We propose a trapped-ion quantum simulation protocol for the nuclear spin dynamics of calcium phosphate Posner molecules — hypothetical biological quantum information carriers proposed by Fisher (2015). The protocol exploits three insights: (1) the Zeeman interaction with magnetic fields can be eliminated via a rotating-frame transformation at zero gate cost; (2) J-coupling between phosphorus-31 nuclei (approximately 0.003 to 0.178 Hz) is sufficiently weak to require only two Trotter steps per simulated second; and (3) dipolar relaxation (approximately 90 to 730 Hz) is treated as a Lindblad noise channel rather than Trotterized. A 4-qubit calcium phosphate dimer simulation requires 6 global Molmer-Sorensen gates per simulated second at 96.9 percent circuit fidelity — achievable on current Quantinuum H2 and IonQ Forte platforms. We identify the spin-free substrate as the unifying architectural principle connecting the Kane quantum computer, the Posner molecule, and trapped-ion quantum simulators. We map the full nuclear-to-biochemical readout chain onto the trapped-ion platform, requiring 7 qubits and 13 to 16 two-qubit gates. We analyze the high-field effect and identify five experimental signatures measurable on current hardware. A landscape survey confirms that no trapped-ion group has published on Posner molecule simulation, establishing this as a novel research direction.