We introduce a modelling framework and computational paradigm called Colonies of Synchronizing Agents (CSAs) inspired by the intracellular and intercellular mechanisms in biological tissues. The model is based on a multiset of agents in a common environment. Each agent has a local state stored in the form of a multiset of atomic objects, which is updated by global multiset rewriting rules either independently or synchronously with another agent. We first define the model then study its computational power, considering trade-offs between internal rewriting (intracellular mechanisms) and synchronization between agents (intercellular mechanisms). We also investigate dynamic properties of CSAs, including behavioural robustness (ability to generate a core behaviour despite agent loss or rule failure) and safety of synchronization (ability of an agent to synchronize with some other agent whenever needed).