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The concept of topology-aware grid applications is derived from parallelized computational models of complex systems that are executed on heterogeneous resources, either because they require specialized hardware for certain calculations, or because their parallelization is flexible enough to exploit such resources. Here we describe two such applications, a multi-body simulation of stellar evolution, and an evolutionary algorithm that is used for reverse-engineering gene regulatory networks. We then describe the topology-aware middleware we have developed to facilitate the "modeling-implementing-executing" cycle of complex systems applications. The developed middleware allows topology-aware simulations to run on geographically distributed clusters with or without firewalls between them. Additionally, we describe advanced coallocation and scheduling techniques that take into account the applications topologies. Results are given based on running the topology-aware applications on the Grid'5000 infrastructure.