The important research advances, in many scientific areas, have been fostered by an improvement of the computational strategies employed. As an example, High Performance Computing enables the collaborative usage of multiple processors to accelerate the resolution of scientific problems, and even to face large problems.

However, there are several scientific applications whose computational requirements can exceed the computing capacities of a single organisation. This way, the recent advances in the bandwidth of the communication networks have leveraged the idea of joining geographically distributed resources, creating a global computing infrastructure known as the Grid.

This thesis combines High Performance Computing and Grid Computing in order to accelerate the execution of scientific applications, and to allow solving problems that can not be solved, in a reasonable time, with the resources of a single organisation.

For that purpose, a system that offers an abstraction layer to simplify the execution of general scientific applications, in Grid infrastructures, has been developed. This system, called GMarte, provides metascheduling functionality for the concurrent execution of parallel applications on resources based on the Globus Toolkit, the standard software in computational Grids. Later, and according to the current trend towards service-oriented architectures, a metascheduler Grid service has been created, featuring interoperability and based on standard technologies. This Grid service offers metascheduling functionality to multiple clients, which use high-level graphical applications to interact with it, using security mechanisms for data protection. This way, it is possible to simplify and foster the usage of Grid technologies for the efficient execution of scientific applications.

The proposed computational approach has been applied to two biomedical applications: the cardiac electrical activity simulation and the protein design with targeted properties. First of all, a parallel simulation system of the action potential propagation on cardiac tissues has been developed. Secondly, an efficient system has been implemented for the design of proteins. In both cases, the usage of High Performance Computing has enabled to accelerate the executions as well as to face larger dimension problems.

Finally, executions of both applications have been performed over different Grid deployments, in order to evaluate the advantages of a strategy that combines both computationally advanced techniques.