The E-cadherin adhesive profile expressed by a tumour is a characterization of the intracellular and intercellular protein interactions that control cell-cell adhesion. Within the intracellular proteins that determine the tumour adhesive profile, Src and PI3 are two essentials to initiate the formation of the E-cadherin adhesion complex. On the other hand, Src has also the capability of disrupting the β-catenin-E-cadherin complex and down-regulating cell-cell adhesion. In this paper, using a multi-scale mathematical model, we study the role of each of these proteins in the adhesive profile and invasive properties of the tumour. To do this, we create three versions of an intracellular model that explains the interplay between the proteins E-cadherin, β-catenin, Src and PI3; and we couple them to the strength of the cell-cell adhesion forces within an individual-cell-based model. The simulation results show how the tumour profile and its aggressive potential may change depending on the intrinsic characteristics of the protein pathways, and how these pathways may influence the early stages of cancer invasion. Our major findings may be summarized as follows. (1) Intermediate levels of Src synthesis rates generate the least invasive tumour phenotype. (2) Conclusions drawn from findings obtained from the intracellular molecular dynamics (here cadherin-catenin binding complexes) to the multi-cellular invasive potential of a tumour may be misleading or erroneous. The conclusions should be validated in a multi-cellular context on timescales relevant for population growth. (3) Monoclonal populations of more cohesive cells with otherwise equal properties tend to grow slower. (4) Less cohesive cells tend to outcompete more cohesive cells. (5) Less cohesive cells have a larger probability of invasion as migration forces can more easily outbalance cohesive forces.