Nonlinear effect of an oscillating electric field on membrane proteins

Abstract

The nonlinear response of a two-state chemical transition to an oscillating electric field is examined. A reaction for which this analysis is particularly relevant is a conformational transition of a membrane protein exposed to an ac electric field. Even a modest externally applied field leads to a very large local field within the membrane. This gives rise to nonlinear behavior. The applied ac field causes harmonics in the polarization and can cause a dc shift in the state occupancy, both of which can be observed and used to determine kinetic parameters. Fourier coefficients are calculated for the enzyme state probability in the ac field, exactly for infinite frequency, and in powers of the field for finite frequency. Kramers–Kronig relations are proved and response functions are given for the leading terms of the harmonics. The results are extended to the spherical symmetry relevant to suspensions of spherical cells, vesicles, or colloidal particles. If the protein catalyzes a reaction, free energy is transduced from the electric field to the output reaction, even if that reaction is electrically silent. Many transport enzymes are ideal examples. The ac field can cause the enzyme to pump ions or molecules through the membrane against an (electro)chemical potential. The efficiency of this energy transduction can be as high as 25%.