The two volumes, LNCS 6686 resp. LNCS 6687, constitute the refereed proceedings of the 4th International Work-Conference on the Interplay between Natural and Artificial Computation, IWINAC 2011, held in La Palma, Canary Islands, Spain, in May/June 2011. The 108 revised full papers presented in LNCS 6686 resp. LNCS 6687 were carefully reviewed and selected from numerous submissions. The first part, LNCS 6686, entitled "e;Foundations on Natural and Artificial Computation"e;, includes all the contributions mainly related to the methodological, conceptual, formal, and experimental developments in the fields of neurophysiology and cognitive science. The second part, LNCS 6687, entitled "e;New Challenges on Bioinspired Applications"e;, contains the papers related to bioinspired programming strategies and all the contributions related to the computational solutions to engineering problems in different application domains, specially Health applications, including the CYTED ``Artificial and Natural Computation for Health'' (CANS) research network papers.