在理論和模擬不同種的實驗方法下,水溶液中離子與離子對的水合結構、水合能、分子動態學是一個長期研究且具吸引力的主題，值得一提的是鈣離子在生物系統上扮演極具影響的角色，另一方面在各組研究顯示鈣離子與水的配位的結果是不一致的。早前的古典力場分子模擬研究指出高濃度電解液中會觀察到過多離子簇生成，其原因來自於使用Lorentz-Berthelot combining rule的方法來估算陽離子與陰離子的蘭納-瓊斯作用力，此近似的方法使用在系統預設值來進行分子動態模擬產生陽、陰離子相互作用力是不當的。
此次的研究，我們採用Luo與Roux所提出的方法來改善鈣離子與氯離子及醋酸根上氧原子的蘭納-瓊斯作用參數，有兩組力場參數需要進行優化，第一組為CHARMM預設參數的鈣離子與氯離子以及鈣離子與醋酸根上氧原子的蘭納-瓊斯作用參數(鈣與水形成五角雙錐體)第二組Lim的參數(鈣與水形成四角反稜柱)。基於使用Lim的鈣離子蘭納-瓊斯參數下，來修正鈣離子與氯離子和醋酸根上氧原子的蘭納-瓊斯作用力，我們模擬結果發現優化後的Lim參數可以重現在近乎飽和濃度下的滲透壓實驗值且鈣離子與氯離子蘭納-瓊斯作用參數還能重現大範圍滲透壓的結果，但在CHARMM預設下鈣離子與氯離子和醋酸根上氧原子的蘭納-瓊斯作用參數卻是辦不到的，並且使用Lim的鈣離子與醋酸根上氧原子的蘭納-瓊斯作用參數在鈣結和蛋白質的模擬上不僅可以符合X-ray結構下的結合點位，同時也擁有著可以接受的鈣氧結合距離，再者，使用我們優化後的Lim鈣離子與氯離子/醋酸根上氧原子蘭納-瓊斯作用力的結果還能支持近期鈣離子與水配位為八的結果，且改善方法容易操作在CHARMM與NAMD的軟體中。

Local hydrated structure, molecular dynamics, and hydration energies of ions and ion-pairs in aqueous solution have long been an attractive topic under investigated in terms of various experimental, theoretical, and simulation methods. Especially, Calcium ions (Ca2+) play an important role in mediating and regulating biological systems. Experimental and simulation results regarding the Ca2+H2O coordination number are pretty diverse. Previous studies have shown that the excess ion cluster formation in concentrated electrolyte solutions observed in classical molecular dynamics simulations (MD) is arisen from the improper cation-anion Lennard-Jones (LJ) interacting parameters, approximated by Lorentz-Berthelot combining rule, which are generally default used in MD simulations. In this study, we follow the same methodology proposed by Luo and Roux1 to determine the Ca2+Cl and Ca2+OAcLJ interaction parameter. Two sets of Ca2+ LJ parameters are used for optimization: CHARMM36 and Lim’s parameters. Based on the Lim’s Ca2+ LJ parameters, the Ca2+Cl and Ca2+oxygen atom of OAc LJ interaction parameter are able to be optimized to reproduce experimentally-measured osmotic pressure at nearly saturated concentration, whereas CHARMM36 Ca2+ LJ parameters are not. Using the optimized Ca2+Cl/Ca2+oxygen atom of OAc LJ interaction parameter, the osmotic pressures of CaCl2 solution at a wide range of concentration and the osmotic pressures of Ca(OAc)2 solution at a saturated concentration are well reproduced. Furthermore, it gives a concentration-independent Ca2+H2O coordination number of 8, which is consistent with the recently experimental results. Using our optimized Ca2+oxygen atom of OAc LJ interaction parameters, we are able to reproduce the structure of x-ray crystallographically determined proteinCa2+ binding sites. Our results can be simply implemented in CHARMM and NAMD softwares for further biomolecule simulations.

References
1. Luo, Y.; Roux, B., Simulation of Osmotic Pressure in Concentrated Aqueous Salt Solutions. The Journal of Physical Chemistry Letters 2010, 1 (1), 183-189.
2. Perney, T. M.; Hirning, L. D.; Leeman, S. E.; Miller, R. J., Multiple calcium channels mediate neurotransmitter release from peripheral neurons. Proceedings of the National Academy of Sciences 1986, 83 (17), 6656-6659.
3. Schneggenburger, R.; Neher, E., Presynaptic calcium and control of vesicle fusion. Current opinion in neurobiology 2005, 15 (3), 266-74.
4. Szent-Györgyi, A. G., Calcium regulation of muscle contraction. Biophysical journal 1975, 15 (7), 707-723.
5. Robertson, W. G., Chemistry and biochemistry of Calcium. In In Calciuin in Human Biolog, Nordin, B. E.-C., Ed. Springer-Verlag: London, 1998; pp 1-26.
6. Draper, D. E., RNA Folding: Thermodynamic and Molecular Descriptions of the Roles of Ions. Biophysical journal 2008, 95 (12), 5489-5495.
7. (a) Megyes, T.; Grosz, T.; Radnai, T.; Bako, I.; Palinkas, G., Solvation of calcium ion in polar solvents: An X-ray diffraction and ab initio study. Journal of Physical Chemistry A 2004, 108 (35), 7261-7271; (b) Pham, V. T.; Fulton, J. L., Ion-pairing in aqueous CaCl2 and RbBr solutions: simultaneous structural refinement of XAFS and XRD data. J Chem Phys 2013, 138 (4), 044201.
8. (a) Babu, C. S.; Lim, C., Empirical force fields for biologically active divalent metal cations in water. J Phys Chem A 2006, 110 (2), 691-9; (b) Mundy, M. D. B. a. C. J., Local Aqueous Solvation Structure Around Ca2+ During Ca2+···Cl− Pair Formation. The Journal of Physical Chemistry B 2016; (c) Saxena, A.; Garcia, A. E., Multisite ion model in concentrated solutions of divalent cations (MgCl2 and CaCl2): osmotic pressure calculations. J Phys Chem B 2015, 119 (1), 219-27; (d) Tsai, H. H.; Chang, C. M.; Lee, J. B., Multi-step formation of a hemifusion diaphragm for vesicle fusion revealed by all-atom molecular dynamics simulations. Biochim. Biophys. Acta 2014, 1838 (6), 1529-35; (e) Tsai, H. H.; Juang, W. F.; Chang, C. M.; Hou, T. Y.; Lee, J. B., Molecular mechanism of Ca(2+)-catalyzed fusion of phospholipid micelles. Biochim. Biophys. Acta 2013, 1828 (11), 2729-38; (f) Tsai, H. H.; Lai, W. X.; Lin, H. D.; Lee, J. B.; Juang, W. F.; 40Tseng, W. H., Molecular dynamics simulation of cation-phospholipid clustering in phospholipid bilayers: possible role in stalk formation during membrane fusion. Biochim. Biophys. Acta 2012, 1818 (11), 2742-55.
9. (a) Hewish, N. A.; Neilson, G. W.; Enderby, J. E., Environment of Ca2+ ions in aqueous solvent. Nature 1982, 297 (5862), 138-139; (b) Probst, M. M.; Radnai, T.; Heinzinger, J. K.; Bopp, P.; Rode, B. M., Molecular Dynamics and X-ray Investigation of an Aqueous CaCI, Solution. J. Phys. Chem. 1985, 89, 753-759; (c) Spångberg, D.; Hermansson, K.; Lindqvist-Reis, P.; Jalilehvand, F.; Sandström, M.; Persson, I., Model Extended X-ray Absorption Fine Structure (EXAFS) Spectra from Molecular Dynamics Data for Ca2+ and Al3+ Aqueous Solutions. The Journal of Physical Chemistry B 2000, 104 (45), 10467-10472; (d) Fulton, J. L.; Heald, S. M.; Badyal, Y. S.; Simonson, J., Understanding the effects of concentration on the solvation structure of Ca2+ in aqueous solution. I: The perspective on local structure from EXAFS and XANES. The Journal of Physical Chemistry A 2003, 107 (23), 4688-4696.
10. Ohtaki, H.; Radnai, T., Structure and dynamics of hydrated ions. Chemical Reviews 1993, 93 (3), 1157-1204.
11. Dudev, T.; Lim, C., Principles Governing Mg, Ca, and Zn Binding and Selectivity in Proteins. Chemical Reviews 2003, 103 (3), 773-788.
12. Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M., Charmm - a Program for Macromolecular Energy, Minimization, and Dynamics Calculations. J. Comput. Chem. 1983, 4 (2), 187-217.
13. Weiner, P. K.; Kollman, P. A., Amber - Assisted Model-Building with Energy Refinement - a General Program for Modeling Molecules and Their Interactions. J. Comput. Chem. 1981, 2 (3), 287-303.
14. Scott, W. R. P.; Hünenberger, P. H.; Tironi, I. G.; Mark, A. E.; Billeter, S. R.; Fennen, J.; Torda, A. E.; Huber, T.; Krüger, P.; van Gunsteren, W. F., The GROMOS Biomolecular Simulation Program Package. The Journal of Physical Chemistry A 1999, 103 (19), 3596-3607.
15. Marcus, Y., A simple empirical model describing the thermodynamics of hydration of ions of widely varying charges, sizes, and shapes. Biophysical chemistry 1994, 51, 11-127.
16. Chitra, R.; Smith, P. E., Molecular Association in Solution:  A Kirkwood−Buff Analysis of Sodium Chloride, Ammonium Sulfate, Guanidinium Chloride, Urea, and 2,2,2-Trifluoroethanol in Water. The Journal of Physical Chemistry B 2002, 106 (6), 1491-1500.
17. (a) Chen, A. A.; Pappu, R. V., Parameters of monovalent ions in the AMBER-99 forcefield: assessment of inaccuracies and proposed improvements. J Phys Chem B 2007, 111 (41), 11884-7; (b) Auffinger, P.; Cheatham, T. E.; Vaiana, A. C., Spontaneous Formation of KCl Aggregates in Biomolecular Simulations: A Force Field Issue? J Chem Theory Comput 2007, 3 (5), 1851-9; (c) Yoo, J.; Wilson, J.; Aksimentiev, A., Improved model of hydrated calcium ion for molecular dynamics simulations using classical biomolecular force fields. Biopolymers 2016, 105 (10), 752-63.
18. Kale, L.; Skeel, R.; Bhandarkar, M.; Brunner, R.; Gursoy, A.; Krawetz, N.; Phillips, J.; Shinozaki, A.; Varadarajan, K.; Schulten, K., NAMD2: Greater scalability for parallel molecular dynamics. J. Comp. Phys. 1999, 151 (1), 283-312.
19. Marchand, S.; Roux, B., Molecular dynamics study of calbindin D9k in the apo and singly and doubly calcium-loaded states. Proteins: Structure, Function, and Bioinformatics 1998, 33 (2), 265-284.
20. Saxena, A.; Sept, D., Multisite ion models that improve coordination and free energy calculations in molecular dynamics simulations. J Chem Theory Comput 2013, 9 (8), 3538-3542.
21. Sakharov, D. V.; Lim, C., Force fields including charge transfer and local polarization effects: Application to proteins containing multi/heavy metal ions. J Comput Chem 2009, 30 (2), 191-202.
22. Huang, J.; MacKerell, A. D., Jr., CHARMM36 all-atom additive protein force field: validation based on comparison to NMR data. J Comput Chem 2013, 34 (25), 2135-45.
23. Robinson, R. A.; Stokes, R. H., Electrolyte solutions. Courier Corporation: 2002.
24. Humphrey, W.; Dalke, A.; Schulten, K., VMD: Visual molecular dynamics. J. Mol. Graph. 1996, 14 (1), 33-38.
25. Klauda, J. B.; Venable, R. M.; Freites, J. A.; O'Connor, J. W.; Tobias, D. J.; Mondragon-Ramirez, C.; Vorobyov, I.; MacKerell, A. D.; Pastor, R. W., Update of the CHARMM All-Atom Additive Force Field for Lipids: Validation on Six Lipid Types. J. Phys. Chem. B 2010, 114 (23), 7830-7843.
26. Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L., Comparison of Simple Potential Functions for Simulating Liquid Water. J. Chem. Phys. 1983, 79 (2), 926-935.
27. Feller, S. E.; Zhang, Y. H.; Pastor, R. W.; Brooks, B. R., Constant-Pressure Molecular-Dynamics Simulation - the Langevin Piston Method. J. Chem. Phys. 1995, 103 (11), 4613-4621.
28. Steinbach, P. J.; Brooks, B. R., New Spherical-Cutoff Methods for Long-Range Forces in Macromolecular Simulation. J. Comput. Chem. 1994, 15 (7), 667-683.
29. Ryckaert, J.-P.; Ciccotti, G.; Berendsen, H. J. C., Numerical integration of the cartesian equations of motion of a system with constraints: Molecular dynamics of n-alkanes. J. Comp. Phys. 1977, 23 (3), 327-341.
30. Brooks, B. R.; Brooks, C. L.; Mackerell, A. D.; Nilsson, L.; Petrella, R. J.; Roux, B.; Won, Y.; Archontis, G.; Bartels, C.; Boresch, S.; Caflisch, A.; Caves, L.; Cui, Q.; Dinner, A. R.; Feig, M.; Fischer, S.; Gao, J.; Hodoscek, M.; Im, W.; Kuczera, K.; Lazaridis, T.; Ma, J.; Ovchinnikov, V.; Paci, E.; Pastor, R. W.; Post, C. B.; Pu, J. Z.; Schaefer, M.; Tidor, B.; Venable, R. M.; Woodcock, H. L.; Wu, X.; Yang, W.; York, D. M.; Karplus, M., CHARMM: The biomolecular simulation program. Journal of Computational Chemistry 2009, 30 (10), 1545-1614.
31. (a) Beglov, D.; Roux, B., Finite representation of an infinite bulk system: Solvent boundary potential for computer simulations. The Journal of Chemical Physics 1994, 100 (12), 9050-9063; (b) Roux, B., Valence selectivity of the gramicidin channel: a molecular dynamics free energy perturbation study. Biophysical journal 1996, 71 (6), 3177-3185.
32. Vyas, M. N.; Vyas, N. K.; Quiocho, F. A., Crystallographic Analysis of the Epimeric and Anomeric Specificity of the Periplasmic Transport/Chemosensory Protein Receptor for D-Glucose and D-Galactose. Biochemistry 1994, 33, 4762-8.
33. Yang, Y. H.; Jiang, Y. L.; Zhang, J.; Wang, L.; Bai, X. H.; Zhang, S. J.; Ren, Y. M.; Li, N.; Zhang, Y. H.; Zhang, Z., et al., Structural Insights into Srap-Mediated Staphylococcus Aureus Adhesion to Host Cells. PLoS pathogens 2014, 10, e1004169.
34. Cates, M. S.; Berry, M. B.; Ho, E. L.; Li, Q.; Potter, J. D.; Phillips, G. N., Jr., Metal-Ion Affinity and Specificity in Ef-Hand Proteins: Coordination Geometry and Domain Plasticity in Parvalbumin. Structure 1999, 7, 1269-78.
35. Nagae, M.; Nozawa, A.; Koizumi, N.; Sano, H.; Hashimoto, H.; Sato, M.; Shimizu, T., The Crystal Structure of the Novel Calcium-Binding Protein Atcbl2 from Arabidopsis Thaliana. J Biol Chem 2003, 278, 42240-6.
36. Apelblat, A.; Korin, E., The Vapour Pressures of Saturated Aqueous Solutions of Magnesium, Calcium, Nickel and Zinc Acetates and Molar Enthalpies of Solution of Magnesium, Calcium, Zinc and Lead Acetates. The Journal of Chemical Thermodynamics 2001, 33, 113-120.
37. Muñoz Noval, Á.; Nishio, D.; Kuruma, T.; Hayakawa, S., Coordination and Structure of Ca(Ii)-Acetate Complexes in Aqueous Solution Studied by a Combination of Raman and Xafs Spectroscopies. Journal of Molecular Structure 2018, 1161, 512-518.