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Knots are commonly found in molecular chains such as DNA and proteins, andthey have been considered to be useful models for structural analysis of thesemolecules. One interested quantity is the minimum number of monomers necessaryto realize a molecular knot. The minimum lattice length $\mbox{Len}(K)$ of aknot $K$ indicates the minimum length necessary to construct $K$ in the cubiclattice. Another important quantity in physical knot theory is the ropelengthwhich is one of knot energies measuring the complexity of knot conformation.The minimum ropelength $\mbox{Rop}(K)$ is the minimum length of an ideallyflexible rope necessary to tie a given knot $K$.  Much effort has been invested in the research project for finding upperbounds on both quantities in terms of the minimum crossing number $c(K)$ of theknot. It is known that $\mbox{Len}(K)$ and $\mbox{Rop}(K)$ lie between$\mbox{O}(c(K)^{\frac{3}{4}})$ and $\mbox{O}(c(K) [\ln (c(K))]^5)$, but unknownyet whether any family of knots has superlinear growth. In this paper, we focuson 2-bridge knots and links. Linear growth upper bounds on the minimum latticelength and minimum ropelength for nontrivial 2-bridge knots or links arepresented:  $\mbox{Len}(K) \leq 8 c(K) + 2$.  $\mbox{Rop}(K) \leq 11.39 c(K) + 12.37$.

Minimum lattice length and ropelength of 2-bridge knots and links