Estimating mutual interactions of genetic networks is mainly to infer the mutual control relationships from multiple genes from the gene expression data. Such correlations are typically expressible in the form of nonlinear simultaneous differential equations. However, most work to date has employed S-systems as an expression of such differential equations, allowing only rough approximations of mass actions, and as such it was difficult to determine the actual correlations between the genes. Instead, we formulate the mutual interactions as actual simultaneous partial differential equations, and automatically determine its structure and coefficients using genetic programming (GP) from a given data series. Parallel implementation of the scheme in a Grid environment using our Jojo Grid programming system for Java has resulted in precise determination of the equations in many cases within some reasonable time.