Rapid increase of data volume from the experiments running at the Large Hadron Collider (LHC) prompted physics computing community to evaluate new data handling and processing solutions. Russian grid sites and universities' clusters scattered over a large area aim at the task of uniting their resources for future productive work, at the same time giving an opportunity to support large physics collaborations. In our project we address the fundamental problem of designing a computing architecture to integrate distributed storage resources for LHC experiments and other data-intensive science applications and to provide access to data from heterogeneous computing facilities. Studies include development and implementation of federated data storage prototype for Worldwide LHC Computing Grid (WLCG) centres of different levels and University clusters within one National Cloud. The prototype is based on computing resources located in Moscow, Dubna, Saint Petersburg, Gatchina and Geneva. This project intends to implement a federated distributed storage for all kind of operations such as read/write/transfer and access via WAN from Grid centres, university clusters, supercomputers, academic and commercial clouds. The efficiency and performance of the system are demonstrated using synthetic and experiment-specific tests including real data processing and analysis workflows from ATLAS and ALICE experiments, as well as compute-intensive bioinformatics applications (PALEOMIX) running on supercomputers. We present topology and architecture of the designed system, report performance and statistics for different access patterns and show how federated data storage can be used efficiently by physicists and biologists. We also describe how sharing data on a widely distributed storage system can lead to a new computing model and reformations of computing style, for instance how bioinformatics program running on supercomputers can read/write data from the federated storage.