By threshold-regulated neural firing and synaptic weight updates in biological neuron–synapse combinations, neural systems can selectively and autonomously encode and process spatiotemporal information. Emulating such an exquisite biological process in electronic devices is a fundamental step toward realizing intelligent neuromorphic systems with self-adaptivity, energy-efficient in-situ edge/parallel computing, and probabilistic inference. Here we report a self-threshold design of prototype artificial axons based on metalloporphyrin, a molecular medium that allows dual electronic/ionic migration in hybrid heterojunction oxide memristors. Threshold behaviors in biological neurons are emulated by introducing metalloporphyrin into alumina-oxide memristors. We show that the memristor achieves smooth, gradual conductive transitions. As a unique feature of such a hybrid system, the endurable current-voltage characteristics of the memristor can be enhanced by altering the metal center to achieve the desired metal–oxygen bonding energy and oxygen migration dynamics. The spike voltage-dependent plasticity is recorded with a positive threshold voltage stemming from the interfacial counterbalance between the vacancy-induced Coulomb force and the external electric field. We further build memristive arrays that directly emulate the self-adaptive and signal-filtering function of the human visual system. These results suggest that the metalloporphyrin platform offers vast opportunities for implementing efficient neural-signal analysis in neuromorphic hardware.