Biological neural networks enable rapid communication between cells, which has inspired the development of artificial smart neuro-mimetic systems. In this work, freestanding elastomeric membranes are fabricated with 3D structured holes to induce nonlinear ion-based transport. These 3D microholes are embedded in a soft polymeric membrane via a grayscale lithographical process and demonstrate ionic rectification, negative differential ionic resistance, ionic conductivity gating, and spiking under an applied electric field bias. The ion transport behavior of these membranes is affected by the shape, size, number, and chemical functionalization of the embedded microholes. The microholes are functionalized with responsive poly(N-isopropylacrylamide) polymer brush layers allowing to alter the electric gating behavior by external stimuli that includes temperature and chemical composition of the surrounding environment. The electrically biased membranes with a linear array of eight equidistantly spaced microholes exhibit synchronous gating of ionic transport through each one. These individual microholes are equipped with circumjacent blocking stretchable electrodes to simultaneously measure the exact onset time delay of the spikes during the synchronous gating. The operation of the freestanding elastomeric membranes with embedded microholes mimics the behavior of neural membranes. Membranotronics will pave the way toward bioinspired soft artificial neuro-mimetic systems mechanically and electrochemically comparable to their biological counterpart.