Protein response to external electric fields: Relaxation, hysteresis, and echo

Dipole moments induced in proteins by external electric fields are studied by molecular dynamics simulations and described in terms of analytical models based on ensembles of Langevin oscillators and Fokker-Planck equations. We investigate through simulations of the protein bovine pancreatic trypsin inhibitor (BPTI) (1) the distribution p(M) of dipole moments as well as the dipole moment autocorrelation function C_M,M(t) at thermal equilibrium, (2) the dielectric constant ∈, (3) the dipole moment ΔM(t) induced by cyclic (piecewise linear or sinusoidally periodic in time) spatially homogeneous fields, demonstrating significant hysteresis behavior, and (4) the dipolar response to a constant homogeneous field applied for about a picosecond. Through a comparison between an analytical model and simulations, we show that the dipolar response (4) can be described by a relaxation characterized by V_M,M(t) in addition to a significant pulse-shaped component, termed the dipole echo. The dipole echo arises from a memory effect of transient increases or decreases of protein vibrational frequencies induced by an external field. The hysteresis behavior (3) under a weak external field is related to the equilibrium properties p(M), C_M,M(t), and ∈; however, discrete structural transitions induced by a strong field also contribute to hysteresis, as demonstrated in a model evoking stochastic motion in a periodically driven bistable potential. In the case of electric fields arising through charge displacements in proteins, e.g., through electronic excitation or photoinduced electron transfer, concomitant dipolar responses in real proteins should resemble those reported here and should be observable by means of sub-picosecond spectroscopy.