We develop a new framework for inferring models of transcriptional regulation. The models in this approach, which we call physical models, are constructed on the basis of verifiable molecular attributes of the underlying biological system. The attributes include, for example, the existence of protein-protein and protein-DNA interactions in gene regulatory processes, the directionality of signal transduction in protein-protein interactions, as well as the signs of the immediate effects of these interactions (e.g., whether an upstream gen activates or represses the downstream genes). Each attribute is included as a variable in the model, and the variables define a collection of annotated random graphs. Possible configurations of these variables (realizations of the underlying biological system) are constrained by the available data sources. Some of the data sources such as factor-binding data (location data) involve measurements that are directly tied to the variables in the model. Othe...