paper.md

title	tags	authors	affiliations	date	bibliography
ELECTRIC: Electric fields Leveraged from multipole Expansion Calculations in Tinker Rapid Interface Code	Tinker molecular dynamics polarizable force fields electric fields	name orcid affiliation Jessica Nash 0000-0003-1967-5094 1, 2 name orcid affiliation Taylor Barnes 0000-0001-9396-1094 1, 2 name orcid affiliation Valerie Vaissier Welborn^[Corresponding author] 0000-0003-0834-4441 2	name index The Molecular Sciences Software Institute, 1880 Pratt Drive, Suite 1100, Blacksburg, VA 24060 1 name index Department of Chemistry, Davidson Hall, Virginia Tech, 1040 Drillfield Drive, Blacksburg, VA 24061 2	July 1, 2020	paper.bib

Summary

Polarizable force fields have changed the landscape of biomolecular simulation, mostly by featuring improved electrostatic potential energy terms [@doi:10.1146/annurev-biophys-070317-033349]. These novel energy functions allow environment-driven changes in charge distribution, which yield simulations with improved geometries and molecular properties. In particular, the AMOEBA polarizable force field exhibits two fundamental changes compared to more traditional fixed charge force fields [@doi:10.1021/ct4003702; @doi:10.1021/acs.jctc.7b01169]. The first one relates to permanent electrostatics, expressed in AMOEBA in terms of atomic multipoles (truncated at quadrupoles) that account for anisotropy in the computed charge distributions. The second one represents polarizability through an induced dipole term that can respond to the chemical environment. These modified terms make the AMOEBA force field more physically grounded than other force fields and is the basis for more realistic simulations of biomolecular systems.

Improved electrostatics with AMOEBA give a unique opportunity to accurately compute electric fields, powerful metrics of catalytic activity in enzymes and other systems [@doi:10.1021/jacs.6b12265; @doi:10.1021/acscatal.7b03151; @natcat]. Electric fields projected onto specific bonds report on the effect of the surroundings (interacting via coulombic interactions, solvent effects, hydrogen bonding or other forces, all mostly electrostatic in nature) on the flow of electrons along these bonds. Therefore, projected electric fields are correlated to the probability of breaking these bonds, making them a useful probe of chemical reactivity.

ELECTRIC [@electric] is a MolSSI Driver Interface (MDI) [@mdi_repo; @barnes_taylor_arnold_2020_3659285] driver that utilizes Tinker [@doi:10.1021/acs.jctc.8b00529] to analyze specific components of electric fields that are modeled using the AMOEBA force field. ELECTRIC parses Tinker trajectories and orchestrates additional Tinker calculations in order to project components of the electric fields onto user-defined bonds (specified by two atoms). It outputs the field in MV/cm, which is the sum of the direct field (from permanent electrostatics) and the induced field (from the induce dipole term), projected onto the bond unit vector (i.e., normalized by the bond length). ELECTRIC enables splitting of the total field into contributions from different components of the system, by molecules or by residues as specified in a reference PDB file. In summary, ELECTRIC was designed to expand quantitative system characterization via the computation of electric fields with user-friendly processing tools of Tinker-AMOEBA simulations.

In practice, the user needs a Tinker trajectory file (i.e., filename.arc), a Tinker input file (i.e., tinker.key) stripped from any keywords corresponding to periodic boundary conditions and a Tinker reference snapshot (filename.xyz - this can be the first frame in filename.arc) where the dimensions of the box, usually printed on line 2, has been deleted. Tinker is then launched as an MDI engine before the ELECTRIC driver. Options regarding the electric fields calculations, such as probe index number, number of frames at the beginning of the trajectory file to skip (equilibration procedure), reference PDB file, etc. are specified as command line arguments when launching the driver. A complete usage procedure is provided in the README file.

Statement of Need

Since electric fields assist the motion of charges such as ions or electrons, they can link structure to function in molecular dynamics simulations. By taking advantage of their additivity property, we can decompose the total electric field into contributions from each system component (protein residues, solvent molecules, etc.). While this approach has already been used to probe electron flow along the bonds that break and form during a catalyzed reaction [@doi:10.1021/jacs.6b12265; @doi:10.1021/acscatal.7b03151], its applicability reaches many other research areas as it can also be used to probe ion transport or electron reorganization upon molecular binding, for example.

Mathematics

The electric field at atom $i$, $\vec{E}^i$, has components defined as: \begin{equation} E^i_x=\sum_jE^{j\to i}x =\sum_j\left( E^{j\to i}{x,\text{perm}} +E^{j\to i}_{x,\text{ind}} \right) \end{equation} where $E^i_x$ is the $x$-component of the electric field on atom $i$, $E^{j\to i}_x$ is the $x$-component of the electric field on atom $i$ due to atom $j$ and "perm" and "ind" refer to permanent and induced fields, respectively.

Each atom $i$ is characterized by permanent atomic multipoles, including a monopole (charge) $q^i$, a dipole ${\mu^i_x,\mu^i_y,\mu^i_z}$ and a quadrupole ${Q^i_{xx}, Q^i_{xx},Q^i_{xy},Q^i_{xz}...Q^i_{zz}}$, such that \begin{equation} E^{j\to i}{x,\text{perm}}=-T_xq^j+\sum{m=y,z}T_{xm}\mu^j_m-\frac{1}{3}\sum_{m=y,z}\sum_{n=y,z}T_{xmn}Q^j_{mn}, \end{equation} and \begin{equation} E^{j\to i}{x,\text{ind}}=\sum{m=y,z}=T_{xm}\mu^j_{\text{ind},m}, \end{equation} where \begin{equation} T_{xy...}=\frac{1}{4\pi\epsilon_0}\nabla_x\nabla_y...\frac{1}{r_{ij}}, \end{equation} as also defined in @doi:10.1021/jacs.6b12265.

Similar equations can be written for the $y$- and $z$-components of the field. The field projected onto a specific bond, say bond $ij$ between atoms $i$ and $j$, is then calculated as:
\begin{equation} E^{ij}\text{proj}=\left( \frac{\vec{E}^i+\vec{E}^j}{2}\right).\vec{u}^{ij}, \end{equation} where $E^{ij}\text{proj}$ is the electric field projected onto bond $ij$ and $\vec{u}^{ij}$ the unitary vector defining bond $ij$.

Acknowledgements

The authors thank Yi Zheng for producing AMOEBA Tinker trajectories to test ELECTRIC and the Virginia Tech Department Faculty Start-up Funds for financial support.

References