Neuromorphic architectures offer great promise for achieving computation capacities beyond conventional Von Neumann machines. The essential elements for achieving this vision are highly scalable synaptic mimics that do not undermine biological fidelity. Here we demonstrate that single solid-state TiO2 memristors can exhibit non-associative plasticity phenomena observed in biological synapses, supported by their metastable memory state transition properties. We show that, contrary to conventional uses of solid-state memory, the existence of rate-limiting volatility is a key feature for capturing short-term synaptic dynamics. We also show how the temporal dynamics of our prototypes can be exploited to implement spatio-temporal computation, demonstrating the memristors full potential for building biophysically realistic neural processing systems.