The emerging Grid infrastructure presents many challenges due to its inherent heterogeneity, multi-domain characteristic, and highly dynamic nature. One critical challenge is providing authentication, authorization and access control guarantees. In this paper, we present the SESAME dynamic context-aware access control mechanism for pervasive Grid applications. SESAME complements current authorization mechanisms to dynamically grant and adapt permissions to users based on their current context. The underling dynamic role based access control (DRBAC) model extends the classic role based access control (RBAC). We also present a prototype implementation of SESAME and DRBAC with the Discover computational collaboratory and an experimental evaluation of its overheads.