Figure 3
From: Specific binding of a polymer chain to a sequence of surface receptors
The mean time (in units of b 2/D, logarithmic scale) to bind the chain to the surface, as a function of the number M of equidistant binding sites. (a) A fixed chain N = 100 segments. The dashed blue line marks the case of M = 1, when only the Nth segment has a binding ligand, reaching for a receptor a = 40b away. As the number of binding sites along the chain increases, the time to bind the final receptor dramatically reduces. (b) A fixed interval between receptors ΔN = 20, so N = MΔN. The plot compares a chain with single binding site at a distance a = 3Nb/20 (solid blue line), and a chain with M = N/ΔN binding sites every 20 monomers, whose receptors are spaced at Δa = a/M = 3b. In both cases, the end of the chain binds at the distance a. The inset illustrates that the typical binding time increases almost linearly with chain length or number of sites, in contrast to the exponential increase of this time for the single-site chain. The dashed black line indicates the line Mτ 1a , which is the strictly single-step zipper binding pathway. The possibility of occasional double steps lowers the binding time of an ‘accelerated zipper’. In both plots, the blue dots represent the exact expression for 〈τ〉; the continuous red line is the plot of (8), where Δa = a/M.
