Stochastic Dynamics of Electrical Membrane with Voltage-Dependent Ion Channel Fluctuations

Brownian ratchet like stochastic theory for the electrochemical membrane system of Hodgkin-Huxley (HH) is developed. The system is characterized by a continuous variable $Q_m(t)$, representing mobile membrane charge density, and a discrete variable $K_t$ representing ion channel conformational dynamics. A Nernst-Planck-Nyquist-Johnson type equilibrium is obtained when multiple conducting ions have a common reversal potential. Detailed balance yields a previously unknown relation between the channel switching rates and membrane capacitance, bypassing Eyring-type explicit treatment of gating charge kinetics. From a molecular structural standpoint, membrane charge $Q_m$ is a more natural dynamic variable than potential $V_m$; our formalism treats $Q_m$-dependent conformational transition rates $\lambda_{ij}$ as intrinsic parameters. Therefore in principle, $\lambda_{ij}$ vs. $V_m$ is experimental protocol dependent,e.g., different from voltage or charge clamping measurements. For constant membrane capacitance per unit area $C_m$ and neglecting membrane potential induced by gating charges, $V_m=Q_m/C_m$, and HH's formalism is recovered. The presence of two types of ions, with different channels and reversal potentials, gives rise to a nonequilibrium steady state with positive entropy production $e_p$. For rapidly fluctuating channels, an expression for $e_p$ is obtained.Comment: 8 pages, two figure

Valley contrasting chiral phonons in monolayer hexagonal lattices

In monolayer hexagonal lattices, two inequivalent valleys appear in the Brillouin zone. With inversion symmetry breaking, we find chiral phonons with valley contrasting circular polarization and ionic magnetic moment. At valley centers, there is a three-fold rotational symmetry endowing phonons with a quantized pseudo angular momentum, which includes spin and orbital parts. From conservation of the pseudo angular momentum, crystal momentum and energy, selection rules in intervalley scattering of electrons by phonons are obtained. The chiral valley phonons are verified and the selection rules are predicted in monolayer Molybdenum disulfide. Due to valley contrasting phonon Berry curvature, one can also detect a valley phonon Hall effect. The valley-contrasting chiral phonon, together with phonon circular polarization, ionic magnetic moment, phonon pseudo angular momentum, valley phonon Hall effect, will form the basis for valley-based electronics and phononics applications in the future