Entanglement and coherence in pure and doped Posner molecules

The potential role of spin in biological systems is a primary topic in quantum biology. However, much of this research focuses on electron spin. A recent hypothesis suggests that nuclear spin may be better suited to biological processes, being less sensitive to decoherence. The hypothesis details how phosphorus nuclei might be prepared in a spin entangled state, how this entanglement is protected by assembly into calcium phosphate (Posner) molecules, and how this entanglement might modulate calcium ion production and concomitant neural activation. In this paper we investigate the robustness of quantum effects such as coherence and entanglement in Posner molecules. We investigate how these effects are directly dependent on specific parameters such as spin-spin coupling strengths and Posner molecule symmetry. We also investigate how lithium isotope doped Posner molecules differentially modulate quantum resources such as coherence and entanglement and whether this is a viable explanation for lithium's mechanism of action in bipolar disease. Finally we illustrate how entanglement might possibly be preserved through exploitation of the biological environment.