Despite substantial research into the biological basis of memory, the precise mechanisms by which experiences are encoded, stored, and retrieved in the brain remain incompletely understood. A growing body of evidence supports the engram theory, which posits that sparse populations of neurons undergo lasting physical and biochemical changes to support long-term memory. Yet, a comprehensive computational framework that integrates biological findings with mechanistic models remains elusive. This work synthesizes insights from cellular neuroscience and computational modeling to address key challenges in engram research: how engram neurons are identified and manipulated; how synaptic plasticity mechanisms contribute to stable memory traces; and how sparsity promotes efficient, interference-resistant representations. Relevant computational approaches -- such as sparse regularization, engram gating, and biologically inspired architectures like Sparse Distributed Memory and spiking neural networks -- are also examined. Together, these findings suggest that memory efficiency, capacity, and stability emerge from the interaction of plasticity and sparsity constraints. By integrating neurobiological and computational perspectives, this paper provides a comprehensive theoretical foundation for engram research and proposes a roadmap for future inquiry into the mechanisms underlying memory, with implications for the diagnosis and treatment of memory-related disorders.

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