  We show that the minimum number of sticks required to construct a non-paneled
knotless embedding of $K_4$ is 9 and of $K_5$ is 12 or 13. We use our results
about $K_4$ to show that the probability that a random linear embedding of
$K_{3,3}$ in a cube is in the form of a M\"{o}bius ladder is $0.97380\pm
0.00003$, and offer this as a possible explanation for why $K_{3,3}$ subgraphs
of metalloproteins occur primarily in this form.
