It is challenging to parameterize the force field for calcium ions (Ca2+) in calcium-binding proteins because of its unique coordination chemistry that involves  surrounding atoms required for its stability. In this work, we extracted a wide variation of Ca2+ binding loop conformations from Ca2+ binding protein calmodulin (CaM) that adopt the most populated ternary structure types from the MD simulations, followed by ab initio quantum mechanical (QM) calculations on the 12 amino acids from entire loop that coordinate the Ca2+ in aqueous solution. Ca2+ charges are derived by fitting to the ESP in the context of  classical or polarizable force field (PFF). We discover that the atom radius of Ca2+ in conventional force fields is too large for the QM calculation to capture the variation in  coordination geometry of Ca2+ in its ionic form and lead to unphysical charges. Specially, we find that the fitted atomic charges of Ca2+ in the context of PFF depend on the coordinating geometry of electronegative atoms from the amino acids in the loop. Although the nearby water molecules do not influence the atomic charge of Ca2+, they are crucial for compensating  the coordination of Ca2+ due to the conformational flexibility in the EF-hand loop. Our method advances the development of force fields for metal ions and the protein binding sites in dynamical environments.
It is challenging to parameterize the force field for calcium ions (Ca2+) in calcium-binding proteins because of their unique coordination chemistry that involves the surrounding atoms required for stability. In this work, we observed wide variation in Ca2+ binding loop conformations of the Ca2+ -binding protein calmodulin (CaM) , which adopts the most populated ternary structures determined from the MD simulations, followed by ab initio quantum mechanical (QM) calculations on all twelve amino acids in the loop that coordinate Ca2+ in aqueous solution. Ca2+ charges were derived by fitting to the electrostatic potential (ESP) in the context of a classical or polarizable force field (PFF). We discovered that the atomic radius of Ca2+ in conventional force fields is too large for the QM calculation to capture the variation in the coordination geometry of Ca2+ in its ionic form , leading to unphysical charges. Specifically, we found that the fitted atomic charges of Ca2+ in the context of PFF depend on the coordinating geometry of electronegative atoms from the amino acids in the loop. Although nearby water molecules do not influence the atomic charge of Ca2+, they are crucial for compensating for the coordination of Ca2+ due to the conformational flexibility in the EF-hand loop. Our method advances the development of force fields for metal ions and protein binding sites in dynamic environments.
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