In the course of understanding biological regulatory networks (BRN), scientists usually start by studying small BRNs that they believe to be of particular importance to represent a biological function, and then, embed them in the whole network. Such a reduction can lead to neglect relevant regulations and to study a network whose properties can be very different from the properties of this network viewed as a part of the whole. In this paper we study, from a logical point of view, the preservation of properties inherited from small BRNs. The signature of BRN, constituted by a graph, is one of the distinctive features on which embeddings can be defined which leads us to give a first condition on the subgraphs ensuring the preservation of properties of the embedded graphs. Key words: Biological regulatory networks, network embedding, property preservation, mathematical modeling, computational tree logic