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Biophys J, May 2000, p. 2349-2363, Vol. 78, No. 5
Boltzmann Theory versus Brownian Dynamics
and
*Protein Dynamics Unit, Department of Chemistry, and
Department of Theoretical Physics, Research School of
Physical Sciences, Australian National University, Canberra, Australian
Capital Territory 0200, Australia
Continuum theories of electrolytes are widely used to
describe physical processes in various biological systems. Although these are well-established theories in macroscopic situations, it is
not clear from the outset that they should work in small systems whose
dimensions are comparable to or smaller than the Debye length. Here, we
test the validity of the mean-field approximation in Poisson
Boltzmann
theory by comparing its predictions with those of Brownian dynamics
simulations. For this purpose we use spherical and cylindrical
boundaries and a catenary shape similar to that of the acetylcholine
receptor channel. The interior region filled with electrolyte is
assumed to have a high dielectric constant, and the exterior region
representing protein a low one. Comparisons of the force on a test ion
obtained with the two methods show that the shielding effect due to
counterions is overestimated in PoissonBoltzmann theory when the ion
is within a Debye length of the boundary. As the ion gets closer to the
boundary, the discrepancy in force grows rapidly. The implication for
membrane channels, whose radii are typically smaller than the Debye
length, is that PoissonBoltzmann theory cannot be used to obtain
reliable estimates of the electrostatic potential energy and force on
an ion in the channel environment.
Biophys J, May 2000, p. 2349-2363, Vol. 78, No. 5
© 2000 by the Biophysical Society 0006-3495/00/05/2349/15 $2.00
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