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Genetic regulatory networks usually encompass a multitude of complex, interacting feedback loops. Being able to model and analyze their behavior is crucial for understanding their function. However, state space explosion is becoming a limiting factor in the formal analysis of genetic networks. This paper explores a modular approach for verification of reachability properties. A framework for component-based modeling of genetic regulatory networks, based on a modular discrete abstraction, is introduced. Then a compositional algorithm to efficiently analyze reachability properties of the model is proposed. A case study on embryonic cell differentiation involving several hundred cells shows the potential of this approach.