The three-dimensional organisation of chromosomes can be probed using methods such as Capture-C. However it is unclear how such population level data relates to the organisation within a single cell, and the mechanisms leading to the observed interactions are still largely obscure. We present a polymer modelling scheme based on the assumption that chromosome architecture is maintained by protein bridges which form chromatin loops. To test the model we perform FISH experiments and also compare with Capture-C data. Starting merely from the locations of protein binding sites, our model accurately predicts the experimentally observed chromatin interactions, revealing a population of 3D conformations.Experimental data sets, simulation data sets and files used to perform simulations are provided in gzipped tarballs. The README gives brief details of each zipped file, and each of these contains a further README with full details.