Proteins fulfil a huge number of functions in any living organism. The dynamics of the protein concentrations in a cell is defined by a regulatory network which usually encompasses a multitude of highly complex feedback loops. Being able to model and analyze its structure and behavior is crucial for understanding the functions of the proteins and their interactions. For a modeling framework to be useful in practice, two factors are crucial: the model must faithfully represent the actual behavior of the network, and it must be supported by analysis algorithms that are efficient enough to cope with complex models, and scale up well. Therefore, this paper makes two different contributions. First, we present a framework for modeling genetic regulatory networks in a modular yet faithful manner based on the mathematically well-founded formalism of differential inclusions. In our approach, the different components of the system (proteins or sets proteins) and the way they constrain each other, are modeled separately and modularly. Second, we propose efficient algorithms to analyze the behavior of the model. The algorithms are compositional in the sense that they verify local properties on the individual components. Sufficient conditions on these local properties and on the constraints between the components then allow to efficiently infer properties of the whole system, such as reachability and existence of equilibrium states. Two case studies show the potential of this approach.