A modified Poisson-Boltzmann equation is developed from statistical mechanical considerations to describe the influence of the transmembrane potential on macromolecular systems [1]. Using a Green's function formalism, the electrostatic free energy of a protein associated with the membrane is expressed as the sum of three terms: a contribution from the energy required to charge the system's capacitance, a contribution corresponding to the interaction of the protein charges with the membrane potential, and a contribution corresponding to a voltage-independent reaction field free energy. The membrane potential, which is due to the polarization interface, is calculated in the absence of the protein charges, whereas the reaction field is calculated in the absence of transmembrane potential. Then, a theoretical framework is elaborated to account for the effect of a transmembrane potential in computer simulations with explicit solvent. It is shown that a simulation with a constant external electric field applied in the direction normal to the membrane is equivalent to the influence of surrounding infinite baths maintained to a voltage difference via ion-exchanging electrodes connected to an electromotive force [2]. It is also shown that the linearly-weighted displacement charge within the simulation system tracks the net flow of charge through the external circuit comprising the electromotive force and the electrodes. Using a statistical mechanical reduction of the degrees of freedom of the external system, three distinct theoretical routes are formulated and examined for the purpose of characterizing the free energy of a protein embedded in a membrane that is submitted to a voltage difference. The two methods are compared and applied to the voltage-gated potassium channel. 1. Roux, B. 1997. Influence of the membrane potential on the free energy of an intrinsic protein. Biophysical J. 73:2980-2989. 2. Roux, B. 2008. The membrane potential and its representation by a constant electric field in computer simulations. Biophys J. 95:4205-4216.