Study of interactions between metal ions and protein model compounds by energy decomposition analyses and the AMOEBA force field

Abstract

The interactions between metal ions and proteins are ubiquitous in biology. The selective binding of metal ions has a variety of regulatory functions. Therefore, there is a need to understand the mechanism of protein-ion binding. The interactions involving metal ions are complicated in nature, where short-range charge-penetration, charge transfer, polarization, and many-body effects all contribute significantly, and a quantitative description of all these interactions is lacking. In addition, it is unclear how well current polarizable force fields can capture these energy terms and whether these polarization models are good enough to describe the many-body effects. In this work, two energy decomposition methods, absolutely localized molecular orbitals and symmetry-adapted perturbation theory, were utilized to study the interactions between Mg/Ca and model compounds for amino acids. Comparison of individual interaction components revealed that while there are significant charge-penetration and charge-transfer effects in Ca complexes, these effects can be captured by the van der Waals (vdW) term in the AMOEBA force field. The electrostatic interaction in Mg complexes is well described by AMOEBA since the charge penetration is small, but the distance-dependent polarization energy is problematic. Many-body effects were shown to be important for protein-ion binding. In the absence of many-body effects, highly charged binding pockets will be over-stabilized, and the pockets will always favor Mg and thus lose selectivity. Therefore, many-body effects must be incorporated in the force field in order to predict the structure and energetics of metalloproteins. Also, the many-body effects of charge transfer in Ca complexes were found to be non-negligible. The absorption of charge-transfer energy into the additive vdW term was a main source of error for the AMOEBA many-body interaction energies.

Many-body effect determines the selectivity for Ca 2+ and Mg 2+ in proteins

“…Due to their computation cost, MD simulations are usually performed with empirical force fields. The large, repulsive many-body energy in Table 1 is not explicitly modeled in additive force fields, while it is included in polarizable force fields since a large portion of the many-body energy comes from polarization (51,52). A comparison between many-body energies from MP2 and the AMOEBA (atomic multipole optimized energetics for biomolecular simulation) force field for several model compounds of protein-metal ion complexes (see SI Appendix, Fig.…”

“…The AMOEBA free energy simulations were performed using the TINKER-OpenMM package (60). The latest AMOEBA parameter was used (51,61,62), which includes modifications detailed in SI Appendix. The parameter file in TINKER format is also included in Dataset S1.…”

Transferable interactions of Li+ and Mg2+ ions in polarizable models

“…In the case of Mg 2+ , we also recalibrate a dimensionless parameter in its polarization term, as done in the development of the original and improved descriptors. [42][43][44] AMEOBA employs a Thole approach 45 to prevent polarization catastrophe, wherein electrostatic interactions are damped in the short range. Damping is applied to only one of the two sites of an interaction pair using ρ = 3a 4π e −ar 3 ij / √ α i α j , where r ij is the distance between two sites with atomic polarizabilities α, and 'a' is a dimensionless width parameter of the damped charge distribution that controls the damping strength.…”

“…34 One approach to improve transferability in MM models is to define cross-terms or separate sets of non-bonded (NB) descriptors for every distinct pair of ion and its coordinating chemical group (ligand). 44,[68][69][70][71][72][73][74] In most applications, [68][69][70][71][72][73][74] the error corrections in this NB-Fix approach are assigned to the Lennard-Jones (LJ) term; however, there is no supporting information of this term being the source of error.…”

Steric “attraction”: not by dispersion alone

“…The resulting attraction between the nuclei of one molecule to the electron density of the other is greater than the electron–electron and nuclei–nuclei repulsion. The crucial role of charge penetration has been demonstrated for a diverse range of chemical systems, including the saturated [ 9 , 28 ] and unsaturated hydrocarbons [ 30 ], nucleic acids [ 31 ], metal ions interacting with proteins [ 32 ], heteroaromatic cores that are the common building blocks for organic semiconductors [ 33 ], cyclophanes [ 34 ], Wilcox torsion balance systems [ 35 ], etc.…”