Biomolecular electrostatics with the linearized Poisson-Boltzmann equation

Electrostatics plays a key role in many biological processes. The Poisson-B oltzmann equation (PBE) and its linearized form (LPBE) allow prediction of electrostatic effects for biomolecular systems. The discrepancies between t he solutions of the PBE and those of the LPBE are well known for systems wi th a simple geometry, but much less for biomolecular systems. Results for h igh charge density systems show that there are limitations to the applicabi lity of the LPBE at low ionic strength and, to a lesser extent, at higher i onic strength. For systems with a simple geometry, the onset of nonlinear e ffects has been shown to be governed by the ratio of the electric field ove r the Debye screening constant. This ratio is used in the present work to c orrect the LPBE results to reproduce fairly accurately those obtained from the PBE for systems with a simple geometry. Since the correction does not i nvolve any geometrical parameter, it can be easily applied to real biomolec ular systems. The error on the potential for the LPBE (compared to the PBE) spans few kT/q for the systems studied here and is greatly reduced by the correction. This allows for a more accurate evaluation of the electrostatic free energy of the systems.