We will present a new model accounting for the spatial organization and the transcription of the genome in the mammalian cell nucleus. In this model, genome regions are represented as sequences of points with marks reflecting their transcriptional activity. The probabilistic distribution of the marked points is written as a Gibbs distribution with several potentials representing different types of interactions between nuclear elements. The considered interactions are: volume exclusion (limiting the local chromatin density), chromatin elasticity (limiting the distance between consecutive points lying on the same chromosome), binding of chromatin to the nuclear envelope, repression of transcription due to local crowding and clustering of highly transcribed genomic regions. In addition to encompass a wide range of interactions compared to previous 3D DNA models, our model takes into account the heterogeneity of the chromatin fibers concerning elasticity, transcription and interactions with the nuclear envelope. More precisely, some interaction parameters vary along the sequence of points. Hence the proposed model is of very high dimension with a number of parameters of the same order as the number of points. An algorithm for simulating the model together with some simulation results will be presented. Finally some issues relative to fitting from genome-wide contact data will be discussed.