Simulation of pH-Dependent Conformational Transitions in Membrane Proteins: The CLC-ec1 Cl-/H+ Antiporter.

Intracellular transport of chloride by members of the CLC transporter family involves a coupled exchange between a Cl- anion and a proton (H+), which makes the transport function dependent on ambient pH. Transport activity peaks at pH 4.5 and stalls at neutral pH. However, a structure of the WT protein at acidic pH is not available, making it difficult to assess the global conformational rearrangements that support a pH-dependent gating mechanism. To enable modeling of the CLC-ec1 dimer at acidic pH, we have applied molecular dynamics simulations (MD) featuring a new force field modification scheme-termed an Equilibrium constant pH approach (ECpH). The ECpH method utilizes linear interpolation between the force field parameters of protonated and deprotonated states of titratable residues to achieve a representation of pH-dependence in a narrow range of physiological pH values. Simulations of the CLC-ec1 dimer at neutral and acidic pH comparing ECpH-MD to canonical MD, in which the pH-dependent protonation is represented by a binary scheme, substantiates the better agreement of the conformational changes and the final model with experimental data from NMR, cross-link and AFM studies, and reveals structural elements that support the gate-opening at pH 4.5, including the key glutamates Gluin and Gluex.

A derivation of Maxwell's equations using the Heaviside notation.

Maxwell's four differential equations describing electromagnetism are among the most famous equations in science. Feynman said that they provide four of the seven fundamental laws of classical physics. In this paper, we derive Maxwell's equations using a well-established approach for deriving time-dependent differential equations from static laws. The derivation uses the standard Heaviside notation. It assumes conservation of charge and that Coulomb's law of electrostatics and Ampere's law of magnetostatics are both correct as a function of time when they are limited to describing a local system. It is analogous to deriving the differential equation of motion for sound, assuming conservation of mass, Newton's second law of motion and that Hooke's static law of elasticity holds for a system in local equilibrium. This work demonstrates that it is the conservation of charge that couples time-varying E -fields and B -fields and that Faraday's Law can be derived without any relativistic assumptions about Lorentz invariance. It also widens the choice of axioms, or starting points, for understanding electromagnetism.This article is part of the theme issue 'Celebrating 125 years of Oliver Heaviside's 'Electromagnetic Theory''.