In eukaryotes, DNA is confined in the cell nucleus. Therefore it is in the nucleus that the main functions involving DNA such as replication, repair and transcription take place. DNA is highly folded in the nucleus: the whole genome extends on about 2 meters while the nucleus is about 5-10 microns. The wrapping of DNA around protein complexes (nucleosomes), forming the chromatin fiber, induces a first level of DNA compaction. However folding at a higher level is necessary to reach observed levels of compaction. Furthermore it is believed that the nucleus is not spatially homogeneous with respect to transcription: the densities of transcription factors and chromatin vary spatially. Conversely the activity of the genome may play a major role in the setup of its spatial organization. In particular, active loci tend to cluster together and could be responsible for establishing chromatin loops. The interplay between the activity and the spatial organization of the genome has been investigated through diverse experimental methods. Modelling approaches have been developed to test hypotheses about rules gouverning the spatial organization. Models are generally stochastic and can be viewed as Gibbs models. Two types of geometry are considered: chains of fixed length segments (random walks) and sequences of points (worm-like chains). Different types of interactions are included: short-range repulsion (volume exclusion), attraction between consecutive points (compaction), long-range attraction between a subset of points (looping). Such models succeed in reproducing global features of the chromatin spatial organization. So far, models are low-dimensional and the chromatin fibers are supposed to be homogeneous. However recent hight-throughput technics are providing data at the scale of the whole genome showing differences between various chromatin regions. Hence current models should be extended involving heterogeneous fibers instead of homogeneous ones. This means that interaction parameters should be specific to each segment or point, leading to models with thousands of parameters! We will sketch such a model. The chromatin fibers will be represented as sequences of points (worm-like chains) where each point interacts specifically with other points and other nuclear components. In order to investigate the interplay between spatial organization and transcriptional activity, the transcription level of each point will be represented in the model as a mark. The different types of interactions to be considered will be modelled by potentials. This model does not raise new theoretical issues concerning Gibbs model. However it is much more complex than standard models. This is due to the number of types of interactions considered in the model, and to the fact that points are allowed to interact specifically with other elements. Several issues relative to simulation and fitting will be discussed.