Forcing substrates through channels

Living cells are defined in part by the possession of a membrane barrier surrounding their perimeter, thereby delineating the border between the inside and the outside. The existence of this barrier, as well as the proteins that mediate exchange of ions and other substrates across it, leads immediately to the question of how transport across the membrane, whether it be active or passive, is achieved and, in particular, how its done selectively. Although some common mechanisms exist, each protein has evolved specific features to optimally transport its particular substrate. The transport process is characterized typically by a substrate pathway along with associated conformational changes in the protein. These changes are often small or even non-existent for passive channels, but can be quite large for active transporters. The substrate pathway can also be characterized by the substrate's free energy along it, known as the potential of mean force (PMF), which dictates the speed of transport and the selectivity. While X-ray crystallography and other experimental structural techniques can provide snapshots of membrane proteins, even in multiple states, they cannot display the dynamics connecting those states. Computational methods, namely molecular dynamics (MD) simulations, provide a means of animating the static structures, allowing for, e.g., the visualization of an entire permeation event of a substrate through a channel or transporter. However, the relevant time scales for many transport processes is beyond that afforded by MD, which is typically limited to a few microseconds currently. As such, methods to accelerate the process of interest in a simulation have been developed. One example is steered molecular dynamics (SMD) (1, 2), a method in which forces are applied to part of the system, e.g., the substrate, to drive it along a predefined direction. Commonly implemented using a constant force or a constant velocity , this method is useful for exploring possible permeation pathways through a membrane protein. However, because the forces imposed are usually orders of magnitude greater than would be experienced in a living system, interpretation of the results is often limited to a qualitative description of the possible behavior of the substrate and protein. For a quantitative picture of transport, one must turn to more advanced methods. For example, the results of multiple SMD simulations combined through application of Jarzynski's equality provides a means of recovering an equilibrium PMF from non-equilibrium events (3, 4, 5, 6, 7). Alternatively, adaptive biasing forces (ABF) can generate quasi-equilibrium …