Chaperone-driven polymer translocation through nanopore: Spatial distribution and binding energy

Chaperones are binding proteins working as a driving force in biopolymer translocation. They bind to the biopolymer near the pore and prevent its backsliding. Chaperones may have different spatial distributions. Recently, we showed the importance of their spatial distribution in translocation and its effects on the sequence dependency of the translocation time. Here we focus on homopolymers and exponential distribution. Because of the exponential distribution of chaperones, the energy dependency of the translocation time will change. Here we find a minimum in translocation time versus binding effective energy (EBE) curve. The same trend can be seen in the scaling exponent of time versus polymer length, [Formula: see text] ([Formula: see text]), when plotted against EBE. Interestingly in some special cases, e.g. chaperones of size [Formula: see text] and with an exponential distribution rate of [Formula: see text], the minimum even reaches to an amount of less than 1 ([Formula: see text]). We explain the possibility of this rare result. Moreover, based on a theoretical discussion we show that, by taking into account the velocity dependency of the translocation on polymer length, one can truly predict the value of this minimum.