Storing long-lived memories via molecular error correction: a minimal mathematical model of Cricks memory switch

Cells store information in part by attaching molecular marks to proteins and DNA. But because marks can be randomly removed (e.g., due to ambient phosphatase activity) and added (e.g., due to ambient kinase activity), information encoding may be poor, and in the worst case marks may only store information on the time scale of molecular turnover. We identify a high-level strategy cells use to maintain encoding fidelity beyond the time scale of turnover-- which we call molecular error correction--and find that it closely resembles an underexplored theoretical proposal by Francis Crick. To assess the effectiveness of molecular error correction, we construct and analyze several minimal mathematical models of molecular memory switches. We find that Crick-like error correction provides an efficient way to improve the lifetime of stored memories, especially compared to redundantly encoding information using a large number of molecules, but that it can yield false positives (and hence low information fidelity) when there is ambient marking activity; given these two competing concerns, the optimal level of error correction is moderate rather than arbitrarily high. We also find that combining error correction with redundant encoding can efficiently and robustly produce memories that last between ten and one hundred times longer than the turnover time scale. Our work provides insight regarding how to model and interrogate noisy molecular memory systems, and suggests that error correction is a design principle of performant molecular memory.