This paper proposes the direct calculation of the microscopic contributions to the magneto-electric coupling, using ab initio methods. The electrostrictive and the Dzyaloshinskii-Moriya contributions were evaluated individually. For this purpose a specific method was designed, combining density functional theory calculations and embedded fragment, explicitly correlated, quantum chemical calculations. This method allowed us to calculate the evolution of the magnetic couplings as a function of an applied electric field. We found that in YMnO3 the Dzyaloshinskii-Moriya contribution to the magneto-electric effect is three orders of magnitude weaker than the electrostrictive contribution. Strictive effects are thus dominant in the magnetic exchange evolution under an applied electric field, and by extension in the magneto-electric effect. These effects however, remain quite small, and the modifications of the magnetic excitations under an applied electric field will be difficult to observe experimentally. Another important conclusion is that it can be shown that the linear magneto-electric tensor is null due to the inter-layer symmetry operations.