38In the crowded cell, a strong selective pressure operates on the proteome to limit the 39 competition between functional and non-functional protein-protein interactions. We 40 developed an original theoretical framework in order to interrogate how this competition 41 constrains the behavior of proteins with respect to their partners or random encounters. Our 42 theoretical framework relies on a two-dimensional (2D) representation of interaction energy 43 landscapes with 2D energy maps that reflect in a synthetic way the propensity of a protein to 44 interact with another protein. We investigated the propensity of protein surfaces to interact 45 with functional and arbitrary partners and asked whether their interaction propensity is 46 conserved during the evolution. Therefore, we performed several thousands of cross-docking 47 behavior of a protein in interaction with hundreds of selected partners and opens the way for 56 further developments to study the behavior of proteins in a specific environment. 57 58 Biomolecular interactions are central for many physiological processes and are of utmost 59 importance for the functioning of the cell. Particularly protein-protein interactions have 60 attracted a wealth of studies these last decades [1-5]. The concentration of proteins in a cell 61 has been estimated to be approximately 2-4 million proteins per cubic micron [6]. In such a 62 highly crowded environment, proteins constantly encounter each other and numerous non-63 specific interactions are likely to occur [7-10]. For example, in the cytosol of S. cerevisiae a 64 protein can encounter up to 2000 different proteins [11]. In this complex jigsaw puzzle, each 65protein has evolved to bind the right piece(s) in the right way (positive design) and to prevent 66 misassembly and non-functional interactions (negative design) [12][13][14][15][16]). 67Consequently, positive design constrains the physico-chemical properties and the evolution of 68 protein-protein interfaces. Indeed, a strong selection pressure operates on binding sites to 69 maintain the functional assembly including the functional partner and the functional binding 70 mode. For example, homologs sharing at least 30% sequence identity almost invariably 71 interact in the same way [17]. Conversely, negative design prevents proteins to be trapped in 72 the numerous competing non-functional interactions inherent to the crowded environment of 73 the cell. Many studies were reported on the relationship between the propensity of proteins for 74 promiscuous interactions and their abundances or surface properties [18][19][20][21]. Particularly, it 75 has been shown that the misinteraction avoidance shapes the evolution and physico-chemical 76properties of abundant proteins, resulting in a slower evolution and less sticky surfaces than 77 what is observed for less abundant ones [18,[22][23][24][25][26]. The whole surface of abundant proteins 78 is thus constrained, preventing them to engage deleterious non-specific interactions that could 79 be of dramatic impac...