Learning in neural networks inspired by brain tissue has been studied for machine learning applications. However, existing works primarily focused on the concept of synaptic weight modulation, and other aspects of neuronal interactions, such as non-synaptic mechanisms, have been neglected. Non-synaptic interaction mechanisms have been shown to play significant roles in the brain, and four classes of these mechanisms can be highlighted: (i) electrotonic coupling; (ii) ephaptic interactions; (iii) electric field effects; and iv) extracellular ionic fluctuations. In this work, we proposed simple rules for learning inspired by recent findings in machine learning adapted to a realistic spiking neural network. We show that the inclusion of non-synaptic interaction mechanisms improves cell assembly convergence. By including extracellular ionic fluctuation represented by the extracellular electrodiffusion in the network, we showed the importance of these mechanisms to improve cell assembly convergence. Additionally, we observed a variety of electrophysiological patterns of neuronal activity, particularly bursting and synchronism when the convergence is improved.