 Facilitated target search

A facilitated target search combines bulk diffusion with lower-dimensional motion on a substrate, such as sliding on DNA. In the scaling model $\tau =A/\lambda +B\lambda$, positive constants $A,B$ balance relocation and local exploration. Differentiation gives ${\lambda }_{\ast }=\sqrt{A/B}$ and ${\tau }_{\min }=2\sqrt{AB}$. These expressions require an accessible optimum within the physically allowed range of sliding lengths.