Space versus Context: Competition for limited neural resources determines engram cell allocation in the hippocampus
Engram cells in hippocampal CA1 represent contextual information associated with events experienced by animals and constitute a cellular substrate of episodic memory. Recent experiments have shown that a subset of hippocampal place cells is recruited as engram cells for individual contexts. However, the principle governing engram cell allocation across contexts remains unclear. Here, we develop an information-theoretic framework that quantifies the trade-off between spatial and contextual information encoded by CA1 neurons. Our theory shows that limited neural resources inevitably create competition among contexts for the recruitment of place cells as engram cells. Solving this optimization problem determines the fraction of engram cells allocated to each context as a function of its occurrence probability. The theory predicts a non-monotonic relationship between context probability and engram allocation, reflecting competition between spatial and contextual information under resource constraints. Consequently, the recruited fraction emerges through a discontinuous transition at a critical probability, reaches a maximum at intermediate probabilities, and decreases for highly frequent contexts. Furthermore, we analytically derive the phase boundary for the emergence of finite engram cell allocation as a function of contextual input strength and the relative importance of contextual information. These findings identify competition for limited neural resources as a key determinant of engram cell allocation and provide experimentally testable predictions for how memory representations are distributed across contexts under resource constraints.