility in modelling such dynamic systems. Models created through our framework are non-executable, and expressly free of simulation implementation concerns. They are a valuable complement and precursor to simulation specifications and implementations, focusing purely on thoroughly exploring the biology, recording hypotheses and assumptions, and serve as a communication medium detailing exactly how a simulation relates to the real biology.

Modelling biological behaviours with the unified modelling language: an immunological case study and critique