Localized potential well vs binding site: Mapping solute dynamics in a membrane channel onto one-dimensional description.

In the one-dimensional description, the interaction of a solute molecule with the channel wall is characterized by the potential of mean force U(x), where the x-coordinate is measured along the channel axis. When the molecule can reversibly bind to certain amino acid(s) of the protein forming the channel, this results in a localized well in the potential U(x). Alternatively, this binding can be modeled by introducing a discrete localized site, in addition to the continuum of states along x. Although both models may predict identical equilibrium distributions of the coordinate x, there is a fundamental difference between the two: in the first model, the molecule passing through the channel unavoidably visits the potential well, while in the latter, it may traverse the channel without being trapped at the discrete site. Here, we show that when the two models are parameterized to have the same thermodynamic properties, they automatically yield identical translocation probabilities and mean translocation times, yet they predict qualitatively different shapes of the translocation time distribution. Specifically, the potential well model yields a narrower distribution than the model with a discrete site, a difference that can be quantified by the distribution's coefficient of variation. This coefficient turns out to be always smaller than unity in the potential well model, whereas it may exceed unity when a discrete trapping site is present. Analysis of the translocation time distribution beyond its mean thus offers a way to differentiate between distinct translocation mechanisms.