The interoperability of e-Science infrastructures like DEISA/PRACE and EGEE/EGI is an increasing demand for a wide variety of cross-Grid applications (EUFORIA, VPH, WISDOM, etc.), but interoperability based on common open standards adopted by Grid middleware is only starting to emerge and is not broadly provided today. In earlier work, we have shown how refined open standards form a reference model, which is based on careful academic analysis of lessons learned obtained from production cross-Grid applications that require access to both, High Throughput Computing (HTC) resources as well as High Performance Computing (HPC) resources. This paper provides insights in several concepts of this reference model with a particular focus on realizing interoperability with the so-called plumbings approach in order to satisfy the different security demands of e-scientists and their cross-Grid applications today and in future. Based on lessons learned over years gained with production interoperability setups and experimental interoperability work between production Grids like EGEE, DEISA, and NorduGrid, we illustrate how open Grid standards (e.g. OGSA-BES, JSDL, GLUE2, and SAML) jointly together with the plumbings concept contribute to the desired vision of a network of interoperable Grid services.