The Intrinsic Radius as a Key Parameter in the Generalized Born Model to Adjust Protein-Protein Electrostatic Interaction.

The generalized Born (GB) model is an extension of the continuum dielectric theory of Born solvation energy and is a powerful method for accelerating the molecular dynamic (MD) simulations of charged biological molecules in water. While the effective dielectric constant of water that varies as a function of the separation distance between solute molecules is incorporated into the GB model, adjustment of the parameters is indispensable for accurate calculation of the Coulomb (electrostatic) energy. One of the key parameters is the lower limit of the spatial integral of the energy density of the electric field around a charged atom, known as the intrinsic radius ρ. Although ad hoc adjustment of ρ has been conducted to improve the Coulombic (ionic) bond stability, the physical mechanism by which ρ affects the Coulomb energy remains unclear. Via energetic analysis of three differently sized systems, here, we clarify that the Coulomb bond stability increases with increasing ρ and that the increased stability is caused by the interaction energy term, not by the self-energy (desolvation energy) term, as was supposed previously. Our results suggest that the use of larger values for the intrinsic radii of hydrogen and oxygen atoms, together with the use of a relatively small value for the spatial integration cutoff in the GB model, can better reproduce the Coulombic attraction between protein molecules.

Coulombic Organization in Membrane-Embedded Rotary Motor of ATP Synthase.

The electrochemical potential difference of protons across the membrane is used to synthesize ATP through the proton-motive rotatory motion of the membrane-embedded region of ATP synthase called Fo. In this study, we illuminate the unsolved proton-motive rotary mechanism of Fo on the basis of atomistic simulation with full description of protein, lipid, and water molecules, and highlight the underlying Coulombic design. We first show that a water channel is spontaneously formed at the interfacial region between the rotor (c-ring) and the stator (a-subunit). The observed water channel is a full channel penetrating the membrane, but a Coulomb barrier by a strictly conserved arginine of the a-subunit dominates at the midpoint of the full channel, preventing proton leakage. Our molecular dynamics simulation further demonstrates that the Coulomb attraction between the arginine and the essential glutamic acid of the c-subunit drives the c-ring rotation. We finally illustrate that the charge-state changes of the glutamic acids, enabled by the electrochemical potential difference of proton and the thermal motion, can produce unidirectional rotation of the c-ring.

Torque generation mechanism in Fo motor of ATP synthase elucidated by free-energy and Coulomb-energy landscapes along the c-ring rotation.

Fo portion of ATP synthase is a proton-motive rotary motor. The Coulombic attraction between the conserved acidic residues in the c-ring and the arginine in the a-subunit (aR) was early proposed to drive the c-ring rotation relative to the a-subunit, and has been actually observed in our previous molecular dynamics simulation with full atomistic description of Fo embedded in the membrane. In this study, to quantify the driving force, we conducted the umbrella sampling (US) and obtained the free-energy landscape for the c-ring rotation. We first show that the free-energy gradient toward the ATP-synthesis direction appears in the deprotonated state of cE. Using the sampled snapshots that cover a wide range of the rotational angle, we further analyzed the rotational-angle dependence of the hydration and the protonation states and obtained the Coulomb-energy landscapes with a focus on the cE-aR interaction. The results indicate that both the Coulombic solvation energy of cE and the interaction energy between cE and aR contribute to the torque generation for the c-ring rotation.

Over-Destabilization of Protein-Protein Interaction in Generalized Born Model and Utility of Energy Density Integration Cutoff.

The generalize Born (GB) model is frequently used in MD simulations of biomolecular systems in aqueous solution. The GB model is usually based on the so-called Coulomb field approximation (CFA) for the energy density integration. In this study, we report that the GB model with CFA overdestabilizes the long-range electrostatic attraction between oppositely charged molecules (ionic bond forming two-helix system and kinesin-tubulin system) when the energy density integration cutoff, rmax, which is used to calculate the Born energy, is set to a large value. We show that employing large rmax, which is usually expected to make simulation results more accurate, worsens the accuracy so that the attraction is changed into repulsion. It is demonstrated that the overdestabilization is caused by the overestimation of the desolvation penalty upon binding that originates from CFA. We point out that the overdestabilization can be corrected by employing a relatively small cutoff (rmax = 10-15 Å), affirming that the GB models, even with CFA, can be used as a powerful tool to theoretically study the protein-protein interaction, particularly on its dynamical aspect, such as binding and unbinding.