The special theme of DCM 2009, co-located with ICALP 2009, concerned Computational Models From Nature, with a particular emphasis on computational models derived from physics and biology. The intention was to bring together different approaches - in a community with a strong foundational background as proffered by the ICALP attendees - to create inspirational cross-boundary exchanges, and to lead to innovative further research. Specifically DCM 2009 sought contributions in quantum computation and information, probabilistic models, chemical, biological and bio-inspired ones, including spatial models, growth models and models of self-assembly. Contributions putting to the test logical or algorithmic aspects of computing (e.g., continuous computing with dynamical systems, or solid state computing models) were also very much welcomed.