The ability for artificially reproducing human brain type signals' processing is one of the main challenges in modern information technology, being one of the milestones for developing global communicating networks and artificial intelligence. Electronic devices termed memristors have been proposed as effective artificial synapses able to emulate the plasticity of biological counterparts. Here we report for the first time a single crystalline nanowire based model system capable of combining all memristive functions - non-volatile bipolar memory, multilevel switching, selector and synaptic operations imitating Ca dynamics of biological synapses. Besides underlying common electrochemical fundamentals of biological and artificial redox-based synapses, a detailed analysis of the memristive mechanism revealed the importance of surfaces and interfaces in crystalline materials. Our work demonstrates the realization of self-assembled, self-limited devices feasible for implementation via bottom up approach, as an attractive solution for the ultimate system miniaturization needed for the hardware realization of brain-inspired systems.