TUPÃ: Electric field analyses for molecular simulations

Abstract

We introduce TUPÃ, a Python-based algorithm to calculate and analyze electric fields in molecular simulations. To demonstrate the features in TUPÃ, we present three test cases in which the orientation and magnitude of the electric field exerted by biomolecules help explain biological phenomena or observed kinetics. As part of TUPÃ, we also provide a PyMOL plugin to help researchers visualize how electric fields are organized within the simulation system. The code is freely available and can be obtained at https://mdpoleto.github.io/tupa/.

Keywords: electric field; electrostatics; force fields; molecular dynamics; molecular mechanics.

Figure 1:

General workflow of TUPÃ and a pseudocode for its basic functions. After the configuration file is parsed, an MDAnalysis universe is built and used to extract atomic positions and charges to calculate $\overrightarrow{E}$ exerted on the probe. The contributions of each residue to $\overrightarrow{E}$ are also calculated.

Figure 2:

Electric field properties exerted by T4 lysozyme. A) Benzene ligand (carbon in orange) bound to T4 lysozyme. B) Time series of $\overrightarrow{E}$ sensed by benzene at its COM. C) Direction of $\overrightarrow{E}$ at the benzene COM (solid cyan vector) and at each benzene carbon atom (translucent cyan vectors). Oxygen lone pairs are shown in green spheres. D) Contribution of each T4 lysozyme residue to the total $\overrightarrow{E}$.

Figure 3:

Electric field properties of KSI electric field exerted at 19NT carbonyl bond. A) Time series of $\overrightarrow{E}$ (cyan), ${\overrightarrow{E}}_{\mathit{\text{proj}}}$ (dark turquoise) and their alignment percentage (red). B) Alignment percentage of electric fields exerted by each KSI residue and the 19NT carbonyl bond axis. Tyr16, Asp40, and Asp103 participate in KSI catalysis.

Figure 4:

Binding mode of 19NT in KSI active site. A) Tyr16 and Asp103 interact with the carbonyl oxygen of 19NT, positioning the substrate-like inhibitor within the active site. B) Electric field exerted by KSI on the carbonyl bond. The C=O bond axis is shown in translucent gray, $\overrightarrow{E}$ in solid cyan, and ${\overrightarrow{E}}_{\mathit{\text{proj}}}$ in translucent dark turquoise.

Figure 5:

Electric field properties of NaK2K ion channel. A) ${\overrightarrow{E}}_{PMz}$ throughout the ion channel as depicted in panel B. Negative values represent a vector pointing downward, while positive values represent a vector pointing upward. B) ${\overrightarrow{E}}_{PMz}$ orientation throughout the ion channel core. Coordinated K⁺ ions K1 to K4 are shown as translucent magenta spheres. C) ${\overrightarrow{E}}_{\mathit{\text{PMKz}}}$ distribution exerted on coordinated K⁺. Full lines represent ${\overrightarrow{E}}_{\mathit{\text{PMKz}}}$ when accounting for the contribution of protein, membrane, and other coordinated ions. Dashed lines represent ${\overrightarrow{E}}_{PKz}$, the electric field without the membrane contribution.

Figure 6:

Electric fields of the T4 lysozyme system. A) Electric field magnitudes (in black) and the respective environment size (in red) as a function of environment radial composition. Standard deviations shown as bars. B) Variation of the environment set with the standard deviation explicitly shown.