Sequences that influence nucleosome positioning in promoter regions, and their relation to gene regulation, have been the topic of much research over the last decade. In yeast, significant nucleosome-depleted regions are found, which facilitate transcription. With the arrival of nucleosome positioning maps for the human genome, it was discovered that in our genome, unlike in that of yeast, promoters encode for high nucleosome occupancy. In this work, we look at the genomes of a range of different organisms, to provide a catalog of nucleosome positioning signals in promoters across the tree of life. We utilize a computational model of the nucleosome, based on crystallographic analyses of the structure and elasticity of the nucleosome, to predict the nucleosome positioning signals in promoter regions. To be able to apply our model to large genomic datasets, we introduce an approximative scheme that makes use of the limited range of correlations in nucleosomal sequence preferences to create a computationally efficient approximation of the full biophysical model. Our predictions show that a clear distinction between unicellular and multicellular life is visible in the intrinsically encoded nucleosome affinity. Furthermore, the strength of the nucleosome positioning signals correlates with the complexity of the organism. We conclude that encoding for high nucleosome occupancy, as in the human genome, is in fact a universal feature of multicellular life.