The ability to learn continuously in artificial neural networks (ANNs) is often limited by catastrophic forgetting, a phenomenon in which new knowledge becomes dominant. By taking mechanisms of memory encoding in neuroscience (aka. engrams) as inspiration, we propose a novel approach that integrates stochastically-activated engrams as a gating mechanism for metaplastic binarized neural networks (mBNNs). This method leverages the computational efficiency of mBNNs combined with the robustness of probabilistic memory traces to mitigate forgetting and maintain the model's reliability. Previously validated metaplastic optimization techniques have been incorporated to enhance synaptic stability further. Compared to baseline binarized models and benchmark fully connected continual learning approaches, our method is the only strategy capable of reaching average accuracies over 20% in class-incremental scenarios and achieving comparable domain-incremental results to full precision state-of-the-art methods. Furthermore, we achieve a significant reduction in peak GPU and RAM usage, under 5% and 20%, respectively. Our findings demonstrate (A) an improved stability vs. plasticity trade-off, (B) a reduced memory intensiveness, and (C) an enhanced performance in binarized architectures. By uniting principles of neuroscience and efficient computing, we offer new insights into the design of scalable and robust deep learning systems.