Behaviour specifications of heterogeneously structured interacting system components in a distributed software architecture are coalgebras based on different endofunctors, whose interaction scenarios must be algebraically specified. We propose to formalise the concrete interaction rules as natural transformations, called coordination laws, and embed these specifications into a bialgebraic representation based on multi-sorted algebraic signatures. If the coordination laws can be transformed into an abstract GSOS format, the approach is compositional, i.e. syntactical operations on the individual components are fully abstract w.r.t. bisimilarity. We obtain resulting operational semantics as a holistic coalgebra, which comprises the behaviour of the individual components and the resulting global behaviour. This guarantees non-intrusiveness for the individual components and, furthermore, enables successive coordination steps building on each other by taking the individual components as initial input and yielding an ultimate compound behaviour as final output.