A neurobiologically constrained deep neural network mimicking cortical area function relevant for sensorimotor, linguistic and conceptual processing was used to investigate the putative biological mechanisms underlying conceptual category formation and semantic feature extraction. Networks were trained to learn neural patterns representing specific objects and actions relevant to semantically ‘ground’ concrete and abstract concepts. Grounding sets consisted of three grounding patterns with neurons representing specific perceptual or action-related features; neurons were either unique to one pattern or shared between patterns of the same set. Concrete categories were modelled as pattern triplets overlapping in their ‘shared neurons’, thus implementing semantic feature sharing of all instances of a category. In contrast, abstract concepts had partially shared feature neurons common to only pairs of category instances, thus, exhibiting family resemblance, but lacking full feature overlap. Stimulation with concrete and abstract conceptual patterns and biologically realistic unsupervised learning caused formation of strongly connected cell assemblies (CAs) specific to individual grounding patterns, whose neurons were spread out across all areas of the deep network. After learning, the shared neurons of the instances of concrete concepts were more prominent in central areas when compared with peripheral sensorimotor ones, whereas for abstract concepts the converse pattern of results was observed, with central areas exhibiting relatively fewer neurons shared between pairs of category members. We interpret these results in light of the current knowledge about the relative difficulty children show when learning abstract words. Implications for future neurocomputational modelling experiments as well as neurobiological theories of semantic representation are discussed.