Protein Dielectrophoresis in Solution

Proteins experience either pulling or repelling force from the gradient of an external electric field due to the effect known as dielectrophoresis (DEP). The susceptibility to the field gradient is traditionally calculated from the solution of the electrostatic boundary-value problem, which requires assigning a dielectric constant to the protein. This assignment is essential since the DEP susceptibility is proportional, in dielectric theories, to the Clausius-Mossotti factor, the sign of which is controlled by whether the protein dielectric constant is below (repelling) or above (pulling) the dielectric constant of water. The dielectric constant is not uniquely or even well-defined for a particle of molecular size and the Clausius-Mossotti factor is shown here to be inadequate for describing the dipolar response of the protein and hydration water. An alternative theory is developed from the standpoint of molecular properties of the protein solute and water solvent. The effective polarity of the protein molecule enters the theory in terms of the variance of its molecular dipole moment and its refractive index. Molecular dynamics (MD) simulations of the protein cytochrome c in solution are performed to calculate the dipolar susceptibilities entering the theory. We find that tumbling of the protein on the nanosecond time scale results in a positive DEP (pulling). The DEP susceptibility for cytochrome c acquired from MD simulations is 10³-10⁴ times higher than predicted by the Clausius-Mossotti factor. Nevertheless, this high DEP susceptibility is fully consistent with empirically confirmed Oncley's equation connecting the protein dipole to dielectric increments of protein solutions. For cytochrome c, high DEP susceptibilities calculated from MD are consistent with experimental dielectric data. We provide a general relation connecting the DEP susceptibility to the dielectric increment of solution.