This paper presents membrane systems as an appropriate model for distributed computing, an efficient and natural environment to present the fundamental distributed algorithms. We support the idea that P systems can become a primary model for distributed computing, particularly for message-passing algorithms. We present the core theory, the fundamental algorithms and problems in distributed computing. We focus on an example describing an immune response system against virus attacks. The example is implemented using a P system library created by the authors to simulate the main functions of a P system, and an MPI program that takes advantage of the highly parallel features provided by the model. The program uses distributed leader election and synchronization algorithms.