ABSTRACT
When a polymer molecule is spatially confined in a volume less than its molecular volume in free solution, the number of polymer conformations is reduced, and at the same time, the intersegment interactions become more pronounced. As a result, the free energy of the molecule generally increases, due to a decrease in chain conformational entropy and an increase in energy arising from the intrachain excluded volume effect. Therefore, as a chain is squeezed from one region in a free solution into another region through a spatially restricting pore or channel, the chain must go through a free energy barrier. The free energy barrier is additionally contributed by the enthalpic interactions between the polymer and the inside walls of the pore that may bear specific chemical decorations. In this chapter, we shall estimate the free energy barriers relevant to the geometries sketched in Figure 5.1 and derive the free energy landscape as a function of the extent of translocation. The translocation process can occur either as a single-file conformation or as a multiply folded conformation depending on the size of the pore. We shall first discuss single-file translocation through a tiny pore embedded in a thin planar membrane (Figure 5.1a) and through a pore connecting two spherical chambers (Figure 5.1b). One of the major features of the single-file translocation process is the free energy penalty associated with the obligatory search by one chain end to find the pore entrance. The examples of Figure 5.1a and b allow us to capture the essential elements of the free energy landscape associated with the translocation process. In experiments involving solid-state nanopores and channels, the spatial restrictions can be big enough to allow multiply folded conformations. We shall also discuss this scenario by considering wider pores (Figure 5.1c) and channels (Figure 5.1d). Here we will explore the effect arising from chain stiffness as well. For a given pore geometry, different stages of translocation by a macromolecule can be written as a composite of several components, such as one part of the chain hanging in the donor compartment, another part hanging in the receiver compartment, and the rest residing inside the pore. We shall summarize key formulas for the free energies of polymer conformations corresponding to these different components, which can be used to construct the free energy landscape for any particular mode of translocation. Our construction of the free energy landscape is based on equilibrium considerations.
