The cuspidine system, La4(Ti2-xGaxO8-x/2)O2 has recently been shown to display significant oxide ion conductivity at elevated temperatures, with evidence for proton conduction at low temperatures in wet atmospheres. In this paper we present a computer modelling study of the La4(Ti2O8)O2 (x=0) end-member. In agreement with experimental studies, the most favourable oxide ion vacancy defect is found at the bridging oxygen position (O3). Oxide ion migration is shown to proceed via a cooperative vacancy migration process with a calculated activation energy of 1.51 eV, in very good agreement with experiment. The computational results for water incorporation suggest that oxygen vacancies are required for water incorporation to occur, which also agrees with experiment, and the most favourable position for the proton is the bridging oxygen (O3).